CFA Practice Question

There are 227 practice questions for this study session.

CFA Practice Question

A portfolio manager took a long position on a 180-day forward contract on the S&P 500 stock index 30 days ago. The no-arbitrage forward price was $1263.87. The index was at $1245. Now (30 days later) the index is still at $1245. Suppose that the continuously compounded dividend yield is 1.45%, and the discrete risk-free rate is 4.6%. neither of these two rates have changed since the contract initiation date. What is the current value of the forward contract?
A. $0, since the index price and two rates are still the same.
B. -$3.11
C. $3.72
Explanation: r = ln(1 + r) = ln(1 + 0.046) = 0.045
Vt(0, T) = Vt(0, T) = St e-δ(T-t) - F(0, T) e-r(T - t) = 1245 x e -0.0145 x (150/365) - 1263.87 e -0.045 x (150/365) ) = -$3.11
This is a loss to the long position.

User Contributed Comments 8

User Comment
danlan2 Discret risk-free rate is 4.6%, so continuous risk-free rate is ln1.046=0.045
danlan2 Dividend yield and risk-free rate are different, so we use both rates.
danlan2 We use dividend yield for index and risk-free rate for forward price.
frankal101 In 30 days the index value must be at least 1245e^(0.046-0.0145)(30/365) (number bigger than 1245). Since it is the same, the return must be negative...
MonkeySee No calculation is needed in this case. Since the situation shows an asset price that has appreciated at a rate of less then the risk free rate, we know it is a loss for the long. Only one answer is negative and therefore is correct.
broadex Why do we discount the index since its the current price? The forward price is 150 days fro m now hence we need to discount by 150 days.
DCPWS Current price includes value of dividends. These must be discounted out since they do not accrue to the holder of the futures.
DevanCFA RFR is higher than div yield and the index hasnt increased, so it will be a neagtive value. is it not that simple?
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