## Forward Contracts On A Security That Provides A Known Dividend Yield

As will be explained in later sections, both currencies and stock indices can be regarded as securities that provide known dividend yields. In this section, we provide a general analysis of forward contracts on such securities.

A known dividend yield means that the income when expressed as a percentage of the security price is known. We will assume that the dividend yield is paid continuously at an annual rate q. To illustrate what this means, suppose that q = 0.05 so that the dividend yield is 5 percent per annum. When the security price is \$10, dividends in the next small interval of time are paid at the rate of 50 cents per annum; when the security price is \$100, dividends in the next small interval of time are paid at the rate of \$5 per annum; and so on.

To value the forward contract, portfolio B in Section 3.2 can be replaced by:

Portfolio B: e~q(T~!> of the security with all income being reinvested in the security

The security holding in portfolio B grows as a result of the dividends which are paid, so that at time T exactly one unit of the security is held. Portfolios A and B are therefore worth the same at time T. From equating their values at time, i, we obtain

and the forward price, F, is given by the value of K that makes / zero:

Note that if the dividend yield rate varies during the life of the forward contract, Equation (3.10) is still correct with q equal to the average dividend yield rate.

### Example 3.7

Consider a 6-month forward contract on a security that is expected to provide a continuous dividend yield of 4% per annum. The risk-free rate of interest (with continuous compounding) is 10% per annum. The stock price is \$25 and the delivery price is \$27. In this case S = 25, K = 27, r = 0.10, q = 0.04, and T - t = 0.5. From Equation (3.9) the value of a long position, /, is given by

From Equation (3.10) the forward price, F, is given by

+1 0 ## Forex Foundry

Tap into the forex secrets of millionaires. Discover The Untold Forex Secrets Used By The World’s Top Millionaires To Generate Massive Amounts Of Passive Incomes To Feed Their Families For Decades. Finally You Can Fully Equip Yourself With These “Must Have” Forex Tools For Creating Financial Freedom And Living A Life Of Luxury.

Get My Free Ebook

### Responses

• Dennis
Is a forward contract a security?
7 years ago