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)
(3.32−2.94)⋅100=$38
$38$190⋅100=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+X∗e−r∗t=P0+S0
3.32+190∗e−0.024∗(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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