Chapter 24
Integrating Derivative Assets and
Portfolio Management
Portfolio Construction, Management, & Protection, 5e, Robert A. Strong
Copyright ©2009 by South-Western, a division of Thomson Business & Economics. All rights reserved.
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,
former chairman and
CEO, Merrill Lynch &
Company
2
Introduction
Chapter is an extended example focusing on risk
management and income generation in a portfolio
context
 Portfolio objectives must be set with or without
derivatives
 Futures and options:

• Can be used in risk management and income generation
• Can be used to adjust the fixed-income portfolio, the
equity portfolio, or both to accomplish the objectives
3
Setting the Stage
 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
4
Setting the Stage (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
5
Fixed Income Securities
TABLE 24-1
Par
YTM(%)
Market
Value
Annual
Income
Duration
Issue
Price(%)
$50,000
US6s18
100
6.00
$50,000
$3,000
5.13
$50,000
US7s19
105
6.10
52,500
3,500
5.69
$50,000
US7s20
105
6.20
52,500
3,500
6.31
$50,000
US7s21
104 ¾
6.30
52,375
3,500
6.88
$50,000
US5.5s22
90 5/8
6.80
45,313
2,750
7.69
$50,000
AB6.3s23
94 5/8
7.00
47,313
3,150
8.01
$50,000
CD7.1s24
100
7.10
50,000
3,550
8.27
$50,000
EF7.3s25
100 7/8
7.20
50,438
3,650
8.63
$50,000
GH7¼s26
99 ½
7.30
49,750
3,625
9.01
$50,000
IJ6¼s27
89 5/8
7.40
44,813
3,125
9.63
$495,002
$33,350
7.48*
$500,000
*Value-weighted average
6
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 Table 24-3)
7
Stock & Bond Portfolio Facts

The final portfolio consists of:
•
•
•
•

$495,002 in bonds
$996,986 in stocks
$3,014 in cash
A total value of $1,495,002
The existing portfolio should yield:
• $33,350 from bonds
• $25,026 from dividends

You are $16,624 short relative to the $75,000 goal
8
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
9
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
10
Maximum Permissible Index Written
 With
Cash as Collateral:
 15% of Index + MVIndex – $ Out of Money
 Total Portfolio Value
• 15% of Index (@ 310): 0.15 x $298.96 x 100 x N
• Market Value of Index (@ 310): + $3.00 x 100 x N
• Out-of-money amount (@ 310): - ($310 - 298.96) x N
With stock as collateral you can write half as
many options
 With fixed income securities the maximum
number written is between these extremes

11
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
3.00
1.75
1.00
Delta
0.435
0.324
0.228
0.151
Maximum
Contracts
171
203
244
301
Income
$83,362
60,900
42,700
30,100
12
Writing Index Calls (cont’d)
 You
decide to write 56 AUG 310 index
calls:
• Generates $3 × 56 × 100 = $16,800 in income
immediately
• The delta of 0.324 indicates that these options
will likely expire worthless
13
Determining the
Portfolio Delta and Beta
 Effective
stock portfolio risk management
requires determination of portfolio delta and
beta
• The equity portion of the portfolio has a beta of
1.08
• Writing index call options always reduces the
portfolio beta
– Short calls carry negative deltas
14
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
15
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
16
Determining the Portfolio
Delta and Beta (cont’d)
 Delta
Contribution of Stock Portfolio
• Index Equivalent x Delta x 100 = Contribution
– 36.02 x 0.578 x 100 = 2,081.96
 Delta
Contribution of AUG 310 Calls
• Contracts x Delta x 100 = Contribution
– 56 x (-0.324) x 100 = -1814.40
 Position
Delta = 2.081.96 – 1814.40 = 267.56
17
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
18
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
19
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
20
Caveats about Black-Scholes Prices
for Away-from-the-Money Options
 The
Black-Scholes Option Pricing Model:
• 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
21
Hedging Company Risk
 Equity
options can be used to hedge
company specific risk
• Company specific risk is in additional to overall
market risk
– e.g., a lawsuit
22
Buying Puts

To hedge against a small price change, it is
necessary to determine how many option
contracts are necessary to bring the position delta
to zero:
shares 1.0
# of contracts 
put delta 100
23
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?
24
Buying Puts (cont’d)
Example (cont’d)
Solution: Calculate the number of contracts needed:
shares 1.0
# of contracts 
put delta 100
1,000 1.0

 55.56
0.18 100
25
Buying Puts and Writing Calls

Hedging a long stock position involves adding
negative deltas to the positive deltas from the
shares
• Long puts and short calls both have negative deltas

Major market movements up or down can result in
significantly different ending portfolio values for
the puts-only scenario compared with the putsand-calls alternative
26
Fixed-Income Portfolio
 T-bond
futures can be used to reduce
interest rate risk by reducing portfolio
duration
• If interest rates rise, the value of a fixed-income
portfolio declines
 T-bond
futures options are a useful
investment
27
Hedging the Bond Portfolio Value 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
28
Hedging the Bond Portfolio Value 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
29
Hedging the Bond Portfolio Value 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?
30
Hedging the Bond Portfolio Value 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

 0.9914
$100,000
 4.91 contracts
31
Hedging the Bond Portfolio
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

The buyer of a futures option has a known and
limited maximum loss
• Buying only the futures contract can result in large losses
32
Hedging the Bond Portfolio 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
33
Hedging the Bond Portfolio with
Futures Options (cont’d)
 The
appropriate hedge ratio for futures
options is:
Portfolio value
1
HR  CF 

$100, 000
Delta
34
Hedging the Bond Portfolio 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?
35
Hedging the Bond Portfolio 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
36
Hedging the Bond Portfolio with
Futures Options (cont’d)
Example (cont’d)
Solution (cont’d): Writing 9 calls will generate $24,187.50:
2 44/64% × $100,000 × 9 = $24,187.50
37
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
38
Managing Cash Drag (cont’d)
 The
hedge ratio is:
Portfolio size
HR 
 Beta
Futures size
39
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?
40
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%
41
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?
42
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
43