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A stock is expected to pay a dividend of $2 per share in three months and in six months
A stock is expected to pay a dividend of $2 per share in three months and in six months. The stock price is $60, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in an eight-month forward contract on the stock. a. What are the forward price and the initial value of the forward contract? b. Five months later, the price of the stock is $56 and the risk-free rate of interest is still 8% per annum. What are the forward price and the value of the long position in the forward contract?
Expert Solution
Solution:
GIven:
Stock Price= $60
Risk free rate of interest per annum= 8%
Dividend per share= $2
a) Forward Price:
Forward price for 8 months contract
Forward price= (stock price-dividend*
)*
Rf= Risk free rate of interest per annum
Rf= 8%
Dividend= $4 ( as received twice in the span of 8 month contract)
T= time period in year
For 8 months:
T=8/12= 0.66
Forward price= (60-4(
)*
Forward Price= (60-4*0.9485)*1.0542
Forward Price= $59.20
Initial value of the contract is 0, as any contract has a value 0 initially.
b)Forward Price 5 months later
Rf= 8%
Time= 5 months= 5/12= 0.416
Forward price= (56-2*(
)*
Forward Price= (56-2*(0.96)*1.033
Forward Price= $55.86
Value of the Contract for long position= (Current stock price- forward price after 5 month)*
Value of the Contract(long position)= (56-55.86)*= 0.14*0.9672= $0.135
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