Chapter 22 – Futures Markets
CHAPTER 22: FUTURES MARKETS
PROBLEM SETS
1. There is little hedging or speculative demand for cement futures, since cement prices are
2. The ability to buy on margin is one advantage of futures. Another is the ease with which one
3. Short selling results in an immediate cash inflow, whereas the short futures position
does not:
Action
Initial CF
Final CF
Short Sale
+P0
–PT
Short Futures
0
F0 – PT
4. a. False. For any given level of the stock index, the futures price will be lower when
the dividend yield is higher. This follows from spot-futures parity:
b. False. The parity relationship tells us that the futures price is determined by the stock
c. True. The short futures position will profit when the market falls. This is a negative
5. The futures price is the agreed-upon price for deferred delivery of the asset. If that price
6. Because long positions equal short positions, futures trading must entail a “canceling
22-2
7. a. The closing futures price for the March contract was 1,477.20, which has a dollar
value of:
Therefore, the required margin deposit is: $36,930
b. The futures price increases by: 1,500.00 – 1,477.20 = 22.80
c. Following the reasoning in part (b), any change in F is magnified by a ratio of
8. a. F0 = S0(1 + rf ) = $150 1.06 = $159
9. a. Take a short position in T-bond futures, to offset interest rate risk. If rates increase,
the loss on the bond will be offset to some extent by gains on the futures.
11. The put-call parity relation states that:
P = C – S0 + X /(1 + rf )T
Chapter 22 – Futures Markets
22-3
12. According to the parity relation, the proper price for December futures is:
13. a. 120 1.06 = $127.20
b. The stock price falls to: 120 (1 – 0.03) = $116.40
14. a. The initial futures price is F0 = 1300 (1 + 0.005 – 0.002)12 = $1,347.58
In one month, the futures price will be:
15. The treasurer would like to buy the bonds today, but cannot. As a proxy for this
purchase, T-bond futures contracts can be purchased. If rates do in fact fall, the treasurer
16. The parity value of F is: 1,300 (1 + 0.04 – 0.01) = 1,339
The actual futures price is 1,330, too low by 9.
Arbitrage Portfolio
CF now
CF in 1 year
Short Index
1,300
−S T − (0.01 × 1,300)
Buy Futures
0
S T − 1,330
Lend
−1,300
1,300 × 1.04
Total
0
9
Chapter 22 – Futures Markets
17. a. Futures prices are determined from the spreadsheet as follows:
Spot price
1,500
Income yield (%)
1.5
Futures prices versus maturity
Interest rate (%)
3.0
Today’s date
1/1/2008
Spot price
1,500.00
Maturity date 1
2/14/2008
Futures 1
1,502.67
Maturity date 2
5/21/2008
Futures 2
1,508.71
Maturity date 3
11/18/2008
Futures 3
1,519.79
Time to maturity 1
0.12
Time to maturity 2
0.39
Time to maturity 3
0.88
LEGEND:
Enter data
Value calculated
See comment
b. The spreadsheet demonstrates that the futures prices now decrease with increased
time to maturity:
Spot price
1,500
Income yield (%)
4.0
Futures prices versus maturity
Interest rate (%)
3.0
Today’s date
1/1/2008
Spot price
1,500.00
Maturity date 1
2/14/2008
Futures 1
1,498.20
Maturity date 2
5/21/2008
Futures 2
1,494.15
Maturity date 3
11/18/2008
Futures 3
1,486.78
Time to maturity 1
0.12
Time to maturity 2
0.39
Time to maturity 3
0.88
LEGEND:
Enter data
Value calculated
See comment
18. a. The current yield for Treasury bonds (coupon divided by price) plays the role of the
b. When the yield curve is upward sloping, the current yield exceeds the short rate.
22-5
19. a.
Cash Flows
Action
Now
T1
T2
Long futures with maturity T1
0
P1 – F( T1)
0
Short futures with maturity T2
0
0
F( T2) – P2
Buy asset at T1, sell at T2
0
–P1
+P2
At T1, borrow F( T1)
0
F( T1)
–F( T1) (1+ rf )( T2–T1)
Total
0
0
F( T2) – F( T1) (1+ rf )( T2–T1)
b. Since the T2 cash flow is riskless and the net investment was zero, then any profits
represent an arbitrage opportunity.
c. The zero-profit no-arbitrage restriction implies that
CFA PROBLEMS
1. a. The strategy that would take advantage of the arbitrage opportunity is a “reverse cash
and carry.” A reverse cash and carry opportunity results when the following
relationship does not hold true:
F0 ≥ S0 (1+ C)
If the futures price is less than the spot price plus the cost of carrying the goods to the
futures delivery date, then an arbitrage opportunity exists. A trader would be able to sell
b.
Cash Flows
Action
Now
One year from now
Sell the spot commodity short
+$120.00
−$125.00
Buy the commodity futures expiring in 1 year
$0.00
$0.00
Contract to lend $120 at 8% for 1 year
−$120.00
+$129.60
Total cash flow
$0.00
+$4.60
Chapter 22 – Futures Markets
22-6
2. a. The call option is distinguished by its asymmetric payoff. If the Swiss franc rises
in value, then the company can buy francs for a given number of dollars to service
its debt, and thereby put a cap on the dollar cost of its financing. If the franc falls,
the company will benefit from the change in the exchange rate.
b. The call option gives the company the ability to benefit from depreciation in the
franc, but at a cost equal to the option premium. Unless the firm has some special
3. The important distinction between a futures contract and an options contract is that the
futures contract is an obligation. When an investor purchases or sells a futures contract, the
investor has an obligation to either accept or deliver, respectively, the underlying commodity
on the expiration date. In contrast, the buyer of an option contract is not obligated to accept
4. a. The investor should sell the forward contract to protect the value of the bond against
rising interest rates during the holding period. Because the investor intends to take a
b. The value of the forward contract on expiration date is equal to the spot price of the
underlying asset on expiration date minus the forward price of the contract:
$978.40 – $1,024.70 = –$46.30
The contract has a negative value. This is the value to the holder of a long position in
Chapter 22 – Futures Markets
c. The value of the combined portfolio at the end of the six-month holding period is:
$978.40 + $46.30 = $1,024.70
The change in the value of the combined portfolio during this six-month period is:
$24.70
The value of the combined portfolio is the sum of the market value of the bond
and the value of the short position in the forward contract. At the start of the six-
month holding period, the bond is worth $1,000 and the forward contract has a
value of zero (because this is not an off-market forward contract, no money
forward contract, the investor has created a fully hedged (and hence risk-free)
position, and should earn the risk-free rate of return. The six-month risk-free rate
of return is 5.00% (annualized), which produces a return of $24.70 over a six-
month period:
($1,000 × 1.05(1/2)) – $1,000 = $24.70
These results support VanHusen’s statement that selling a forward contract on the
underlying bond protects the portfolio during a period of rising interest rates. The loss
5. a. Accurate. Futures contracts are marked to the market daily. Holding a short position
on a bond futures contract during a period of rising interest rates (declining bond
prices) generates positive cash inflow from the daily mark to market. If an investor in
b. Inaccurate. According to the cost of carry model, the futures contract price is adjusted
upward by the cost of carry for the underlying asset. Bonds (and other financial
instruments), however, do not have any significant storage costs. Moreover, the cost