SECTION VI: Futures
Required Readings
Notes 6
Chap. 11 (p.341-346; 349-353; 365-367)
Chap. 22 (p.924-931)
Chap. 23 (p.938-954; 962-967)
Topic VI.a: Taxonomy of a Commitment
Topic VI.b: Hedging with futures
Topic VI.c: Speculating with futures
Topic VI.d: Case Study-Portfolio Hedging
Suggested problems and practice
questions
Practice problems:
4, 5, 6 pp.977-978
Practice questions:
2,7 p.974-975
Session VI: Futures in portfolio Management
Learning Outcomes:





Define and differentiate between forward and futures
List, define and contrast the different futures exchanges and quotations
Analyze and interpret the effect of margin requirements in futures trading
List, define, analyze and interpret the different techniques that use futures for hedging bond
and equity portfolio
Define and apply the different techniques that use futures for speculating and positioning the
systematic risk of a portfolio
Pre-assessment Questions:
How would you rate your understanding of the following:
The difference between forward and futures
[ ] Excellent
[ ]Good
[ ]fair
[ ]Slight
[ ]Little or none
The different futures exchanges and quotations
[ ] Excellent
[ ]Good
[ ]fair
[ ]Slight
[ ]Little or none
The affect of margin requirements in futures trading
[ ] Excellent
[ ]Good
[ ]fair
[ ]Slight
[ ]Little or none
The different techniques that use futures for hedging bond and equity portfolio
[ ] Excellent
[ ]Good
[ ]fair
[ ]Slight
[ ]Little or none
The different techniques that use futures for speculating and positioning the systematic risk of
a portfolio
[ ] Excellent
[ ]Good
[ ]fair
[ ]Slight
[ ]Little or none
Estimated Time to Complete: 6 hours
Post-assessment Questions:
How would you rate your understanding of the following:
The difference between forward and futures
[ ] Excellent
[ ]Good
[ ]fair
[ ]Slight
[ ]Little or none
The different futures exchanges and quotations
[ ] Excellent
[ ]Good
[ ]fair
[ ]Slight
[ ]Little or none
The affect of margin requirements in futures trading
[ ] Excellent
[ ]Good
[ ]fair
[ ]Slight
[ ]Little or none
The different techniques that use futures for hedging bond and equity portfolio
[ ] Excellent
[ ]Good
[ ]fair
[ ]Slight
[ ]Little or none
The different techniques that use futures for speculating and positioning the systematic risk of
a portfolio
[ ] Excellent
[ ]Good
[ ]fair
[ ]Slight
[ ]Little or none
Summary: In this section the student is introduced to the concept of derivative security. In a first
topic, the taxonomy of futures and forward contracts is addressed; market, quotations, contract
size and margin requirements are explained. In the second topic, the concept of hedging with
futures is described; decision matrices that summarize the simultaneous positions in commodity,
bonds and indexes and corresponding futures are explained; methods to implement an imperfect
hedge are derived. In the third topic, speculation with those highly leveraged financial products
is overviewed; the student also looks at the techniques to modify the beta and/or the duration of a
portfolio using futures contracts.
Topic VI.a: Taxonomy of a Commitment
Learning outcomes:



Define and differentiate between forward and futures
List, define and contrast the different futures exchanges and quotations
Analyze and interpret the effect of margin requirements in futures trading
Reading: p.341-346 and p. 938-942
Forward and Futures contracts are commitments, one is traded OTC while the other is traded
on regulated exchanges<LINK: Trading>. Futures are liquid, standardized, traded in organized
exchanges, guarantied by a clearinghouse, and have a delivery date which is typically the third
Friday of the delivery month. Further, futures require an initial margin of 2% to 10% (depending
on the client) and are marked to market daily against a maintenance margin smaller or equal to
the initial margin (to avoid default). Forwards are tailor made contracts that are exchanged
through a market maker; they do not require any margin and are not marked to market. The
delivery date are custom, and the contract is typically not liquid and not guarantied.
<START LINK: Trading>
<END LINK: Trading>
A forward contract is a legal agreement in which a buyer agrees to purchase an asset from a
seller at a specified future date at an agreed upon price. A Futures Contract is a highly liquid
and regulated version of a forward contract. The future price is the price, set today, at which the
asset will be traded in the future. The date on which the transaction is to be consummated is the
maturity (or expiration) date. The price at which the sale will be made is the forward or futures
contract price and is different from the current spot (cash) price, except at maturity.
