Equivalent Option Positions

In the past couple of months, I authored three commentaries talking about covered straddles. There was the blog on Bombardier (April 18, 2016), another on energy stocks (May 3, 2016) and finally one on gold stocks (May 9, 2016). I call it the double up double down approach to investing.

Without re-hashing the specifics of the previous discussions I wanted to take a fresh look at the structure of the strategy. While not as appealing – editorially speaking – as the double up double down vernacular, selling two puts instead of one covered straddle results in the same risk reward characteristics. Selling short two puts is more efficient; one trade ticket, one commission, easier exit strategy all with the same result.

The point is all option positions have equivalent alternatives. Any strategy, no matter how complex, can be set up using one or two possibilities. The foundation of Equivalent Option Positions is the Equivalent Shares Position (ESP) discussed in last weeks’ blog.

To make the point, let’s return to our hypothetical XYZ stock framed with the following assumptions;

XYZ is trading at $50 per share and does not pay a dividend
XYZ six month 50 call is trading at $3.00 with a delta of 0.60
XYZ six month 55 call is trading at $1.00 with a delta of 0.40
XYZ six month 50 put is trading at $3.00 with a delta of 0.60
XYZ six month 45 put is trading at $1.00 with a delta of 0.40
The short term interest rate for a credit balance is effectively zero

If we wanted to execute an at-the-money covered call, we would buy XYZ and write say the XYZ six month 50 calls at $3.00. If XYZ is above $50 in six months the shares will be called away. The six month return if called is 6% ($50 purchase price + $3.00 per share premium divided by $50 purchase price – 1 = 6% return).

If instead we sell a cash secured at-the-money put option, we would also receive $3.00 per share. We would earn no interest on the account balance that is being used to support the short put. If the stock closes above $50 per share the put will expire worthless and the six-month return would be 6%.

In effect the two positions have the same risk reward characteristics. The maximum risk with both positions occurs if XYZ decline to zero. The best case return on both positions is the same at any price point above $50 per share.

Same with the covered straddle. We buy XYZ and write the six-month 50 calls at $3.00 and the six-month 50 puts at $3.00 per share. In this case we also have to set aside sufficient capital to secure the short put. Total premium is $6.00 per share which results in a total return on invested capital (note invested capital is $10,000, $5,000 to buy 100 shares of XYZ that covers the call and $5,000 in cash to secure the short put) is 6%. Obviously these are approximations. In point of fact, you could hold other securities in your account to cover the margin requirements, for the short put which was the assumption I was making when I talked about the covered straddles in the previous blogs. But, from the perspective of risk and return metrics these figures are applicable.

Traders could implement an equivalent covered straddle position by doing the following’; write two cash secured puts or execute two covered calls against a 200 share position in XYZ. Each position assumes that no margin is being used.

If we break down each position into its component parts it becomes apparent all three approaches provide equivalent results. The covered straddle is just a covered call and a cash-secured put. The covered call position is equivalent to a naked put position, and the naked put in the covered combination is the same as the naked put in our earlier example.

Any option strategy that can be structured using calls, can also be structured using puts. It is the interchangeability of option strategies that allows professional floor traders to take offsetting positions when providing liquidity to the market.

With that in mind, the accompanying table looks at a partial list of equivalent positions.

Long stock is equivalent to Long call + short put
Buy call is equivalent to Long stock + long put
Buy put is equivalent to Short stock + long call
Buy stock + sell call (covered call) is equivalent to
Sell call is equivalent to Short stock + short put
Buy 100 shares sell two calls (ratio write) is equivalent to Short 100 shares + sell 2 puts
Buy 100 shares + sell call + sell put is equivalent to Short 2 puts, long 2 covered calls