Workshop 2

Fair Value

Whenever a futures contract is priced at the cost of the asset plus the risk-free cost of carry, we say that contract is trading at fair value.

Cost of carry is fairly easy to figure out. All we have to do is convert the risk-free rate of interest to a decimal point by dividing by 100, then add one, and then multiply it by the total contract value. In the previous example, 5% is .05 as a decimal so we'd multiply $5,000 by 1.05 = $5,250. Therefore, we would expect to see the one-year futures contract trading for this amount (fair value).

If the time period is longer than one year, we simply multiply by 1.05 again for each additional year. For example, we would expect to see a two-year futures contract trading for $5,000 x (1.05) x (1.05) = $5,512.50.

Notice how 1.05 was just "repeated" twice, which is mathematically the same thing as raising it to the second power. Instead, we could say $5,000 x (1.05)² = $5,512.50. The raised "2" is called an exponent. Most financial, engineering or scientific calculators can accommodate them. If you have a calculator that can tabulate using exponents, you will probably see a key that looks like y^x. That is the one you will use to figure out these problems. Exponents give us a nice shortcut method for figuring otherwise tedious problems.

We can even use fractional years with exponents. What is the fair value of a 1-1/2 year contract? That would be $5,000 x (1.05)^1.5 = $5,379.65

Here's one for you to try...

Assume an underlying stock is trading for $100 and the risk-free interest rate is 6%. What would you expect the price to be of a one-year futures contract?