Rm 8-1

Risk ManagementUniversity of Economics, Kraków, 2012

Tomasz Aleksandrowicz

market risk management

techniques: hedging & diversificationmeasuring market risk

derivatives summary matrix

risk category options futures forwards swaps

equity stock option index future (e.g. DIJA)

repo (repurchase agreement) equity swap

interest rate e.g. basis swap e.g. Euribor future

FRA (forward rate agreement)

interest rate swap

foreign exchange FX option FX future FX forward FX swap

commodity e.g. gold option e.g. weather derivatives forward contract commodity swap

hedging

hedging

• protects assets against unfavourable movements in value of the underlying asset

• investment position intended to offset potential losses of organization’s financial exposures

• it is to reduce the volatility of the asset value changes / cash flow

• using assets that have negative or weak correlation• using derivatives and/or short selling

correlation

• known as the correlation coefficient• ranges between -1 and +1, where:– -1 - perfect negative correlation - two securities moves

opposite direction– 0 - no correlation (random relation)– +1 - perfect positive correlation - two securities moves

same direction

• perfectly correlated securities are rare, rather some degree of correlation

correlation table (example)

Google Microsoft Ford Motor AT&T

JP Morgan Chase

Merck & Inc.

Exxon Mobile

Walt Disney

Google 0.26 0.35 0.4 0.64 0.06 0.16 0.34

Microsoft 0.26 0.57 0.35 0.61 0.34 0.83 0.79

Ford Motor 0.35 0.57 0.62 0.61 0.28 0.72 0.62

AT&T 0.4 0.35 0.62 0.55 0.39 0.6 0.58

JP Morgan Chase

0.64 0.61 0.61 0.55 0.43 0.73 0.68

Merck & Inc. 0.06 0.34 0.28 0.39 0.43 0.5 0.54

Exxon Mobile 0.16 0.83 0.72 0.6 0.73 0.5 0.8

Walt Disney 0.34 0.79 0.62 0.58 0.68 0.54 0.8

basic hedging methods

• pair of stock with negative correlation• derivatives (options, features/forwards, swaps, etc.)• short selling

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short selling

• difference: long position and short position• short selling is selling of borrowed assets• profit is difference between price at borrow date and

price of re-purchase• short selling is widely treated as speculative

technique• short selling is regulated by financial regulators

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example 1: stock A onlydate investment quantity price value total value of

investment

start day stock A 100 100 10,000 10,000

next day up stock A 100 105 10,500 10,500

next day down

stock A 100 95 9,500 9,500

example 2: stock A hedge by stock Bwith negative correlation of stock B (-0,4)

date investment quantity price value total value of investment

start day stock A 50 100 5,000 10,000

start day stock B (-0.4) 100 50 5,000


next day up stock B (-0.4) 100 49 4,900

next day down

stock A 50 95 4,750 9850

next day down

stock B (-0.4) 100 51 5,100

example 3: stock A put option hedgeput (sell) option at price of 100


start day stock A 99 100 9,900 9,999

start day put option A (100)

99 1 99


next day up put option A (100)

100 0 0

next day down

stock A 99 95 9,405 9,900

next day down

put option A (100)

99 5 495

example 4: stock A hedge short sellshort selling of stock B with positive correlation (0,8)


start day stock A 50 100 5,000 10,000

start day short stock C (0.8)

100 50 5,000


next day up short stock C (0.8)

100 48 4,800

next day down

stock A 50 95 4,750 9,950

next day down

short stock C (0.8)

100 52 5,200

hedging strategies output summary

strategy start value of investment

value next day up value next day down

stock A only 10,000 10,500 9,500

stock A + stock B (-0.2) 10,000 10,150 9,850

stock A + put option A 9,999 10,395 9,900

stock A + short stock C (0,8) 10,000 10,050 9,950

hedging issues

• precise calculation and smart decisions needed• brokerage fees and commissions (additional costs)• complexity of the derivatives – risk of

misunderstanding or misconduct• complexities associated with the tax and accounting

consequences• combined with leverage is so-called ‘weapon of mass

destruction

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diversification

diversification

• diversification means reducing risk by investing in a variety of assets (within one or more asset class)

