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# how to calculate annualized return for short option positions

Discussion in 'Options' started by teachamantofish, Dec 17, 2017.

1. ### teachamantofish

I've been writing a number of JS charts to graph my trading performance, and I'd like to calculate my annualized return performance by week. That is, if I make 5% on a trade in a month, that's about 218% per year. Of course, losses magnify the same way.

If I buy options or stocks, calculating annualized return is easy, but what if I sell premium? I'm not sure how to approach the problem. Some example trades:

30 DTE: sold 80 BCRX 5.00 calls @ .11 (owned the stock). Profit: 880
30 DTE: sold 40 DVAX 20.00 calls @.65 (owned the stock. Profit: 2600

So I thought about somehow using return on risk, but my trades are often covered and at least defined in one direction. there's not any risk if the stock appreciates is called away: I made money on the stock and premium. Of course the stock won't go to zero either.

The only thing I've thought of so far is to pick a likely range of price movement and multiply that by the number of underlying shares. So if my average price movement range is +20% for all my underlying stocks, then selling my 80 calls above when BCRX was at 4.80 would be 9,600(.96 x 8000). So then the profit would be 9.1% for the month.

That seems high.

Is there a better way?

2. ### stepandfetchit

Return on risk seems to be most appropriate.
It seems you assume a covered call has no risk? Your risk is your long stock position, which can go to zero, if not protected! -- This process only makes sense for Defined risk strategies, so the Long stock becomes linked to the Call Write for the Covered Call.

IgorVI likes this.
3. ### teachamantofish

Well it's unreasonable to think the stock would go to zero. A logical range would reflect real world price movements. On high IV biotech, I've seen -80% and plus 110%, but most stock moves 5-10%. When dealing with 20-30 trades per month, I need to choose some baseline if I go this route. . .

4. ### spindr0

Calculation on long options is easy.

I see 3 choices for naked puts depending on your exposure.

1) Cash secured
2) 50% margin as if you were doing the synthetic covered call (adj by premium)
3) Approx 20% as per Reg T minimum margin requirement (see http://www.cboe.com/LearnCenter/pdf/margin2-00.pdf)

Naked calls is not as easy since the maximum loss is unknown and the margin varies based on the pricing variables (primarily the underlying's value).

For consistency with both, I would use either the approx Reg T margin formula (see link) or the time premium divided by the stock's price. .

5. ### teachamantofish

The second option is how I choose the trade. I usually choose trades that net me 5%+ if the stock gets called in 30 days ( e.g. sell 5.00 call @ 11 when BCRX is 4.80 means I'd make 6.4% in a month if the stock is called).

Maybe that's the way to go. However, I'll peruse the margin doc some more and plug in some real world examples to see what makes sense.

6. ### ironchef

This is how I calculate my profit/loss for buy-write or cash secured put (I only give you my buy-write case):

If I do a buy write (selling covered call), at the end of the period, either the call is ITM or ATM/OTM.

1. If the underlying is called, my profit will be the call premium minus transaction costs. Cost base is stock price - call premium so percentage gain can be calculated.

2. If the underlying is not called, I can liquidate (or mark to market) and calculate the total profit/loss. Cost base is again stock price - call premium.

3. Similar logic as 2 if I close out early or roll.

4. Return % is profit/loss divide by cost base and can easily be annualized.

At the end of the year, I totaled up my profits, compare that to buy and hold the underlying. If my profit is > buy and hold, I consider my trades a win. If it is less than buy and hold, I consider my trades a loss.

Keeping score this way made me realized that mechanically selling calls and puts returned less than buy and hold after transaction costs were included.

I don't know if this is what you were asking, if not, just ignore my post.

7. ### teachamantofish

thanks. Comparing to a buy and hold scenario is a worthwhile analysis. One point though:

For #1, isn't the profit: Called price - cost basis + premium?

If you sell an option at a 5 strike and the stock cost you 4.90 and the premium was .10, then 5-4.90+.10 = .20

Or is that what you said?

8. ### ironchef

Yes, that was what I said.

9. ### spindr0

That is not correct for selling an ITM covered call for which the profit is the extrinsic value (time premium). The correct formula for all situations is as teachamantofish suggested: Strike + Premium - Underlying Cost

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10. ### jjapp

For the naked shorts couldn't you use some multiple of the IV to calculate maximum likely move? There are clearly some problems with that (fat tails) but you could be conservative on the multiple. For example, use something like 5 or 6 x the standard deviation to calculate max moves and then take your result with a bit of skepticism to account for the spikes beyond that.

#10     Dec 18, 2017
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