The Economist magazine just published an article that talked about "synthetic" hedge funds, or replicating hedge fund returns using factor models. The original research cited can be found here. (For those of you who want a primer on factor models, I have written an article on this topic previously.) The seven factors are (are you ready?):

1) excess return on the S&P 500 index;

2) a small minus big factor constructed as the difference of the Wilshire small and large

capitalization stock indices;

3) excess returns on portfolios of lookback straddle options on currencies;

4) excess returns on portfolios of lookback straddle options on commodities;

5) excess returns on portfolios of lookback straddle options on bonds;

6) the yield spread of the US ten year treasury bond over the three month T-bill, adjusted for the duration of the ten year bond;

7) the change in the credit spread of the Moody's BAA bond over the 10 year treasury bond, also appropriately adjusted for duration.

According to the researchers, factors 3)-5) are constructed to replicate the maximum possible return to trend-following strategies on their respective underlying assets.

See, it is not that difficult to run a hedge fund after all!

## Saturday, March 24, 2007

## 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.

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.

## Sunday, March 04, 2007

### Maximizing Compound Rate of Return vs Maximizing Sharpe ratio

A reader, Mr. A. Goldstein, made a very useful observation about my article "Maximizing Compound Rate of Return". In that article I argued that if your goal is to maximize the compound rate of return, you should maximize the quantity

Mr. Goldstein also suggested a beta arbitrage strategy which he has allowed me to share with my readers in a future post.

*m – s*, where m is the short-term (1-period) rate of return, and^{2}/2*s*is its standard deviation. In general, this is not the same as maximizing the Sharpe ratio of a strategy. However, Mr. Goldstein pointed out that, if you also optimize the leverage of your strategy using Kelly's criterion, then maximizing Sharpe ratio does in fact maximize the compound rate of return also. This follows from a calculation in section 7 of Dr. Edward Thorpe's paper www.bjmath.com/bjmath/thorp/paper.htm.Mr. Goldstein also suggested a beta arbitrage strategy which he has allowed me to share with my readers in a future post.

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