ML0329-01.zip

April 1st, 2022

600577 – RM Lecture1-2019.pptx

Risk ManagementIntroduction – Part I

Lecture 1

Prof. Youwei Li

Lecture Plan

Why risk management is important?

The risk management process

Principles of risk management decisions

Why Risk Management is important?

Risk is all pervasive – affects every individual and every organisation.

There is no choice but to manage risk.

Therefore, risk management is increasingly seen as a key management function within organisations.

The Risk Management ProcessSource: Crouhy, et.al, p.2

Simple Example

A manufacturer has the opportunity to make a lucrative but very dangerous inflammable chemical

How to control the risk?

Simple Example

Risk Avoidance – prevent risks from coming into existence e.g. don’t manufacture the product.

Risk Transfer – Buy appropriate Insurance.

Simple Example

Risk Mitigate

Reduce chance of a fire – lots of safety training for workers

Reduce losses if fire occurs e.g. install a sprinkler system

Keep

decide to accept the risk given the return

Simple Example

Evaluate and compare the performance of each risk mitigation:

Risk avoidance

Risk transfer

Risk mitigate

Keep risk

1.8

Financial Principles

What principles are used to make financial decisions about risk?

Principle 1: The Risk-Return Trade-off

Would you invest your savings in the stock market if it offered the same expected return as your bank?

We won’t take on additional risk unless we expect to be compensated with additional return.

Higher the risk of an investment, higher will be its expected return.

Dow Jones Industrials headed for its biggest weekly loss since 2008 after giving back early gains, having traded in a wide 600-point range in just the first 90 minutes of the Friday 9th of February 2018 session.

The Risk-Return Trade-off

Risk vs Return

There is a trade off between risk and expected return

The higher the risk, the higher the expected return

Historic price of S&P 500

Risk vs Return-measure return

Historical Volatility – annualised standard deviation

Risk is measured by the standard deviation of the returns on an asset, based on either historical returns or expected future returns.

Risk vs Return-measure risk

Expected Return & Expected Standard Deviation

Expected Return, E(R) :

Standard Deviation, Sd:

Risk vs Return

i =1

Ri pi

i =1

Ri pi

R = expected return, Ri = return if event i occurs

pi = probability of event i occurring, n = number of events

The Expected Return

The Expected Standard Deviation

Risk vs Return, Example (Hull (2007), table 1.1, page 2)

Imagine that you have $100,000 to invest for one year. One alternative is to buy Treasury bills yielding 5% [ E(R)=5% ], with no risk [ σ=0 ].

Other is to buy an equity investment shares with the risk and return described in table below:

Which product would you like to invest?

The greater the risk taken, the higher the expected return.

Probability	Expected Return
0.05	+50%
0.25	+30%
0.40	+10%
0.25	–10%
0.05	–30%

5% probability of getting a 50% return

25% probability of getting -10% (negative) return

Expected Return

Expected Return per year [E(R)]=?

E(R) = 0.05×0.50+0.25×0.30+0.40×0.10+0.25x(-0.10)+0.05(-0.30)=0.10

This shows that in return for taking some risk you are able to increase your expected return per annum from 5% offered by treasury bills to 10%.

If things work out well, your return per annum could be as high as 50%. However, the worst-case outcome is a -30% return, or a loss of $30.000=$100.000×0.30.

Probability	Expected Return
0.05	+50%
0.25	+30%
0.40	+10%
0.25	–10%
0.05	–30%

Quantifying Risk

How do you quantify the risk you take when choosing an investment?

A convenient measure that is often used is the standard deviation of return over one year. This is:

Sd=

Where R is the return per annum. The symbol E denotes expected value, so that E(R) is the expected return per annum.

Expected Return

Probability	Expected Return
0.05	+50%
0.25	+30%
0.40	+10%
0.25	–10%
0.05	–30%

Sd=

E(R) = 0.05×0.50+0.25×0.30+0.40×0.10+0.25x(-0.10)+0.05(-0.30)=0.10

Principle 2: All Risk is Not Equal

Some risk can be diversified away, and some cannot.

The process of diversification can reduce risk, and as a result, measuring a project’s or an asset’s risk is very difficult.

A project’s risk changes depending on whether you measure it standing alone or together with other projects the company may take on.

All Risk is Not Equal

Total risk can be divided into systematic and unsystematic risk.

Systematic risk is due to factors, such as changes in interest rates, business cycles and government policy – affects all investments.

Unsystematic risk is specific to a given share.

Unsystematic risk decreases as the number of investments in a portfolio increases: this is called portfolio diversification of risk.

The concept of diversification

Total risk falls as number of investments rises

Diversification of risk

The amount of risk diversification depends on correlation between returns and hence on the value of the correlation coefficient (CC)

+1: no diversification of unsystematic risk

0: partial diversification of unsystematic risk

-1: full diversification of unsystematic risk

Correlation and Diversification

Diversification of a 2 asset portfolio-Hypothetical returns: ACE plc

Hypothetical returns: Bravo plc

Two-asset portfolio: ACE & Bravo

Perfect negative correlation cc=-1

Time(years)

–15

–

Return %

–10

Bravo

Ace

Portfolio

Another Two-asset portfolio: ACE & Clara

Perfect positive correlation cc=1

Time(years)

–10

–

Return %

–15

–20

Clara

Portfolio

Ace

Principle 3: The Time Value of Money

A dollar received today is worth more than a dollar to be received in the future.

Because we can earn interest on money received today, it is better to receive money earlier rather than later.

Because we could lose value due to inflation

Principle 4: Efficient Capital Markets

The values of securities at any instant in time fully reflect all publicly available information.

Prices reflect value and are right.

Price changes reflect changes in expected cash flows (and not cosmetic changes such as accounting policy changes). Good management decisions drive up the stock prices and bad management decision drive down the stock price.

Categories of Risk

Market Risk

Foreign exchange risk (fluctuations in exchange rates)

Interest rate risk

Commodity price risk

Equity risk

Credit Risk

Operational Risk

Liquidity risk

Systematic risk

Other risks/challenges

Country risk (changes in government regulations, unstable government, economic changes)

Cultural risk (differences in language, traditions, ethical standards, etc.)

etc

Interactions of several risks

The interactions of several risks can alter or magnify the potential impact to an organization.

An organization may have both commodity price risk and foreign exchange risk. If both markets move adversely, the organization may suffer significant losses as a result.

There are two components to assessing financial risk:

Potential loss as a result of a particular rate or price change

Estimate of the probability of such an event (a) occurring

Risk and Uncertainty

Generally we will assume risk can be quantified.

For example, throw a die – don’t know what number will come up but we do know the probability of each is 1/6.

Knightian uncertainty is risk that is immeasurable, not possible to calculate.

Do we really know the distribution of say stock prices in a year’s time?

Black Swan events – totally unexpected e.g. 9/11.

Background Reading

Dionne G. (2015) Risk management: History, definition and critique

Stulz R. M. ((1996) Rethinking Risk Management, Journal of Applied Corporate Finance, Vol. 9, Issue 3, pp8-25.

Thank you!

Next week:

Risk ManagementIntroduction – Part II

1265.42

0.01758

1287.87

Returns

approxLn

exampleLn

–

æö

ç÷

èø

æö

==-

ç÷

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DateCloseAdj CloseS&P500return

15/06/20111265.421265.42-0.017585608

14/06/20111287.871287.870.012532883

13/06/20111271.831271.830.000668552

10/06/20111270.981270.98-0.014078468

09/06/2011128912890.007350455

08/06/20111279.561279.56-0.004195756

07/06/20111284.941284.94-0.000956785

06/06/20111286.171286.17-0.010818524

03/06/20111300.161300.16-0.009781564

02/06/20111312.941312.94-0.001225504

01/06/20111314.551314.55-0.023048299

31/05/20111345.21345.20.010537033

27/05/20111331.11331.10.004072589

26/05/20111325.691325.690.003945345

25/05/20111320.471320.470.003178158

24/05/20111316.281316.28-0.000827749

23/05/20111317.371317.37-0.011997246

20/05/20111333.271333.27-0.007718007

19/05/20111343.61343.6

year

per

intervals

time

number

obsevation

number

returns.

interval

end

price

asset

Where

)

(

–



–R

)

i =1

σ =

[

]

()()

ERER

–

222222

()0.05(0.50)0.25(0.30)0.40(0.10)0.25(0.1

0)0.05(0.30)0.046

=+++-+-=

Sd = 0.0460.100.1897 (18.97%)

Risk

Number of

Investments

8-12 30

Unsystematic

Systematic

0 0

123

678Time

(years)

−10

−

Return %

123

678Time

(years)

−10

−

Return %

123

567

8Time

(years)

–15

–

Return %

123

567

8Time

(years)

–15

–

Return %

BUSS1000_S1 2022_Case Study_Instructions and Rubric_FINAL.pdf

BUSS1000: Future of Business – Semester 1, 2022 Assessment Instructions

Assessment Name

Individual/Group

Assessment Conditions

LOs Length Weight Due Time Due Date Closing Date

Case Study Individual Compulsory 1,2,3,4, 6

2000 words

25% 10:00am 28 March 2022

7 April 2022

Case Study: Coles Group

Your Task: You need to prepare a report on Coles Group (https://www.colesgroup.com.au/home/).

Coles Group

This report should consist of two sections:

Part 1: Role of Business in Society (Approx. 500 words)

What is Coles’ dominant orientation towards society? Profit Maximisation or Creating Shared Value or something else? Take a stance and explain your arguments with the help of evidence.

Part 2: Strategy Evaluation (Approx. 1500 words)

In this section, analyse Coles’ competitive environment by applying the PESTLE framework. Your response should demonstrate your ability to integrate various factors of PESTLE framework.

Important points:

• Scope: You need to consider the organization as a whole. In other words, you need to consider all the operating markets of Coles Group.

• Format: We are NOT expecting any specific format. Also, do not add any cover page or do not repeat the question before your response (simply state Part 1 and Part 2). 2000 words count towards every words in your response document. Please remember that you are presenting the report from a general manager’s perspective (practitioner style), but it must still contain full academic references.

• Evaluation: Each paper is graded against the rubric. Ensure you have looked at the rubric carefully prior to beginning your paper, and prior to submitting.

• Research: Should be using relevant, quality research, not based simply on the organisations webpages. It is important to use high quality sources, including ABDC peer reviewed journal articles.

• Reference: Thorough and regular referencing adds academic weight to your arguments. Statements not

backed up by data and/or appropriate business theory/frameworks carry less weight. Referencing adds rigour,

integrity and believability to your arguments – doing this as often as possible will enhance your paper by

demonstrating your business knowledge with credible sources.

• Word count and structure: The above word counts include references. References should appear at the end

of the paper and comply with APA 7th standard.

Assessment criteria:

Please make sure you read the rubric (pages 3-5) carefully as this is what will be used to grade your paper.

Requirements for submission:

• Your case study must be submitted on the BUSS1000 Canvas site under “Assignments” (submission will open two weeks prior to the deadline).

• Appropriate word length – the word length for this report is 2000 words. Normal word count penalties apply when the report word length (including headings, in-text reference and Reference list) should not exceed word limit of 2000 words or +10% that is maximum of 2200 words – refer Penalties below for appropriate URL. Note that the word limit includes in-text referencing and the reference list at the end of the document.

• Appropriate referencing throughout the case study, in-text and in the Reference list, using the latest version of APA 7th Edition Referencing. The University of Sydney has an APA 7th Edition guide which can be found

here: https://libguides.library.usyd.edu.au/ld.php?content_id=49237993 . • Case study must be submitted as a Word file document (.doc, .docx)

• The submission should have a file name in thee following format “BUSS1000_S1 2022_Case Study_SID”, so an example could be “BUSS1000_S1 2022_Case Study_123456789”

• Late penalties will apply after the due date and time 10:00am on 28 March, 2022.

