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rate is 5% and the expected dividend yield on the S&P 500 is 2%, what should the one-
year maturity futures price be?
13. It is now January. The current interest rate is 5%. The June futures price for gold is
$346.30, while the December futures price is $360.00. Is there an arbitrage opportunity
here? If so, how would you exploit it?
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Fifth Edition




593
16 Futures Markets


14. The Chicago Board of Trade has just introduced a new futures contract on the stock of
Brandex, a company that currently 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 stock 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?
15. The multiplier for a futures contract on the stock market index is $250. The maturity of
the contract is one year, the current level of the index is 1,200, 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 1,210.
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 one-month holding-period return if the initial margin on the contract is
$15,000.
16. Futures contracts and options contracts can be used to modify risk. Identify
the fundamental distinction between a futures contract and an option contract,
and briefly explain the difference in the manner that futures and options modify
portfolio risk.
17. Suppose an S&P index portfolio pays a dividend yield of 2% annually. The index
currently is 1,200. The T-bill rate is 5%, and the S&P futures price for delivery in one
year is $1,243. Construct an arbitrage strategy to exploit the mispricing and show that
your profits one year hence will equal the mispricing in the futures market.
18. a. How should the parity condition (Equation 16.2) 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 16.2.
19. The one-year futures price on a particular stock-index portfolio is 406, the stock index
currently is 400, the one-year risk-free interest rate is 3%, and the year-end dividend
that will be paid on a $400 investment in the index portfolio is $5.
a. By how much is the contract mispriced?
b. Formulate a zero-net-investment arbitrage portfolio and show that you can lock in
riskless profits equal to the futures mispricing.
c. Now assume (as is true for small investors) that if you short sell the stocks in the
market index, the proceeds of the short sale are kept with the broker, and you do not
receive any interest income on the funds. Is there still an arbitrage opportunity
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(assuming you don™t already own the shares in the index)? Explain.
d. Given the short-sale rules, what is the no-arbitrage band for the stock-futures price
relationship? That is, given a stock index of 400, how high and how low can the
futures price be without giving rise to arbitrage opportunities?
20. The S&P 500 index is currently at 1,400. You manage a $7 million indexed equity
portfolio. The S&P 500 futures contract has a multiplier of $250.
a. If you are temporarily bearish on the stock market, how many contracts should you
sell to fully eliminate your exposure over the next six months?
b. If T-bills pay 2% per six months and the semiannual dividend yield is 1%, what is
the parity value of the futures price? Show that if the contract is fairly priced, the
Bodie’Kane’Marcus: V. Derivative Markets 16. Futures Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




594 Part FIVE Derivative Markets


total risk-free proceeds on the hedged strategy in part (a) provide a return equal to
the T-bill rate.
c. How would your hedging strategy change if, instead of holding an indexed portfolio,
you hold a portfolio of only one stock with a beta of 0.6? How many contracts would
you now choose to sell? Would your hedged position be riskless? What would be the
beta of the hedged position?
21. The margin requirement on the S&P 500 futures contract is 10%, and the stock index is
currently 1,200. Each contract has a multiplier of $250. How much margin must be put
up for each contract sold? If the futures price falls by 1% to 1,188, what will happen to
the margin account of an investor who holds one contract? What will be the investor™s
percentage return based on the amount put up as margin?
22. The multiplier for a futures contract on a certain stock market index is $500. The
maturity of the contract is one year, the current level of the index is 400, and the risk-
free interest rate is 0.5% per month. The dividend yield on the index is 0.2% per month.
Suppose that after one month, the stock index is at 410.
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 $15,000.
23. You are a corporate treasurer who will purchase $1 million of bonds for the sinking
fund in three months. You believe rates soon will fall and 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
actually can buy the bonds? Will you be long or short? Why?




WEBMA STER
Contract Specifications for Financial Futures and Options
Go to the Chicago Board of Trade site at http://www.cbot.com. Under the Knowledge
Center item find the contract specifications for the Dow Jones Industrial Average
Futures and the Dow Jones Industrial Average Options. Then, answer the following
questions:
1. What contract months are available for both the futures and the options?
2. What is the trading unit on the futures contract?
3. What is the trading unit on the option contract?
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Obtain current prices on the Dow Jones Industrial Average Futures Contract. This can
be found under Equity Futures quotes.
4. What is the futures price for the two delivery months that are closest to the
current month? (Use the last trade for price.)
5. How does that compare to the current price of the Dow Jones Industrial
Average?
6. What are the prices for the put and call options that are deliverable in the same
months as the futures contracts? Choose exercise prices as close as possible to
the futures price.
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Fifth Edition




