Risk ManagementUniversity of Economics, Kraków, 2012

Tomasz Aleksandrowicz

market risk management

techniques: hedging & diversificationmeasuring market risk: value at risk (VaR)

derivatives summary matrix

hedging

hedging

• investment position intended to offset potential losses

Hedgeing (I)

transaction to reduce or eliminate an exposure to risk• an investment position intended to offset potential losses of

other investment• the idea is to protects assets against unfavourable movements

in value of the underlying asset• hedging on stock, industry, market, country level• hedging is wiedly using derivatives

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Hedgeing (II)

• crucial element is negative correlation of assets• financial instruments bought as a hedge transfer risk to

different party• tend to has opposite-value movements to the underlying• It can reduce the variability of the asset value changes / cash

flow

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Hedging tools / methods

• short selling• options• features/forwards• swaps• other derivatives

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Short selling

• long position vs 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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stock price hedgeing

• Two companies from same industry as trader is interested in Asset A and want to hedge industry risk

• Day1: trader creates a portfolio– Asset A price: $5, position of 100 = $5000– Asset B price: $10, short position of 50 = $5000

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stock price hedgeing

• Two companies from same industry as trader is interested in Asset A and want to hedge industry risk

• Day1: trader creates a portfolio– Asset A price: $5, position of 100 = $5000– Asset B price: $10, short position of 50 = $5000

• Day 2: industry good news– Asset A price: $6, value $6000, profit $1000– Asset B price: $12, value $5500, loss $600

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stock price hedgeing

• Two companies from same industry as trader is interested in Asset A and want to hedge industry risk

• Day1: trader creates a portfolio– Asset A price: $5, position of 100 = $5000– Asset B price: $10, short position of 50 = $5000

• Day 2: industry good news– Asset A price: $6, value $6000, profit $1000– Asset B price: $12, value $5500, loss $600

• Day3: industry crash– Asset A price: $3, value $3000, loss $2000 – Asset B price: $6, value $3000, profit $2000

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hedging issues

• usual high brokerage fees and commissions• 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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hedging

diversification

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)

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portfolio creation process

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portfolio types

• market portfolio – all tradable assets on market• main index portfolio – all main index assets• efficient portfolio – portfolio with:– maximum expected return for a given level of risk– minimum risk for a given expected return

• optimal portfolio – collection of securities that provides an investor with the highest level of expected return

• zero-risk portfolio - constant return portfolio18

diversification (I)

• diversification means reducing risk by investing in a variety of assets

• 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 • correlation values:[-1,1]

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two assets portfolio

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two assets portfolio

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divrsification (II)

• 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 (III)

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Asset specific risk – variance / sd

• specicfic risk could be measured by variance and standard deviation of the asset

• sd and var how far a set of numbers are spread out from each other (from mean/expected value)

• variance:

• standard deviation (sq root ov variance):

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Assets historical return and sd

Based on annual returns from 1926-2004

Avg. Return SDSmall Stocks 17.5% 33.1%Large Co. Stocks 12.4% 20.3%L-T Corp Bonds 6.2% 8.6%L-T Govt. Bonds 5.8% 9.3%U.S. T-Bills 3.8% 3.1%

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Asset systematic risk - beta factor

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

• the systematic risk is measured by the beta coefficient, or β.• variation in asset/portfolio return depends on return of market portfolio

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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 (5 yr)

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.31Heinz.H.J

.41ExxonMobil

.57Pfizer

.66sMcDonald'

.67PepsiCo

1.00Airlines Delta

1.05Ford

1.18GE

2.14 er DellComput

3.30Amazon

BetaStock

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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