Derivatives - risk-free rate impact on equity forward value

CFA Level II Derivatives
#1

I’m using CFA Institute Textbook to study derivative.
And on page p376 there is a question I couldn’t understand. Here is the question:

Troubadour next considers an equity forward contract for Texas Steel, Inc. (TSI). Information regarding TSI common shares and a TSI equity forward contract is presented in Exhibit 2.
Exhibit 2 Selected Information for TSI
■■
The price per share of TSI’s common shares is $250.
The forward price per share for a nine-month TSI equity forward contract is $250.562289.
Assume annual compounding.
■■
Troubadour takes a short position in the TSI equity forward contract. His supervisor asks, “Under which scenario would our position experience a loss?”

6 The most appropriate response to Troubadour’s supervisor’s question regarding the TSI forward contract is:
A a decrease in TSI’s share price, all else equal.
B an increase in the risk-free rate, all else equal
C a decrease in the market price of the forward contract, all else equal.

For answer B, I thought the formula for the value of short position in the equity forward contract is:
Vshort = PV(F0(T) - Ft(T) / (1+Rf)^(T-t)
So if risk-free rate increases, the value of the short position should decrease?
Am I not considering other aspects?
Could anyone help on this issue? Thanks!

#2

You value a forward by entering into an offsetting position and discounting the future payoff. In your equation, Ft(T) would be greater than F0(T) because the new, higher Rf increases the forward price. That means at expiration you have a loss and your numerator is negative. The fact that Rf shows up in the denominator is irrelevant for the question–it only serves to discount whatever gain/loss there is.

#3

Thanks for your detailed explanation! :slight_smile: