Stock A has a spot price of $50.It is expected to appreciate by 2% over the next quarter.The risk-free rate for the next quarter is 2% in continuously-compounded and annualized terms,and the quarterly continuous dividend payment is also 2% in continuously-compounded and annualized terms.The three-month forward price is
A)$50.00
B)$50.25
C)$50.50
D)$50.75

Question

Quizplus · Accepted Answer

The forward price of a stock that pays continuous dividends can be calculated using the formula: $F = S_0e^{(r-q)T}$, where $F$ is the forward price, $S_0$ is the spot price, $r$ is the risk-free rate, $q$ is the dividend yield, and $T$ is the time to maturity (in years). Here, $S_0 = $50$, $r = 2\%$, $q = 2\%$, and $T = 0.25$ years (since it's for the next quarter). Plugging these values into the formula gives $F = $50e^{(0.02-0.02)0.25} = $50e^0 = $50$.

Stock a Has a Spot Price of $50