Chapter 24 Integrating Derivative Assets and Portfolio Management

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Chapter 24Integrating Derivative Assets and
Portfolio Management
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Introduction

• Futures and options
• Can be used in risk management and income
  generation
• Can be integrated into the portfolio management
  process

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Portfolio Objectives

• Portfolio objectives must be set with or without
  derivatives
• 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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Portfolio Objectives (contd)

• 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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Portfolio Objectives (contd)

• Assume (contd)
• 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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Portfolio Construction

• Fixed-income securities
• Stocks

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Fixed-Income Securities

• The fund holds ten fixed-income securities

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Stocks

• 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
• Linear programming can be used to determine the
  solution (see next slide)

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Stocks (contd)

• 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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Determining Unmet Income Needs

• The existing portfolio should generate
• 33,350 from bonds
• 25,026 from dividends
• You are 16,624 short relative to the 75,000 goal

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Writing Index Calls

• 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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Writing Index Calls (contd)

• Eligible options are identified (all with August
  expiration)

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Writing Index Calls (contd)

• You determine the maximum contracts you can write
  using stock as collateral

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Writing Index Calls (contd)

• 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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Risk Management

• Stock portfolio
• Hedging company risk
• Fixed-income portfolio

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Stock Portfolio

• Determining the portfolio delta and beta
• Caveats about prices from the popular press
• Caveats about Black-Scholes prices for
  away-from-the-money options

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Determining the Portfolio Delta and Beta

• The equity portion of the portfolio has a beta of
  1.08
• Writing index call option always reduces the
  portfolio beta
• Short calls carry negative deltas
• It is important to know the risk level of the
  portfolio

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Determining the Portfolio Delta and Beta (contd)

• First, determine the hedge ratio for the stock
  portfolio

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Determining the Portfolio Delta and Beta (contd)

• The stock portfolio is theoretically equivalent
  to 36.02 at-the-money contracts of the index
• 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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Determining the Portfolio Delta and Beta (contd)

• Determine the delta contributions of the stock
  and the short options

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Determining the Portfolio Delta and Beta (contd)

• Lastly, estimate the resulting portfolio beta

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Determining the Portfolio Delta and Beta (contd)

• The stock portfolio combined with the index
  options
• Has a slightly positive position delta
• Has a slightly positive beta
• The total portfolio is slightly bullish and will
  benefit from rising market prices

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Caveats About Prices from the Popular Press

• 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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Caveats About Black-Scholes Prices

• 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
• To calculate delta, it may be preferable to
  calculate implied volatility for the option you
  are investigating

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Hedging Company Risk

• Introduction
• Buying puts
• Buying puts and writing calls

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Introduction

• 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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Buying Puts

• 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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Buying Puts (contd)

• 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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Buying Puts (contd)

• Example (contd)
• Solution Calculate the hedge ratio

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Buying Puts and Writing Calls

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

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Fixed-Income Portfolio

• Hedging the bond portfolio value with T-bond
  futures
• Hedging the bond portfolio with futures options

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Hedging With T-Bond Futures

• 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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Hedging With T-Bond Futures (contd)

• Determine the hedge ratio

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Hedging With T-Bond Futures (contd)

• Determine the number of contracts you need to
  sell to hedge

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Hedging With T-Bond Futures (contd)

• 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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Hedging With T-Bond Futures (contd)

• Example (contd)
• Solution You need to sell 5 contracts to hedge
  completely

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Hedging With Futures Options

• 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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Hedging With Futures Options (contd)

• 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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Hedging With Futures Options (contd)

• Futures options do not require the good faith
  deposit associated with futures
• You could buy T-bond futures puts instead of
  going short T-bond futures to hedge the bond
  portfolio

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Hedging With Futures Options (contd)

• The appropriate hedge ratio for futures options
  is

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Hedging With Futures Options (contd)

• 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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Hedging With Futures Options (contd)

• Example (contd)
• Solution The hedge ratio indicates you need to
  write 9 contracts to hedge

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Hedging With Futures Options (contd)

• Example (contd)
• Solution (contd) Writing 9 calls will generate
  24,187.50
• 2 44/64 x 100,000 x 9 24,187.50

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Managing Cash Drag

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

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Managing Cash Drag (contd)

• The hedge ratio is

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Managing Cash Drag (contd)

• 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 SP 500 index (your benchmark)
  earned 8 percent, with cash earning 2.0 percent.
• What is the return on your portfolio?

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Managing Cash Drag (contd)

• Example (contd)
• 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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Managing Cash Drag (contd)

• Example (contd)
• 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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Managing Cash Drag (contd)

• Example (contd)
• Solution The hedge ratio indicates you should
  buy 146 SPX futures