Sunday, March 16, 2008

Dummies Guide to Leverage (Calculated Risk)

How Debt Bites Back Click on image for full cartoon at the WaPo site.

Here is a simplistic cartoon from the WaPo showing how leverage can boost returns - and can also lead to disaster. How Debt Bites Back (hat tip David).

This cartoon shows leverage of 30 to 1; I think 14 to 1 is more typical.

Using the other numbers in the cartoon, 14 to 1 leverage would result in 36% return from the hedge fund when all is going well (before the hedge fund manager's cut).

And of course a 36% return will attract more investors, and allow the hedge fund to borrow more money (with the same leverage) - and pay the hedge fund manager larger fees. As the cartoon points out, because of the credit issues, this ends up being a losing strategy for investors - but the cartoon misses the final point - this is still a winning strategy for the hedge fund manager!

Back in 2005, Professor Hamilton wrote: Hedge fund risk

Psst-- want to earn a 41% annual return over a decade? Then read on.

... let me tell you about [a] fund ... called CDP, which was described by MIT Professor Andrew Lo in an article published in Financial Analysts Journal in 2001.

1992-1999 was a good time to be in stocks-- a strategy of buying and holding the S&P 500 would have earned you a 16% annual return, with $100 million invested in 1992 growing to $367 million by 1999. As nice as this was, it pales in comparison to CDP's strategy, which would have turned $100 million into $2.7 billion, a 41% annual compounded return, with a positive return in every single year.

Want to learn more? CDP stands for "Capital Decimation Partners", a hypothetical fund created by Professor Lo in order to illustrate the potential difficulty in evaluating a fund's risk if all you had to go on was a decade of stellar returns. The strategy whereby CDP would have amassed a hypothetical fortune was amazingly simple-- it simply sold put options on the S&P 500 stock index (SPX).

Buying put options is a way that an investor can buy insurance against the possibility of a big loss. For example, the S&P 500 index is currently valued around 1250. You can buy an option (the 1150 March 2006 put) that will pay you $100 for every point that the S&P is below 1150 on a specified date in March. Such an insurance policy would today cost you about $750. If you've bought enough puts to balance the equity you have invested long, you have nothing to fear if the market goes below 1150, because every dollar you lose on your main holdings you can gain back from your put option.

But what about the person who sold you that put? They have now assumed all of your downside risk. Lo's Capital Decimation Partners would use its capital to meet the margin requirements (which guarantee to the exchange that CDP could in fact make the payments to the buyer of the put), and roll over the proceeds to make even bigger bets. Essentially it was thus using leverage to turn the relatively small proceeds from selling these puts into a huge return on the capital invested.

Of course, if you play that game long enough, eventually the market will make a big enough move against you that your capital used to meet margin requirements gets completely wiped out, giving you a long-run guaranteed return on your investment of -100%. But over the 1992-99 period, Lo's hypothetical fund dodged that bullet and ended up turning in a whopping performance.

Lo gives a variety of other examples of funds that could go for a long period with very high returns and yet entail enormous risks. They all have this feature of pursuing investments that have a high probability of a modest return and a very small probability of a huge loss. By leveraging such investments, one can achieve a very impressive record as long as that low probability disastrous event does not occur.
And when the hedge fund does go under (the low probability event occurs), no one asks the hedge fund manager to return their fees. A short term winning strategy, with "a long-run guaranteed return on investment of -100%", is still a potential winning strategy for a hedge fund manager.

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