Input:
Interest
Rate
0.058
FV of
Dividends
21
Current
Answers:
a. Expected level of
index in 6 mths?:
1600.55
Problem 23-5
Consider the futures contract written on the S&P 500 index and maturing in 6 months. The interest rate is 3% per 6-month period, and the future
value of dividends expected to be paid over the next 6 months is $15. The current index level is 1,425. Assume that you can short sell the S&P
index.
a.Suppose the expected rate of return on the market is 6% per 6-month period. What is the expected level of the index in 6 months? (Round your
answer to 2 decimal places.)
Level
Expected
Input:
Value of
S&P 500
1179
Cost per
contract
33
Avg NYSE
stock
price
48
Transactio
Answers:
Transactio
Transactio
n cost per
share
S&P 500
multiplier
Input:
Value of
S&P 500
1097
Value of
portfolio
10200000
S&P 500
Answers:
a. Long or
short?
Short
c. # of
contracts?
Problem 23-7
You manage a $16.5 million portfolio, currently all invested in equities, and believe that the market is on the verge of a big but
short-lived downturn. You would move your portfolio temporarily into T-bills, but you do not want to incur the transaction costs
of liquidating and reestablishing your equity position. Instead, you decide to temporarily hedge your equity holdings with S&P
500 index futures contracts.
a.Should you be long or short the contracts?
multiplier
Beta of
portfolio
Inputs:
Problem 23-8
A manager is holding a $1 million stock portfolio with a beta of 1.25. She would like to hedge the risk of the portfolio using the S&P 500 stock index
Inputs:
Spot price
If < 1; rate
higher in
US
If > 1; rate
higher in
Europe
Problem 23-10
Suppose that the spot price of the euro is currently $1.30. The 1-year futures price is $1.35. Is the interest rate higher in the United
States or the euro zone?
Inputs:
Spot price
of the
British
pound
1.70
Answer:
Forward
Problem 23-11
Assume the spot price of the British pound is currently $2.00. If the risk-free interest rate on 1-year government bonds is 4% in
the United States and 6% in the United Kingdom, what must be the forward price of the pound for delivery 1 year from now?
(Round your answer to 3 decimal places. Omit the “$” sign in your response.)
Forward price
rate on 1-
year
Inputs:
# of
per
contract
5000
Answer:
Problem 23-13
Farmer Brown grows Number 1 red corn and would like to hedge the value of the coming harvest. However, the futures contract is traded on
the Number 2 yellow grade of corn. Suppose that yellow corn typically sells for 90% of the price of red corn. If he grows 100,000 bushels, and
bushels
grown
yellow
corn
Inputs:
Basis pts.
Difference
Par value 100
Closing
futures
price
99.96
Initial
futures
price
Answer:
Profit or
Problem 23-14
Return to Figure 23.7 . Suppose the LIBOR rate when the first listed Eurodollar contract matures in January is .40%. What will be the profit or los s to
Libor rate 0.04
Initial
futures
price
Input:
to a change in
20 yr bonds
4.875
Answer: Δy 0.00039
duration of 5
yr bonds
duration of T-
bond futures
Number
Dollar
amount of 5
Problem 23-15
Yields on short-term bonds tend to be more volatile than yields on long-term bonds. Suppose that you have estimated that the yield on
Inputs:
Answer:
Dollars’
Problem 23-16
A manager is holding a $1 million bond portfolio with a modified duration of 8 years. She would like to hedge the risk of theportfolio by
short-selling Treasury bonds. The modified duration of T–bonds is 10 years. How many dollars’ worth of T-bonds should she sell to
Inputs:
Answer:
Forward
Problem 23-18
If the spot price of gold is $1,500 per troy ounce, the risk-free interest rate is 2%, and storage and insurance costs are zero,
what should be the forward price of gold for delivery in 1 year? (Round your answer to 2 decimal places. Omit the “$” sign
Inputs:
spot price
2.95
ROR on
mkt per
month
0.016
Risk-free
rate per
month
0.009
CAPM 0.0118
FV of corn
in 3 mths
2.86922
Answer:
FV of
storage
costs in 3
mths
$0.12
FV of corn
in 3 mths
yes if the
Problem 23-20
Suppose that the price of corn is risky, with a beta of .5. The monthly storage cost is $.03, and the current spot price is $5.50,
Storage
cost
Current
Expected
Inputs:
# of Euros 2100000
US yield
Answer:
Swap rate
Problem 23-21
Suppose the U.S. yield curve is flat at 4% and the euro yield curve is flat at 3%. The current exchange rate is $1.50 per euro.
PV of sum $7,867,383.08
Inputs:
Value of
Answer:
Problem 23-22
Desert Trading Company has issued $100 million worth of long-term bonds at a fixed rate of 7%. The firm then enters into
an interest rate swap where it pays LIBOR and receives a fixed 6% on notional principal of $100 million. What is the firm’s
notional
Inputs:
LIBOR 0.04
swap
5
Answer:
Problem 23-24
Suppose that at the present time, one can enter 5-year swaps that exchange LIBOR for 8%. An off-market swap would then be defined as a swap of
LIBOR for a fixed rate other than 8%. For example, a firm with 10% coupon debt outstanding might like to convert to synthetic floating-rate debt by
principal
payment
payments
Inputs:
Contract
multiplier
250
Value of
S&P 500
1575
Current
semi-annual
interest rate
0.031
annual
dividend
available
from short
% access to
short saale
profit 1462.81
Answers:
a. Fraction
of
proceeds
available
0.730
Problem 23-26
Consider these futures market data for the June delivery S&P 500 contract, exactly 6 months hence. The S&P 500 index is at 1,350,
and the June maturity contract is at F0= 1,351.
a.If the current interest rate is 2.2% semiannually, and the average dividend rate of the stocks in the index is 1.2% semiannually,
b-1.Suppose that you in fact have access to 90% of the proceeds from a short sale. What is the lower bound on the futures price
that rules out arbitrage opportunities? (Do not round intermediate calculations. Round your answer to 2 decimal places.)