595
16 Futures Markets


1. a. The payoff on the put looks like that on the short futures contract when the asset price falls SOLUTIONS TO
below X or F0, but when the asset price rises above F0, the futures payoff turns negative whereas
< Concept
the value of the put cannot fall below zero. The put (which must be purchased) gives you upside
potential if the asset price falls but limits downside risk, whereas the futures gives you both CHECKS
upside and downside exposure.
b. The payoff on the written call looks like that on the short futures contract when the asset price
rises above F0, but when the asset price falls, the futures payoff is positive, whereas the payoff
on the written call is never positive. The written call gives you downside exposure, but your
upside potential is limited to the premium you received for the option.


Short futures Buy (long) put Write (sell) call
Payoff, profit Payoff Payoff




PT PT PT
F0 X X




2. The clearinghouse has a zero net position in all contracts. Its long and short positions are offsetting,
so that net cash flow from marking to market must be zero.
3.
T-Bond Price in March

$102.91 $103.91 $104.91
Cash flow to purchase bonds ( 2,000 PT) $205,820 $207,820 $209,820
Profits on long futures position 2,000 $0 2,000
Total cash flow $207,820 $207,820 $207,820


4. The risk would be that the index and the portfolio do not move perfectly together. Thus, risk
involving the spread between the futures price and the portfolio value could persist even if the
index futures price were set perfectly relative to index itself.
5.
Action Initial Cash Flow Time-T Cash Flow
$280(1.005)6
Lend $280 $280 $288.51
Sell gold short 280 ST
Long futures 0 ST $288
Total $0 $0.51 risklessly
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Essentials of Investments, Management Companies, 2003
Fifth Edition




SIX
PA RT
ACTIVE INVESTMENT
MANAGEMENT
assive investment, or indexing, is the pre- Active management attempts to exploit

P ferred strategy for those who believe mar- market inefficiency that potentially could arise
kets are efficient. While administration of from market frictions or less-than-fully rational
passive portfolios requires an efficient organiza- investor behavior. Chapter 19 explores the
tional structure, there is comparatively less need emerging field of behavioral finance and lays
for knowledge of investments in managing index down the fundamentals of behavior that may
portfolios. In contrast, active management takes affect security prices. We also catalogue and ex-
it on faith that markets are not always efficient plain certain techniques known as technical
and that, at least occasionally, bargains are to be analysis aimed at uncovering deviations from
found in security markets. Active managers must market efficiency in order to improve investment
apply asset valuation and portfolio theory to performance.
client portfolios. Regardless of why prices may not reflect all
Professional management of active invest- relevant information, efficient exploitation of se-
ments begins with a contractual relationship curity mispricing calls for balancing investment in
between client and portfolio manager. The eco- underpriced securities with diversification. How
nomic needs of clients must be articulated and should this balance be struck? The answer is in-
their objectives translated into an operational fi- separable from the quandary of how to assess
nancial plan. For this purpose, the Association of the performance of an active portfolio. Accord-
Investment Management and Research (AIMR) ingly, Chapter 20 begins with the theory of per-
designed a framework for financial planning that formance evaluation and proceeds to suggest
can be understood by lay clients. Chapter 17 fa- portfolio management techniques to achieve the
miliarizes you with this framework. goal of superior performance.
Investments originate with a savings plan Investing across borders is conceptually a
that diverts funds from consumption to invest- simple expansion of portfolio diversification. Yet
ment. How much should an individual household this pursuit confronts the effects of political risk
save? Taxes and inflation complicate the relation- and uncertain exchange rates on future perform-
ship between how much you save and what you ance. These issues, unique to international in-
will be able to achieve with your accumulating in- vestment, are addressed in Chapter 21.
vestment fund. Chapter 18 formulates a compre-
hensive household savings/investment plan.




>
17 Investors and the Investment Process
18 Taxes, Inflation, and Investment Strategy
19 Behavioral Finance and Technical Analysis
20 Performance Evaluation and Active Portfolio Management
21 International Investing


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Essentials of Investments, Management Investment Process Companies, 2003
Fifth Edition




17
INVESTORS AND THE
INVESTMENT PROCESS


AFTER STUDYING THIS CHAPTER
YOU SHOULD BE ABLE TO:


> Specify investment objectives of individual and institutional
investors.

> Identify constraints on individual and institutional investors.


> Compare and contrast major types of investment policies.




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