Penalties:

• Late submission penalty is in line with the Business School policy which can be found at: http://sydney.edu.au/business/currentstudents/policy

• Word length is in line with the Business School policy which can be found at: http://sydney.edu.au/business/currentstudents/policy

• Academic dishonesty and plagiarism is in line with the Business School policy which can be found at: http://sydney.edu.au/business/currentstudents/policy

Feedback:

• Feedback will be provided for each part based on the marking criteria,

• Feedback for the case study will be shown as comments.

• The case study will be marked in accordance with the Business School policy.

• Overall, feedback will be provided through the following: ✓ Specific comments on each assessment segments ✓ Overall comments based on each part of the report ✓ By attending tutor consultation hour and asking for additional feedback aimed at achieving better

grades in the future. Learning outcomes for this case study include: LO1, LO2, LO3, LO4, LO6

BUSS1000 – Case Study Rubric

Task Description: For this assignment you will be undertaking a case study of a provided organization. You will be required to undertake general and academic research, apply theoretical frameworks, and critically analyse the context and/or organisation. Please see Canvas for the full list of assignment instructions once they are uploaded.

ASSESSMENT CRITERIA

100% 90% 80% 70% 60% 50% 40% 20% 0%

Part 1. Role of Business in Society 15 marks (GQ Information and digital literacy And GQ Critical Thinking and Problem Solving)

The analysis demonstrates a flawless ability to correctly identify, select, analyse and critique all relevant information, enabling a very robust and un-questionable argument.

The analysis demonstrates an outstanding ability to correctly identify, select, analyse and critique all relevant information, enabling a strong, well-explored and justified argument.

The analysis demonstrates a good ability to correctly identify, select, analyse and critique relevant information, enabling a well-thought-out argument.

The analysis demonstrates an ability to correctly identify, select and analyse relevant information to support a good argument.

The analysis demonstrates a basic ability to correctly identify and select relevant social and ethical information. Argument could be further strengthened & less descriptive.

The analysis demonstrates an attempt to identify some reliable social and ethical information, however, is somewhat descriptive. Depth, strength of argument &/or accuracy are therefore lacking.

The analysis is superficial due to being descriptive with little connection between evidence and theory, building a weak argument.

The analysis is lacking or extremely superficial, demonstrating a weak understanding of the different orientations businesses may adopt.

No evidence of appropriate analysis.

Part 2. Competitive Environment Evaluation 60 marks (GQ Information and digital literacy And GQ Critical Thinking and Problem Solving)

The analysis demonstrates a flawless ability to correctly identify, select, analyse and critique all relevant information, enabling a very robust and un-questionable argument.

The analysis demonstrates an outstanding ability to correctly identify, select, analyse and critique all relevant information, enabling a strong, well-explored and justified argument.

The analysis demonstrates a good ability to correctly identify, select, analyse and critique relevant information, enabling a well-thought-out argument using theory well.

The analysis demonstrates an ability to correctly identify, select and analyse relevant information to support a good argument using theory appropiately.

The analysis demonstrates a basic ability to correctly identify and select relevant information. Argument could be further strengthened & less descriptive.

The analysis demonstrates an attempt to identify some relevant information, however, is somewhat descriptive. Depth, strength of argument &/or accuracy are therefore lacking.

The analysis is superficial due to being descriptive with little connection between evidence and theory, building a weak argument.

The analysis is lacking or extremely superficial, demonstrating a weak understanding of the relevant theory.

No evidence of appropriate analysis.

ASSESSMENT CRITERIA

100% 90% 80% 70% 60% 50% 40% 20% 0%

Clarity of expression Effective communication in the form of professional writing skills 10 marks (GQ Communication skills)

The writing showed flawless use of business writing style. The use of sections was thoughtful. Information was presented in a flawlessly clear & organised manner with no room for improvement. You have followed APA 7th edition guideline in your referncing without any error.

The writing showed an exceptional level of business writing style. The organisation and formatting of information into the report sections was very clear and organised with clear expression assisting the strength of the overall argument. You have followed APA 7th edition guideline in your referncing.

The writing showed a very good understanding of business writing style with fluent language and good expression. The organisation & formatting of information into the report sections was logical & purposeful.

The writing showed a good understanding of business writing style and use of report sections/categories. However, there is scope for a tighter structure to make for a clearer and more organised report.

The writing largely demonstrated business writing style. Information was appropriately categorised within the report sections however there was significant room for improvement in tightening structure and organisation.

Although the meaning was generally apparent, the writing demonstrated a very basic business style. Information was mainly categorised into appropiate report sections.

The writing demonstrated minimal business style. The meaning was not always understandable, and/or There was little organisation of ideas & information within appropriate report sections.

The writing had little or no business style. It was unclear to the extent that the meaning was not understandable. There was no organisation of ideas & information within report sections.

The writing was not effective & with no business writing skills displayed.

Research: Quality of sources and effective use demonstrated 15 marks (GQ Information and digital literacy And GQ Critical Thinking and Problem Solving And GQ Integrated professional, ethical, and personal identity)

Sources used from outside the class including more than two high quality peer reviewed academic business journal references. Additional high-quality relevant research is evident. Source quality and credibility has been critically considered. Overall research is exceptional and could not be improved.

Various sources from outside the class, including more than two peer reviewed academic business journal references are used exceptionally well to support argument. Additional relevant research incorporates credible and high quality sources.

Sources from outside the class including at least two peer reviewed academic business journal references used well to support argument. Additional relevant research incorporates credible and high quality sources.

Sources from outside the class including two peer reviewed academic business journal refences are effectively used. Additional relevant research is evident.

Sources from outside the class are used including two peer reviewed academic business journal references, however, there is limited use or over-use of the same sources which limits quality.

Minimum requirement met that sources have been used from outside Unit’s resources including one peer reviewed academic business journal reference (<10 years old).

Sources from outside the class have been used but have not included one peer reviewed academic business journal reference (<10 years old).

No materials from the Unit’s resources have been used.

Material from outside or inside the class have not been used.

Word Count Penalty Late Penalty Appendix/Appendices

Where the report’s word length is exceeded, the student will lose 10% of the total marks when the submission is 10% above the word length. 10% will be lost for each 10% over-length thereafter.

If the report is submitted late, a penalty of 5% (equating to 5 marks out of a total 100 marks) per day will be applied up to 10 calendar days, after which a mark of zero is applied.

The word limit for this assessment is 2000 words. The appendix/appendices exceeded this word limit & therefore have not been considered.

Case Study: Coles Group

RM Lecture 10 Credit Default Swaps 2019.pptx

Risk ManagementCredit Default Swaps andAsset Backed Securities

Lecture 10

Prof Youwei Li

Session Plan

Credit default swaps

Asset backed securities

Revision

Commercial Credit Risk and the Rating of Individual Credit

Commercial credit risk is the largest and most elementary risk faced by many banks, and it is a major risk for many other kinds of financial institutions and corporations as well.

Plus assessing commercial credit risk is a complicated task:

determining how likely it is that an event of default will happen; and

how costly will turn out to be if it does occur.

Therefore, no surprise to find that there are many different approaches to the problem.

Many uncertain elements are involved in determining both how likely it is that an event of default will happen; and how costly will turn out to be if it does occur.

Credit Default Swaps

A huge market with over $40 trillion of notional principal

Buyer of the instrument acquires protection from the seller against a default by a particular company or country (the reference entity)

Credit Default Swaps

Example: Buyer pays a premium of 90 bps per year for $100 million of 5-year protection against company X defaulting

90 x0.01% x 100million = 0.9million pa

Premium is known as the credit default spread. It is paid for life of contract or until default

If there is a default, the buyer has the right to sell bonds with a face value of $100 million issued by company X for $100 million (Several bonds are typically deliverable)

Credit Default Swaps

In practice for settlement the seller may settle on a cash basis.

Pay buyer cash of 100(1-R) where R is the recovery rate.

i.e. put buyer in the same position as if there had been no default.

Recovery Rate

The recovery rate for a bond is usually defined as the price of the bond immediately after default as a percent of its face value

Recovery Rates(Moody’s: 1982 to 2006)

CDS Structure

Default

Protection

Buyer, A

Default

Protection

Seller, B

90 bps per year

Payoff if there is a default by reference entity=100(1-R)

Recovery rate, R, is the ratio of the value of the bond issued by reference entity immediately after default to the face value of the bond

Other Details

Payments are usually made quarterly in arrears

In the event of default there is a final accrual payment by the buyer

Settlement can be specified as delivery of the bonds or in cash

Suppose payments are made quarterly in the example just considered. What are the cash flows if there is a default after 3 years and 1 month and recovery rate is 40%?

3 years – last payment

3 years 3 months next

payment due

Default 3 years 1 months

Cash Flows on Default – Buyer

Buyer has to make payments up to exact date of default.

Will have already have made payments for the first three years.

Normal quarterly payment

= 100M x 0.9/100 x 0.25 = 225,000

One months payment to make

= 225,000 x1/3 = 75,000

Cash Flows on Default – Seller

Recovery Rate 40%.

Recovery $40m

Thus seller pays $60m

Attractions of the CDS Market

Allows credit risks to be traded in the same way as market risks

Previously banks that made loans were stuck with them until they expired.

Can be used to transfer credit risks to a third party

Insurance companies (say) can take these on as an investment.

Attractions of the CDS Market

Can be used to diversify credit risks

In theory should be safer to spread risk across many parties.

Before crisis they encouraged much more credit risk to be taken on and much of it was highly correlated so systematic risk greatly increased.

Overall effect counterproductive.

Asset Backed Securities – Another way to transfer credit risk

Security created from a portfolio of loans, bonds, credit card receivables, mortgages, auto loans, aircraft leases, etc.

Asset Backed Securities – Another way to transfer credit risk

Usually the income from the assets is tranched.

A “waterfall” defines how income is first used to pay the promised return to the senior tranche, then to the next most senior tranche, and so on.

Possible Structure

Asset 1

Asset 2

Asset 3



Asset n

Principal=$100

million

SPV

Tranche 1

(equity)

Principal=$5 million

Yield = 30%

Tranche 2

(mezzanine)

Principal=$20 million

Yield = 10%

Tranche 3

(super senior)

Principal=$75 million

Yield = 6%

Asset Backed Securities – Why Do it?

More demand for highly rated (safe) instruments.

Overall can sell portfolio for more if repackage some of it as very safe.

Issuers tent to persuade rating agencies to give good credit ratings – AAA.

The Mezzanine Tranche is Most Difficult to Sell…

Subprime Mortgage Portfolio

Equity Tranche (5%)

Not Rated

Mezzanine Tranche (20%)

BBB

Super Senior Tranche (75%)

AAA

Equity Tranche (5%)

Mezzanine Tranche (15%) BBB

Super Senior Tranche (80%)

AAA

The mezzanine tranche is repackaged with other similar mezzanine tranches

The Credit Crunch

Between 2000 and 2006 mortgage lenders in the U.S. relaxed standards (liar loans, NINJAs)

Interest rates were low

Demand for mortgages increased fast

Mortgages were securitized using ABSs and ABS CDOs

The Credit Crunch

In 2007 the bubble burst

House prices started decreasing. Defaults and foreclosures, increased fast.

Fundamental Problem

Banks no longer responsible for the consequences of their own lending.

Only concerned whether they could pass on loans profitably to a special purpose vehicle (SPV).

Rating agencies work with historic data but this was no longer applicable – defaults much higher than previously and very highly correlated.

Summary

Asset Backed securities and CDOs are very useful.

Appropriate pricing is very sensitive to the underlying assumptions – default probabilities of underlying assets and correlations between underlying assets especially in times of stress.

