Question

Let’s consider an one-year forward contract on a certain dividend-paying stock. The current price of the stock is $100, and the stock is known to pay dividend twice in three and nine months from now. Each time, the dividend amount will be the 1% of the stock price at that time. Assume that risk-free interest rate is 4% per annum with quarterly compounding. Then, in theory, the one-year forward price on the stock should be $__________.?

Answer 1

Risk free rate per quarter =4%/4 = 1%

Let the stock price today is S0 , stock price after 3 months is S3,

stock price after 9 months be S9 and that after 12 months be S12

Expected value of S3 = S0*1.01 = 100*1.01 = $101

Expected Dividend after 3 months D3 = $101*1% = $1.01

Expected value of S9 = (S3-D3)*1.01^2 = (101-1.01)*1.01^2 = $101.999 or $102

Expected Dividend after 9 months D9 = $102*1% = $1.02

Expected value of S12 or the Forward Price

= (S9-D9)*1.01 = (102-1.02)*1.01 = $101.9898 or $101.99

In theory, the one-year forward price on the stock should be $101.99