• it means: don't put all your eggs in one basket• diversified portfolio will have less risk than the

weighted average risk of its elements• often less risk than the least risky of its parts• crucial element is selection of assets with low

correlation

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specific and systematic risk

• difference: specific risk and systematic risk• individual, specific securities are much more risky

than the market• specific risk can be lowered by diversification• systematic risk is a limit for diversification efficiency –

can not be eliminated by diversification

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diversification and risk

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measurement of specific risk

• specicfic risk could be measured by standard deviation (SD)• SD tells how far a set of numbers are spread out from each

other (from mean/expected value)• standard deviation (sq root ov variance):

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long-run historical return and SD

Avg. Return SDSmall Stocks 17.5% 33.1%Large Co. Stocks 12.4% 20.3%L-T Corp Bonds6.2% 8.6%L-T Govt. Bonds 5.8% 9.3%U.S. T-Bills 3.8% 3.1%

based on 80yr data (1926-2004)

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measurement of systematic risk

• can be measured as the sensitivity of a stock’s return to fluctuations in returns on the market portfolio

• is measured by the beta coefficient, or β.

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b = % change in asset return

% change in market return

Beta factor interpretation

• if = 0b– asset is risk free

• if = 1b– asset return = market return

• if > 1b– asset is riskier than market index

• if < 1b– asset is less risky than market index

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Beta factor sample

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stock bGoogle 1.19

Microsoft 1.00

Ford Motor 2.92

AT&T 0.46

JP Morgan Chase 1.66

Merck & Inc. 0.30

Exxon Mobile 0.61

Walt Disney 1.37

example: two assets portfolio

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example: two assets portfolio

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example: two assets portfoliostart price Mon Tue Wed Thu Fri SD

stock A (100% - 100 shares) 100 105 110 112 108 103

portfolio value 10000 10500 11000 11200 10800 10300 3.6469

stock B (100% - 200 shares) 50 52 53 52 53 54

portfolio value 10000 10400 10600 10400 10600 10800 0.8367

start price Mon Tue Wed Thu Fri SD

stock A (50% - 50 shares) 100 105 110 112 108 103

stock B (50% - 100 shares) 50 52 53 52 53 54

portfolio value 10000 10450 10800 10800 10700 10550 2.2418

modern portfolio theory

• portfolio - collection of securities that together provide an investor with an attractive trade-off between risk and return

• portfolio theory - concept of making security choices based on portfolio expected returns and risks (risk-return trade-off)

• capital asset pricing model (CAPM) and many other mathematical models and concepts used for portfolio management

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portfolio creation process

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portfolio types

• market portfolio – all tradable assets on market• main index portfolio – all index assets (e.g. DIJA)• efficient portfolio – where:– maximum expected return for a given level of risk– minimum risk for a given expected return

• zero-risk portfolio - constant low-return portfolio with no risk

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measuring risk: value at risk

VaR (I)

• Market risk not much in Basel II scope• VaR (Value-at-Risk) – standard market risk method• In its simplest form: market VAR takes the banks’s

market risks and estimates how much they might lose over a given time period

• Example: if bank has a one-day, 99% VaR of $50 million, then 99 days out of 100 it should not expect to lose more than $50 million.

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VaR (II)

• The volatility of the underlying asset– e.g. equity or bond price, currency rate

• A matrix of correlations– e.g. the historical price relationships between equities, interest rates,

currencies, credit spreads, and so on);

• A liquidation period – e.g. one day, one week, one month or however long a firm thinks it

will take to unwind or neutralize its risk

• A statistical confidence level – e.g. 95% or 99%

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VaR problems

• VAR does not tell how big the loss might be on the 100th day

• it is based on historical correlations which can break down in times of market stress,

• it is based on statistical assumptions (which may or may not become true)

• VAR can really only be used for marked-to-market portfolios (revalued every day)

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Business

Rm 8-1