Futures contract are traded on organized exchanges <LINK: EXCHANGES AND
UNDERLYING>. Those “commitments” to buy or sell an underlying asset at a future date are
traded in regional exchanges depending on the nature of the underlying asset. Futures are traded
on commodities and financial securities. Commodities like grains, metals, and meat make up the
traditional (commodities) segment of the futures market. Although a large portion of this market
is concentrated in the agricultural segment of our economy, there's also a very active market for
various metals and petroleum products. As the prices of commodities go up and down in the
market, the respective futures contracts behave in much the same way; thus, if the price of corn
goes up, the value of corn futures contracts rises as well. Whereas commodities deal with
physical assets, financial futures deal with financial assets, such as stocks, bonds, and currencies.
Even though the nature of the underlying assets may differ, both are traded in the same place: the
futures market. Financial futures are the newcomers, but this segment of the market has grown to
the point where the volume of trading in financial futures now far exceeds that of commodities.
<START LINK: EXCHANGES AND UNDERLYING>
Underlying Asset
Exchange
Physical Commodities
Corn, soybean meal, soybean oil, wheat
Chicago Board of Trade
Cattle-feeder, cattle-live, hogs, pork bellies,
Chicago Mercantile Exchange
lumber, heating oil
Cocoa, coffee, sugar-world, sugar-domestic
Cocoa, Sugar, and Coffee Exchange
Copper, gold, silver
New York Commodity Exchange
Crude oil, heating oil, gasoline, natural gas,
New York Mercantile Exchange
platinum
Underlying Asset
Exchange
Financial Securities
Yen, German mark, Canadian dollar, Swiss
International Monetary Market (Chicago
franc, British pound, Mexican peso, Australian Mercantile Exchange)
dollar, Treasury bills, Eurodollars (LIBOR)
Treasury bonds, Treasury notes, Municipal
Chicago Board of Trade
bond index, federal funds, Major Market Index
Eurodollar, British gilt, German bonds,
London International Financial Futures
Euromarks, Eurofrancs, Eurolira, FT-SE 100
Exchange
Index
<END LINK: EXCHANGES AND UNDERLYING>
Futures (Hog, gold, interest rates, currencies, etc..) have similar quotations<LINK: typical
quotation table>. Futures are identified through symbols, which consist of the ticker for the
commodity, the month code and a year code. Be aware that expiration months and dates vary.
Please check a financial newspaper to see what expiration months are currently being
offered<LINK: EXPIRATION MONTH CODE AND CONTRACT SIZE >. You can also get
real quotes at the Chicago Mercantile Exchange and the Chicago Board of Trade. Check the
daily quotation for the S&P500 and S&P400 futures <LINK: S&P500 and S&P400 futures
quotations> and notice that those contracts mature the third Friday of each three months (March,
June, September and December). The third Fridays of expirating months are also known as the
triple witching day: stock options, stock index options, and stock index futures expire pratically
at the same time and cause volatility in the stock market. Be aware that the size of a contract
varies; for example T-bond futures are in $100,000 per contracts; S&P500 and S&P400 futures
are $250 and $500 times the index, respectively.
