Sunday, March 18, 2007

Is increasing beta or increasing leverage a better way to increase returns?

In my previous post, I reported an astute observation from my reader Mr. Goldstein that maximizing compound rate of return, maximizing leverage, and maximizing Sharpe ratio are all tightly connected. This makes intuitive sense because the higher the Sharpe ratio of a strategy, the smaller the drawdown, and therefore the higher the leverage you can apply to it in order to maximize compound return.

Mr. Goldstein also made another very interesting observation. He noted that there are usually 2 ways to increase the returns of a portfolio of stocks: either by picking high-beta stocks, or by increasing the leverage of the portfolio. In both cases, we are taking on more risk in order to generate more returns. But are these 2 ways equal? Or is one better than the other? It turns out that there is some research out there which suggests increasing leverage is the better way, due to the fact that the market seems to be chronically under-pricing high-beta stocks. This gives rise to a strategy called "Beta Arbitrage": buy low-beta stocks, short high-beta stocks, and earn a positive return.

I myself have not studied this form of arbitrage in depth, and therefore can neither endorse nor criticize it. However, if this research is correct, it does argue against including too many volatile stocks in your portfolio or trading strategy. If you want to take on more risk and generate higher return, just turn the knob and increase your leverage and therefore book size.


Anonymous said...

Dr. Chan-
First off, I rather enjoy your site - thanks for the posts.

I came across this study a while back and thought it was an interesting piece of research. I put up a comment about it on my site, but also posed the question about the impact of market cap on this observation. Small caps have the heuristic of outperforming the market, so it seems they may provide a way to artificially leverage a portfolio, also due to their high risk. Since high beta stocks may not provide the expected return as consistently as low beta stocks, could low beta small caps be the best way to manage this? Or would the results be consistent and, on a risk adjusted basis, would it show that large cap low beta are better?

I may look into this but would be interested to hear your thoughts.

Matt aka cpptrader

my link and comments:

Ernie Chan said...

Dear Matt,
Your made a great point. According to the research I cited, the lower return is indeed due to beta, and not to market cap. So I would expect that given the same beta, small cap stocks will still outperform large cap stocks.

There is one caveat: one cannot indefinitely increase leverage on a portfolio of small cap stocks due to liquidity constraint.

Hope this answers your question?