Rm 8-1

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Rm 8-1

  1. 1. Risk ManagementUniversity of Economics, Kraków, 2012 Tomasz Aleksandrowicz
  2. 2. market risk management techniques: hedging & diversification measuring market risk
  3. 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) swapforeign exchange FX option FX future FX forward FX swap e.g. weather commodity e.g. gold option forward contract commodity swap derivatives
  4. 4. hedging
  5. 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. 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. 7. correlation table (example) JP Ford Merck & Exxon Walt Google Microsoft AT&T Morgan Motor Inc. Mobile Disney ChaseGoogle 0.26 0.35 0.4 0.64 0.06 0.16 0.34Microsoft 0.26 0.57 0.35 0.61 0.34 0.83 0.79FordMotor 0.35 0.57 0.62 0.61 0.28 0.72 0.62AT&T 0.4 0.35 0.62 0.55 0.39 0.6 0.58JPMorgan 0.64 0.61 0.61 0.55 0.43 0.73 0.68ChaseMerck &Inc. 0.06 0.34 0.28 0.39 0.43 0.5 0.54ExxonMobile 0.16 0.83 0.72 0.6 0.73 0.5 0.8WaltDisney 0.34 0.79 0.62 0.58 0.68 0.54 0.8
  8. 8. basic hedging methods• pair of stock with negative correlation• derivatives (options, features/forwards, swaps, etc.)• short selling 8
  9. 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 9
  10. 10. example 1: stock A only date investment quantity price value total value of investmentstart day stock A 100 100 10,000 10,000next day up stock A 100 105 10,500 10,500next day stock A 100 95 9,500 9,500down
  11. 11. example 2: stock A hedge by stock Bwith negative correlation of stock B (-0,4) date investment quantity price value total value of investmentstart day stock A 50 100 5,000 10,000start day stock B (-0.4) 100 50 5,000next day up stock A 50 105 5,250 10,150next day up stock B (-0.4) 100 49 4,900next day stock A 50 95 4,750 9850downnext day stock B (-0.4) 100 51 5,100down
  12. 12. example 3: stock A put option hedgeput (sell) option at price of 100 date investment quantity price value total value of investmentstart day stock A 99 100 9,900 9,999start day put option A 99 1 99 (100)next day up stock A 99 105 10,395 10,395next day up put option A 100 0 0 (100)next day stock A 99 95 9,405 9,900downnext day put option A 99 5 495down (100)
  13. 13. example 4: stock A hedge short sellshort selling of stock B with positive correlation (0,8) date investment quantity price value total value of investmentstart day stock A 50 100 5,000 10,000start day short stock C 100 50 5,000 (0.8)next day up stock A 50 105 5,250 10,050next day up short stock C 100 48 4,800 (0.8)next day stock A 50 95 4,750 9,950downnext day short stock C 100 52 5,200down (0.8)
  14. 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 9,500stock A + stock B 10,000 10,150 9,850 (-0.2) stock A + put 9,999 10,395 9,900 option Astock A + short 10,000 10,050 9,950 stock C (0,8)
  15. 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 15
  16. 16. diversification
  17. 17. diversification• diversification means reducing risk by investing in a variety of assets (within one or more asset class)• it means: dont 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 17
  18. 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 18
  19. 19. diversification and risk 19
  20. 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): 20
  21. 21. long-run historical return and SD 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%based on 80yr data (1926-2004) 21
  22. 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 22
  23. 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 23
  24. 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. 25. example: two assets portfolio 25
  26. 26. example: two assets portfolio 26
  27. 27. example: two assets portfolio start price Mon Tue Wed Thu Fri SDstock A (100% - 100 shares) 100 105 110 112 108 103portfolio value 10000 10500 11000 11200 10800 10300 3.6469stock B (100% - 200 shares) 50 52 53 52 53 54portfolio value 10000 10400 10600 10400 10600 10800 0.8367 start price Mon Tue Wed Thu Fri SDstock A (50% - 50 shares) 100 105 110 112 108 103stock B (50% - 100 shares) 50 52 53 52 53 54portfolio value 10000 10450 10800 10800 10700 10550 2.2418
  28. 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 28
  29. 29. portfolio creation process 29
  30. 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 30
  31. 31. measuring risk: value at risk
  32. 32. 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. 33
  33. 33. 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% 34
  34. 34. 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) 35

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