Workshop 2

Fair Value

Topics covered include:

• Fair value concepts and calculations
• Cash-and-carry arbitrage
• Reverse-cash-and-carry arbitrage

In the course, we learned about fair value and how it affects the market opening for stocks. This relationship is important to understand since futures trade nearly 24 hours a day, and you may wish to place a trade based on the indications of the market. If your interpretation about fair value is wrong, you will end up on the wrong side of the trade!

Let's start the workshop by making sure you understand the concept of cost-of-carry, since that is the starting point for understanding fair value.

Cost of Carry

Whenever you purchase anything there is an implied, and often overlooked, economic cost associated with owning it. Because you purchased the item, that money is now gone and cannot be used for anything else. That forgone use is called an opportunity cost since you pass up that opportunity to purchase the other good. In finance, that opportunity cost is the money that could be earned at the risk-free rate since we know for sure that is the minimum that is given up.

For example, many people in Florida are retired and own their homes outright. It is not uncommon to hear some remark that there is no cost to them since there is no mortgage payment. Not true. There is a forgone opportunity cost with the money that is tied up in the home. Had they not purchased the home, that money could have been left in a risk-free interest bearing account. If someone lives in a $500,000 home that is fully paid for and risk-free interest rates are 5% per year, that home owner is missing out on $500,000 x 5% = $25,000 per year in interest payments on money they used to purchase the house. Of course, they wouldn't have a home anymore but they would receive $25,000 in interest per year.

This is not to say that you shouldn't own a home outright. The point is that there is a cost associated with owning it even if it's fully paid for. This cost is called the cost of carry, which is simply the "cost" to own or "carry" the asset through time. Notice how it's easy to overlook the cost since no money changes hands, but that doesn't mean the cost is not there.

Because futures contracts are a guaranteed purchase and sale of an asset at a future date, the owner of the asset must be compensated for the risk-free rate of interest. For example, assume you own 100 shares of a $50 stock and interest rates are 5%. If you enter into a one-year single stock futures contract to sell those shares, the buyer of the contract must compensate you for the lost interest. Had you not entered the futures contract, you could sell the stock today, take the $5,000 and earn $250 interest in one year. But because your money is tied up in the stock, you are unable to do so.

Now, you may think "What if the seller doesn't actually own the underlying asset?" Using the above example, isn't it possible to speculate on a downturn in the stock and just sell the contract without actually owning the shares? If that's the case, why should the seller be compensated for the risk-free rate of interest? If the seller does not own the shares, he has an unhedged position and is at risk of having to sell the underlying asset for a much higher price at expiration. But that doesn't mean the buyer doesn't have to compensate them for the risk-free rate. The buyer always benefits by the risk-free rate when the payment is deferred. If the buyer wants to be assured of being able to take control of the stock for $50 in the future, he would have to buy it for $50 today and hold it for one year, and thus miss out on the interest. Because the seller is assuring them delivery for $50, he needs to be compensated for the lost interest.

The point is that, because futures contracts are guaranteed deferred purchases and sales, they are usually priced higher than the current asset by the risk-free rate of interest.

If you own 100 shares of stock at $50 and interest rates are 5%, you should be willing to sell a one-year futures contract for $5,250 ($5,000 plus 5% interest). Once again, the reason is that you really have two choices in selling the stock. First, you could sell the stock today and invest the $5,000 at 5%, which would grow to $5,250 at the end of the year. Second, you could enter the futures contract and sell the stock for $5,250 at the end of the year. Both methods net the same amount.