<START LINK: typical quotation table>
Month
Expiration
(3rd Friday of
the month)
Open
Hi
opening
price
Lo
Settlement
Settle price
(Average of the
day)
Net Change
change in
settle price
Open Interest
number of outstanding
contracts (times 2 to
get all contracts
outstanding
<END LINK: typical quotation table>
<START LINK: EXPIRATION MONTH CODE AND CONTRACTs SIZE>
Month
January
February
March
April
May
June
EXPIRATION MONTH CODES
Code
Month
F
July
G
August
H
September
J
October
K
November
M
December
Description
Treasury Bonds
5 Yr Treasury Notes
Treasury Bills
Libor
Eurodollar
Muni-Bond
Dow Jones Industrial Average
S&P 500 Index
Nasdaq 100 Index
Nikkei 225 Index
U.S. Dollar Index
Code
N
Q
U
V
X
Z
Contract Size
100,000
100,000
1,000,000
3,000,000
1,000,000
1,000
10
250
100
5
1,000
Russell 2000 Index
Corn
Oats
Soybeans
Soybean Meal
Wheat-CBT
Cattle-Feeder
Cattle-Live
Hogs
Pork Bellies
Lumber
Cocoa
Coffee
Sugar-World
Cotton
Orange Juice
Copper-High
Gold
Platinum
Silver
Crude Oil
Heating Oil No 2
Gasoline-NY Unleaded
Natural Gas
Japanese Yen
Deutschmark
British Pound
Canadian Dollar
Swiss Franc
Mexican Peso
Australian Dollar
500
5,000
5,000
5,000
100
5,000
50,000
40,000
40,000
40,000
80,000
10
37,500
112,000
50,000
15,000
25,000
100
50
5,000
1,000
42,000
42,000
10,000
12.5 Mil
125,000
62,500
100,000
125,000
500,000
100,000
<END LINK: EXPIRATION MONTH CODE AND CONTRACT SIZE>
<START LINK: S&P500 and S&P400 futures quotations>
S&P 500
Index
Daily Prices As of :- Friday, 25
February
Date
2/25/00
2/25/00
2/25/00
2/25/00
2/25/00
2/25/00
2/25/00
2/25/00
2/25/00
Composite
2/24/00
Cash
Mar 00
Jun 00
Sep 00
Dec 00
Mar 01
Jun 01
Sep 01
Dec 01
Volume
130148
Open
High
Low
Last
Chge
0
135600
137150
139200
139100
0
146820
0
0
Open_Int
387076
136214
136650
138350
140190
142220
144420
146820
149220
151620
132915
133250
135100
136890
138920
141120
143520
145920
148320
133336
133810
135580
137460
139460
141560
143860
146160
148460
-2007
-1720
-1740
-1730
-1760
-1860
-1960
-2060
-2160
Prev.
Volume
0
119828
10139
128
45
6
2
0
0
Prev.
Open_Int
0
352678
28610
2823
2683
163
110
5
3
S&P Midcap
400
Daily Prices As of :- Friday, 25
February
Date
2/25/00
2/25/00
2/25/00
2/25/00
Composite
2/24/00
Open
High
Low
Mar 00
45350
Jun 00
0
Sep 00
0
Dec 00
0
Volume Open_Int
769
13215
45550
45220
45430
45640
44650
45220
45430
45640
Last Chge
44650
45220
45430
45640
-630
-630
-630
-630
Prev.
Prev.
Volume Open_Int
769
13214
0
0
0
0
0
0
<END LINK: S&P500 and S&P400 futures quotations>
In the same vein as the positions one could take in the spot (cash) market, you can be short or
long in the forward or futures market. A short futures or forward position is the commitment to
sell an underlying security at a Future price. A long futures or forward position is the
commitment to buy an underlying asset at a future price. The clearinghouse needs some
guaranties that the trader is not going to default his commitment; thus margins are required. For
example, assume you are short 2 “December S&P 400 futures contracts” for 924.5 (an S&P 400
contract is for 500 times the index). The total value of the position is 2 times 500 times 924.5 or
$924,500. Let ‘s assume that your initial margin is 5% or $46,225 and your maintenance margin
is 4.5% (--i.e., 41,602.50). A margin call will occur if the futures price climbs to 930 <LINK:
MARGIN>. Notice that there is a huge leverage effect; in the previous example, you only put a
fraction down for margin (5%) versus 50% if you had invested in stocks.
<START LINK: MARGIN>
Day F.Price
Gain (loss)
Equity
Debt Position
Margin Call
0
1
2
3
4
4
5
6
924.5
0
926 2 x 500 x (-1.5)= (1,500)
924
2 x 500 x 2= 2000
927 2 x 500 x (-3) = (3,000)
930
(3,000)
930
929
925
0
1,000
4,000
46,225
878,275
44,725
878,275
46,725
878,275
43,725
878,275
878,275
40,725
(<41,602.50)
46,225
47,225
51,225
924,500
0
923,000
Restricted
925,000
Over margined
922,000
Restricted
919,000 CALL: + $5,500 from
your pocket to cover the
requirements
878,275
0
0
878,275 925,500
Over margined
878,275 929,500
Over margined
<END LINK: MARGIN>
Futures contracts control large amounts of the underlying commodity or financial instrument
and, as a result, can produce wide price swings and very attractive rates of return (or very
unattractive losses). Such returns (or losses) are further magnified because all trading in the
futures market is done on margin. Whereas a speculator's profit is derived directly from the wide
price fluctuations that occur in the market, hedgers derive their profit from the protection they
gain against adverse price movements.