Crisis was to a large extent caused by these assumptions being incorrect.

Class Mean(%)

Senior Secured 54.44

Senior Unsecured 38.39

Senior Subordinated 32.85

Subordinated 31.61

Junior Subordinated 24.47

Class	Mean(%)
Senior Secured	54.44
Senior Unsecured	38.39
Senior Subordinated	32.85
Subordinated	31.61
Junior Subordinated	24.47

RM Lecture 10 Revision 2021.pptx

Risk ManagementRevision

Lecture 10

Prof Youwei Li

Assignment and Revision

What to Revise

Lecture Slides

Handouts

Tutorial Examples

Textbook

Don’t need to go beyond this

Formula sheet and Normal Tables on Canvas

Assignment – Format

Answer all questions

Mainly essay based

Basic Knowledge

Fundamental concepts in the first two lectures.

Risk Return, diversification.

Arbitrage and its importance in Derivative Pricing.

Futures and Forwards – what are the payoffs.

Uses for hedging and speculation.

Basic Knowledge

Basic properties of options:

Terminology: American, European etc.

Writing/buying

What are the payoffs? Why would you do it?:

(hedging, speculation)

What variables determine option prices?

Major Topics for Revision

Topics

Principles of risk management decisions

Categories of risks

Main type of derivatives – define/describe them,

what are their payoffs? When are they useful?

Foreign exchange risk management

Topics

Controlling Interest Rate Risk (Altering business activities/derivatives

Credit Rating – Companies and Countries: How calculated? How ratings change over time?

Topics

Quantitative approaches to risk management: Greeks, VAR, Stress testing, back testing, expected shortfall.

How can VAR be calculated?

Topics

Past Derivatives Problems

Credit crunch 2008-09

The 2020 stock market crash from 20 February to 7 April 2020; Negative oil futures prices 20-21 April 2020

What can be done about them?

Topics

All the seminar calculations.

Swaps

Caps, Floors, Collars

Arbitrage arguments to value the forward prices of different assets

Be able to do numerical calculations

Topics

Use Black-Scholes formula to calculate price of European call and put options

How can model be adapted to deal with dividends and American Options?

Practice using the formula.

Thank you!

Good Luck with the Assignment

RM Lecture 2 – 2019.pptx

Risk ManagementIntroduction – Part II

Lecture 2

Prof Youwei Li

Lecture Plan

Credit Risk

Equity risk

Operational Risk

Liquidity risk

Systematic risk

Interest rate risk

Yield curve risk

Credit RiskSee Horcher (2005), pp. 39-45; Hull (2007), chapter 11.

In general, credit risk is a concern when money is owed or must rely on another organization to make a payment to it or on its behalf.

Organizations are exposed to credit risk through all business and financial transactions that depend on the payment or fulfilment of obligations of others.

Default risk

Counterpart pre-settlement risk

Counterpart settlement risk

Sovereign or country risk

Concentration risk

Legal risk

Credit Risk1. Default Risk

Arises from money owed, either through lending or investment, that the borrower is unable or unwilling to repay.

The amount at risk is the defaulted amount, less any amount that can be recovered from the borrower.

In many cases the default amount is most or all of the advanced funds.

Credit Risk2. Counterparty Pre-Settlement Risk

Counterparty exposure arises from the fact that if the counterparty defaults or otherwise does not fulfil its obligations under the terms of a contractual agreement, it might be necessary to enter into a replacement contract at far less favourable prices.

The amount at risk is the net present value of future cash flows owed to the organization, presuming that no gross settlements would be required.

Credit Risk3. Counterparty Settlement Risk

Arises at the time that payments associated with a contract occur, particularly cross payments between counterparties. It has the potential to result in large losses because the entire amount of the payment between counterparties may be at risk if a counterparty fails during the settlement process.

Depending on the nature of the payment, the amount at risk may be significant because the notional amount could potentially be at risk.

Credit Risk4. Sovereign or Country Risk

Sovereign risk encompasses the legal, regulatory, and political exposures that affect international transactions and the movement of funds across borders.

It arises through the actions of foreign governments and countries and can often result in significant financial volatility.

Exposure to any nondomestic organization involves an analysis of the sovereign risk involved.

In areas of political instability, sovereign risk is particularly important.

Credit Risk5. Concentration Risk

Is a source of credit risk that applies to organizations with credit exposure in concentrated sectors.

An organization that is poorly diversified, due to its industry or regional influences, has concentration risk.

Concentration risk is most effectively managed with the addition of diversification, where possible.

Credit Risk6. Legal Risk

The risk that a counterparty is not permitted or able to enter into transactions, particularly derivatives transactions, is known as legal risk.

The risk that an individual employed by an entity has sufficient authority to enter into a transaction, but that the entity itself does not have sufficient authority, has also caused losses in derivatives transactions.

As a result, organizations should ensure that counterparties are legally authorized to enter into transactions.

Operational Risk

Operational Risk:

Human Error and Fraud

Processes and Procedural Risk

Technology and System Risk

It arises from human error and fraud, processes and procedures, and technology and systems.

It is one of the most significant risks facing an organization because of the varied opportunities for losses to occur and the fact that losses may be substantial when they occur.

Equity Price Risk

Affects corporate investors with equities or other assets the performance of which is tied to equity prices.

Firms may have equity exposure through pension fund investments, for example, where the return depends on a stream of dividends and favourable equity price movements to provide capital gains.

The exposure may be to one stock, several stocks, or an industry or the market as a whole.

Equity price risk also affects companies’ ability to fund operations through the sale of equity and equity-related securities. Equity risk is thus related to the ability of a firm to obtain sufficient capital or liquidity.

Liquidity Risk

Liquidity impacts all markets. It affects the ability to purchase or sell a security or obligation, either for the hedging purposes or trading purposes, or alternatively to close out an existing position.

Liquidity can also refer to an organization having the financial capacity to meet its short-term obligations.

Another form of liquidity risk is the risk that an organization has insufficient liquidity to maintain its day-to-day operations.

Systemic Risk

Systemic risk is the risk that a failure of a major financial institution could trigger a domino effect and many subsequent organizational failures, threatening the integrity of the financial system.

Aside from practicing good risk management principles, systemic risk is difficult for an individual organization to mitigate.

Higher volumes, especially for foreign exchange and securities trading, increase liquidity, which has benefits to market participants.

Systemic risk can also arise from technological failure or major disaster.

Interest Rate Risk

Arises from fluctuating interest rates.

The following techniques can be used to reduce interest rate exposure and the resulting need for derivatives:

Global cash netting

Intercompany lending

Embedded options

Changes to payment schedules

Asset-liability management

Interest Rate Risk 1. Global cash netting

When an organization has cash flows in multiple currencies, some parts of the organization may have excess cash while others may need to drawn down on available lines of credit.

A cash forecast for specific currencies will enable surplus and shortages to be forecast and managed more accurately. On a centralized basis, it may be possible to pool funds from divisions or subsidiaries and make them available to other parts of the organization.

Interest Rate Risk 2. Intercompany lending

A longer-term approach to managing funding shortages and surpluses across an organization is intercompany lending. When one part of an organization requires long-term funding, and another part has excess cash available for investment purposes, the combination of the two may reduce interest costs and permit more control over the borrowing process.

Expert assistance is necessary to ensure that legal, tax, and regulatory restrictions or prohibitions do not exist.

Interest Rate Risk 3. Embedded Options

Embedded options are granted to securities holders or contract participants and provide them with certain rights. The granting of permission to buy or sell something is an option, and it has value.

Embedded options commonly consist of redemption, call, or similar features in corporate debt securities. Embedded options may also exist in contractual pricing agreements with customers or suppliers or fixed-priced commodity contracts.

The option holder is the party to whom the benefits accrue. The option grantor is the party that has an obligation as a result of the embedded option.

Interest Rate Risk 3. Embedded Options

The use of securities with features such as a call provision provides debt issuers with alternative method for managing exposure to interest rates.

Callable debt combines the debt component, which would provides an option to the issuer. If interest rates decline, the issuer can retire the higher-interest debt through the call provision and subsequently reissue lower-interest debt.

The issuer will incur a cost for the call option through the call price premium or the coupon.

Interest Rate Risk 4. Changes to Payment Schedules

Changes to payment schedules may permit an organization to maintain cash balances for longer periods, reducing the need for funding and therefore exposure to interest rates.

Changes to supplier/vendor payment schedules may permit a longer payment cycle, reducing the need for borrowing

Changes to customers payment schedules may increase the speed with which funds are collected, reducing the need for borrowing (changing the methods of payment encouraging electronic alternatives to paper checks).

Changes to contractual long-term payments, such as royalties and license agreements, to quarterly from annually, for example.

Interest Rate Risk 5. Asset-Liability Management

In financial institutions, the management of assets and liabilities is a key requirement for managing interest rate risk.

Asset-liability management involves the pairing or matching of assets (customer loans and mortgages in case of a financial institution) and liability (customers deposits) so that changes in interest rates do not adversely impact the organization.

This practice is commonly known as “gap management” and often involves duration matching.

Interest Rate Determinants

Nominal Interest Rate = Real interest rate + Inflation risk premium + Default Risk premium + Maturity Premium + Liquidity Premium

Thus the nominal rate or quoted rate for securities is driven by all of the above risk premium factors. Such knowledge is critical when companies set an interest rate for their issues.

Real and Nominal Returns

What is the real rate of return, if inflation is 5% and the quoted rate is 11.3%

11.3%-5%= 6.3%

Real Rate is 6.3%

Term Structure of Interest Rates or Yield to Maturity

The graph shows the relationship between a debt security’s rate of return and the length of time until the debt matures, where the risk of default is held constant.

The graph could be upward sloping (indicating longer term securities command higher returns), flat or inverted (longer term securities command lower returns compared to short-term securities).

The graph changes over time. Upward sloping curve is most commonly observed.

Yield Curve Risk

Results from changes in the relationship between short and long-term interest rates.

In a normal interest rate environment, the yield curve has an upward-sloping shape, that is, longer-term interest rates are higher than shorter-term interest rates because of higher risk to the lender.

In an inverted/flatten yield curve environment, demand for short-term funds pushes short-term rates above long-term rates (recent financial crisis).

The steepening or flattening of the yield curve changes the interest rate differential between maturities, which can impact borrowing and investment decisions and therefore profitability.

Yield Curve Risk

A steeper yield curve results in a greater interest rate differential between short-term and long-term interest rates, which makes the rolling over debt forward more expensive.

The inability to forecast the rollover rate with certainty has the potential to impact overall profitability of the investment or project

Yield Curve Risk

A short-term money market investor is exposed to the possibility of lower interest rates when current holdings mature.

Investors who purchase callable bonds are exposed to reinvestment risk. If callable bonds are called by the issuer because interest rates have fallen, the investor will have proceeds to reinvest at subsequently lower rates.

Callable bonds can be redeemed at the option of the issuer prior to maturities.

Yield Curve Risk

A borrower that issues commercial paper to finance longer-term projects is exposed to the potential for higher rates at the rollover or refinancing date.

As a result, matching funding duration to that of the underlying project reduces exposure to refunding risk.

Derivatives and Interest Rate Risk

Derivatives are financial instruments whose value is ‘derived’ from other instruments. E.g, interest rates, currency, commodities, stocks etc.

Crucial for risk management.

Main Types of Derivatives

A forward contract is an legally binding agreement between two parties to exchange something at a set price in the future.

Normally Over the Counter (OTC) – don’t have to be standardised.

Forwards are not marketable

Once a firm enters into a forward contract there is no convenient way to trade out of it.

A futures contract is similar to a forward contract.

Difference is traded on exchanges – have to be standardised.

Futures are marketable

An option contract is similar to futures contract, involving a predetermined price and contract duration.

