2
$\begingroup$

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)

$(3.32-2.94) \cdot 100 = \$38$

$\dfrac{\$38}{\$190\cdot100} = 0.2\%$

Annualized Return = $0.2\%\cdot12=2.4\%$

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?

$C_0+X*e^{-r*t} = P_0+S_0$

$3.32+190*e^{-0.024*(1/12)} = 2.94 + 190 = 192.94$

Thanks for any clarification.

$\endgroup$
  • 1
    $\begingroup$ When are the premiums paid? Also when is the 19000 paid? Thx $\endgroup$ – dm63 Mar 22 at 3:16
  • $\begingroup$ All at the exact same moment. Theoretically no friction and perfectly liquid. $\endgroup$ – Daniel Sims Mar 22 at 3:33
  • $\begingroup$ Now, or in one month? $\endgroup$ – dm63 Mar 22 at 3:34
  • 1
    $\begingroup$ You are indeed somehow extracting the equity funding cost (which on top of risk-free funding rate could include dividend yield, repo margins) from call put parity. $\endgroup$ – Quantuple Mar 22 at 11:18
  • 1
    $\begingroup$ You are welcome just note that the CP parity actually writes $C_0 - P_0 = DF(0,T) ( F(0,T) - S_0 )$ where $F(0,T)$ is the equity forward price (related to equity funding cost) and $DF(0,T)$ the discount factor (related to cash or collateral funding cost) $\endgroup$ – Quantuple Mar 22 at 18:22
4
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ I agree that there is no arbitrage, as the formula holds perfectly: 3.32 + 189.62 = 2.94 + 190 || 3.32 = 2.94 + .38 I believe you are correct because by paying 19,000 I am essentially lending at the risk free rate. (Easier for me to understand as an arbitrageur would need to pay 38 to borrow the 19,000 if the trade were reversed - Selling Put, Buying Call, Selling Stock.) Thank you for taking the time to answer this question. $\endgroup$ – Daniel Sims Mar 22 at 14:07

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.