Question

Suppose that you enter into a three-month forward contract on a non-dividend-paying stock when the stock price is $60 and the risk-free interest rate (with quarterly compounding) is 8% per annum.
What is equivalent continuously compounding rate?

Answer 1

Answer:

The equivalent continuously compounding rate is 0.02%

Explanation:

Forward price of the contract in 3 months:

F = S x e^(r*t)

Expected equity market return of the stock in 3 months:

E(r) = F/S -1 = e^(r*t) -1 = e^(8%*1/4) - 1 = 0.0202 or 2.02%

Annual market rate or Annual market rate premium with rf as the risk-free interest rate per annum with quarterly compounding.

r = E(r) - rf = 2.02% - 8%/4 = 0.02%

The quarterly compounded rate (rq) is given by:

rq= 4 x [(r/2 + 1)^(1/2) - 1]

where r as the annual market risk rate.

Apply the above formula to the question:

rq=4 x [(0.02%/2 + 1)^(1/2) -1] = 0.0002 or 0.02%