Synthetic Long with Options

Hi All -

I just want to make sure I’m thinking about this correctly.

The S&P 500 ETF, ticker SPY, closed Friday at 210.01. This means, at close, I could have bought 100 shares for $21,001.

Alternatively, I could have sold a $210 strike put and purchased a $210 strike call - the July expiry premiums were $3.62 and $2.68, respectively. Which means, I would have received a net premium of $0.94 (or had a negative outlay) and the breakeven price for me would have been $210 + (-$0.94) = $209.06.

So … I could use options to create a synthetic long with an effective cost basis of $209.06 or buy stock for $210.01, which seems as though it would generate an arbitrage opportunity (sell short the stock, use options to create synthetic long) until you consider the dividends. The ETF pays dividends the option holder does not receive.

So, am I correct in saying that the difference between the ETF price and the options is the present value of the anticipated dividend on the ETF?

Hmm… something is not making sense to me. For September expiry, here are the premiums at close listed on Scottrade.

Strike price $201: Put = 3.75 ; Call = 11.69

Strike price $220: Put = $12.55 ; Call = $1.00

So… if you

  1. go synthetic long using the $220 strike (Sell the $220 put and buy the $220 call) for net premium income of $11.55 ($12.55 - $1)

AND

  1. go synthetic short using the $201 strike (Sell the $201 call and buy the $201 put) for net premium income of $7.94 ($11.69 - $3.75)

Your options are guaranteed to cost $19 at expiry but you collected $19.49 upfront … time value or just stale pricing maybe?

SPY goes ex-div next week. You’ll owe the dividend if you’re short the shares. Dividend is likely ~$1, hence the price difference.

Hello. If these options were European, this discrepancy should not exist. The difference here is probably because the 201 Call can be exercised before the ex-dividend date in June. American calls and puts are rarely exercised (and in fact, if you assume continuous dividends, they will not be exercised). However, with discrete dividends, if (approximately) delta*dividend cash amount > time value, exercise is optimal. The 201 (in-the-money) call might offer an optimal exercise choice on June 18 or September 17. Hence, it’s value is greater than that of a European call, and you are paid more to go short that call.

The 220 Call, on the other hand, is out-of-the-money. It is unlikely to offer an optimal exercise choice. Therefore, buying this call, as you described, costs less than you would have had to pay for a call with a high chance of early exercise.

Note that if all options were European, you would receive less than $19 up front, due to discounting. Stale prices might also have been an issue, but 49 cents is probably a lot for that, given how liquid SPY options are.