Chapter 24
Integrating Derivative Assets and
Portfolio Management
1
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
2
Outline
 Introduction
 Setting
the stage
 Meeting an income constraint
 Risk management
 Managing cash drag
3
Introduction
 Futures
and options:
• Can be used in risk management and income
generation
• Can be integrated into the portfolio
management process
4
Setting the Stage
 Portfolio
objectives
 Portfolio construction
5
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
6
Portfolio Objectives (cont’d)
 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
7
Portfolio Objectives (cont’d)
 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
8
Portfolio Construction
 Fixed-income
securities
 Stocks
9
Fixed-Income Securities
 The
fund holds ten fixed-income securities:
10
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)
11
12
Stocks (cont’d)
 The
final portfolio consists of:
• $495,002 in bonds
• $996,986 in stocks
• $3,014 in cash
• A total value of $1,495,002
13
Using SAS for
Linear Programming
14
Meeting an Income Constraint
 Determining
unmet income needs
 Writing index calls
15
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
16
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
17
Writing Index Calls (cont’d)
 Eligible
options are identified (all with
August expiration):
Striking Price
Premium
305
4.13
310
3
315
1.75
320
1
Current level of the Index = 298.96
Delta
0.435
0.324
0.228
0.151
18
Writing Index Calls (cont’d)
 You
determine the maximum contracts you
can write using stock as collateral:
Striking
Price
305
310
315
320
Premium
4.875
3
1.75
1
Delta
0.435
0.324
0.228
0.151
Maximum
Contracts
171
203
244
301
Income
$83,362
60,900
42,700
30,100
19
Writing Index Calls (cont’d)
 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
20
Risk Management
 Stock
portfolio
 Hedging company risk
 Fixed-income portfolio
21
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
22
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
23
Determining the Portfolio
Delta and Beta (cont’d)
 First,
determine the hedge ratio for the stock
portfolio:
Portfolio value
HR 
 Beta
Contract value
$996,975

 1.08  36.02
$298.96 100
24
Determining the Portfolio
Delta and Beta (cont’d)
 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
25
Determining the Portfolio
Delta and Beta (cont’d)
 Determine
the delta contributions of the
stock and the short options:
26
Determining the Portfolio
Delta and Beta (cont’d)
 Lastly,
estimate the resulting portfolio beta:
Initial portfolio delta Final portfolio delta

Initial portfolio beta Final portfolio beta
2, 081.96 267.56

1.08
Beta
Beta  0.14
27
Determining the Portfolio
Delta and Beta (cont’d)
 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
28
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
29
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
30
Hedging Company Risk
 Introduction
 Buying
puts
 Buying puts and writing calls
31
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
32
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:
Stock value
1
HR 

Put value
Delta
33
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?
34
Buying Puts (cont’d)
Example (cont’d)
Solution: Calculate the hedge ratio:
Stock value
1
HR 

Put value
Delta
1, 000  $56
1


100  $55 0.18
 56.57 contracts
35
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
36
Fixed-Income Portfolio
 Hedging
the bond portfolio value with Tbond futures
 Hedging the bond portfolio with futures
options
37
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
38
Hedging With
T-Bond Futures (cont’d)
 Determine
the hedge ratio:
Pb  Db
HR  CFctd 
Pf  D f
where Pb  price of bond portfolio as a percentage of par
Db  duration of bond portfolio
Pf  price of futures contract as a percentage
D f  duration of cheapest-to-deliver bond eligible for delivery
CFctd  conversion factor for the cheapest-to-deliver bond
39
Hedging With
T-Bond Futures (cont’d)
 Determine
the number of contracts you
need to sell to hedge:
Portfolio value
Number of contracts 
 HR
$100, 000
40
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?
41
Hedging With
T-Bond Futures (cont’d)
Example (cont’d)
Solution: You need to sell 5 contracts to hedge completely:
Portfolio value
Number of contracts 
 HR
$100, 000
$495, 002

 0.8215
$100, 000
 4.91 contracts
42
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
43
Hedging With
Futures Options (cont’d)
 The
buyer of a futures option has a known
and limited maximum loss
• Buying only the futures contract can result in
large losses
44
Hedging With
Futures Options (cont’d)
 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
45
Hedging With
Futures Options (cont’d)
 The
appropriate hedge ratio for futures
options is:
Portfolio value
1
HR  CF 

$100, 000
Delta
46
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?
47
Hedging With
Futures Options (cont’d)
Example (cont’d)
Solution: The hedge ratio indicates you need to write 9
contracts to hedge:
Portfolio value
1
HR  CF 

$100, 000
Delta
$495, 002
1
 0.91

$100, 000 0.583
 8.933
48
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
49
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
50
Managing Cash Drag (cont’d)
 The
hedge ratio is:
Portfolio size
HR 
 Beta
Futures size
51
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?
52
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%
53
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?
54
Managing Cash Drag (cont’d)
Example (cont’d)
Solution: The hedge ratio indicates you should buy 146
SPX futures:
Portfolio size
HR 
 Beta
Futures size
0.07  $600, 000, 000

1.0
1150.00  $250
 146.09
55