I am doing some research on stock options at the moment as part of my Masters thesis. Specifically, on the performance of options on the Nikkei 225 index. Rather than being options to buy or sell a particular share, these options are to buy or sell the “basket” of 225 shares represented by the Nikkei 225 index. They therefore offer an opportunity to speculate on the direction of the Japanese share market as a whole, rather than any one company.
Some information about options for those of you not familiar with the concept: An option is a contract that provides the right, but not the obligation for the holder to buy (or sell, depending on the type) a certain amount of shares at a certain price until a certain pre agreed time. There are two types of options, puts and calls. Put options allow one to sell shares at a certain price. They thus act as a sort of insurance/downside protection. If one held 100 shares of Toshiba which were trading at ¥100, one may be able to buy an option that allows one to sell those shares at ¥80 for the next three months. This means that even if Toshiba drops to ¥70 in two months time, one will still be able to sell the shares for ¥80.
Call options give the right to buy shares at a certain price. If one held a call option on Sumitomo group shares with an agreed price (know as the strike price) of ¥200, then no matter how high Sumitomo group shares rose, one would still be able to buy them for ¥200 each within the agreed timeframe.
Obviously, as these options act as a sort of insurance against future changes in share prices, they can have significant value. So when one buys an option from someone else, in order to induce that counterparty to take the risk that these “insurance” contracts may be used in the future, the counterparty must be compensated with a premium. This is the price of an option, and it varies according to many different things, such as interest rates, the underlying asset type, “fear” in the market, length to expiration of option etc..
It has been documented in several academic papers that options, particularly put options, on share indexes have tended historically to be “overpriced”. Meaning that those who sold these contracts made profits disproportional to the risk they were undertaking. There are numerous theories as to why which I won’t go into in this post.
Anyway, as there seems to be some evidence that index options and especially index put options are overpriced, I thought it would be good to analyse their return in the Japanese market. Japanese shares have performed poorly for the past 20 years, and since put options tend to do well when the underlying asset performs badly, it would be quite a rigorous result if selling put options still turned out to be profitable in such a market. Unfortunately I was only able to get the data on Nikkei 225 options from March 2006 to the present. Data is available from the middle of 1989 onwards but it would cost around ¥230,000. I can’t afford that at the moment, though should I find myself in a more secure financial position I would be happy to purchase such data to more rigorously test my theories.
But even taking the subsegment of March 2006 to the present, the Nikkei index itself (like most of the rest of the world’s share indices) has performed poorly. Thus it should be a reasonably strong test of options selling strategies. In this case one would also expect call selling to be profitable, as call options do poorly in falling markets.
So when deciding to sell options, even when one has decided the type (put or call) to sell, one is still left with the issue of which of the many strike price and expiration date combinations to choose. The strike price is the price that the option seller agrees to accept/pay from/to the buyer of the option for the share in question, regardless of the market price of the share. The buyer has the option to force the seller to do this transaction, but the buyer does not have to execute the transaction if he does not wish to do so. Obviously he will only execute the trade if the option strike price is better than the market price. The option will also expire at some agreed date, and all else equal, it will lose value as that date approaches. Some options can be exercised at any time between purchase and the expiration date, whereas some can only be exercised on the expiration date. In the case of options of the Nikkei 225, they are of the latter type.
An option with a strike price that is currently “in the money”, meaning that for a put the strike price is higher than the market price, or for a call the strike price is lower than the market price, will be priced significantly higher than an option that is “out of the money”. Why would anyone buy an option that has a strike price less favorable than the market price? Because the option still provides a level of insurance until the expiration date that even if the market price of the underlying security moves unfavorably, one’s losses will not exceed a certain level.
In general, it has been found that “out of the money” options tend to be overpriced, while “at the money” or “in the money” options are more of a toss up. In my testing program that I wrote I am able to test strategies at varying levels of “moneyness” and in general I found those conclusions to be correct.
I also tested the relative profitability of selling options with different amounts of time left until expiration. 1, 2 and 3 months to expiration were tested. 1 month to expiration seemed to consistently be a far superior selling strategy than either of the other two.
In addition to testing put selling and call selling strategies, I also tested selling both at the same time. This strategy is know as a strangle (or a straddle, depending on the strike prices involved). It has the interesting property, that if one sells both an out of the money put and an out of the money call with the same expiration date, at the expiration date one of them will always expire worthless, and it’s possible that both of them will. This significantly reduces the volatility of the strategy, as the infrequent but often massive one off losses that occur when selling out of the money options are attenuated by both the premium received from the other option that expires worthless and by the fact that one is selling only half the amounts of each option relative to a single option based strategy.
My first graph includes the performance of the Nikkei and the 3 option selling strategies. Each option selling strategy is the average of 11 different strategies based on different levels of moneyness (all out of the money, but to varying degrees). I could’ve cherry picked the most profitable level of moneyness for each strategy, but I thought it would be fairer to show the average performance of a wide array of out of the money strategies. Just to be clear, all of the 11 individual option strategies that make up each of the average strategies (33 strategies total) in this graph were profitable by themselves (i.e. I am not averaging them as an attempt to mask massive levels of volatility and differences in performance between them.) The time period in question is March 2006 to June 2010. Click on the images for full resolution.
As can be seen, one would be much better off selling options, of either type or both, than investing in the Nikkei itself. After 4 and a third years one would be up between 16% and 21% depending on the option strategy taken, while the Nikkei was down around 38%. Selling puts was actually more profitable than selling calls, despite the overall downward trend in the index. Selling both was almost as profitable as just selling puts. The huge drop in the performance of the put selling strategies occurred when Lehman brothers was allowed to go bankrupt in the latter half of 2008 which caused the massive worldwide market collapse. Interestingly the premiums paid for options exploded after this, allowing the put strategies to recover quickly and the call strategies to make huge gains. The later huge drop for the call selling strategy occurred after the market bottomed out and turned up in March 2009.
Notice that I have written “no leverage”. When selling options one needs to hold a cash reserve so that if the position moves against oneself, there will be sufficient cash at hand to payout to the option purchaser. In the case of put options, I defined a no leverage strategy to be one in which one held enough reserves so that if the index fell to 0 on option expiration date, one would have enough cash to payout in full. The index going to 0 is the maximum potential loss scenario for a put seller.
In the case of call selling it is actually impossible to define a “no leverage” level of selling, as there is theoretically no limit to how high an index can rise. So I arbitrarily defined a “no leverage” strategy as holding enough cash to be able to payout even after a 100% rise in the index.
In either case protecting against a 100% move in the index every month is a most conservative strategy. I tested the strategies with reserves enough to cope with a 50% move:
Note the scale on the left increases with each graph.
A less conservative approach increases the volatility of the options strategies but allows for significantly higher returns. Interestingly the strategies that involve selling both types of options have overtaken the put option selling strategies, benefitting from the “spike moderating” effect I described earlier.
Reducing the reserve level to 35%:
Here we see that although all three sets of selling strategies have increased their returns, the strategies involving selling both have benefitted to a much greater extent. The put selling strategies have now fallen behind the call selling ones as the hit after the Lehman failure exerts an increasingly disproportionately destructive effect.
Reducing to 25%:
Amazingly selling both types of options would on average earn a 97% return over the period. Increasing leverage is making the performance of the put selling strategies worse however, they now return less than when no leverage was used at all. The call selling strategies only note a very small increase in return, being close to the point where massive one month losses begin to overwhelm the benefits of additional leverage.
Finally, taking it to a 20% reserve level:
Many of the put selling strategies were completely wiped out at this level, so they couldn’t be included. The call selling strategies now only return about what they returned when the “no leverage” strategy was pursued, having reached the damagingly volatile level of leverage that the put based strategies reached in the previous graph. The spectacular rise to 5 times the initial investment only to fall off a cliff, losing on average 3.5 times the initial investment in only one month is rather nauseating. The selling both strategies managed to still improve returns, now finishing with a 124% average return.
Beyond this level of leverage the call selling strategies quickly all collapse. Some of the both selling strategies start to deteriorate in performance and eventually they start to collapse around a 15% reserve level.
In the end I am left with the conclusion that selling 1 month to expiration out of the money strangles on the Nikkei 225 seems to be a most scandalously profitable activity, at the very least worthy of significant further investigation. The nature of the strategy results in much lower volatility than selling puts or calls alone, allowing the seller to hold much lower levels of reserves and therefore make much greater profits. I would be able to make a more authoritative conclusion had I access to a longer dataset, but the current findings are most positively suggestive.