Synthetic Long Asset vs put-call parity

In the CFA curriculum it states that you can make up a synthetic long asset by buying a call and selling a put on the asset, with equal exercise price and expiration date.

Whatever happened with the PV(X) in the put-call parity formula??

That’s a good question. The risk profile (or P/L profile) of combining, say, an at-the-money long call on AAPL with an at-the-money short put on AAPL, of the same tenor and strike, would be equivalent to just buying 100 shares of AAPL outright. Put-call parity says that a owning a call and shorting the put at the same strike/expiration would equal being long the stock and short the risk-free asset of X/(1+r)^t. I suppose that in theory the risk-free requirement would be reflected in the market price for that combined short put and long call? Maybe someone else on the forum can shed more light on the discrepancy.

They forgot it.

EnricB, I’m going to take a second whack at this from a practitioner’s perspective. We know that put-call parity says a long call and short put at the same strike = long the underlying asset and short the risk-free asset. Given current market prices for the 130 calls/puts (using the nearest strike to being at-the-money in the March 17, 2017 expiration cycle) and the current value of AAPL stock ($132.12), we can rearrange the put-call parity formula to see what the present value of the risk-free asset must equal for parity to hold with the market prices. Doing that brings you to a value of -$25. If you bought a 130 call, sold a 130 put, and shorted 100 shares of AAPL stock, you’re left with a -$25, or what has to be the present value of short position in a risk-free asset. So if -$25 is that number, I suppose we could back into what the implied risk-free rate must be given current market prices and a strike price of 130 with 33 days remaining to expiration. I realize this doesn’t outright answer your question, but thought you might find it insightful!