A variety of trading strategies can be used with commodities contracts, including speculating,
spreading, and hedging. Regardless of whether investors are in a long or a short position, they
have only one source of return from commodities and financial futures: appreciation (or
depreciation) in the price of the contract. Rate of return on invested capital is used to assess the
actual or potential profitability of a futures transaction. There are three types of financial futures:
currency futures, interest rate futures, and stock-index futures. The first type deals in different
kinds of foreign currencies. Interest rate futures, in contrast, involve various types of short and
long-term debt instruments. Stock-index futures are pegged to broad movements in the stock
market, as measured by such indexes as the S&P 500 and the NYSE Composite Index. These
securities can be used for speculating, spreading, or hedging. They hold a special appeal to
investors who use them to hedge other security positions. For example, interest rate futures
contracts are used to protect bond portfolios against a big jump in market interest rates, and
currency futures are used to hedge the foreign currency exposure that accompanies investments
in foreign securities.
Topic VI.b: Hedging with futures
Learning outcomes:

List, define, analyze and interpret the different techniques that use futures for hedging
bond and equity portfolio
Reading: p.349-353, p.365-367, p.924-931, p. 943-945, p. 949-954, and p. 962-967
You need to be aware of the Notations used throughout the course; they are consistent with other
references. The Futures Price is the price, set today, at which the asset will be traded in the
future—i.e., F(0,T). It has a maturity of T and in a future date, the maturity would be, of course
be T-t. S(0) is the current price of the underlying asset and S(t) would be the price at time t of the
underlying asset. Example--What are S(t), S(T), F(t,T), and F(T,T)?
S(t) is the price of the underlying asset at time t; S(T) is the price of the underlying asset at
maturity; F(t,T) is the price of a futures at time t that has T-t left to maturity; F(T,T) is the price
of a futures at time T that has T-T (or 0, it is dead) left to maturity, it is of course equal to S(T).
The Basis is difference in price between spot and future market—i.e., B(t,T)=S(t)-F(t,T);
because prices are expected to change in the future, futures prices and spot prices will not equal.
Thus, a basis risk exist and affect futures traders who take positions in one or both markets. For
example, What are B(0,T) and B(T,T)? B(0,T) is S(0) minus F(0,T); it is today’s basis; B(T,T) is
S(T) minus F(T,T) or zero; of course, at maturity, futures and spot prices are the same.
Arithmetic conventions: the Buyer is long or “+”, he is looking for a price appreciation; the
Seller is short or “-“, he is looking for a price depreciation. For example, assume that a buyer
and seller agree on a futures price of $45 or F(0,T). At expiration, the underlying security is
priced at $53 or S(T). The Buyer makes $8.00 or “+F(0,T)-S(T)”: At t=0, Buyer went long (+) on
the futures contract and At t=T, Buyer bought at F(0,T) from seller and sold it on the spot (-) at
S(T) to realize the profit. The Seller loses $8.00 or “–F(0,T)+S(T)”: At t=0, seller went short (-)
on the contract and At t=T, seller rushed to buy at S(T) on the spot, and sold at a committed
F(0,T) to buyer.<LINK: Decision Matrix>
<START LINK: Decision Matrix>
BUYER:
Time On the futures market
t=0
-45 (buy future commitment)
t=T
+53 (sell in the spot; notice: spot price =futures price at maturity)
Total +8
SELLER:
Time On the futures market
t=0
+45 (sell future commitment)
t=T
-53 (sell in the spot; notice: spot price =futures price at maturity)
Total -8
<END LINK: Decision Matrix>
Hedges are created by combining a long and short position in the same asset on the futures and
the spot markets to reduce or eliminate the price fluctuation risk. A buying (long) hedge is design
to protect the buyer against a price increase. In a long hedge, one combines a short commodity
holding with a long futures or forward position. A selling (short) hedge will protect a seller
against a falling price. In a short hedge, one holds a short futures or forward position against the
long position on the commodity. For Example, a farmer expects to harvest 40,000 bushels of
wheat in August. It costs him about $3.05 a bushel to plant and harvest the crop. An August
futures price of $3.45 is available. The farmer wants to lock the price by building a selling
(short) hedge by selling 8 of these August futures contracts (each contract is for 5,000 bushels,
hence 8 contracts will cover the entire 40,000 bushels!). When August comes, the spot drops to
$3. As a result, the farmer covers his loss on the spot with his short position on the futures: The
farmer is short in futures as he makes a commitment to sell at a future date, and long in spot as
he actually owns the wheat. As a result he will receive a gain of $18,000 on the futures market
and lose $2,000 on the spot<LINK: DECISION MATRIX>.This is an example of perfect hedge,
it is rare in practice as quantity or quality of products harvested may differ from the one specified
in the futures contracts; furthermore, maturity of crops do not always match futures contract
expirations.
