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?

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%