Risk Latte - Leveraged Bet - a negative skew trade

Leveraged Bet - a negative skew trade

Rahul Bhattacharya
March 2, 2007

If you borrow lots of money to buy stocks, chances are that sooner or later you'll blow up. This is because your trade displays all the characteristics of a "negative skew" trade.

Jonathan Lau had borrowed heavily to bet on Hong Kong stocks a couple of weeks ago. And then he had gone long on a large number of big name china stocks listed in Hong Kong . It was one of the biggest margin trading account that our legendary broker friend, Irvin Matlock had in the brokerage house K-alpha Securities. For the last two days the Hong Kong stocks, like stocks all over the world, and especially in Asia , took a severe hammering. Today, at around noon, Mr. Lau became incommunicado and Irvin and K-alpha became the talk of the town. It seems that there were quite a few margin accounts like Jonathan Lau's in K-alpha, with margins sometimes reaching as high as 70% (yes, it came as a surprise to us as well that even today one can get such a high financing from brokers to buy stocks).

The brokerage, K-alpha will soon release a 25 page analysis of the fundamental state of the Chinese and global economy and try to explain away some of the humongous losses that its clients had suffered, not to mention its own loss thanks to clients like Mr. Jonathan Lau who have jumped the margin calls. And in that 25 page analysis not once will the word “skew” be mentioned, let alone "negative skew".

What happens when you borrow money to buy stocks? You essentially short a put option. And because you short a put option you trade displays all the characteristics of a negative skew. That is what happened at K-alpha.

This is the simplest leveraged trade that has existed since the advent of stock markets and one that practically every hedge fund manager more or less follows at some point in his career, regardless of whatever strategy he employs. They borrow money and buy stocks, to make potentially large gains for very little they put up from their own pocket.

The fundamental Black-Scholes option equivalence relationship states that a put option is equivalent to selling short a risky asset (stock) and lending money at a riskfree rate. Note that lending money at risk free rate is equivalent to buying risk-free government bonds, which we will simply denote as bonds. In the math identities below a plus sign represents a long (bought) position and a minus sign represents a short (sold) position.

The conjugate of the above relationship is:

Shorting (selling) bonds has the same effect as borrowing money. This means that if you borrow money (at the risk-free rate) and go long on the asset (stock) then that trade is equivalent to going short on a put. In other words, you are selling a put option; which is what a leveraged bet is.

Actually, leveraged equity (equity bought using borrowed money) is a combination of long call and short put. A call option is equivalent to buying a risky asset and borrowing money at a risk-free rate.

Therefore, a long call and a short put will have a payoff of:

Short option trades will make frequent small gains and infrequent large losses. This is called the left tail risk or negative skew. This also means that the normal distribution of returns for the investor is not symmetrical and there is a chance that in a small period of time (a small pocket of time considering the entire investment horizon) the investor will take a big hit. This is a blowup . No matter how savvy an investor or a trader you are, if you are running with a negative skew, you are bound to blow up, and the bigger the skew the bigger the blow up. It is a simple mathematical fact of life.

But Mr. Lau, and the likes of him are not a rarity. In fact, they are the everywhere. It is interesting to note that most investors prefer negative skew over a positive skew. Though there is an abundance of mathematical and economic literature on this you can test this hypothesis by simply looking around you. And the most interesting part is that some of the savviest of derivative traders prefer negative skew trade.

Why? Well, the answer to this why could be very interesting and may take us to a realm beyond that of financial theory.

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