<START LINK: DECISION MATRIX>
Time
June
August
On the “spot” market
-$3.05/bushel or
-40,000 x 3.05 = -$122,000
$3.00/bushel or
40,000 x 3.00 = $120,000
Total
-2,000
Balance +16,000
On the futures market
$3.45/bushel or
40,000 x 3.45 = $138,000
-$3.00/bushel or
-40,000 x 3.00 = -$120,000
(notice: spot price =futures price at maturity)
+18,000
<END LINK: DECISION MATRIX>
For Example, you are managing a $100,000 (face value) portfolio in T-BONDS priced at 98-10
or $98,312.5. In June, you are concern with a forthcoming increase in interest rates (within the
next 6 months, around November…may be). Hence, you enter into a short hedge to “lock” the
value of your portfolio for the next seven month. You are interested in December T-bond futures
priced at 97-0 ($97,000). You make the commitment to sell those December T-bonds—i.e. you
are short on December T-bonds Futures. On November 15th interest rates increase and your Tbond portfolio drops to $96,250; however your December futures contract price drops to 95-10
or $95,312.5. Even though your portfolio dropped by $2,062.5, you gained $1,687.5 in the
futures market<LINK: DECISION MATRIX>.
<START LINK: DECISION MATRIX>
Date
June 1st
Cash Market
You hold $100,000 face value T-bonds
with a current market value of
-$98,312.5 --100,000 x (98+10/32)%
You are long on T-Bonds
Nov. 15th
Interest rates increase and the T-bond
is worth 96-8. Sell your T-bonds at 968--i.e., +$96,250
You lost 96,250-98,312.5=-$2,062.5
on the Cash Market
-$375
Bottom
Line
Balance
Futures Market
You are interested in December T-bond
futures priced at 97-0--i.e., +$97,000. You
make the commitment to sell those
December T-bonds at this price: you are
short on December T-bonds Futures
The December T-bill futures is worth 9510. Close (buy) your short position at 9510--i.e., -$95,312.5
You Gain 97,000-95,312.5=+$1,687.5 on
the Futures Market
<END LINK: DECISION MATRIX>
Let’s consider another example, you are managing $5 million of common stock portfolio. You
are concern that the market will go down in the next three months. The current 3-month S&P400
index futures is selling at 200. Then, you are long in the “cash” market; to protect yourself, you
will go short in the futures market (short hedge). The portfolio amounts $5,000,000 and the price
of 1 contract is $500 per index point; if the value of one contract is $100,000 (200 x 500), you
need 50 (5,000,000/100,000) contracts to “hedge” the whole $5,000,000. Assume that the
portfolio value falls to $4 million two months after and that the S$P400 index futures falls
simultaneously at 170. As a result of the short hedge, you gain $750,000 in the futures market
and lose $1,000,000 in the cash market<LINK: DECISION MATRIX>.
<START LINK: DECISION MATRIX>
Time
On the “spot” market On the futures market
Today
-$5,000,000
200 x 500 x 50= $5,000,000
2 month after +$4,000,000
170 x 500 x 50= -$4,250,000
(notice: spot price =futures price at maturity)
Total
-1,000,000
+750,000
Balance
-250,000
<END LINK: DECISION MATRIX>
In perfect hedges, if you want to know how much contract to buy in order to hedge your
portfolio, you just have to divide the amount you want to hedge by the value of a contract.
