Expected future gains

[wrongsaidfred]

Hi David,

I was looking at one of the problems in the Hull Ch 5-6 problem set and you used the expression "expected future gain" and say that it is equal to E(St) - Fo. In McDonald, they say that the NPV of an investment is E(St)*e(-alpha*t) - So. If you discount the expected future gain by multiplying by e^(-rt) you get something very close, but not exactly the NPV.

Should these be equal or am I making a bad assumption somewhere?

Thanks,
Mike

 

[David Harper CFA FRM]

Hi Mike,

I think they should equate but the fallacy i perceive is, when you discount the expected future gain, only the F0 can be discounted at the risk-free rate, because F0 = S0*exp(rT). However, if we assume alpha = growth = discount:
E(St) = S0*exp(alpha*T) = S0*exp(r*T)*exp[(alpha-r)*T], such that discounted E(St) by only exp(-rt) gets you:
E(St)*exp(-rT) = S0*exp[(alpha-r)*T]

In this way, i think the two formula do synch up:
F0 discounts at riskfree rate to S0, but
E(St) discounts at alpha because it is not riskfree

Hope that helps, David

 

[wrongsaidfred]

It certainly does help.

Thank you.

Mike