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Investments

Zvi Bodie, Alex Kane, Alan J. Marcus

Chapter 22

Futures Markets - all with Video Answers

Educators

Chapter Questions

Problem 1

Why is there no futures market in cement?

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Problem 2

Why might individuals purchase futures contracts mather than the underlying asset?

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00:36

Problem 3

What is the difference in cash flow between short-selling an asset and entering a short futures position?

Abby Kennedy
Abby Kennedy
Numerade Educator

Problem 4

Are the following statements true or false? Why?
a. All else equal, the futures price on a stock index with a high dividend yield should be higher than the futures price on an index with a low dividend yield.
b. All else equal, the futures price on a high-beta stock should be higher than the futures price on a low-beta stock.
c. The beta of a short position in the S\&P 500 futures contract is negative.

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Problem 5

What is the difference between the futures price and the value of the futures contract?

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02:05

Problem 6

Evaluate the criticism that futures markets siphon off capital from more productive uses.

Norman Atentar
Norman Atentar
Numerade Educator

Problem 7

$a$. Turn to the Mini-S\&P 500 contract in Figure 22.1. If the margin requirement is $10 \%$ of the futures price times the contract multiplier of $$\$ 50$$, how much must you deposit with your broker to trade the December maturity contract?
b. If the December futures price increases to 4.400 , what percentage return will you carn on your investment if you entered the long side of the contract at the price shown in the figure?
c. If the December futures price falls by $1 \%$, what is your percentage return?

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Problem 8

a. A futures contract on a non-dividend-paying stock index with current value 150 has a maturity of one year. If the T-bill rate is $3 \%$, what should the futures price be?
b. What should the futures price be if the maturity of the contract is three years?
c What if the interest rate is $6 \%$ and the maturity of the contract is three years?

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Problem 9

Determine how a portfolio manager might use financial futures to hedge risk in each of the following circumstances:
a. You own a large position in a relatively illiquid bond that you want to sell.
b. You have a large gain on one of your Treasuries and want to sell it, but you would like to defer the gain until the next tax year.
c. You will receive your annual bonus next month that you hope to invest in long-term corporate bonds. You believe that bonds today are selling at quite attractive yields, and you are concerned that bond prices will rise over the next few weeks.

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Problem 10

Suppose the value of the S\&P 500 stock index is currently 4,000 .
a. If the 1-year T-bill rate is $3 \%$ and the expected dividend yield on the S\&P 500 is $2 \%$, what should the 1-year maturity futures price be?
b. What if the T-bill mate is less than the dividend yield, for example, $1 \%$ ?

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Problem 11

Consider a stock that pays no dividends on which a futures contract, a call option, and a put option trade. The maturity date for all three contracts is $T$, the exercise price of both the put and the call is $X$, and the futures price is $F$. Show that if $X=F$, then the call price equals the put price. Use parity conditions to guide your demonstration.

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Problem 12

It is now January. The current interest rate is $2 \%$. The June futures price for gold is $$\$ 1,500$$, whereas the December futures price is $$\$ 1,510$$. Is there an arbitrage opportunity here? If so, how would you exploit it?

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Problem 13

FinTrade has just introduced a single-stock futures contract on Brandex stock, a company that currendly pays no dividends. Each contract calls for delivery of 1,000 shares of stock in one year. The T-bill rate is $6 \%$ per year.
a. If Brandex stock now sells at $$\$ 120$$ per share, what should the futures price be?
b. If the Brandex price drops by $3 \%$, what will be the change in the futures price and the change in the investor's margin account?
c. If the margin on the contract is $$\$ 12,000$$, what is the percentage return on the investor's position?

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Problem 14

The multiplier for a futures contract on a stock market index is $$\$ 50$$. The maturity of the contract is one year, the current level of the index is 4,500 , and the risk-free interest rate is $.5 \%$ per month. The dividend yield on the index is $.2 \%$ per month. Suppose that after one month, the stock index is at 4,550 .
a. Find the cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition always holds exactly.
b. Find the holding-period return if the initial margin on the contract is $$\$ 10,000$$.

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Problem 15

You are a corporate treasurer who will purchase $\mathrm{S1}$ million of bonds for the sinking fund in three months. You believe rates will soon fall, and you would like to repurchase the company's sinking fund bonds (which currently are selling below par) in advance of requirements. Unfortunately, you must obtain approval from the board of directors for such a purchase, and this can take up to two months. What action can you take in the futures market to hedge any adverse movements in bond yields and prices until you can actually buy the bonds? Will you be long or short? Why? A qualitative answer is fine.

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Problem 16

The S\&P portfolio pays a dividend yield of $1 \%$ annually. Its current value is 4,000 . The T-bill rate is $4 \%$. Suppose the S\&P futures price for delivery in one year is 4,100 . Construct an arbitrage strategy to exploit the mispricing and show that your profits one year hence will equal the mispricing in the futures market.

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01:17

Problem 17

The Excel Application box in the chapter (available in Connect; link to Chapter 22 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, 2023. Assume the interest rate is $3 \%$ per year and a stock index currently at 2,000 pays a dividend yield of $2.0 \%$. Find the futures price for contract maturity dates of (i) February 14, 2023; (ii) May 21, 2023; and (iii) November 18, 2023.
b. What happens to the term structure of futures prices if the dividend yield is higher than the risk-free rate? For example, what if the dividend yield is $4 \%$ ?

Breanna Ollech
Breanna Ollech
Numerade Educator

Problem 18

a. How should the parity condition (Equation 22.2) for stocks be modified for futures contracts on Treasury bonds? What should play the role of the dividend yield in that equation?
b. In an environment with an upward-sloping yield curve, should T-bond futures prices on more-distant contracts be higher or lower than those on near-term contracts?
c. Confirm your intuition by examining Figure 22.1.

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Problem 19

Consider this arbitrage strategy to derive the parity relationship for spreads: (i) enter a long futures position with maturity date $T_1$ and futures price $F\left(T_1\right)$ : (ii) enter a short position with maturity $T_2$ and futures price $F\left(T_2\right)$; (iii) at $T_1$. when the first contract expires, buy the asset and borrow $F\left(T_1\right)$ dollars at rate $r_f$ (iv) pay back the loan with interest at time $T_2$.
a. What are the total cash flows to this strategy at times $0, T_1$, and $T_2$ ?
b. Why must profits at time $T_2$ be zero if no arbitrage opportunities are present?
c. What must the relationship between $F\left(T_1\right)$ and $F\left(T_2\right)$ be for the profits at $T_2$ to be equal to zero? This relationship is the parity relationship for spreads.

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