Forward parity arbitrage

CFA Level II Derivatives
#1

So the problem says to determine if the forward contract is priced correctly using put-call-forward parity. The option exercise price is 90, the risk-free rate is 5%, the options and the forward expire in 2 years and the put price is 3, the call price is 15.25 and the forward contract is priced at 101.43.

I worked using the parity formula that a synthetic put is overpriced vs the actual put. The synthetic works out to 4.88 vs actual put of 3.

So I would have sold the synthetic put and bought the actual put. Which would work out to buy the put,sell the call, sell the bond and long the forward.

But the answer says buy the put, sell the call, buy the bond and long the forward???

surely this is incorrect?

#2

Clearly it’s incorrect.

The long call and long bond are on the same side of the equation. You’ll either buy both or else sell both.

#3

Thanks Magician, that makes me feel a lot better. Thought I was going mad.

#4

You may well be; this merely _ isn’t _ evidence that you are.