### Pricing Financial Forwards and Futures

After completing this reading, you should be able to:

• Differentiate between investment and consumption assets.
• Define short-selling and calculate the net profit of a short sale of a dividend-paying stock.
• Describe the differences between forward and futures contracts and explain the relationship between forward and spot prices.
• Calculate the forward price given the underlying asset’s spot price and describe an arbitrage argument between spot and forward prices.
• Distinguish between the forward price and the value of a forward contract.
• Calculate the value of a forward contract on a financial asset that does or does not provide income or yield.
• Explain the relationship between forward and futures prices.
• Calculate a forward foreign exchange rate using the interest rate parity relationship.
• Calculate the value of a stock index futures contract and explain the concept of index arbitrage.

## Investment Asset vs. Consumption Asset

An investment asset is an asset held for the purposes of investing. The holder takes a position in the asset in the hope of earning an income or capital gain. Examples include stocks and bonds issued by various financial institutions.

A consumption asset is an asset primarily held for the purpose of consumption, and not for investment or resale. Examples include oil, coffee, tea, corn, e.t.c.

## Short-selling

Short selling involves the sale of a security which the investor does not own. The investor borrows the security from the owner, the lender, with a promise to return it as of a specified date. But why would anyone want to short sell?

The short seller has reason to believe that the security is overpriced or there are some other factors that make it highly likely that the security will lose value in the near future. Their goal, therefore, is to sell high and buy low and get to keep the difference (profit).

When the short sale is closed out, the short seller must return the security to the lender. The lender may also request to have the asset even before closeout, depending on the initial agreement. There’s always the risk that the security’s price will actually rise, forcing the investor to reacquire it at a higher price and thus make a loss.

Short sales are transacted through a broker. The short seller must deposit some collateral to guarantee the eventual return of the security to the owner. In addition, the short seller is required to pay all accrued dividends to the lender. Thus, the net profit is equal to:

$$Net\quad profit=sale\quad price–borrowing\quad price–dividend\quad paid.$$