Financial Derivatives
Problem Set 2
Spring 2016
Advanced Futures Strategies
1.
Suppose IBC stock is selling at $80 per share. Also, the T-bill rate with 180 days to
maturity is 5%. Construct a synthetic futures contract with maturity in 180 days and
futures price of $82. In equilibrium, what should be the price of this futures
contract? What does that tell us about the expected return from holding the stock?
What difference would it make if the stock were expected to pay dividends?
2.
Again, suppose IBC stock is selling at $80 per share, and the T-bill rate with 180
days to maturity is 5%. In the previous problem, you constructed a synthetic futures
contract with maturity in 180 days and futures price of $82. Now, create a portfolio
of put and call options that is equivalent to the futures contract. Suppose the
standard deviation for the stock’s return is 25% over the period involved here. Use
the options calculator to compute the value of the put and the call in your equivalent
portfolio.
3.
Again, suppose IBC stock is selling at $80 per share, the standard deviation for the
stock is 25%, and the T-bill rate with 180 days to maturity is 5%. Construct a
synthetic put option with 180 days to expiration and exercise price of $40. Suppose
you wanted to use this in a manner equivalent to having an insurance policy to
protect against the stock price falling below $40. Explain how you would maintain
the protection with a $40 floor as the stock price moves. Repeat with a floor of $60.
4.
Refer again to problem 3. Could you establish “insurance” with a floating protection
level, so that the present value of the exercise price is always exactly half the current
stock price? Would this be harder or easier to maintain than the insurance strategy
described in problem 3?
5.
Attached is an article from the Wall Street Journal (3/27/01: C5) about a proposal to
offer futures contracts on individual stocks. These so-called Universal Stock Futures
(USFs) are described as providing a useful new tool for investors, particularly for
individual investors who might find it difficult to sell stocks short. Theoretically,
one could replicate these futures contracts synthetically (refer to problem 1) or with
option spreads (see problem 2). Discuss the practical difficulties of each of these
alternatives.
6.
Explain how the repurchase agreement plays a role in the pricing of futures
contracts. What is the implied repo rate?
7.
On January 28, the T-bill futures contract expiring on March 17 (not a leap year) was
priced at 93 (IMM Index). The T-bill maturing at that time was priced at a discount
of 7.10 and the T-bill maturing on June 16 at a discount of 7.17. Determine the
implied repo rate. Is there an arbitrage opportunity?
8.
Suppose you are managing a diversified stock portfolio with beta of 1.10. Describe
how you could use index futures contracts to change the beta of your position to
0.55.
Prof. Kensinger
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Financial Derivatives
9.
Problem Set 2
Spring 2016
Suppose you are managing a stock portfolio worth $12,500,000. It has a beta of
1.25. During the next three months, you fear there might be a correction in the
market that could take the market down about 5%. To reduce the risk of loss if this
happens, you would like to reduce the beta of your portfolio to 1. A stock index
futures contract with the appropriate expiration is priced at 1250 with a multiplier of
250.
a)
Should you buy or sell futures? How many contracts should you use?
b)
Suppose that after a while a “correction” similar to the one you feared actually
occurs. Your portfolio has fallen in value to $11,750,000. The price in the
market index future you sold has fallen to 1181.25, and you unwind the hedge.
Determine the profit on the futures contract and the overall portfolio return over
the life of the hedge. How close did you come to the desired result?
10. Suppose you are a multi-national company with supplies of crude oil stored in several
nations. You observe the following prices:
•
•
•
Euro per Dollar exchange rate is 0.60 spot and 0.62 for 180-day forward.
German interest rate is 5% compounded daily.
U.S. interest rate is 3% compounded daily.
Explain how you could take advantage of this situation using just your oil
inventories, without changing the total amount of oil you own worldwide. You
won’t need to borrow money or invest in bonds in either country. Just assume
that oil futures markets are in equilibrium in both countries.
Prof. Kensinger
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Financial Derivatives
Problem Set 2
Spring 2016
Nasdaq, Liffe Plan Stock-Futures Venture
By SILVIA ASCARELLI
Staff Reporter of THE WALL STREET JOURNAL
March 27, 2001
Page C5
LONDON-The Nasdaq Stock Market and the London International Financial Futures and
Options Exchange, or Liffe, said they will jointly introduce single-stock futures in the
U.S. later this year.
The rare trans-Atlantic partnership depends on an anticipated change in U.S.
regulations, which is expected by year end. U.S. investors have been barred from
investing in single-stock futures, known at Liffe as Universal Stock Futures, or USFs,
because of fears of market manipulation. With such contracts, investors commit
themselves to buying or selling a security at a set price on a certain date. Among other
things, investors can use singlestock futures for short sales. In a short sale, an investor
borrows a security, sells it and hopes to buy it back later at a lower price, pocketing the
difference.
Attracting Nasdaq is a coup for Liffe, which only three years ago was in disarray after
the bulk of trading in futures on German government bonds, Liffe's biggest product,
shifted to the rival Swiss-German Eurex exchange. The accord with Nasdaq gives Liffe
access to a huge new group of potential investors in single-stock futures, which were
introduced by Liffe in London two months ago.
Trading currently averages about 200 contracts a day in each of 30 USFs currently
listed on Liffe, or about half the average daily volume in each of the 98 individual equity
options contracts now traded on the exchange. That is small stuff for Liffe, which trades
nearly 750,000 contracts every day, mostly tied to bonds and money markets, but Which
is trying to boost its stock-reIated business.
It also represents a new foothold in Europe for Nasdaq, which is expected to announce
its intent to take a majority stake in Easdaq, a floundering pan-European market
patterned after Nasdaq, later this week. But Nasdaq has otherwise struggled to establish
itself in Europe, and securities firms refused to back an earlier plan to launch a new
pan-European exchange that would have been known as Nasdaq Europe.
Executives from the two exchanges said they could eventually take their partnership to
Asia, where Nasdaq is already operating a stock market with the Osaka Stock Exchange.
The UPS currently traded on Liffe are based on some of the biggest stocks in Britain,
continental Europe and the U.S., including Nasdaq-listed stocks like Microsoft Corp. and
Cisco Systems Inc. The exchange plans to add an additional 10 next month. Liffe
Chairman Brian Williamson said the exchange is aiming for about 100 USFs by year end.
UPS are aimed at individual investors, who generally can't short stocks, as well as at
institutional investors.
The partnership will use Liffe's Connect electronic trading system and will trade
during the U.S. business day. Executives declined to disclose other terms of the deal.
While Mr. Williamson confidently predicted that USFs mark a revolution in equity
trading, other exchanges have struggled with similar concepts. Eurex, the world's biggest
Prof. Kensinger
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Financial Derivatives
Problem Set 2
Spring 2016
derivatives market, lists about 90 "Lepos," or low exercise price options, which it says
function in the same way as USFs. Originally launched in Switzerland as a way to avoid
stamp duty, the options have attracted no trading for a few years, a spokesman said.
Prof. Kensinger
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