2. © 2004 South-Western Publishing 1 Chapter 16 Financial Engineering and Risk Management

3. 2 Outline Introduction and background Financial engineering Risk management

4. 3 Introduction and Background Financial engineering: – Is a relatively new derivatives endeavor – Has led directly to improvements in the process of risk management

5. 4 Introduction and Background (cont’d) Risk management awareness is associated with various phrases: – Asian flu – Global contagion – Orange County “We take the risks because of the potential reward”

6. 5 Financial Engineering Synthetic put Engineering an option Gamma risk

7. 6 Synthetic Put Financial engineering is the popular name for constructing asset portfolios that have precise technical characteristics In the early days of the CBOE there were no puts; only calls traded – Can construct a put by combining a short position in the underlying asset with a long call – Synthetic puts were the first widespread use of financial engineering

8. 7 Synthetic Put (cont’d) + = short stock +long call = long put

9. 8 Engineering an Option There are a variety of tactics by which wealth can be protected without disturbing the underlying portfolio – Shorting futures provides downside protection but precludes gains from price appreciation – Writing a call provides only limited downside protection – Buying a put may be the best alternative

10. 9 Engineering an Option (cont’d) StrategyAdvantagesDisadvantages Short futuresLow trading fees; Easy to do Lose upside potential; Possible tracking error Write callsGenerate incomeLose most upside potential; Inconvenience if exercised; Limited protection Buy putsReliable protection Premium must be paid; Hedge may require periodic adjustment

11. 10 Engineering an Option (cont’d) Extensive purchase of individual equity puts is inefficient in a large portfolio – Portfolio may contain dozens of stocks, resulting in numerous trading fees, managerial time, and high premium cost – Index options or futures options are best suited

12. 11 Engineering an Option (cont’d) Financial Engineering Example Assume that T-bills yield 8% and market volatility is 15%. Black’s options pricing model predicts the theoretical variables for a 2-year XPS futures put option with a 325.00 striking price as follows: Striking price = 325.00 Index level = 326.00 Option premium = $23.15 Delta = -0.388 Theta = -0.011 Gamma = 0.016 Vega = 1.566

13. 12 Engineering an Option (cont’d) Financial Engineering Example Linear programming models can be utilized to obtain the desired theoretical values from existing call and put options. The greater the range of striking prices and expirations from which to choose, the easier the task.

14. 13 Engineering an Option (cont’d) Financial Engineering Example Available XPS Options Linear Programming Synthetic Put With Desired Theoretical Values

15. 14 Engineering an Option (cont’d) The tough part of engineering an option is dealing with the dynamic nature of the product – To keep the engineered put behaving like a “real” one, it is necessary to adjust the option positions that comprise it (dynamic hedging) – How frequently you should reconstruct the portfolio to fine-tune delta depends on the rest of your market positions and the magnitude of the trading fees you pay

16. 15 Engineering an Option (cont’d) Primes and Scores  PRIME is the acronym for “Prescribed Right to Income and Maximum Equity”  SCORE stands for “Special Claim on Residual Equity”  PRIMEs and SCOREs were arguable the first of the engineered hybrid securities  Securities provided investors a means of separating a stock’s income and capital appreciation potential

17. 16 Engineering an Option (cont’d) Primes and Scores (cont’d) Americus Trust Unit PRIMESCORE Common Stock

18. 17 Gamma Risk There are several ways to engineer derivatives products that differ with regard to their cost and their robustness Gamma risk measures: – How sensitive the position is to changes in the underlying asset price – The consequences of a big price change

19. 18 Gamma Risk (cont’d) An options portfolio with a gamma far from zero will rattle apart when the market experiences stormy weather

20. 19 Gamma Risk (cont’d) Gamma Risk Example Suppose we hold 10,000 shares of a $60 stock and want to temporarily move to a position delta of zero.

21. 20 Gamma Risk (cont’d) Gamma Risk Example (cont’d) Options Data CallsPuts StrikePremiumDeltaGammaPremiumDeltaGamma 50$11.240.8800.019$0.63-0.1210.019 60$4.510.5650.037$3.84-0.4450.038 70$1.310.2440.029$10.71-0.7870.033

22. 21 Gamma Risk (cont’d) Gamma Risk Example (cont’d) Alternative Solution A PositionQuantityDeltaGammaPremium Stock+10,000 -- 60 Call-100-5,650-370+$45,100 60 Put+98-4,361+372-$37,632 -11+2+$7,468

23. 22 Gamma Risk (cont’d) Gamma Risk Example (cont’d) Alternative Solution B PositionQuantityDeltaGammaPremium Stock+10,000 -- 50 Call-114-10,032-217+$128,136 -32-217+$128,136

24. 23 Gamma Risk (cont’d) Gamma Risk Example (cont’d)  Both solutions have an initial position delta close to zero  Solution B has the attraction of bringing in a great deal more than Solution A  Solution B’s negative gamma may be hurt by a fast market  Assume the underlying stock price rises by 5% to $63

25. 24 Gamma Risk (cont’d) Gamma Risk Example (cont’d) Options Data CallsPuts StrikePremiumDeltaGammaPremiumDeltaGamma 50$13.960.9270.012$0.36-0.0740.013 60$6.380.6680.032$2.68-0.3390.033 70$2.140.3360.033$8.47-0.6870.035

26. 25 Gamma Risk (cont’d) Gamma Risk Example (cont’d) Alternative Solution A: 5% Increase in Stock Price PositionQuantityNew DeltaChange in Option Value Gain or Loss Stock+10,000 -+$30,000 60 Call-100-6,680+$1.87-$18,700 60 Put+98-3,322-$1.16-$11,368 -2+$68

27. 26 Gamma Risk (cont’d) Gamma Risk Example (cont’d) Alternative Solution B: 5% Increase in Stock Price PositionQuantityNew DeltaChange in Option Value Gain or Loss Stock+10,000 -+$30,000 60 Call-114-10,568+$2.72-$31,008 -568-$1,008

28. 27 Gamma Risk (cont’d) Gamma Risk Example (cont’d)  Solution A is preferable because:  Its position delta remains near the target figure of zero  Its value changed by only $68, while the other portfolio declined by over $1,000

29. 28 Risk Management Managing company risk Managing market risk

30. 29 Managing Company Risk Many modern portfolio managers actively practice some form of delta management – Delta management refers to any investment practice that monitors position delta and seeks to maintain it within a certain range – Delta is a direct measure of the “degree of bullishness” represented in a particular security position or portfolio

31. 30 Managing Company Risk (cont’d) Bullish Out of the Fully Market 0% + + 100%Invested - - Bearish Position Delta

32. 31 Managing Market Risk Most institutional use of SPX futures is to reduce risk rather than eliminate it – If you completely eliminate risk, returns should be modest

33. 32 Managing Market Risk (cont’d) Delta management of market risk involves futures puts and calls – A long futures contract has a delta of 1.0 – Call options have deltas near 1.0 if they are deep-in-the-money and near zero if they are far out-of-the-money

34. 33 Managing Market Risk (cont’d) Delta management of market risk involves futures puts and calls (cont’d) – Puts have deltas near –1.0 when deep-in-the- money and near zero if far out-of-the-money – When the striking price is near the price of the underlying asset, the option delta will be near 0.5 (for calls) or –0.5 (for puts)