Pratically, a portfolio does not have a corresponding futures contract available. So, when the
underlying asset and the futures are not exactly the same, you are in a situation of imperfect
hedge
In the case of Bond portfolios, you don’t have many choices for bond index futures. So, if your
portfolio includes bonds with different duration, or a mix of corporate, municipal or other bonds,
the number of contracts that need to be issued for an hedge are the ratio of equivalency times the
amount you want to hedge by the value of a contract<LINK: BOND IMPERFECT HEDGE>.
<START LINK: BOND IMPERFECT HEDGE>
Hedge Ratio   =
n  
D modS
S
 i 
D modF
F
amount to hedge
value of 1 contract
Where Dmods is the modified duration of the portfolio, Dmodf is the modified duration of the
futures, beta is the “beta yield” or the relative difference in interest rates affect between futures
and spot markets (we’ll assume that it equals 1).
<END LINK: BOND IMPERFECT HEDGE>
For Example, suppose an investment banker underwrites the issue of a bond that will be sold in
3 months. He has set the indenture and expect to sell the animal at par! The total issue amounts
to 10,000,000 (or 10,000 bonds). Yet, he is concerned about a rise in interest rates. Thus, he
hedges the new issue in the T-BOND futures market. He knows that the bond is far from being a
T-BOND, but futures on this bond are not traded. Knowing that the a T-Bond futures contract
covers 100,000, he finds that the right amount of contracts to be sold to hedge the new issue
should be 82 contracts<LINK: TABLE 1>.
<START LINK: TABLE 1>
Yield Coupon m maturity Duration
Price
BOND
8.25% 8.25% 2
15
8.516292224
100
T_BOND (FUT) 7.70%
8%
2
20
10.04494771 103.0625
8.52
 8.18
8.25%
(1 
)
2
10.05
Dmod F 
 9.68
7. 7%
(1 
)
2
Assuming Beta = 1,
8.18
100
Hedge Ratio   =
1
 0.819
9.68
103.06
10,000,000
n  0.819 
 82 contracts
100,000
Then, the hedge ratio is 0.82 or 82 contracts are to be sold (remember he is long in the bond
market!)
Dmod S 
<END LINK: TABLE 1>
You manage a fund; you plan to sell $100,000,000 (face value) of a type of bonds in 2 months
from now to reallocate the assets of the portfolio. You decide to build a hedge to lock the cash
you will receive. That is, you build a short hedge by selling 1,108 T-Bond futures <LINK:
TABLE 2>
<START LINK: TABLE 2>
Yield Coupon m maturity Duration
7.48% 7.25% 2
26 11.45268584
7.89%
8% 2
20 9.952213432
Price
97.375
101.125
BOND
T_BOND (FUT)
11.45
Dmod S 
 11.04
7.48%
(1 
)
2
9.95
Dmod F 
 9.57
7.89%
(1 
)
2
Assuming Beta = 1,
11.04
97.375
Hedge ratio   =
 1
 1.111
9.57
101.125
The hedge ratio is 1.111 or you will have to short
100,000,000
n  1.111 
 1111 contracts
100,000
1,111 contracts (you are long in the bond market!)
<END LINK: TABLE 2>
Equity portfolio can also be hedged using index futures; in reality, there are only index futures
and your portfolio is not exactly the same as the index! Thus, in the same vein as with bond
futures, the number of contracts to purchase to hedge a portfolio of stock is related to how your
portfolio is correlated to the chosen index <LINK: FORMULA>.
<START LINK: FORMULA>
N=portfolio value/contract value x βportfolio
Where βportfolio is the beta of your portfolio compared to the chosen index.
<END LINK: FORMULA>
S&P400 futures are traded at the CME. Purchasers place funds in a margin account (Initial
margin requirements of $6,000 for speculators and $2,500 for hedgers). Prices are marked to
market (a change in value is added or subtracted from the margin account). Maintenance Margin
requires an increase of $2500 for speculators and $1400 for hedgers. For Example, suppose that
in mid-December you own a portfolio worth $3,243,750; you expect the market to plunge within
the next 6 months; thus, you sell June S&P 500 futures contracts which currently trade at a
settlement price of 617.00. The value of a single contract is $308,500--i.e., 500 x 617-- your
portfolio has a beta of 1.15 with the S&P400; then, you decide to short 12 contracts, as you are
long in the equity market<LINK: SOLUTION>
<START LINK: SOLUTION>
 Value of Portfolio 
N* = 

 Value of 1 contract 
 $3,243,750 / $308,500  1.15
 12.09
<END LINK: SOLUTION>
Topic VI.c: Speculating with futures
Learning outcomes:

Define and apply the different techniques that use futures for speculating and positioning
the systematic risk of a portfolio
Reading: p.349-353, p.365-367, p.924-931, p.938-954, and p.962-967
Each time you take a position in a market, you speculate! Rather than hedging (offsetting long
and short positions), an investor may engage into speculation by assuming the price fluctuation
risk in order to have a chance to make a large gain. Remember that gains and loss are magnified
by the use of leverage (margin). For example you believe that the price of corn will go from $3
per bushel to $4 in three month from now. We are in June and the September futures is at $3.25.
