The document discusses various techniques for managing market risk, including hedging using derivatives and diversification. It provides examples of how different derivatives like options, futures, forwards and swaps can be used for hedging equity, interest rate, foreign exchange, and commodity risk. The document also discusses measuring market risk using value at risk and the limitations of VAR. It provides examples of portfolio creation and how diversification across assets with low correlation can reduce overall risk.

1. Risk Management
University of Economics, Kraków, 2012
Tomasz Aleksandrowicz

2. market risk management
techniques: hedging & diversification
measuring market risk

3. derivatives summary matrix
risk category options futures forwards swaps
index future (e.g. repo (repurchase
equity stock option equity swap
DIJA) agreement)
e.g. Euribor FRA (forward rate interest rate
interest rate e.g. basis swap
future agreement) swap
foreign exchange FX option FX future FX forward FX swap
e.g. weather
commodity e.g. gold option forward contract commodity swap
derivatives

4. hedging

5. 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

6. 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

7. correlation table (example)
JP
Ford Merck & Exxon Walt
Google Microsoft AT&T Morgan
Motor Inc. Mobile Disney
Chase
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 0.64 0.61 0.61 0.55 0.43 0.73 0.68
Chase
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

8. basic hedging methods
• pair of stock with negative correlation
• derivatives (options, features/forwards, swaps, etc.)
• short selling
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9. 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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10. example 1: stock A only
date 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 stock A 100 95 9,500 9,500
down

11. example 2: stock A hedge by stock B
with 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 A 50 105 5,250 10,150
next day up stock B (-0.4) 100 49 4,900
next day stock A 50 95 4,750 9850
down
next day stock B (-0.4) 100 51 5,100
down

12. example 3: stock A put option hedge
put (sell) option at price of 100
date investment quantity price value total value of
investment
start day stock A 99 100 9,900 9,999
start day put option A 99 1 99
(100)
next day up stock A 99 105 10,395 10,395
next day up put option A 100 0 0
(100)
next day stock A 99 95 9,405 9,900
down
next day put option A 99 5 495
down (100)

13. example 4: stock A hedge short sell
short selling of stock B with positive correlation (0,8)
date investment quantity price value total value of
investment
start day stock A 50 100 5,000 10,000
start day short stock C 100 50 5,000
(0.8)
next day up stock A 50 105 5,250 10,050
next day up short stock C 100 48 4,800
(0.8)
next day stock A 50 95 4,750 9,950
down
next day short stock C 100 52 5,200
down (0.8)

14. hedging strategies output summary
strategy start value of value next day up value next day
investment down
stock A only 10,000 10,500 9,500
stock A + stock B
10,000 10,150 9,850
(-0.2)
stock A + put
9,999 10,395 9,900
option A
stock A + short
10,000 10,050 9,950
stock C (0,8)

15. 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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16. diversification

17. 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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18. 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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19. diversification and risk
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20. 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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21. long-run historical return and SD
Avg. Return SD
Small 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%
based on 80yr data (1926-2004)
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22. 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.
% change in asset return
b= % change in market return
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23. Beta factor interpretation
• if b = 0
– asset is risk free
• if b = 1
– asset return = market return
• if b > 1
– asset is riskier than market index
• if b < 1
– asset is less risky than market index
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24. Beta factor sample
stock b
Google 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 24

25. example: two assets portfolio
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26. example: two assets portfolio
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27. example: two assets portfolio
start 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

28. 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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29. portfolio creation process
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30. 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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32. measuring risk: value at risk

33. 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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34. 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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35. 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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