Comparison between buying a stock and selling a naked put

Question

Suppose one wants to invest in company X, whose stock is selling for, say, $100/share. What are the differences in profit potential between buying 100 shares and repeatedly selling a naked put at whatever the current price is?

In more detail:

Suppose the stock goes up. Then one lets the put expire (or buys it back) and sells another one. If the stock has weekly options it seems likely that selling puts will make far more money than holding the stock. The repeated put premium will almost always outpace the rate at which the stock rises. You might miss big jumps, but I suspect you will make up for it by the week-by-week profit.

Suppose the stock goes down. One should then buy the put back and sell another one at a lower price for a longer price period. For example, suppose the stock declines by to $95. One could very likely sell a put at, say $97 for a somewhat longer period that would cover the cost of buying back the original put. If the stock continues to go down, one would do it again, ... and again. Eventually one might find oneself short a rather long term put. (Of course if one just owed the stock one would be stuck with the loss.)

I suspect that there will be enough variation in the stock price that one can remain fairly even and not committed to too long a period. Eventually the stock will go up. One can then reverse course, buy back the longer term put and sell a shorter term one, perhaps at a higher price.

My question is whether anyone knows of any studies that have been done of this sort of strategy.

I would think that one would want to try this strategy primarily on stocks that one would otherwise want to hold as a long term investment.

Thanks.

Answer 1

Yes, of course there have been studies on this. This is no more than a question about whether the options are properly priced. (If properly priced, then your strategy will not make money on average before transaction costs and will lose once transaction costs are included. If you could make money using your strategy, on average, then the market should - and generally will - make an adjustment in the option price to compensate.)

The most famous studies on this were conducted by Black and Scholes and then by Merton. This work won the Nobel Prize in 1995. Although the Black-Scholes (or Black-Scholes-Merton) equation is so well known now that people may forget it, they didn't just sit down one day and write and equation that they thought was cool. They actually derived the equation based on market factors.

Beyond this "pioneering" work, you've got at least two branches of study. Academics have continued to study option pricing, including but not limited to revisions to the original Black-Scholes model, and hedge funds / large trading house have "quants" looking at this stuff all of the time. The former, you could look up if you want. The latter will never see the light of day because it's proprietary.

If you want specific references, I think that any textbook for a quantitative finance class would be a fine place to start. I wouldn't be surprised if you actually find your strategy as part of a homework problem.

This is not to say, by the way, that I don't think you can make money with this type of trade, but your strategy will need to include more information than you've outlined here. Choosing which information and getting your hands on it in a timely manner will be the key.

Answer 2

I sell a put for a strike price at the market. The stock rises $50 over the next couple months. I've gotten the premium, but lost the rest of the potential gain, yet had the downside risk the whole time.

There's no free lunch.

Edit - you can use a BS (Black-Scholes) calculator to create your own back testing. The calculator shows a 1% interest rate, 2% yield, and 15% volatility produce a put price almost identical to the pricing I see for S&P (the SPY ETF, specifically) $205 put. No answer here, including mine, gave any reference to a study. If one exists, it will almost certainly be on an index, not individual stocks. Note that Jack's answer referencing PUTX does exactly that. The SPY ETF and it put options. My suggestion here would, in theory, let you analyze this strategy for individual stock options as well.

For SPY - With SPY at 204.40, this is the Put you'd look at -

12 times the premium is $33.36 or 16% the current price. The next part of the exercise is to see how the monthly ups and downs impact this return. A drop to $201 wipes out that month's premium.

It happens that it now March 18th, and despite a bad start to the year, we are at break-even YTD. A peek back shows

• Dec 15 - $205.03
• Jan 15 - $187.81
• Feb 12 - $186.63
• Mar 18 - $204 - current price

In Dec you picked up $2.87 premium, (1.4% the current price then) but in Jan, it closed for a loss of $12. Ouch. Now, if you started in January, you'd have picked up 2 month's premiums and today or Monday sell the 3rd. You'd have 2.8% profit so far, vs the S&P break even.

Last, for now, when selling a naked put, you have to put up margin money. Not sure how much, but I use percent of the value of underlying stock to calculate returns. That choice is debatable, it just keeps percents clean. Else you put up no money and have infinite return.

Answer 3

Why do all this work yourself? Pay a modest price to have a professional do this for you. Look at the tickers PUTX, PUTW.

Answer 4

Option prices are computed by determining the cost of obtaining the option returns using a strategy that trades the underlying asset continuously. It sounds like what you are describing is rapidly trading the option in order to obtain returns similar to those of the stock. The equality goes both ways.

If the option is appropriately priced, then a strategy that replicates stock returns using the option will cost the same as buying the stock.

Because you can't trade continuously, you won't actually be able to replicate the stock return, and it may seem like you are making arbitrage profit (puts may seem abnormally expensive), but you do so by bearing tail risk (i.e., selling puts loses more money than owning the associated stock if an unusually bad event occurs).