But the person holding an option has the right, not the obligation, to exercise the put or the call.

Main Types of Derivatives – Forward

It is an “over-the-counter” agreement between two parties to lock in an interest rate for a short period of time.

The period is typically one month or three months, beginning at a future date.

Borrower buys an FRA to protect against rising interest rates, while a lender sells an FRA to protect against declining interest rates.

Main Types of Derivatives – Forward

At the beginning of the period covered by the FRA, the reference rate is compared to FRA rate.

If the reference rate is higher, the FRA seller pays a compensating payment (the settlement amount) to the FRA buyer. If the reference rate is lower, the FRA buyer pays the FRA seller.

The notional contract amount is used for calculating the settlement amount but is not exchanged.

Main Types of Derivatives – Forward

Example: A firm needs to borrow $10million in 3 months. The firm has bought a 3×6 FRA @ 4%.

FRA rate4.00%

Reference (actual) rate5.00%

Difference (5%-4%) 1.00%

(1.00%*90 days)/360 days * $10,000,000 = $25,000

Settlement amount paid by FRA seller, usually at the beginning of the period) is

$25,000 *1/(1+5%*0.25)= $24,691.36

Main Types of Derivatives – Forward

A company needs to borrow $100 million in 3 months time. However, the treasurer of the company is concerned that interest rates may rise, and therefore she decided to buy a 3×6 FRA at 4% interest rate (the term 3×6 indicates that the FRA term begins 3 months from the trade date and ends six months from the trade date).

a) Suppose that at the beginning of the FRA term (in 3-months time) the LIBOR rate is at 4.2%. What is settlement payment underlying the FRA contract for this circumstance? Who will have to pay for the FRA, the company or its counterparty?

Main Types of Derivatives – Forward

b) Compute the settlement payment underlying the FRA assuming that at the beginning of the FRA term the LIBOR interest rate is 2.5%. Who will have to pay for the FRA, in this case?

check tutorial 1-Q11 solutions

Main Types of Derivatives – Forward

FRAs can be closed out at current market value. Since both parties have an obligation under a FRA, closing out the contract involves unwinding it through an offsetting transaction.

The buyer of a FRA will sell an offsetting FRA, while the seller of a FRA will buy an offsetting FRA, with a resultant gain or loss.

Main Types of Derivatives – Futures

Interest rate futures are exchange-traded forwards. They permit an organization to manage exposure to interest rates or fixed income prices by locking in a price or rate for a future date.

Transacted through a broker, there are commissions to buy or sell and margin requirements.

Interest rate futures may be based on a benchmark interest rate (LIBOR usually), index, or fixed income instrument.

Bond futures:

Allow investors to hedge existing bond position, or to replicate bond positions, without buying or selling the underlying bonds.

They are used in asset allocation strategies and portfolio management.

They can assist in the management of long-term interest rates.

Main Types of Derivatives – Swaps

Transacted “over-the-counter” market, interest rates swaps are related to forwards and futures but facilitate interest rate hedging over a longer time interval. Common swaps include:

Asset swaps (swap income from two assets)

Basis swaps (swap based on interest rates)

Zero-coupon swaps (swap based on capital values only)

Forward interest swaps (swap based on anticipated interest rates)

The swap is an agreement between two parties to exchange their respective cash flows at specified future times according to certain specified rules. Most commonly, this involves a fixed rate payment exchanged for a floating rate payment (Plain Vanilla).

An Example of a “Plain Vanilla” Interest Rate Swap

An agreement by Microsoft to receive 6-month floating rate (based on the annual LIBOR) & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million

Next slide illustrates cash flows

———Millions of Dollars———

LIBOR

FLOATING

FIXED

Net

Date

Rate

Cash Flow

Mar.5, 2011

4.2%

Sept. 5, 2011

4.8%

+2.10

–2.50

–0.40

Mar.5, 2012

5.3%

+2.40

–2.50

–0.10

Sept. 5, 2012

5.5%

+2.65

–2.50

+0.15

Mar.5, 2013

5.6%

+2.75

–2.50

+0.25

Sept. 5, 2013

5.9%

+2.80

–2.50

+0.30

Mar.5, 2014

6.4%

+2.95

–2.50

+0.45

Cash Flows to Microsoft

Interest Rate Swaps

Closing Out an Interest Rate Swap

Interest rate swaps must be settled at the market value to be terminated.

The market value of a swap at any time after its commencement is the net present value of future cash flows between the counterparties.

Swap termination involves the calculation of settlement amount representing the net present value of all future obligations by each counterparty.

This net payment is made to the counterparty with unrealized gains in the swap.

For additional information See Horcher, p. 64.

RM Lecture 4 – 2019.pptx

Risk Management

Lecture 4

Prof Youwei Li

Learning Objectives

Calculate how money grows over a time: simple interest & compound interest

Be able to move money through time: present value & future value

Future value and present value of annuity & perpetuity

Portfolio theory: CAPM, SML

Simple Interest

In simple interest calculation, interest is earned only on principal.

Example: Compute simple interest on $100 invested at 6% per year for three years.

1st yearinterest is $6.00

2nd yearinterest is $6.00

3rd year interest is $6.00

Total interest earned: $18.00

Compound Interest

Compounding is when interest paid on an investment during the first period is added to the principal; then, during the second period, interest is earned on the new sum (that includes the principal and interest earned so far).

Compound Interest

Example: Compute compound interest on $100 invested at 6% for three years with annual compounding.

1st year interest is $6.00 Principal is $106.00

2nd year interest is $6.36 Principal is $112.36

3rd year interest is $6.74 Principal is $119.10

Total interest earned: $19.10

Difference of the interst earned: interest earned on all interest earned previously

Simple vs Compound Interest

Simple interest is interest paid on the original principal only (i.e.$18)

compound interest is the interest earned not only on the original principal (i.e.$18), but also on all interests earned previously (i.e. $1.1)

Difference of the interst earned: interest earned on all interest earned previously

Future Value

Is the value a certain amount of sum will grow to in a certain number of years when it is compounded at a specific rate.

Future Value can be computed using formula, table, calculator or spreadsheet.

Future Value – using Formula

FVn = PV (1 + i) n

Where FVn = the future of the investment at the end of “n” years

i = the annual interest (or discount) rate

n = number of years

PV= the present value, or original amount invested at the beginning of the first year

Future Value Example

Example: What will be the FV of $100 in 2 years at interest rate of 6%?

FV2= PV(1+i)2 = $100 (1+.06)2

$100 (1.06)2 = $112.36

Upward sloping curve shows the growth level of the amount of initial deposit

A steeper increase of money value with higher interest rate than a lower interest rate

Increasing Future Value

Future Value can be increased by:

Increasing number of years of compounding (n)

Increasing the interest or discount rate (i)

Increasing the original investment (PV)

See examples on next slide

Changing I, N, and PV

a) You deposit $500 in a bank for 2 years … what is the FV at 2%? What is the FV if you change interest rate to 6%?

FV at 2% = 500*(1.02)2 = $520.2

FV at 6% = 500*(1.06)2 = $561.8

b) Continue same example (6%), but change time to 10 years. What is the FV now?

FV at 6% = 500*(1.06)10= $895.42

c) Continue same example (6%, 10 years), but change contribution to $1500. What is the FV now?

FV at 6% = 1,500*(1.06)10 = $2,686.27

Present value reflects the current value of a future payment or receipt.

It can be computed using the formula, table, calculator or spreadsheet.

Present Value

Present Value – Using Formula

PV = FVn {1/(1+i)n}

Where PV = the present value of the future sum of money

FVn = the future value of the investment at the end of

n years

n= number of years until payment is received

i = the interest rate

PV Example

What will be the present value of $500 to be received 10 years from today if the discount rate is 6%?

PV = $500 {1/(1+.06)10}

= $500 (1/1.791)

= $500 (.558)

= $279

Take 10% for example, $90 deposit will be worth $100 in 2 years time with 10% interest rate; $40 deposit will be worth $100 in 20 years time with 10% interest rate

A steeper decrease of money value with higher interest rate than a lower interest rate

Annuity

An annuity is a series of equal amount payments for a specified number of years.

Ordinary annuity payments occur at the end of each period.

Compound Annuity

Saving or investing an equal sum of money at the end of each year for a certain number of years and allowing it to grow.

Future Value of an Annuity – Example

What will be the FV of 5-year $500 annuity compounded at 6%?

FV5 = $500 (1+.06)4 + $500 (1+.06)3 +$500(1+.06)2 +

$500 (1+.06) + $500

= $500 (1.262) + $500 (1.191) + $500 (1.124)+

$500 (1.060) + $500

= $631.00 + $595.50 + $562.00 + $530.00 + $500

= $2,818.50

Growth of a 5yr $500 Annuity Compounded at 6%

500

Present Value of an Annuity

Pensions, insurance obligations, and interest owed on bonds are all annuities. To compare these three types of investments we need to know the present value (PV) of each.

PV can be computed using calculator, tables, spreadsheet or formula.

Present Value of an Annuity

What amount must you invest today at 6% compounded annually so that you can withdraw $500 at the end of each year for the next 5 years?

PV5 = $500/ (1+.06)5 + $500 (1+.06)4 +$500(1+.06)3 +

$500/ (1+.06)2 + $500/(1+.06)

= $500/ (1.338)+ $500/ (1.262) + $500/(1.191) + $500/(1.124)+

$500/(1.06)

= $373.69 + $396.20+ $419.82 + $444.84.+471.70

= $2106.25

Making Interest Rates Comparable

We cannot compare rates with different compounding periods. For example, 5% compounded annually versus 4.9 percent compounded quarterly.

To make the rates comparable, we need to compute the annual percentage yield (APY) or effective annual rate (EAR).

Quoted rate versus Effective rate

Quoted rate could be very different from the effective rate if compounding is not done annually.

Example: $1 invested at 1% per month will grow to $1.126825 (=$1.00(1.01)12) in one year.

Thus even though the interest rate may be quoted as 12% compounded monthly.

The annual percentage yield (APY) or effective annual rate (EAR) is 12.68%

APY/EAR = (1+quoted rate/m)m – 1

Where m = number of compounding periods

= (1+.12/12)12 – 1

= (1.01)12 – 1

= 0.126825 or 12.6825%

Quoted rate versus Effective rate

The more frequent the compounding periods in a year, the higher the future value will be.

Finding PV and FV with Non-annual periods

If interest is not paid annually, we need to change the interest rate and time period to reflect the non-annual periods while computing PV and FV.

i = stated rate / numbers of compounding periods in a year

n = total compounding periods

Example

10% a year, with quarterly compounding for 10 years.

i = 10% / 4 = 2.5% or 0.025

n = 10*4 = 40 periods

Finding PV and FV with Non-annual periods

The formula for calculating the future value of an ordinary annuity (where a series of equal payments (PMT) are made at the end of each of multiple periods) is:

The formula for calculating the present value of an ordinary annuity is:

Perpetuity

A perpetuity is an annuity that continues forever

The present value of a perpetuity is

PV = PP/i

PV = present value of the perpetuity

PP = constant amount provided by the perpetuity

i = annuity interest (or discount rate)

Example: What is the present value of $2,000 perpetuity discounted back to the present at 10% interest rate?

= 2000/0.10 = $20,000

Perpetuity

Expected Cash Flows and Expected Return

The expected benefits or returns of an investment come in the form of cash flows.

Cash flows are used to measure returns (not accounting profits).

The expected cash flow is the weighted average of the possible cash flow outcomes, such that the weights are the probabilities of various outcomes.

