Question

You own a dividend-paying stock currently worth $150 and plan to sell it in 250 days. In order to hedge against a possible price decline, you wish to take a short position in a forward contract that expires in 250 days. The risk-free rate is 5.25%. Over the next 250 days, the stock will pay dividends according to the following schedule:

Days to next dividend Dividends per share

30 $1.20

120 $1.20

210 $1.20

Assume that the forward price of a contract established today and expiring in 250 days is $151.53. It is now 70 days since you entered the forward contract and the stock price is $160. The value of the forward contract at this point is $ .

Answer 1

70 days are already over so,

number of days left = 250 - 70 = 180

step - 1:

now we have to calculate number of days for next dividend:

number of days untill next dividend = 120 - 70 = 50

number of days untill further dividend = 210 - 70 = 140

step - 2:

here we have to calculate the number of days from dividend payment date to expiring period of 250days

number of days left from now = 250 - 70 = 180

number of days left from next dividend to expiry  = 180 - 50 = 130

number of days left from next dividend to expiry= 180 - 140 = 40

step - 3:

in this step we have to convert the above days into years dividing them by 360 (it is assumed to be 360 days we can alternatively take 365 days)

number of years = 180 / 360 = 0.5

number of years = 130 / 360 = 0.361111

number of years = 40 / 360 = 0.111111

step - 4:

here we calculate futurevalues using formula

future value = present value(1+r)^n

here r = risk free rate = 5.25%

n = number of years

current Stock price = 151.53

future value of current stock price = 160(1 + 0.0525)^0.5 = 164.1463

future value of $1.20 dividend = 1.20(1 + 0.0525)^0.361111 = 1.2224

future value of $1.20 dividend = 1.20(1 + 0.0525)^0.111111 = 1.2068

so value of forward contract = future value of current stock price - futurevalues of dividends

= 164.1463 - 1.2224 - 1.2068

= $161.72(rounded to two decimals)