You can buy 10 of these futures contracts (each of these contracts is for $5,000). If you are right
and the spot goes to $4 in September, you will make $37,500 (10 times 0.75 times 5000), putting
only $10,000 ($1,000 per contract or less than 7%) as an initial margin; which corresponds to
375% profit. A spot speculation would have brought a $50,000 (10 times 1 times 5000) profit
with an initial investment of $150,000 (10 times 3 times 5000); which corresponds to a return of
33%.
Active portfolio managers are considered speculators as they “play” with the beta of their
portfolio: by buying or selling index futures, the beta of a portfolio can be increased or
decreased. Remember that you would like a high beta in a rising economy and a low beta in a
recessing economy<LINK: Mathematical Explaination>.
<START LINK: Mathematically Explaination >
 portfolio  %equity   equity  % Futures   futures
Where, βfutures =1 when you use Index futures (for example the S&P400)
number of contracts  contract size x futures price
%futures 
, thus
portfolio value
 portfolio  %equity   equity  portfolio value
number of contracts 
contract size  futures price
<START LINK: Mathematically Explaination >


For Example, you have a $25 million equity portfolio consisting of $22.5M in stocks and $2.5M
in T-bills. Current beta of equity portion is 0.95. You want to increase it to increase to 1.10. An
S&P400 futures contract is quoted at 476.6 . You need to be long 26 contracts <LINK:
CALCULATION>
<START LINK: CALCULATION>
N=[1.1-(22.5/25) X .95] X 25,000,000/(500 X 476.6)=25.7
It is positive thus buy 26 contracts (you cannot buy 25.7 contracts).
<END LINK: CALCULATION>
Bond portfolio’s duration can also be manipulated according to interest rate expectation. Recall
that the duration of a portfolio is the weighted average of each bond’s duration; then by shorting
T-Bond futures you can decrease the overall portfolio duration to a target. Inversely, if you want
to increase the portfolio duration, buy T-Bond futures. As in increasing the Beta of a portfolio,
these “tactical” procedures are cheaper than rebalancing (selling and buying securities) the whole
portfolio: Transaction costs in the futures market are lesser than in the spot; also the leverage
allowed frees cash for more efficient allocation.
Topic VI.d: Case Study-Portfolio Hedging
This case deals with stock index futures and demonstrates how they can be used to hedge a
portfolio of common stock. The case requires to set up a hedge and in so doing, examines some
of the critical dimensions of a successful hedge transaction.
Jim Parker and his wife, Polly, live in Birmingham, Alabama. Like many young couples today,
the Parkers are a two-income family; Jim and Polly are both college graduates and hold wellpaying jobs. Jim has been an avid investor in the stock market for a number of years and over
time has built up a portfolio that is currently worth nearly $175,000. The Parkers' portfolio is
well diversified, although it is heavily weighted in high-quality, mid-cap growth stocks. The
Parkers reinvest all dividends and regularly add investment capital to their portfolio. Up to now,
they have avoided short selling and do only a modest amount of margin trading. Their portfolio
has undergone a substantial amount of capital appreciation in the last 18 months or so, and Jim is
eager to protect the profit they have earned. And that's the problem, because Jim feels the market
has pretty much run its course and is about to enter a period of decline. He has studied the market
and economic news very care- fully and does not believe the retreat will be of major magnitude
or cover an especially long period of time. He feels fairly certain, however, that most, if not all,
of the stocks in his portfolio will be adversely affected by these market conditions-though they
certainly won't all be affected to the same degree (some will drop more in price than others). Jim
has been following stock-index futures for some time and believes he knows the ins and outs of
these securities pretty well. After careful deliberation, Jim and Polly decide to use stock-index
futures-in particular, the S&P MidCap 400 futures contract-as a way to protect (hedge) their
portfolio of common stocks.
