# Am I doing the math for this covered call/long put strategy correctly? What risks do I run with this strategy?

In this trade, I write an in-the-money covered call and buy an in-the-money put (as an example) on GM, expiring in September 2014. The call premium is \$10.02 with a strike of \$26, and the put premium is \$4.17 for a strike of \$37. GM's share price is \$35.10, and I plan to write 1 call and buy 1 put.

My commissions are \$7.95 per trade and \$0.75 per contract. Here are the legs of the trade as I calculate them:

1. I buy 100 shares at \$35.10, which costs

``````-(100 * 35.10 + 7.95) = -\$3,517.95
``````
2. I buy one put contract (\$37 strike) at \$4.17, which costs

``````-(100 * 4.17 + 7.95 + 0.75) = -\$425.70
``````
3. and I write a call option (\$26 strike), which earns me the premium minus costs (I don't pay a separate 7.95 commission because I already paid it when I bought the shares, per my broker's policy)

``````100 * 10.02 - 0.75 = \$1,001.25
``````

The total cost of the trade is therefore

``````    -\$3,517.95 + -\$425.70 + \$1,001.25 = -\$2,942.40
``````

Assuming I sell the shares immediately at expiration if the covered call isn't assigned (which I may or may not do), here's the profit/loss I calculate for four levels of the share price at expiration (or at any point in time when the call option is assigned):

1. Share price: \$20 (below the strike of the covered call). I exercise the put:

``````100 * (37 - 20) - 7.95 - 0.75 = \$1,691.30
``````

keep the premium from the call option (`\$1,001.25`), and liquidate my shares immediately

``````100 * 20 - 7.95 = \$1,992.05
``````

this gives me profit of of

``````1,691.30 + 1,992.05 + 1,001.25 - 2,942.40 = \$1,742.20
``````
2. Share price: \$30 (above call's strike price, below current share price and put strike). Exercise put:

``````100 * (37 - 30) - 7.95 - 0.75 = \$691.30
``````

keep call premium, and sell shares when call is assigned:

``````100 * 26 = \$2600
``````

for profit of

``````691.30 + 2600 + 1001.25 - 2942.40 = \$1350.15
``````
3. Share price: \$35.10 (unchanged). Exercise put:

``````100 * (37 - 35.10) - 7.95 - 0.75 = \$181.3
``````

keep call premium, and sell shares when call is assigned:

``````100 * 26 = \$2600
``````

for profit of

``````181.3 + 2600 + 1001.25 - 2942.40 = \$840.15
``````
4. Share price: \$40 (above call and put strike prices). Put expires worthless, keep call premium, and sell shares when call is assigned:

``````100 * 26 = \$2600
``````

for profit of

``````2600 + 1001.25 - 2942.40 = \$658.85
``````

Is this math correct? What risks do I run with this strategy?

• @JoeTaxpayer Thanks for the edit. that makes it simpler to follow the math, you're right. All the math is pretty simple but it seemed weird that there was no way to lose money, and my minimum gain (\$658.85) given the initial investment of \$2,942.40 is about 22% which is awfully high for such a low-risk trade (if I understand the risks properly) Commented Mar 19, 2014 at 17:35
• Note that the call is probably a deep in the money option, so I suspect this would create a straddle for tax purposes under §1092. That could suspend your holding period and render dividends non-qualified, as well as placing limitations on your ability to take a tax loss.
– NL7
Commented Apr 18, 2014 at 15:16
• Yes, correct. You had me fooled too, adding the call premium once at the time of opening the trade and then again at the time of liquidating. Commented Oct 14, 2014 at 18:55
• No, the math is not correct. Ignoring the commissions, the BE point is \$33.75 with a maximum gain of \$775 and a maximum loss of \$325. Your trade is a "guts" long stock collar which is equivalent to a bearish vertical spread and would be better placed as a vertical since it involves less B/A slippage and fewer commissions. Also, by selling the deep ITM call, you run the risk of early assignment. The quick calculation of P&L for your numbers is (put strike*100 - \$2,942,40) versus (call strike*100 - \$2,942.40). Commented Jan 30, 2019 at 0:27

You own the stock at \$29.42

At \$40, the stocks is called at \$26. You can't add the call premium, as it's already accounted for. The trade is biased towards being bearish on the stock. (I edited and added the graph the evening I answered)

Not the pretiest graph, but you get the idea. With that \$29.42 cost, you are in the money till about \$30, then go negative until the most you lose is \$3.42.

• Hardly. I know idiots. Instead of asking first, they'd trade and with a successful stock move, find they lost money. You thought it too good to be true and asked the question. The idiot doesn't ask. Commented Mar 19, 2014 at 17:58
• The stock is in-the-money at any price since it will always be above the call strike or below the put strike or both. Ignoring all of the commissions, the break even is \$33.75 and the position goes negative above that price. Commented Jan 30, 2019 at 0:41

FYI: GM has an earnings announcement on April 24th.

