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Chapter 5: Q12I (page 589)

The Excel Applications box in the chapter (available at www.mhhe.com/bkm ; link to Chapter 17 material) shows how to use the spot-futures parity relationship to find a “term structure of futures prices,” that is, futures prices for various maturity dates.

a. Suppose that today is January 1, 2012. Assume the interest rate is 1% per year and a stock index currently at 1,200 pays a dividend yield of 2%. Find the futures price for contract maturity dates of February 14, 2012, May 21, 2012, and November 18, 2012.

b. What happens to the term structure of futures prices if the dividend yield is lower than the risk-free rate? For example, what if the interest rate is 3%?

Short Answer

Expert verified

Answer

a.

$1,198.67

$1,195.30

$1,189.43

b.

$1,201.31

$1,204.66

$1,210.55

Step by step solution

01

Calculation of future price ‘a’

Based on the input template:

Spot price S0
1200
Futures price vs maturity

Income yield(d) (%)

2



Interest (r)(%)

1



Today's date

01-01-2012

Spot Price

$1,200

Maturity date 1

02-14-2012

Futures 1

$1,198.67

Maturity date 2

05-21-2012

Futures 1

$1,195.30

Maturity date 3

11-18-2012

Futures 1

$1,189.43





Time to maturity 1

0.11



Time to maturity 2

0.39



Time to maturity 3

0.88



Time to maturity is calculated by dividing the number of days from today’s date to maturity date by 365(number of days in year).

Formula used: F0 = S0 (1 + r - d)T

02

Calculation of future price ‘b’

Based on the input template (if dividend rate was lower than risk free rate):

Spot price
1200

Futures price vs maturity

Income yield (%)

2




Interest (%)

1




Today's date

01-01-2011


Spot Price

$1,200

Maturity date 1

02-14-2012


Futures 1

$1,201.31

Maturity date 2

05-21-2012


Futures 1

$1,204.66

Maturity date 3

11-18-2012


Futures 1

$1,210.55






Time to maturity 1

0.11




Time to maturity 2

0.39




Time to maturity 3

0.88




Time to maturity is calculated by dividing the number of days from today’s date to maturity date by 365(number of days in year).

Formula used: F0=S01+r-dT

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Most popular questions from this chapter

You are attempting to formulate an investment strategy. On the one hand, you think there is great upward potential in the stock market and would like to participate in the upward move if it materializes. However, you are not able to afford substantial stock market losses and so cannot run the risk of a stock market collapse, which you recognize is also possible. Your investment adviser suggests a protective put position:

Buy shares in a market-index stock fund and put options on those shares with three months until expiration and exercise price of \(1,040. The stock index is currently at \)1,200. However, your uncle suggests you instead buy a three-month call option on the index fund with exercise price \(1,120 and buy three-month T-bills with face value \)1,120.

a. On the same graph, draw the payoffs to each of these strategies as a function of the stock fund value in three months. (Hint: Think of the options as being on one “share” of the stock index fund, with the current price of each share of the index equal to \(1,200.)

b. Which portfolio must require a greater initial outlay to establish?

( Hint: Does either portfolio provide a final payoff that is always at least as great as the payoff of the other portfolio?)

c. Suppose the market prices of the securities are as follows:

Stock Fund

\)1200

T -bill (Face value \(1,120

\)1080

Call (Exercise price \(1,120

\)160

Put (Exercise price \(1040

\)8

Make a table of profits realized for each portfolio for the following values of the stock price in three months: S T = \(0, \)1,040, \(1,120, \)1,200, and $1,280. Graph the profits to each portfolio as a function of S T on a single graph.

d. Which strategy is riskier? Which should have a higher beta?

The hedge ratio of an at-the-money call option on IBM is .4. The hedge ratio of an at-the-money put option is -6. What is the hedge ratio of an at-the-money straddle position on IBM?

You write a call option with X = \(50 and buy a call with X = \)60. The options are on the same stock and have the same expiration date. One of the calls sells for \(3; the other sells for \)9.

a. Draw the payoff graph for this strategy at the option expiration date.

b. Draw the profit graph for this strategy.

c. What is the break-even point for this strategy? Is the investor bullish or bearish on the stock?

A corporation has issued a $10 million issue of floating-rate bonds on which it pays an interest rate 1% over the LIBOR rate. The bonds are selling at par value. The firm is worried that rates are about to rise, and it would like to lock in a fixed interest rate on its borrowings. The firm sees that dealers in the swap market are offering swaps of LIBOR for 7%. What swap arrangement will convert the firm’s borrowings to a synthetic fixed-rate loan? What interest rate will it pay on that synthetic fixed-rate loan?

We showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? Use the put-call parity relationship as well as a numerical example to prove your answer.
See all solutions

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