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1 Chapter 24 Integrating Derivative Assets and Portfolio Management

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2 Life wasn’t designed to be risk-free. They key is not to eliminate risk, but to estimate it accurately and manage it wisely. - William A. Schreyer

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3 Outline u Introduction u Setting the stage u Meeting an income constraint u Risk management u Managing cash drag

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4 Introduction u Futures and options: Can be used in risk management and income generation Can be integrated into the portfolio management process

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5 Setting the Stage u Portfolio objectives u Portfolio construction

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6 Portfolio Objectives u Portfolio objectives must be set with or without derivatives u Futures and options can be used to adjust the fixed-income portfolio, the equity portfolio, or both to accomplish the objectives

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7 Portfolio Objectives (cont’d) u Assume: You are newly responsible for managing a corporate in-house scholarship fund The fund consists of corporate and government bonds and bank CDs The fund has growth of income as the primary objective and capital appreciation as the secondary objective

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8 Portfolio Objectives (cont’d) u Assume (cont’d): A one-time need requires income generation of $75,000 during the next year An account is opened with the deposit of cash and the existing fixed-income securities for a value of about $1.5 million Trading fees are paid out of a small, separate trust fund

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9 Portfolio Construction u Fixed-income securities u Stocks

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10 Fixed-Income Securities u The fund holds ten fixed-income securities:

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11 Stocks u You decide to include stocks in the portfolio for $1,000,000 so that: The portfolio beta is between 1.05 and 1.15 The investment in each stock is between 4 and 7 percent of the total You avoid odd lots u Linear programming can be used to determine the solution (see next slide)

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13 Stocks (cont’d) u The final portfolio consists of: $495,002 in bonds $996,986 in stocks $3,014 in cash A total value of $1,495,002

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14 Using SAS for Linear Programming

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15 Meeting an Income Constraint u Determining unmet income needs u Writing index calls

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16 Determining Unmet Income Needs u The existing portfolio should generate: $33,350 from bonds $25,026 from dividends u You are $16,624 short relative to the $75,000 goal

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17 Writing Index Calls u You want to write index call options to generate the additional needed income: Write short-term out-of-the-money calls to avoid exercise Determine implied volatilities of the options Use the implied volatilities to determine the option deltas Determine the number of options you can write

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18 Writing Index Calls (cont’d) u Eligible options are identified (all with August expiration): Striking PricePremiumDelta 3054.130.435 31030.324 3151.750.228 32010.151 Current level of the Index = 298.96

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19 Writing Index Calls (cont’d) u You determine the maximum contracts you can write using stock as collateral: Striking PricePremiumDelta Maximum ContractsIncome 3054.8750.435171$83,362 31030.32420360,900 3151.750.22824442,700 32010.15130130,100

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20 Writing Index Calls (cont’d) u You decide to write 56 AUG 310 index calls: Generates $3 x 56 x 100 = $16,800 in income immediately The delta of 0.324 indicates that these options will likely expire worthless

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21 Risk Management u Stock portfolio u Hedging company risk u Fixed-income portfolio

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22 Stock Portfolio u Determining the portfolio delta and beta u Caveats about prices from the popular press u Caveats about Black-Scholes prices for away-from-the-money options

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23 Determining the Portfolio Delta and Beta u The equity portion of the portfolio has a beta of 1.08 u Writing index call option always reduces the portfolio beta Short calls carry negative deltas u It is important to know the risk level of the portfolio

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24 Determining the Portfolio Delta and Beta (cont’d) u First, determine the hedge ratio for the stock portfolio:

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25 Determining the Portfolio Delta and Beta (cont’d) u The stock portfolio is theoretically equivalent to 36.02 at-the-money contracts of the index u Next, calculate the delta of a hypothetical index option with a striking price of 298.96 Assume the delta is 0.578

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26 Determining the Portfolio Delta and Beta (cont’d) u Determine the delta contributions of the stock and the short options:

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27 Determining the Portfolio Delta and Beta (cont’d) u Lastly, estimate the resulting portfolio beta:

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28 Determining the Portfolio Delta and Beta (cont’d) u The stock portfolio combined with the index options: Has a slightly positive position delta Has a slightly positive beta u The total portfolio is slightly bullish and will benefit from rising market prices

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29 Caveats About Prices from the Popular Press u Nonsynchronous trading is the phenomenon whereby comparative prices come from different points in time Prices for less actively traded issues may have been determined hours before the close of the market When you consider strategies involving away from the money options, you should verify the actual bid/ask prices for a security

