Chapter 26 Managing Risk 683
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Northern Refineries suffers a cumulative loss of $2,400,000 if the January price is $2.60. That’s
the bad news; the good news is that it can sell and deliver heating oil for $2.60 per gallon. Its net
revenues are $2,600,000 − 200,000 = $2,400,000, or $2.40 per gallon, the futures price in Septem-
ber. Again, you can easily check that Northern’s net selling price always ends up at $2.40 per gallon.
Arctic does not have to take delivery directly from the futures exchange, and Northern Refin-
eries does not have to deliver to the exchange. They will probably close out their futures positions
just before the end of the contract, take their profits or losses, and buy or sell in the spot market.^13
Taking delivery directly from an exchange can be costly and inconvenient. For example,
the NYMEX heating-oil contract calls for delivery in New York Harbor. Arctic Fuels will be
better off taking delivery from a local source such as Northern Refineries. Northern Refiner-
ies will likewise be better off delivering heating oil locally than shipping it to New York. Both
parties can nevertheless use the NYMEX futures contract to hedge their risks.
The effectiveness of this hedge depends on the correlation between changes in heating-oil prices
locally and in New York Harbor. Prices in both locations will be positively correlated because of
a common dependence on world energy prices. But the correlation is not perfect. What if a local
cold snap hits Arctic Fuels’s customers but not New York? A long position in NYMEX futures
won’t hedge Arctic Fuels against the resulting increase in the local spot price. This is an example
of basis risk. We return to the problems created by basis risk later in this chapter.
Trading and Pricing Financial Futures Contracts
Financial futures trade in the same way as commodity futures. Suppose your firm’s pension
fund manager thinks that the French stock market will outperform other European markets
over the next six months. She forecasts a 10% six-month return. How can she place a bet? She
can buy French stocks, of course. But she could also buy futures contracts on the CAC index
of French stocks, which are traded on the Euronext exchange. Suppose she buys 15 six-month
futures contracts at 5,000. Each contract pays off 10 times the level of the index, so she has a
long position of 15 × 10 × 5,000 = €750,000. This position is marked to market daily. If the
CAC goes up, the exchange puts the profits into your fund’s margin account; if the CAC falls,
the margin account falls too. If your pension manager is right about the French market, and
the CAC ends up at 5,500 after six months, then your fund’s cumulative profit on the futures
position is 15 × (5,500 − 5,000) × 10 = €75,000.
If you want to buy a security, you have a choice. You can buy for immediate delivery at
the spot price or you can “buy forward” by placing an order for future delivery at the futures
price. You end up with the same security either way, but there are two differences. First, if
you buy forward, you don’t pay up front, and so you can earn interest on the purchase price.^14
Second, you miss out on any interest or dividend that is paid in the meantime. This tells us the
relationship between spot and futures prices:
Ft = S 0 (1 + rf − y)twhere Ft is the futures price for a contract lasting t periods, S 0 is today’s spot price, rf is the
risk-free interest rate, and y is the dividend yield or interest rate.^15 The following example
shows how and why this formula works.
(^13) Some financial futures contracts prohibit delivery. All positions are closed out at the spot price at contract maturity.
(^15) This formula is strictly true only for forward contracts that are not marked to market. Otherwise the value of the future depends on
the path of interest rates over the life of the contract. In practice this qualification is usually not important, and the formula works for
futures as well as forward contracts.
(^14) In the Appendix to Chapter 19 we pointed out that companies effectively earn the after-tax interest rate when they lend and pay the
after-tax interest rate when they borrow. Therefore, when we value the leverage provided by a forward contract, we should also use the
after-tax rather than the pretax rate. You will generally see the formula for the value of a forward contract written without a tax term.
For convenience we have followed that convention here, but when valuing a forward contract remember to use the after-tax rate. See
S.C. Myers and J. Read, “Real Options, Taxes, and Financial Leverage,” NBER Working Paper No. 18148, June 2012.