Saturday, August 1, 2015

Should Put/Call Parity result in Zero Return or the Risk-Free Rate?


Sorry in advance if this is a basic question. I'm examining some potential at-the-money put/call arbitrage. What I found surprised me somewhat:


            Bid   Ask    Mid
ATM Call = 3.31 x 3.33 (3.32)
ATM Put = 2.93 x 2.95 (2.94)


Expiration = ~ 1 Month

Underlying Stock Price = 190.00

The resulting Put/Call Parity return is equal to:



(Sell Call, Buy Put, Buy 100 Shares of Underlying)


(3.322.94)100=$38


$38$190100=0.2%


Annualized Return = 0.2%12=2.4%




This return is very close to the current stated treasury 'risk-free' rate of 2.48%


I would have expected the return on Put/Call Parity to be zero, however, since the combination of assets is risk-free at that point it would make sense that it pays exactly the risk-free rate.


Is it expected that I should see this risk-free rate of return or should I be seeing zero return?


Is this some other component of return - is this an arbitrage opportunity?


Am I merely seeing an algebraically extracted risk free rate from the put call parity formula?


C0+Xert=P0+S0


3.32+190e0.024(1/12)=2.94+190=192.94


Thanks for any clarification.



Answer




You should see the risk free rate as the return on the strategy. That’s because you actually have to invest money , namely usd 19000 minus usd 38, for the one month period. Hence, there is no arbitrage in the market data you observe.


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