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30 Caveats About Black-Scholes Prices u The Black-Scholes OPM: Works well for near-the-money options Works less accurately for options that are substantially in the money or out of the money u To calculate delta, it may be preferable to calculate implied volatility for the option you are investigating

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31 Hedging Company Risk u Introduction u Buying puts u Buying puts and writing calls

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32 Introduction u Equity options can be used to hedge company specific risk Company specific risk is in additional to overall market risk –E.g., a lawsuit

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33 Buying Puts u To hedge 100 percent of a stock position, it is necessary to calculate a hedge ratio to determine the number of contracts needed:

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34 Buying Puts (cont’d) Example You own 1,000 shares of a stock currently selling for $56 per share. Put options are available with a premium of $0.45 and a $55 striking price. The put delta is –0.18. How many options should you purchase to hedge your position in the stock from a downfall due to company specific risk?

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35 Buying Puts (cont’d) Example (cont’d) Solution: Calculate the hedge ratio:

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36 Buying Puts and Writing Calls u Buying puts may be too expensive Consider writing calls in addition to buying puts –Long puts and short calls both have negative deltas u Including both puts and calls in a portfolio can result in substantially different ending portfolio values

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37 Fixed-Income Portfolio u Hedging the bond portfolio value with T- bond futures u Hedging the bond portfolio with futures options

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38 Hedging With T-Bond Futures u T-bond futures can be used to reduce interest rate risk by reducing portfolio duration Chapter 23 If interest rates rise, the value of a fixed-income portfolio declines

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39 Hedging With T-Bond Futures (cont’d) u Determine the hedge ratio:

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40 Hedging With T-Bond Futures (cont’d) u Determine the number of contracts you need to sell to hedge:

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41 Hedging With T-Bond Futures (cont’d) Example A fixed-income portfolio has a value of $495,002. Using the cheapest-to-deliver bond, you determine a hedge ratio of 0.8215. How many T-bond futures do you need to sell to completely hedge this portfolio?

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42 Hedging With T-Bond Futures (cont’d) Example (cont’d) Solution: You need to sell 5 contracts to hedge completely:

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43 Hedging With Futures Options u A futures option is an option giving its owner the right to buy or sell a futures contract A futures call gives its owner the right to go long a futures contract A futures put gives its owner the right to go short a futures contract

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44 Hedging With Futures Options (cont’d) u The buyer of a futures option has a known and limited maximum loss Buying only the futures contract can result in large losses

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45 Hedging With Futures Options (cont’d) u Futures options do not require the good faith deposit associated with futures u You could buy T-bond futures puts instead of going short T-bond futures to hedge the bond portfolio

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46 Hedging With Futures Options (cont’d) u The appropriate hedge ratio for futures options is:

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47 Hedging With Futures Options (cont’d) Example A fixed-income portfolio has a value of $495,002. MAR 98 T-bond futures calls are available with a premium of 2-44 and a delta of 0.583. The underlying futures currently sell for 91. How many calls do you need to write to hedge? What is the income this strategy generates?

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48 Hedging With Futures Options (cont’d) Example (cont’d) Solution: The hedge ratio indicates you need to write 9 contracts to hedge:

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49 Hedging With Futures Options (cont’d) Example (cont’d) Solution (cont’d): Writing 9 calls will generate $24,187.50: 2 44/64% x $100,000 x 9 = $24,187.50

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50 Managing Cash Drag u A portfolio suffers a cash drag when it is not fully invested Cash earns a below-market return and dilutes the portfolio return u A solution is to go long stock index futures to offset cash holdings

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51 Managing Cash Drag (cont’d) u The hedge ratio is:

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52 Managing Cash Drag (cont’d) Example You are managing a $600 million portfolio. 93% of the portfolio is invested in equity, and 7% is invested in cash. Your equity beta is 1.0. During the last year, the S&P 500 index (your benchmark) earned 8 percent, with cash earning 2.0 percent. What is the return on your portfolio?

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53 Managing Cash Drag (cont’d) Example (cont’d) Solution: The return on your total portfolio is 7.58% (42 basis points below the market return): (0.93 x 0.08) + (0.07 x 0.02) = 7.58%

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54 Managing Cash Drag (cont’d) Example (cont’d) Assume a distant SPX futures contract settles for 1150.00. How many futures contracts should you buy to make your portfolio behave like a 100 percent equity index fund?

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55 Managing Cash Drag (cont’d) Example (cont’d) Solution: The hedge ratio indicates you should buy 146 SPX futures:

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