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Further Lessons in Leverage



"A History of Hedge Funds" talked about some of the background issues for these vehicles of investment (actually "trading" is a better word). Hedge funds are being viewed by many sources of funds, even endowments and pensions, as an asset class to be considered in the mix of their asset allocation decisions: hedge funds exhibit quantifiable return to risk characteristics just like other asset classes. I want to now delve a little deeper into how a hedge fund generates this profile and how leverage plays an important part.

Let's look at an example from a convertible bond position, one of ours. I have described the basics of convertible bond trading in previous pieces, so I will jump right into how leverage affects returns and risk.

We consider the LAMR 2.875% convertible bonds of 2010 fairly cheap and expect them to accrete over time. The bonds are currently trading at around $92.5 while we think they should accrete to fair value of $96.75 over one year's time. This accretion is the primary driver of returns and is equal to (96.75 - 92.5)/92.5 = 4.6% (it is due solely to an increase in the price of the imbedded option). The other components that drive returns are the coupon payments on the bonds (2.9%) and short rebate on the stock (.003 %). As you will see, we short stock against the bonds to protect against stock risk; when we are short stock, we get a small credit for the cash balance that this generates. The total expected return using no leverage (borrowing money to increase the size of the position) is then around 8%.

We are not making a prediction on anything but the volatility of the stock, so we want to reduce or even eliminate as many extraneous risks as possible. That costs money. When we buy these bonds we are taking four primary risks: stock risk, credit risk, general interest rate risk, and volatility risk (from the imbedded long call option). We want to isolate and assume the volatility risk, and so will spend some money (out of the return) to mitigate the other risks. We sell stock at a ratio equal to the delta of the imbedded option times the conversion ratio. This costs nothing (if you consider the probability of the stock going up the same as going down). The credit risk will cost around 1.6% to significantly reduce through a credit default swap. The general interest rate risk will cost .25% to eliminate.

Net this all together and we expect to earn 6.1% on this position for a year. The only risk we are now taking is volatility risk (we could be right or wrong on this).

Now we introduce leverage. We borrow money from our prime broker and buy more of this position. If we double the position, the expected return goes to 10.8% (the return does not double because we pay 1.35% on borrowed funds). In this case we are going to put up half cash and borrow the rest. If we go up to three to one leverage (borrow two thirds of the notional amount) the expected return goes to 15.6% (don't try to linearly calculate this: it gets a little complicated as certain costs change relative to others).
So why don't we just keep leveraging this position to make more money? If we use ten to one leverage the expected return is 48.7%!

The reason is risk. Remember we still have volatility risk and we could be very wrong on that: the expected return could turn into losses of the same magnitude. There are also some hidden risks that could become very real under certain scenarios like the risk of a special dividend paid by the company or what if our counter party defaults on the credit default swap (this happened in 1987 and 1998)?

In the end the determining factor in sizing this position is the simple but time tested notion of "how much risk for how much return". I must assign a probability to being right or being wrong on volatility. I am naturally risk averse and so assign these probabilities to adjust for the fact that I hate losses even more than I like gains. Other managers would look at this completely differently and do the opposite. Some managers do not even look at credit risk as a short option like we do. In that case they would not factor in the cost of eliminating it and get a much better return for risk profile than we would.

One very dangerous process that occurs is what I call "return leverage". In our above example, let's say that the bonds were not all that cheap, trading at $94.50 instead of $92.50. In this case instead of an un-leveraged expected return of 6.1% it is 3.8%. In this case I would not even be a buyer, rather a seller and wait until they get cheaper, where the expected return warrants the expected risk. Some managers instead will lever even more to make the return acceptable.

All this is why I hold in such high regard men like Irv Kessler, Mark Kelner, and Dan Asher. The most successful traders in the world, like Paul Tudor Jones, exhibit this quality. They have always focused on risk before return and their actions over many market environments have proven this focus to be correct. I compared Irv Kessler to John Merriweather yesterday and may have misspoken for I do not know Mr. Merriweather. I was more commenting on his past actions than his abilities. He may have learned very well the lessons of leverage.

Let us hope others have as well.

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