Expected Cash flow (X) = ΣPi*xi

Where: Pi = probabilities of outcome i

xi = cash flows in outcome i

Expected Cash Flows and Expected Return

Measuring the Expected Cash Flow and Expected Return on $10,000 Investment

State of the economy	Probability of the states	Cash flow from the investment	% Return (Cash Flow/Inv. Cost)
Economic Recession	20%	$1,000	10% ($1,000/$10,000)
Moderate Economic Growth	30%	1,200	12% ($1,200/$10,000)
Strong Economic Growth	50%	1,400	14% ($1,400/$10,000)

Expected Cash Flow

Expected Cash flow = Σ Pi*xi

= 0.2*1000 + 0.3*1200 + 0.5*1400

= $1,260 on $10,000 investment

Expected Rate of Return

We can also determine the % of expected return on an investment. Expected Return is the weighted average of all the possible returns, weighted by the probability that each return will occur.

Expected Return (%) = Σ Pi*ki

Where: Pi = probabilities of outcome i

ki = expected % return in outcome i

Measuring the Expected Cash Flow and Expected Return on $10,000 Investment

State of the economy	Probability of the states	Cash flow from the investment	% Return (Cash Flow/Inv. Cost)
Economic Recession	20%	$1,000	10% ($1,000/$10,000)
Moderate Economic Growth	30%	1,200	12% ($1,200/$10,000)
Strong Economic Growth	50%	1,400	14% ($1,400/$10,000)

Expected Return (%) = Σ Pi*ki

Where: Pi = probabilities of outcome i

ki = expected % return in outcome i

= 0.2(10%) + 0.3 (12%) + 0.5(14%)

= 12.6%

Expected Rate of Return

Expected Risk (recap)

Risk refers to potential variability in future cash flows.

The wider the range of possible future events that can occur, the greater the risk. Thus, the returns on common stock is more risky than returns from investing in a savings account in a bank.

Standard deviation (S.D.) is one way of measuring risk. It measures the volatility or riskiness of portfolio returns.

Risk & Return: Historical Perspective (1990-2005)

Portfolio Theory

Portfolio refers to combining several assets.

Portfolio theory works out the ‘best combination’ of assets to hold to get the best return but reduce total risk.

Portfolio Theory

The market rewards diversification.

Through effective diversification, we can lower risk without sacrificing expected returns and we can increase expected returns without having to assume more risk.

Asset Allocation

Asset allocation refers to diversifying among different kinds of asset types (such as treasury bills, corporate bonds, common stocks).

An asset allocation decision has to be made today – the payoff in the future will depend on the mix chosen before, which cannot be changed.

Hence asset allocation decisions are considered the “most important decision” while managing an investment portfolio.

In 2015, $1,000 invested in the stock market will have earned less than $1,000 invested in banks

In 2014, $1,000 in stocks will have earned higher returns

History shows asset allocation matters and that taking high risk does not always pay off!!!

Of course, the decision has to be made today for the future and that is why asset allocation decisions determine who will be the “winners” in the financial market!!!

Example

Diversification can improve the risk-return characteristics of a portfolio.

Required Rate of Return

Investor’s required rate of returns is the minimum rate of return necessary to attract an investor to purchase or hold a security.

This definition considers the opportunity cost of funds, i.e. the foregone return on the next best investment.

Required Rate of Return

ksecurity=krf + krp

Where:

ksecurity= required return rate

krf = risk-Free Rate

krp = risk Premium

Risk-Free Rate

This is the required rate of return or discount rate for risk-less investments.

Risk-free rate is typically measured by Treasury bill rate.

Risk Premium

Additional return we must expect to receive for assuming risk.

As risk increases, we will demand additional expected returns.

Capital Asset Pricing Model (CAPM)

CAPM equates the expected rate of return on a stock to the risk-free rate plus a risk premium for the systematic (or market) risk.

CAPM provides for an intuitive approach for thinking about the return that an investor should require on an investment, given the asset’s systematic (or market) risk.

According to

If the required rate of return for the perfect diversified market portfolio km is 12%, and the krf is 5%, the market risk premium kmrp for the market would be 7%.

kmrp = km – krf

Capital Asset Pricing Model

krp = k – krf

Capital Asset Pricing Model

What is the require return for a single security?

CAPM suggests that Beta is a factor in required return of a selected security

1.52

Beta is the risk that remains for a company even after diversifying the portfolio:

A stock with a Beta of 0 has no systematic risk

A stock with a Beta of 1 has systematic risk equal to the “typical” stock in the marketplace

A stock with a Beta exceeding 1 has systematic risk greater than the “typical” stock

Most stocks have betas between 0.60 and 1.60.

Capital Asset Pricing Model

Example:

Market risk = 12%

Risk-free rate = 5%

Market risk premium =7%

5% + β*(12% – 5%)

If β = 0,Required rate = 5%

If β = 1,Required rate = 12%

If β = 2,Required rate = 19%

This 7% risk premium would apply to any security having systematic risk equivalent to the general market, or beta of 1.

In the same market, a security with Beta of 2 would provide a risk premium of 14%.

The Security Market Line (SML)

SML is a graphic representation of the CAPM, where the line shows the appropriate required rate of return for a given stock’s systematic risk.

The Security Market Line

RM Lecture 5 – notes.pdf

Risk Management Lecture 5 – Notes

Futures and Forwards

Compound Interest

Continuously Compounded Interest Rates

In derivatives work it is normal to use continuously compounded interest rates. With

continuous compounding, an amount A invested for n years at rate R grows to

AeRn

Where e = 2.71828

So at a rate of 5% continuously compounded a sum of £100 grows to 100e0.05

after a year

i.e. £105.13.

After 2 years it would grow to 100e2*0.05

= £110.52.

After 0.1 years it would grow to 100e0.1*0.05

=£100.50

Discounting at a continuously compounded rate R for n years involves multiplying by

e-Rn

So at a 10% continuously compounded rate of interest the discounted value of £100

payable in one year is 100e-0.1

= £90.48

Connection between Continuously Compounded Interest Rates and Periodically

Compounded Interest Rates

If an interest rate R is compounded m times per annum the terminal value of an amount A

invested for n years at rate R is

A(1+R/m)mn

The more frequently a given interest rate is compounded the more it tends to a

continuously compounded rate as shown in the table below:

(In mathematical terms as m tends to 0, (1+R/m)m

tends to eR)

Effect of compounding frequency on the value of £100 at the end of one year when

the interest rate is 5% per annum

Compounding Frequency Value of £100 at end of year

(£)

Annually (m=1) 105.000

Semiannually (m=2) 105.063

Quarterly (m=4) 105.095

Monthly (m=12) 105.116

Weekly (m=52) 105.125

Daily (m = 365) 105.127

Continuously 105.127

Conversion from Continuously Compounding Rates to Periodically Compounding

Rates

If Rc is a continuously compounded rate and Rm is the same rate with compounding m

times per year

We know that an amount A should grow to the same amount after 1 year under both

interest schedules

So AeRc

= A(1+Rm/m)m

So rearranging the equation

Rc = m.ln(1+Rm/m)

Rm = m(eRc/m

–1)

Determination of Forward Prices

Assumptions

In this section assume that the following are true for some market participants:

1. There are no transaction costs for trading. 2. Money can be borrowed or lent at the same risk-free rate of interest. 3. All net trading profits are taxed at the same rate.

These assumptions are approximately true for many of the largest market participants

(such as investment banks) so the reasoning in this section is a valid approach to

determining forward prices.

Notation

T is the time to maturity

r is the risk free rate

F0 is the forward price

S0 is the price of the asset underlying the forward contract

Forward Price for an Investment Asset providing no income

Assets such as non-dividend paying stocks and zero-coupon bonds fall into this category.

If F0  S0erT

, arbitrageurs can buy the asset and short forward contracts on the asset.

They will borrow S0 at rate r to buy the asset and will repay S0erT

thus if F0  S0erT

they

will make a guaranteed profit.

If F0  S0erT

, arbitrageurs can short the asset and buy forward contracts on the asset. By

shorting the asset they will obtain S0 which they can invest at rate r to have S0erT

at time

T thus if F0  S0erT

they will make a guaranteed profit.

Thus F0 = S0erT

-(1)

Note: Short sales are not possible for all investment assets but the above reasoning still

holds as people who hold the asset purely for investment purposes will find it attractive to

sell the asset and take a long position in a forward contract if the forward price is too low.

Forward Price for an Investment Asset providing a known income

Assets such as stocks paying a known dividend and coupon-bearing bonds fall into this

category.

Let the asset provide income with a present value of I during the life of the forward

contract

If F0  (S0 – I)erT

, arbitrageurs can buy the asset and short forward contracts on the asset.

If, F0  (S0 – I)erT

, arbitrageurs can short the asset and buy forward contracts on the

asset.

Thus F0 = (S0 – I)erT

-(2)

Forward Price for an Investment Asset providing a known yield

Let the q be the average yield per annum on an asset during the life of the forward

contract

Suppose we buy N units of the asset and invest the income from the asset in the asset.

The income from the asset causes our holding to grow at a continuously compounded rate

q. By time T the holding has grown to Neqt

units of the asset.

If F0  S0e(r-q)T

, arbitrageurs can buy the asset and short forward contracts on the asset.

If F0  S0e(r-q)T

, arbitrageurs can short the asset and buy forward contracts on the asset.

Thus F0 = S0e(r-q)T

(3)

Stock indices and foreign currencies can be regarded as important special cases of assets

falling into this category.

For stock indices, q is the dividend yield on the index.

For foreign currencies, the foreign currency can be regarded as the asset held and thus the

risk-free interest rate on the foreign currency rf can be regarded as the yield on the asset

held. This gives the formula F0 = S0e(r-rf)T

Forward Price for Commodities

Storage Costs can be regarded as negative income. If U is the present value of all storage

costs that will be incurred during the life of a forward contract we can modify equation

(2) to give

Thus F0 = (S0 + U)erT

-(4)

RM Lecture 6 – 2019.pptx

Risk ManagementThe Greeks

Lecture 6

Prof Youwei Li

The “Greek letters” (or the “Greeks”)

A financial institution that sells an option to a client in the over-the-counter market is often faced with the problem of managing its risk.

If the option happens to be the same as one that is traded on an exchange market, the financial institution can neutralize its exposure by buying on the exchange the same option as it has sold.

But when the option has been tailored to the needs of a client and does not correspond to the standardized products traded by exchanges, managing its risk is difficult.

The “Greek letters” (or the “Greeks”)

“Greek letters” is an alternative approach to manage option risk.

Each Greek letter measures a different dimension of the risk in an option position.

Traders can manage the Greeks so that all risks are acceptable.

Greeks-example

There are several measures of option price sensitivity each with respect to a different variable:

Delta

Gamma

Theta

Rho

Vega

Before measuring the risk in an option position by using these Greek letters, let us review what is a call option

Options Revision

A call option is an option to buy a certain asset by a certain date for a certain price (the strike price)

Here is an example of a long call on Microsoft at Expiry

Long Call on Microsoft at Expiry

Value of a call option on Microsoft:

strike price = $140

-5

100

120

140

160

180

200

Profit ($)

Terminal

stock price ($)

On the expiry date, the underlying stock price was $200, the investor can purchase such stock at $140 , so the profit was $60.

We also use the Balck-sholes model for pricing the stock options.

Before Expiry – Black-Scholes Model Pricing Formula: European non-dividend-paying stock

The European Call/Put Option on a non-dividend-paying stock

BSOPM can find the value of an option at any point in its life.

BSOPM can also find how that value changes with any one of the underlying variables.

–

Call option value equals spot price of the asset (times) an area from standard distribution table (d1)– strike price of the option (divided by) e to the risk free rate (times) time then (times) another area from standard distribution table (d2)

Put option value is equal to strike price of the option (divided by) e to the risk free rate (times) time standard distribution (-d2) taken away from spot price of the asset (times) standard distribution (-d1

K e^-rt: looks a big math here, but actually it is the present value of the exercise (strike) price discounted today at risk free rate of return. Since black scholes uses continues discounting module, so this e stands for exponational.