I think you were trying to create a safe trade by profiting if GM's price fell within a probable range. The chart of the Iron Condor captures just about a standard deviation of movement. So as long as GM is between 31.28 - 37.22 in 34 days you keep the max profit of \$110. Note this trade is a net credit, when placing it you get \$110 less fees.

Also by selling the deep in the money call I take it you were trying to make the most of your capital.

The chart below shows a standard covered call compared to short put vertical. Note the short put vertical simulates the covered call position and it is a net credit trade as well. When you drop the order you get \$111 less fees.

• what platform is this? My platform's graphs are dreary, these are pretty!
– CQM
Commented Apr 19, 2014 at 17:04
• Dough - the visual options trading platform. Their website makes use of TD Ameritrade's API. If you have a TD Ameritrade account you can trade with dough. Commented May 12, 2014 at 3:18

Your math is not correct. In addition, you've made this much harder to visualize by including commissions.

Your long stock collar costs you \$29.25 (-\$35.10 + \$10.02 - \$4.17).

Below \$26, your short call expires and your long put can be exercised. So at \$20, you net \$7.75 by selling the stock via the put (\$37.00 - \$29.25)

At \$30, you are assigned on your \$26 call and your put is worth \$7 (-\$29.25 + \$26.00 + \$7.00) for a gain of \$3.75

At \$33.75, you are assigned on your \$26 call and your put is worth \$3.25 (-\$29.25 + \$26.00 + \$3.25) for no gain or loss. This is your break even price.

At \$40.00, you are assigned on your \$26 call and your put is worthless (-\$29.25 + \$26.00) for a loss of \$3.25. Any share price above \$37.00 incurs the maximum loss of \$3.25

Now, you can adjust the P&L of any expiration price calculation by the total commissions paid

One risk with this approach is the net purchase of volatility premium.

• If there is substantial realized volatility and you are able to capture it, then this risk can provide additional relative returns (meaning you will tend to have larger gains and smaller losses), but it requires a mechanism to realize those benefits
• If this were a hold-until-expiration strategy, this risk would probably create a very substantial drag on returns

Extrinsic values:

• long put: \$2.27/share = \$4.17 premium - (\$37 strike - \$35.10 underlying = \$1.90 intrinsic)
• short call : \$0.92/share = \$10.02 premium - (\$35.10 underlying - \$26 strike = \$9.10 intrinsic)
• net: \$1.35/share paid

That net purchase of \$1.35/share extrinsic premium is a considerable part of what is at risk of being lost. If the underlying rises to close at \$37/share at expiration:

• \$4.17/share is the full loss on the put
• the \$1.90 intrinsic paid at open did not materialize at expiration
• the \$2.27 extrinsic will always be gone when held to expiration
• \$0.98/share is the loss you will take on the short call due to negative delta
• \$11/share "loss" (\$37 underlying - \$26 strike) is the missing credit on the stock sale at assignment due to delta (compared to selling at market)
• \$9.10 "gain" is the intrinsic credit collected at open which offsets the missing credit at assignment
• \$0.92 gain is the extrinsic credit collected at open (your compensation for underwriting and management).
• \$1.90/share is the gain on the shares due to positive delta (\$37 underlying at expiration - \$35.10 long entry)

So you can see that the long extrinsic value is a major part of the losses:

• \$2.27/share out of a total \$5.15 loss is due to extrinsic
• this scenario is where 1) underlying moves against your net delta positioning, 2) long intrinsic value never materializes, and 3) long extrinsic value decays without being realized
• the full net \$1.35/share extrinsic purchase can/will be lost (eg, when excluding/neutralizing the effects of delta in the example above). This fact supports some arguments:
• Actively trading to extract realized volatility
• Not a great argument for using the ATM/ITM put to provide negative delta because you can add negative delta using the underlying and/or moving strikes on the call -- however these have drawbacks, so this is not a clear-cut rejection of the counterargument
• Not a great argument for using the long put to cap losses on upside moves (when adding negative delta) because very likely that can be achieved for lower cost
• "moving up" the call and put strikes to balance volatility exposure
• using a position like this to hedge against short volatility elsewhere in the portfolio

If I wanted a position like this:

• I would most certainly buy less volatility (and likely do the opposite and net sell volatility to improve the strategy's longer-term expected value).
• Also, if I were net buying volatility, I would put on the trade when I would be able to actively swing trade it to extract the extrinsic value out of it to reduce the risk of losing too much extrinsic premium.
• This isn't advice; it's an example of a thought process to address this particular risk.