Explain why the Parkers would want to use stock-index futures to hedge their stock
portfolio, and note how they would go about setting up such a hedge. Be specific. What
alternatives do Jim and Polly have to protect the capital value of their portfolio? What are
the benefits and risks of using stock-index futures for such purposes (as hedging vehicles)?
The reason for the hedge is to protect the capital invested in the stock portfolio-if the market
does indeed drop, then the capital value of the Parker portfolio is likely to decline as well.
Setting up a short hedge with stock index futures would (fully or partially) protect the capital
investment since a short sale appreciates in value as the market declines; thus, the capital lost in
the portfolio should be offset by the profit made from the short position. Parker should set up the
hedge by short selling (one or more) S&P 400 Midcap futures contracts, probably with an
expiration date that is near-or slightly longer than-the time he thinks it will take for the market to
complete its drop.
Parker has several alternatives, including: 1) Short-selling all or most of the portfolio against the
box; 2) Buying puts on all or most of his stocks; or 3) Using stock index options to hedge his
portfolio in much the same way that he's doing with stock index futures. The first two
alternatives are the least attractive since they would be cumbersome and costly to set up; not so
with the stock index option hedge: this tactic has merit and definitely should be considered by
Parker. Another alternative is to use futures options-i.e., to buy puts on stock index futures
contracts. The benefits of hedging with stock index futures are the amount of protection
purchased with such low cost/investment, and the ease of setting up the hedge (with a single
instrument that captures the behavior of the whole market). The major risk of course, is that the
market won't perform as expected (in other words, it goes up rather than down and as a result,
the investor will miss any profits that might be made, as long as the hedge remains in place); in
addition, it's possible that the stock portfolio will not perform like the market and as such, the
hedge itself will be less than effective.
Assume that S&P MidCap 400 futures contracts are currently being quoted at 325.60. How
many contracts would the Parkers have to buy (or sell) to set up the hedge? Say the value
of the Parker portfolio dropped 12% over the market retreat. To what price must the
stock-index futures drop in order to cover that loss? Given that a $6,000 margin deposit is
required to buy or sell a futures contract, what would be the Parkers' return on
investment?
The short hedge can be set up by short selling one S&P 400 Midcap futures contract; at a quote
of 325.60, the underlying value of one contract will fall slightly short of covering the value of
Parker's $175,000 portfolio:
Value of the S&P 400 Midcap futures contract = 325.60 x $500 = $162,800
Value of Parker Portfolio = $175,000 - ($175,000 x . 12) = $154,000
Since the Parker portfolio lost $21,000 and since each point in a S&P400 Composite contract is
worth $500, the index would have to drop 42 points (21,000 / 500) to a new price of 283.60
(325.6 – 42)
Given that a $6,000 margin deposit is required to buy or sell a single S&P 400 futures contract,
the Parkers' return on invested capital if the price of the futures contract changed by 42 points
would be (500 x 42)/6000=350%
Assume that the value of the Parker portfolio declined by $32,000, while the price of an
S&P 400 futures contract moved from 325.60 to 277.60. (Assume that Jim and Polly short
sold one futures contract to set up the hedge.) Add the profit from the hedge transaction to
the new (depreciated) value of the stock portfolio. How does this amount compare to the
$175,000 portfolio that existed just before the market started its retreat? Why did the
stock-index futures hedge fail to give complete protection to the Parker portfolio? Is it
possible to obtain perfect (dollar-for-dollar) from these types of hedges?
Profit from futures contract: (325.60 - 297.60) x $500 = $24,000
Value of portfolio ($175,000 - 32,0000)
+ Profit from short hedge
Net
$143,000
24.000
$167,000
Because of the portfolio short hedge, the net value of the portfolio dropped by only $8,000.
The stock index futures hedge failed simply because the Parker portfolio did not behave exactly
like the S&P 400 Midcap Index. But that's the nature of the animal; for rarely would we expect
even a well-diversified portfolio to behave exactly like the market and as such, short of pure
luck, (theoretically) perfect protection is possible to obtain by using hedge ratio. In fact, about
the only way to obtain a guaranteed perfect hedge is to build a portfolio of stocks exactly like
that in the S&P 400 Midcap Index.