N(d1) bying n(d1) unites of the underlying assets; selling N(d2) units of underlying assets.

The formula of d1 is natural log of spot price divided by strike price (plus) the risk free rate (plus) 0.5 (times) variation of the underlay asset (times) time /(divided) standard variation (times) square root of time

Here a couple of things I want to mention here:

Option prices are a function of 5 factors: stock price, exercise (strike) price, time to expiration, volatility of underlying stock, risk free rate

there are the 5 factors that are going to black-scholes option pricing model

Whenever you see this T for time in black scholes model, it is going to be number of years. So if you have an option with one month to expiration, T is 1/12. it would be some fraction or desemal.

The other thing is volatility, we don’t know what the volatility is, so this is our best guess of the how volatile the stock is going to be in the coming year. We make sure we put this in decimal. So if we forecast the standard deviation is 25%, so we put 0.25.

E.g. Graph value against stock price before expiry (part way through its life).

Purpose of the Greeks

Traders need to understand the risk of an option before expiry date, so that they can manage or hedge the risk efficiently.

The Greeks enable option positions to be hedged efficiently

Example

A bank has sold for $300,000 a European call option on 100,000 shares of a non-dividend paying stock

S0 = $49, K = $50, r = 5%, s = 20%,

T = 20 weeks, m = 13%

The Black-Scholes value of the option is $240,000

How does the bank hedge its risk to lock in a $60,000 profit?

Mu: expected stock return

Example-Naked & Covered Positions

Naked position

Take no action

Covered position

Buy 100,000 shares today

1.11

Can both strategies leave the bank exposed to limited risk?

What is the risk inherent in the naked position?

What is the risk inherent in the covered position?

Example-Naked & Covered Positions

Naked position

Bank will lose if price of stock rises substantially before the option expires

The Bank will have to buy 100,000 shares in the market in 20 weeks and deliver them for a price of $50

If price of stock is $60 cost is $1,000,000

Overall loss of $1,000,000 – option premium = $700,000

Note naked position is alright if stock falls

Covered position

Bank will lose if the stock price drops substantially – It will lose on the stocks it holds

If price of stock drops to $40 it will have lost $900,000 on its stock position – this loss will have more than offset the $300,000 option premium

Note – covered position is alright if option is exercised

1.12

Purpose of the Greeks

The Greeks enable option positions to be hedged efficiently.

Consider Delta initially.

Delta

Delta (D) is the rate of change of the option price with respect to the underlying stock price

Option

price

Slope = D

Stock price

Delta

For a call option:

For a put option:

Partial derivatives with respect to S

Delta

Delta indicates the number of shares of stock required to mimic the returns of the option

E.g., a call delta of 0.80 means it will act like 0.80 shares of stock

If the stock price rises by $1.00, the call option will advance by about $ 80 cents

Delta

For a European option, the absolute values of the put and call deltas will sum to one

So if call delta is 0.80 put delta will be -0.20

(put delta is negative because if stock price goes up put price will go down)

In the BSOPM, the call delta is exactly equal to N(d1)

Delta

The delta of an out-of-the-money option approaches zero as time passes

Near expiry probably will not be exercised so option price insensitive to changes in stock.

The delta of an in-the-money option approaches 1.0 as time passes

Near expiry almost certainly will be exercised so moves in line with stock price (see slide).

Out of the money call option with a strike price higher than market price of underlying assets- value of the stock is lower than the option strike price

Out of the money put option with a strike price smaller than market price of underlying stock- value of option is lower than the stock price

Probability (exercise option)=0 option price is insensitive to changes in stock price

In of the money call option with a strike price lower than market price of underlying

In of the money put option with a strike price higher than market price of underlying stock

Probability (exercise option)=1 option price is align to changes in stock price

Hedge Ratio

Delta is the effective hedge ratio

Assume 1 short call option position has a delta of –0.25. If someone owns 1 share of the stock, short (selling) 4 calls results in a theoretically perfect hedge

OR, if short 1 option owning 0.25 shares would hedge

Consider original example – don’t need to fully cover option positions

You don’t need to cover exactly stock positions, you can tailor the numbers of shares or numbers of option holding

Theta

Theta (Q) is the rate of change of the option price with respect to the passage of time

– Theta

Theta

Theta is a measure of the sensitivity of an option to the time remaining until expiration:

Theta (cont’d)

It always negative, means always working against you as an option buyer not as an option seller

It shows the money that you are going to loss because you get closer to expiration.

A theta of –5.58, for example, means the option will lose 5.58p in value over the course of a year (0.02p per day).

It is the most important part of pricing period for option.

Gamma

Gamma is the second derivative of the option price with respect to the stock price

Gamma is the first derivative of delta with respect to the stock price

Gamma is also called curvature

Gamma (cont’d)

Gamma Addresses Delta Hedging Errors Caused By Curvature

Stock price

S’

Call

price

C’

C’’

The slope shows the first order changes of option price with respect to the changes of stock price

But looking, at the option price curve, it is not a straight line, it is actually a curve line towards right

So based on the first movement of the stock price, another increase in stock price also bring extra profit for option

1% increase in the underlying stock, call option profit will be 0.54%

1% another increase in the underlying stock, profit will be (0.54+0.1)%

1% reduction in the underlying stock, put option profit will be 0.54%

1% another reduction in the underlying stock, profit will be (0.54+0.1)%

Gamma (cont’d)

Gamma is a measure of how often option portfolios need to be adjusted as stock prices change and time passes

Gamma shows an option’s delta changes as the stock price changes

Options with gammas near zero have deltas that are not particularly sensitive to changes in the stock price

Vega

Vega (n) is the rate of change of option price with respect to volatility of the underlying stock

Vega is positive for both long calls and long puts

Vega is

gradient

Rho

Rho is the rate of change of the option price with respect to the interest rate

The least important of the Greeks – unless an option has an exceptionally long life, changes in interest rates only have a modest effect on its price

Rho

is gradient

In sum

Delta: Change in option price per dollar change in underlying asset

Theta: Change in option price per time change

Gamma: Change in delta per dollar change in underlying asset

Vega: Change in option price per X% change in volatility

Rho: Change in option price per X% change in interest rate

Greeks and Option Positions

Greeks can be used to manage positions in options as well as individual options.

Traders and investment managers use Greeks to create combinations of options to produce desired payoffs.

Hedging with Delta, Gamma, &Vega

Delta D can be changed by taking a position in the underlying asset

To adjust G (Gamma) & n (Vega) it is necessary to take a position in an option or other derivative

Delta hedging involves creating a position with zero delta. Because the delta of the underlying asset is 1, one way of hedging is to take a position of negative delta in the underlying asset for each long option being hedged.

Once an option position has been made delta neutral, the next stage is often to look at its gamma. .

Both delta and gamma hedging are based on the assumption that volatility of the underlying asset is constant. In practice, volatilities do change over time. The trader can make the opoition vega neutral.

Delta Neutrality

In practice, the sophisticated option traders usually rebalance options continually to maintain a delta neutral position

Delta neutrality means the combined deltas of the options to be zero

Delta neutrality strategy means that you are neutral about the future prospects for the market

Do not want to have either a bullish or a bearish position

Traders or portfolio managers try to rebalance their portfolio to maintain delta neutrality

Delta Neutrality

Institutional traders establish large neutral positions such as straddles and strangles.

Writing a straddle: short both a put and a call with the same striking price, expiration date, and underlying security

Writing a Straddle

Short straddle

Stock price at

option expiration

$40

Writing a Straddle

This market neutral strategy is specifically designed for low volatility conditions where stocks are inactive and you can collect a premium.

Price<40, put option exercised, you have to buy stocks from the option holder at $40

Price >40, call option exercised, you have to sell stocks with $40 to option holders, but pay higher price to get stocks first

Gamma Neutrality

Once an option position has been made delta neutral, the next stage is often to look at its gamma.

A gamma near zero means that the option position is robust to changes in market factors.

Gamma netrual

Vega Neutrality

Delta and gamma hedging are both based on the assumption that the volatility of underlying asset is constant.

However, volatility do change over time. A trader who wishes to hedge an option opposition against volatility changes can make the position vega neutral.

Traders usually ensure that their portfolios are delta-neutral at least once a day. But it is usually not feasible to maintain gamma and vega neutrality on a regular basis.

Gamma netrual

Hedging vs Creation of an Option Synthetically

When we are hedging we take positions that offset D, G, n, etc.

When we create an option synthetically we take positions that match D, G, & n

Hedging vs Creation of an Option Synthetically

Portfolio managers are sometimes interested in creating put options synthetically for the purposes of insuring an equity portfolio.

By trading the portfolio: equities vs risk-free securities

By trading index futures: equities vs index futures

Such type of portfolio insurance works well under normal conditions, but not in stressed conditions (Black Monday 1987) when it is unable to sell either stocks or index futures fast enough.

1.43

Market declines, increasing sold index futures

012

201

Call: ()()

Put: ()()

Where:

cSNdKeNd

pKeNdSNd

ddT

–

=—

æö

ç÷

èø

æö

ç÷

èø

==-

–

RM Lecture 7 – 2019.pptx

Risk ManagementValue-At-Risk

Lecture 7

Prof Youwei Li

Introduction to VAR

Measures such a delta, gamma and vega represent different aspects of the risk in a portfolio consisting of options and other financial assets.

Financial institutions usually calculate each of these measures each day for every market variable to which it is exposed.

These risk measures provide valuable information for the financial institution’s traders, but they are of limited use to senior management.

Introduction

Value at risk (VaR) is an attempt to provide a single number summarizing the total risk in a portfolio of financial assets for senior management.

It has become widely used by corporate treasurers and fund managers as well as by financial institutions.

Bank regulators also use VaR in determining the capital a bank is required to keep for the risks it is bearing.

Introduction

VaR was devised at JP Morgan.

In the aftermath of the 1987 stock market crash, the CEO demanded that the market risk team produced a simple report of the potential losses for the next trading day – on a single page and delivered no later than 45 minutes after market close.

Nowadays, it is a major activity for the bank to help clients to calculate VaR of their financial asset portoflios .

Devise: design

The VaR Measure1. Introduction

Definition

VaR is the largest likely loss from market risk (expressed in currency units) that an asset or portfolio will suffer over a time interval and with a degree of certainty selected by the user (Choudhry (2006), p.32)

VaR is a measure of the amount that could be lost from a position, portfolio etc. VaR is generally understood to mean the maximum loss an investment could incur at a given confidence level over a specified time horizon. (Wilmott (2006)

The VaR Measure1. Introduction

When using the VaR measure, an analyst is interested in making a statement of the following form:

“I am X percent certain that there will not be a loss of more than V dollars in the next N days”

Where:

V is the VaR of the portfolio. It is a function of two parameters: the time horizon, N days, and the confidence level, X percent. It is the loss level over N days that has a probability of only (100-X) percent of being exceeded.

Bank regulators require banks to calculate VaR for market risk with N=10 and X=99.

The VaR Measure1. Introduction

VaR is an attractive measure because it is easy to understand. In essence, it asks the simple question:

“How bad can things get?”

This is the question all senior managers want to answer. They are very comfortable with the idea of compressing all the Greek letters for all the market variables underlying a portfolio into a single number.

The VaR Measure2. Calculation

The calculation of VaR estimate follows four steps:

Determine the time horizon over which the firm wishes to estimate a potential loss

This horizon is set by the user,

In practice time horizons of 1 day to 1 year is the most common.

Select the degree of certainty required, which is the confidence level that applies to the VaR estimate

For banks a confidence level of 95% is usually enough,

Regulators may require 99% confidence level

Senior management and shareholders are often interested in the potential loss arising from catastrophe situations, such as a stock market crash, so for them a 99% confidence level is more appropriate.

