On page 438 of the book, question 8, says that forward commitments provide “linear payoffs.” I don’t understand what this means. Can someone explain? For example in a future, you go long and say I will buy x in 6 months at $50. What is the linearity in that?
Same question, B) is wrong because forward commitments depend on the outcome or payoff of an underlying asset. But I don’t see why that is the case since with a future you agree now what price you will pay for x asset on the future date. So how does the forward commitment depend on the outcome of the underlying asset?
I will use a forward contract, where the forward price = $50 in 6 months. Yes, you pay $50 no matter what, but whether it’s a gain or loss to you depends on the asset price at expiration.
Forward Payoff at expiration, V(T) = S(T) - 50
If you plot a graph where the vertical axis is V(T) and the horizontal axis is S(T), then you will observe a linear line.
You can try plotting this points out (arbitrarily selected):
S(T) = 40 --> V(T) = 40 - 50 = -10
S(T) = 45 --> V(T) = 45 - 50 = -5
S(T) = 50 --> V(T) = 50 - 50 = 0
S(T) = 55 --> V(T) = 55 - 50 = +5
S(T) = 60 --> V(T) = 60 - 50 = +10
For options, the payoff is non-linear. e.g. For call option, the payoff is horizontal when underlying price < strike price but upward sloping when underlying price > strike price.
Call Payoff at expiration, V(T) = max(0, S(T) - X)