Risk Latte - Going for the Leverage in Options

Going for the Leverage in Options

Rahul Bhattacharya
September 7, 2006

Last year a private banker had advised one of his very modestly wealthy clients (amongst the lowest stratum of "high net worth clients") to put a large part of his holdings in Asian equities and equity index linked funds. This year with the markets delivering extraordinary returns the client should have been jubilant and celebrating. Instead in one of the quarterly meetings with the banker he was sulking and was pretty unhappy. What was the reason? Some of his friends had made far more money dabbling in equity options than he did by investing directly in equities. And what was worse, his friends had not only made much more money than he did but also invested far less than he did and that too without the aid of a private banker.

Anyone investing - buying - in equities, any equities, last year would be making a lot of money today and has every reason to be happy. But anyone buying options - actually, long term options - on the same equities would indeed be making significantly more money than their peers who bought straight equities and that too with very little outlay. How is that possible?

It is possible because of what we call the " leverage" factor of options. But let's get some facts straight before talking about leverage of options. It is not always easy to buy options beyond six months in one go and because of liquidity factors the cost of buying long terms options can be significantly higher than what is predicted by theoretical models.

So how can the leverage of options help in superior returns? Let's first look at the nature of our friend's problem above. Suppose you had bought one contract of Nikkei225 (Japanese stock index) on August 25, 2005. The value of the index on that day was 12, 405. You bought it to hold on for one year. On August 25, 2006, a year later the Nikkei225 index was at 15,938 and therefore the return on your holding would be around 28%. It does not matter whether you invested one dollar (or in this case One Yen or a Million Yen) the percentage return for you will be the same. For exposition let' assume that you'd invested JPY 1 million. Then after a year on August 25, 2006 your profit on the investment would be JPY 280,000. That is an extraordinary annual return and you have every reason to be happy.

Now let us say that your friend wanted to invest his money in Nikkei225 options rather than the index itself. So he bought one contract of one year at the money call option on Nikkei225. The option parameters on August 25, 2005 were, spot was 12, 405, strike price was 12, 405 (since it is at the money), risk free rate was 1.5% (a rough approximation) and the option volatility was 15% (another rough assumption). Let's say that there is no dividend yield on Nikkei225 (incorrect assumption, but will suffice for this example) and that volatility of the options will remain constant throughout the life of the option, i.e. one year. If we plug in the above values in a standard Black-Scholes calculator we will get a value of 832 points.

And since one point of the index is equal to 500 Yen the total outlay on buying one contract of one year ATM call option on Nikkei225 would be JPY416,065. Therefore, your friend's total investment is half of your investment.

On August 25, 2006 the Nikkei225 index finished at 15,938. Thus the terminal payoff of the option (we are assuming that it is cash settled a few days before this date and there is no delivery of the contract) at maturity is 3,533 points (remember the strike is 12,405). This translates into a monetary value of JPY1.766 million or an annualized return of around 325%. What do you say to this? No wonder our friend was not so happy!

Leverage is the percentage by which an option's price changes for a 1% change in the stock price. A major reason for popularity of options amongst investors for the last three decades has been this "leverage" factor. Options are leveraged instruments and often this leverage is increased many fold by investors, especially when they trade or invest in out of the money options. Leverage is generally not a desirable property in any financial instrument or investment and it enhances the risk of the investment. But the good thing about buying (and not selling) options is that the maximum loss is floored at the amount investment. Thus the leverage in the options cannot force a investment value to go below zero, i.e. lose more than you invested like stocks bought with margin, or leveraged loans, etc. If S is the stock price with a dividend yield of and C and P are call and put option prices then:

Leverage of Calls =

Leverage of Puts =

Suppose you buy a highly liquid non-dividend paying stock which is trading for $100 today. If tomorrow the stock goes to $101 then you make a return of 1% over one day.

Now suppose you buy a one month at the money (ATM) option on the same stock from a broker or your bank. Say the option is fairly priced using a Black-Scholes model (where we use 30 divided by 360 as the maturity) using 1.5% risk free rate and 15% annualized volatility and offered to you by the broker for $1.79. This represents, using the above formula, a leverage of 29 times. And if tomorrow the stock goes to 101 then using a 29 day period (30 days less one day) the option price from the model comes out to be $2.32 which represents almost 30% daily return. Of course, we have assumed that the model price will approximate the market's traded price (which in most of the cases is not true) but even if the market approximates the model's price by 66% probability you can see the effect of leverage. Leverage makes a huge difference to your upside when you buy options. The downside of the option seller is similarly magnified hugely due to leverage - that is why so many people say options are so damn risky! Leverage can be devastating for anyone selling options and his or her losses would be unlimited.

Therefore if you are an ordinary investor, you can go for the leverage in options, but only BUY options. Never ever think of selling options!

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