The VaR Measure (cont.)2. Calculation

Create a probability distribution of likely returns for the instrument or portfolio under consideration

Several methods may be used. The easiest is a distribution of recent historical returns for the asset or portfolio which often looks like the curve associated with the normal distribution.

Calculate the VaR estimate

This is done by observing the loss amount associated with that area beneath the normal curve at the critical confidence interval value that is statistically associated with the probability chosen for the VaR estimate in Step 2.

The Time Horizon: VaR has two parameters: the time horizon in days, and the confidence interval, X. In practice, analysts almost invariably set N = 1 in the first instance. This is because there is not enough data to estimate directly the behaviour of market variables over time longer than one day. The usual assumption is:

Note: this formula is exactly true when the changes in the value of the portfolio on successive days have independent identical normal distributions with mean zero. In other cases, it is an approximation.

Calculating VaR

Historical Simulation

Model-Building

Historical Simulation

My name is Robert Hudson. I am lecturer and Module Manager

Calculating VaR -Historical Simulation

Create a database of the daily movements in all market variables.

The first simulation trial assumes that the percentage changes in all market variables are as on the first day

Historical Simulation continued

We are at end of day m, we want to simulate what might happen on the next day m+1

Suppose we use m days of historical data

Let v1 be the value of a variable on day 1

The (m+1) th trial assumes that the changes of the market variable are as on the 1st day, so the value of day m+1 is

Calculating VaR -Historical Simulation

The second simulation trial assumes that the percentage changes in all market variables are as on the second day

and so on

Historical Simulation continued

We are at end of day m, we want to simulate what might happen on the m+2 day

Suppose we use m days of historical data

The (m+2)th trial assumes that the changes in all market variables are as on the 2nd day, so the value on (m+2) day is, is

Generate 500 Scenarios of what might happen on day 501

My name is Robert Hudson. I am lecturer and Module Manager

Historical

Date

Libor

FT All Share

$/£

………

0.05

4000

1.51

0.05

4010

1.53

0.0525

4050

1.51

499

0.06

3500

1.39

500

0.06

3550

1.40

Example – Scenario 1/ 501st day

Libor 0.06 x 0.05/0.05 = 0.06

(V500 x V1/ V0)

FT ALL Share 3550 x 4010/4000 = 3559

(V500 x V1/ V0)

$/£ 1.40 x 1.53/1.51 = 1.42

(V500 x V1/ V0)

Scenario

Number

Libor

FT All Share

$/£

………

Portfolio Value £m

0.06

3559

1.42

0.063

3585

1.38

25.7

499

500

Example – Scenario 500/ 1000th day

What are the value on Scenario 500/ the 1000th day?

Historical

Date

Libor

FT All Share

$/£

………

0.05

4000

1.51

0.05

4010

1.53

0.0525

4050

1.51

499

0.06

3500

1.39

500

0.06

3550

1.40

Example – Scenario 500/ 1000th day

Libor 0.06 x 0.06/0.06 = 0.06

(V500 x V500/ V499)

FT ALL Share 3550 x 3550/3500 = 3601

(V500 x V500/ V499)

$/£ 1.40 x 1.40/1.39 = 1.41

(V500 x V500/ V499)

VaR from Scenarios

When the portfolio value has been calculated for all scenarios, we can work out VaR for 500 scenarios.

If 500 scenarios and looking for 99% VaR look at the drop in value occurring with the 5th (500*1%) worst scenario.

2008 Crisis and using Scenarios

Maybe Financial Institutions weren’t looking back far enough.

Prof Clarkson (Cass) – if engineers built bridges based on ten years of wind data they would be in big trouble if it blew down in a ‘20 year’ storm.

Model Building Approach

My name is Robert Hudson. I am lecturer and Module Manager

Calculating VaR – The Model-Building Approach

The main alternative to historical simulation is to make assumptions about the probability distributions of the portfolio return

This is known as the model building approach or the variance-covariance approach

Microsoft Example

We have a position worth $10 million in Microsoft shares

The volatility (standard deviation) of Microsoft is 2% per day (about 32% per year)

Therefore, one standard deviation changes of the value of Microsoft shares per day : 2%*$10million=$20,000

Daily Standard changes in value is $200,000=2%*10,000,000

Microsoft Example continued

We use N=10 and X=99

(10 day period and 99% confidence)

The one standard deviation of the change in the value of portfolio in 10 days is

10 days standard diviation of return 2 10^(1/2)=6.3%

10 days changes in value 10 million*6.3%

Microsoft Example continued

We assume that the expected change in the value of the portfolio is zero (This is OK for short time periods)

We assume that the change in the value of the portfolio is normally distributed

Since N(2.33)=0.99, the VaR is

A 1% probability that a normally distributed variable will decrease in value by more than 2.33 SD

99% CERTAIN THAT A NORMALLY SITRIBUTED VARIABLEWILL NOT DECREASE IN VALUE BY MORE THAN 2.33SD

AT&T Example

Consider a position of $5 million in AT&T

The daily volatility of AT&T is 1% (approx 16% per year)

The S.D per 10 days is

The VaR at 99% confidence level is

Portfolio

Now consider a portfolio consisting of both Microsoft and AT&T

Suppose that the correlation between the returns is 0.3

S.D. of Portfolio

A standard result in statistics states that

In this case sX = 200,000 and sY = 50,000 and r = 0.3. What is the standard deviation of the change in the portfolio value in one day?

VaR for Portfolio

The 10-day 99% VaR for the portfolio is

The benefits of diversification are

(1,473,621+368,405)–1,622,657=$219,369

The Linear Model

We assume

The daily change in the value of a portfolio is linearly related to the daily returns from market variables

The returns from the market variables are normally distributed

The General Linear Model continued

δP – Change in value of whole portfolio in a day.

δxi – Return on asset i in a day.

αi – Amount in asset i.

ρij – correlation between asset i and asset j.

Delta

Revision – delta measures the number of stocks needed to mimic the returns of an option

Linear Model and Options

Similar when there are many underlying market variables

where Di is the delta of the portfolio with respect to the ith asset

δP – Change in value of whole portfolio in a day.

δSi – Change in stock price i in a day.

Si – Stock price i.

δxi – Return (percentage) on stock price i in a day.

Example

Consider an investment in options on Microsoft and AT&T. Suppose the stock prices are 120 and 30 respectively and the deltas of the portfolio with respect to the two stock prices are 1,000 and 20,000 respectively

As an approximation

where dx1 and dx2 are the percentage changes in the two stock prices

Merits of Historical Simulation and Model Building

Historic simulation has the advantage that historical data determines the joint probability distribution of the market variables.

Historical simulation may be computationally slow

Historical simulation does not easily allow for volatility to be updated

Merits of Historical Simulation and Model Building

The model building approach can produce results quickly (if done analytically rather than by Monte Carlo simulation). It is possible to change parameters to allow for changes in volatility

The model building approach has a disadvantage if it assumes that market variables have a multivariate normal distribution which is often not justified.

Potential Problems of VaR

Some researchers have argued that VaR may tempt traders to choose a portfolio with a return distribution similar to that in Figure 18.2.

In addition, some assets may have heavy tails compared to a normal distribution.

The portfolios in Figures 18.1 and 18.2 have the same VaR, but the portfolio in Figure 18.2 is much riskier because potential losses are much larger.

Potential Problems of VaR

A measure to that deals with that problem is the “expected shortfall”.

Whereas VaR asks the question how bad can things get?”, expected shortfall asks: “If things do get bad, how much can the company expect to lose?”

Expected shortfall is the expected loss during an N-day period conditional that an outcome in the (100-X) percent left tail of the distribution occurs.

For example, with X=99 and N=10, expected shortfall is the average amount the company loses over a 10-day period when the loss is in the 1% tail of the distribution.

Potential Problems of VaR

For example, with X=99 and N=10, expected shortfall is the average amount the company loses is greater than the loss in the 1% tail of the distribution.

Partly Moving to Expected Shortfall

For banks’ trading books (not the other parts of their business), the regulators are now requiring banks to move to use expected shortfall by end of 2019.

Basel Committee of Bank Supervision consultative paper (2012): Fundamental Review of Trading Book.

Next Week

Stress testing

Banking Regulation

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RM Lecture 8 – 2019.pptx

Risk ManagementStress-Testing, Bank Regulation

Lecture 8

Prof Youwei Li

Session Plan

Back testing

Stress testing

Bank Regulation

Derivatives Problems II

Back Testing

Back-Testing

The process of testing a trading strategy based on relevant historical data to ensure its viability before the trader puts any actual capital in risk.

Back-testing in Value at Risk:

measures the accuracy of the VaR calculation. Tests how well VaR estimates would have performed in the past.

Back-Testing in VaR

VaR: measures the maximum amount of loss over a specified time horizon with a given confidence level.

Back-testing in VaR: compares the predicted losses from the calculated VaR with the actual losses realized at the end of the specified time horizon.

Back-Testing in VaR

For example

We could ask the question: How often was the actual 10-day loss greater than the10 day& 99% VaR = $10 million ?

If it did happen much more than 1% there is a problem!

Example – Long-Term Capital Management (LTCM)

Investment Strategy of Convergence Arbitrage

Compare theoretical prices of similar securities

Buy cheap one, sell expensive one

Built up heavy exposure to illiquid bonds

Long-Term Capital Management L.P. (LTCM) was a management firm based in , that used absolute-return trading strategies combined with high financial .

The core strategy of LTCM can be described as "convergence-arbitrage" trades, trying to take advantage of small differences in prices among near-identical bonds. Compare, for instance, a corporate bond yielding 10% and an otherwise identical Treasury bond with a yield of 7%. The yield spread of 3% represents some compensation for credit risk.

If the corporate borrower does not default, a trade that is long the corporate bond and short the Treasury bond would be expected to return 3% for every dollar in the first bond.

The key is that eventually the two bonds must converge to the same value.

Example – LTCM

In 1998 Russia defaulted on its debt causing a ‘flight to quality’ in the bond market

Huge losses for LTCM which had to be bailed out by Barclays, Credit Suisse, Deutsche Bank, Goldman Sachs, etc.

when the Russian government defaulted on their domestic local currency bonds. This came as a surprise to many investors because according to traditional economic thinking of the time, a sovereign issuer should never need to default given access to the printing press. There was a flight to quality, bidding up the prices of the most liquid and benchmark securities that LTCM was short, and depressing the price of the less liquid security they owned.

By the end of August, the fund had lost $1.85 billion in capital

The losses of LTCM were much larger than were predicted by VaR.

Myron Scholes made the following points:

Correlation patterns and variances may change dramatically when market is very volatile

Variables that are not normally highly correlated may become highly correlated

Example-LTCM

Testing the Validity of a Bank’s VaR

The validity of a bank’s estimated VaR is assessed by comparing the actual daily trading gains or losses to the estimated VaR over a particular period (like back-testing).

If the VaR is estimated properly, only 1 percent of the actual losses are worse than the estimated VaR (if VaR is calculated using 99% confidence level).

The bank would be concerned (as would regulators) if the actual results from the trading businesses were frequently worse than the estimated VaR.

Limitations of VaR

The VaR model was generally not effective at detecting the risk of banks during the credit crisis.

The VaR model failed to recognize the degree to which the value of bank assets (such as mortgages or mortgages-backed securities) could decline under adverse conditions.

The use of historical data from before 2007 did not capture the risk of mortgages because investments in mortgages during that period normally resulted in low defaults.

Limitations of VaR

Thus, the VaR model was not adequate for predicting the possible estimated losses.

Many banks experienced larger losses than they thought was possible in 2008, and they had to use up some of their capital to absorb these losses.

Thus, their capital proved to be deficient.

1.12

Stress Testing

This involves testing how well a portfolio performs under some of the most extreme market moves seen in the past

E.g. the 1987 crash, the 1992 Sterling crisis, 9/11, 1998 Russian Default, Credit crunch etc.

HBOS Example

HBOS was one of the five largest UK banks (one of the largest in the world).

It was formed in 2001 by merger of as Halifax and Bank of Scotland.

Effectively failed in the financial crisis.

excessive risk-taking.

HBOS Example

Forced to merge with Lloyds bank.

Brought down Lloyds (a pre tax loss of £10.8bn in 2008) – had to be rescued by the government.

Causes of HBOS failure

The board failed to instil a culture within the firm that balanced risk and return appropriately and it lacked sufficient experience and knowledge of banking.

There was a flawed and unbalanced strategy and a business model with inherent vulnerabilities arising from an excessive focus on market share, asset growth and short-term profitability.

An over-exposure to highly cyclical commercial real estate (CRE) at the peak of the economic cycle.

1.17

Bank-Imposed Stress Tests to supplement the VaR

A Bank wants to estimate the loss that would occur in response to an extreme adverse market event.

First, it identifies an extreme event that could occur, such as an increase in interest rates on one day that is 10 standard deviations from the mean daily change in interest rates. (The mean and standard deviation of daily interest rate movements may be based on a recent historical period, such as 300 days.)

The bank then uses this scenario along with the typical sensitivity of its trading businesses to such a scenario to estimate the loss on its trading businesses as a result.

Bank-Imposed Stress Tests to supplement the VaR

It may then repeat this exercise based on a scenario of decline in the market value of stocks that is 10 standard deviations from the mean daily change in stock prices.

It may even estimate the possible losses in its trading businesses from an adverse scenario in which interest rates increase and stock prices decline substantially on a given day.

Bank Regulation

Global Bank Regulations

Each country has a system for monitoring and regulating commercial banks, although the division of regulatory power between the central bank and other regulators varies among countries.

Differences in regulatory restrictions can allow some banks a competitive advantage in a global banking environment.

Global Bank Regulations (cont.)

US commercial banks could not deal in securities from 1932 to 1999 under the Glass-Steagall Act (1932). Gramm–Leach–Bliley Act of 1999 largely repealed Glass-Steagall. There were wave of mergers between commercial and investment banks. Some commentators blame this for financial crisis.

Historically, Canadian banks were not as restricted in offering securities services as U.S. banks Recently, Canadian banks have began to enter the insurance industry.

Global Bank Regulations (cont.)

European banks have had much more freedom than U.S. banks in offering securities services such as underwriting corporate securities. Many European banks are allowed to invest in stocks.

UK banks have taken over many insurance companies and many have large investment banking arms.

Japanese commercial banks have some flexibility to provide investment banking services, but not as much as European banks.

Japanese banks are allowed to use depositor funds to invest in stocks of corporations. Thus Japanese banks are not only creditors of firms, but are also their shareholders.

How Regulators Monitor Banks?

A supervisory rating system originally developed in the US in 1979 to classify a bank’s overall condition, which together comprise the Camels ratings, so named for the acronym that identifies the six characteristics:

Capital adequacy

Asset quality

Management

Earnings

Liquidity

Sensitivity

Rating 1 Indicates strong performance and risk management practices that consistently provide for safe and sound operations.

Rating 2 Reflects satisfactory performance and risk management practices that consistently provide for safe and sound operations.

Rating 3 Represents performance that is flawed to some degree and is of supervisory concern

Rating 4 Refers to poor performance that is of serious supervisory concern.

Rating 5 Considered unsatisfactory performance that is critically deficient and in need of immediate remedial attention

Limitations of the CAMELS Rating System –

The CAMELS rating system is essentially a screening device. Because there are so many domestic banks (e.g. over 8,000 US banks), regulators do not have the resources to closely monitor each bank on a frequent basis.

The rating system identifies what are believed to be the problem banks. Over time, some problem banks improve and are removed from the “problem list”, while others may deteriorate further and ultimately fail. Still other banks are added to the problem list.

Limitations of the CAMELS Rating System –

Although examinations by regulators may help to detect problems experienced by some banks in time to save them, many problems still go unnoticed, and by the time they are detected, it may be too late to find a remedy.

Because financial ratios measure current or past performance rather than future performance, they do not always detect problems in time to correct them.

The task of assessing a bank is as much an art as it is a science. Subjective opinion must complement measurements to provide the best possible evaluation of a bank.

Limitations of the CAMELS Rating System

Any system used to detect financial problems may misjudge in one of two ways:

It may classify a bank as safe when in fact it is failing, or

It may classify a bank as in very risky when in fact it is safe.

The first type of mistake is more costly, because some failing banks are not identified in time to help them.

To avoid this mistake, bank regulators could lower their benchmark composite rating. However, if they did, many more banks would be on the problem list requiring close supervision, and regulators’ limited resources would be spread too thin.

Corrective Action by Regulators

When a bank is classified as a problem bank, regulators thoroughly investigate the cause of its deterioration. Corrective action is often necessary. Regulators may examine such banks frequently and thoroughly and discuss with bank management possible remedies to cure the key problems.

For example regulators may request that a bank boost its capital level or delay its plans to expand.

They can require that additional financial information be periodically updated to allow continued monitoring.

They have the authority to remove particular officers and directors of a problem bank if doing so would enhance the bank’s performance.

They even have the authority to take legal action against a problem bank if the bank does not comply with their suggested remedies. Such a drastic measure is rare, and would not solve the existing problems of the bank.

CAMEL assessment 1-Capital Adequacy1. capital requirement

Under the 1996 amendment to the Basel Accord, the capital requirements on large banks who have substantial trading businesses (such as interest rate derivatives, foreign exchange derivatives, and underwriting services) to

apply value-at-risk model

reflect their exposure to general market risk such as interest rates, stock prices, and exchange rates.

Capital Adequacy 1. capital requirement

The VaR model can be applied in various ways to determine capital requirements.

In general, a bank defines the VaR as the estimated potential loss from its trading business that could result from adverse movements in market prices.

Regulators typically use a 99 percent confidence level, meaning that there is a 99 percent chance that a loss on a given day will be more favorable than the VaR estimated.

Capital Adequacy1. capital requirement

When applied to a daily time horizon, the actual loss from a bank’s trading businesses should not exceed the VaR estimated loss on more than 1 out of every 100 days.

Banks estimate the VaR by assessing the probability of specific adverse market events (such as abrupt change in interest rates) and the possible sensitivity response to those events.

Banks with a higher maximum loss based on a 99 percent confidence interval are subject to higher capital requirements.

Capital Adequacy 2. The case of the Bank of England (BoE)

The Bank of England model review process includes discussion of the following areas:

The mathematics of the model and underlying assumptions

Systems and controls

Risk management, reporting procedures and limits

Staffing issues

Reconciliation and valuation procedures

The setting of capital requirements

Certain conditions and standards need to be met prior to recognition of the model. These standards vary according to the size of the bank institution and the type of the model being used.

The review process takes the form of an on-site visit with follow-up of any outstanding issues to be met before recognition can be granted

Capital Adequacy 2. The case of the Bank of England (BoE)

The Bank of England adopted the following procedure:

The European Union (EU) Capital Adequacy Directive (CAD) has been in place since January 1996 – UK banks ultimately governed by this. .

UK banks wishing to use their own VaR model for calculating capital requirements under CAD must have it recognized by – the BoE;

No particular type of model is prescribed and banks may use models based on back-testing, variance-covariance matrices, Monte Carlo simulation or simple aggregation of risk numbers.

If using their own models banks must be able to calculate the CAD requirement on a date randomly chosen by the BoE supervisor, and notify the supervisor of the calculation the following day

The bank will then be required to calculate its capital requirement both according to the standard method and its own VaR model.

Capital Adequacy

This focus on daily price movements forces banks to continuously monitor their trading positions so that they are immediately aware of any losses.

Many banks now have access to the market values of their trading businesses at the end of every day. If banks used a longer-term horizon (such as month), larger losses might build up before being recognized.

Back-Testing

This is the process of comparing VaR risk estimates to actual portfolio performance.

Each business day firms should compare the 1-Day VaR measure calculated by their model and the actual 1-Day change in the portfolio value.

For each actual loss greater than predicted, an “Exception” is reported.

For multiple exceptions a plus factor of between 0 and 1 is applied to the formula used to calculated the banks’ capital requirement. The higher the number of “Exceptions” the higher the capital banks will be required to put aside to deal with unfavorable moves in the value of their portfolio of assets.

Regular Stress Tests during the Credit Crisis

Regulators can impose stress tests on banks. Stress testing of bank capital may be frequently applied in the future to ensure that banks have sufficient capital.

Regulators closely monitor bank capital levels during periods of weak economic conditions, because banks may need to rely on their capital to cushion losses and avoid bankruptcy.

In April 2009, US regulators applied stress tests to the 19 largest bank holding companies to determine if the banks had enough capital.

One of the stress tests applied to banks in April 2009 involved forecasting the likely effect on the banks’ capital levels if recession existing at that time lasted longer than expected.

Regular Stress Tests during the Credit Crisis

Since many of the banks were already incurring losses at the time, this adverse scenario would cause them to incur larger losses and to incur losses farther into the future.

As a result, the banks would have to periodically use a portion of their capital to cover their losses, resulting in a reduction in their capital over time.

US Regulators then focused on banks that did not do well on the stress tests in April 2009 in order to ensure that these banks would have sufficient capital even if the recession lasted for a longer period of time.

These banks could attempt to raise capital by issuing stock to the public. However, if they believed that they would not be able to raise sufficient funds from issuing stock to the public, they could issue preferred stock to the Federal Reserve.

Basel Committee on Banking Supervision- Basel Accords

Basel Concordat 1975

Supervisory responsibilities of home country and host country regulators for multinational companies

Basel Accord 1988 (Basel I)

Credit risk, leverage risk

Capital ratio

Basel Committee on Banking Supervision- Basel Accords

Basel Accord 2004 (Basel II)

Three Pillars: minimum capital, supervisory review framework, and market discipline on transaction disclosure.

Basel Accord 2010 (Basel III)

Reaction to the 2008 Crisis being introduced over the period to 2018.

Evolutionary rather than revolutionary.

Broadly the same approach and methods but tougher in that Banks are required to hold more capital.

RM Lecture 9 Credit Rating 2019.pptx

Risk ManagementCredit Rating (Corporations, Countries)

Lecture 9

Prof Youwei Li

Session Plan

Credit rating of Corporations

Credit rating of Countries

Commercial Credit Risk and the Rating of Individual Credit

Commercial credit risk is the largest and most elementary risk faced by many banks, and it is a major risk for many other kinds of financial institutions and corporations as well.

Plus assessing commercial credit risk is a complicated task:

determining how likely it is that an event of default will happen; and

how costly will turn out to be if it does occur.

Therefore, no surprise to find that there are many different approaches to the problem.

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Country	Rating	Confirmed
Belgium	AA-	30 Nov 2018
Germany	AAA
Ireland	A+	14 Dec 2018
Italy	BBB (negative watch)	22 Feb 2019
UK	AA (negative watch)	20 Feb 2019

Quarter	Revenues (USD)	Exchange rate	Revenues (CAD)
1 (actual)	10.000.000	1,5280	15.280.000
2 (actual)	10.000.000	1,4326	14.326.000
3(actual)	10.000.000	1,3328	13.328.000
4(estimated)	10.000.000	1,2910	12.910.000

Exchange rate (USD/CAD)	LiabilityUSD
0,6500	$6.500.000,0
0,7000	$7.000.000,0
0,7500	$7.500.000,0
0,8000	$8.000.000,0
0,9000	$9.000.000,0

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