We have devoted a lot of blog space in the past examining the pros and cons of the Capital Asset Pricing Model (CAPM). The model predicts the amount of excess return (return above the risk-free rate) of an arbitrary portfolio that can be ascribed to a relationship (called beta[1]) to the excess returns on the underlying market portfolio.

We continue our journey into the wonderland of alpha, taking up with leverage and the Efficient Frontier. We documented last time that a mix of a risky portfolio and the risk-free rate (Rf) yields a linear Capital Asset Line (CAL) within risk-return space. When the mix is varied to decrease the amount of Rf, the riskiness and expected return of the portfolio increase. The mirror image occurs as we increase the relative percentage of Rf in the portfolio mix. We can even borrow at the risk-free rate to purchase additional risky assets for our portfolio – one form of a practice known as leverage. Continue reading “Modern Portfolio Theory – Part Two” »

Our risk/return series continues with a review of Modern Portfolio Theory (MPT). We’ve already looked at alpha, beta, efficient markets, and returns. Our ultimate goal is to evaluate the role of alpha in hedge fund profitability, how to replicate hedge fund results without needing alpha, and finally how you can start your own cutting-edge hedge fund using beta-only replication techniques.

MPT suggests that a portfolio can be optimized in terms of risk and return by carefully mixing individual investments that have widely differing betas. Recall that beta is return due to correlation with an overall market (known as systematic risk). To take a trivial example, if you hold equal long and short positions in the S&P 500 index, your portfolio would have an overall beta of (.5 * 1 + .5 * -1) = 0. There would be no risk, but in this case, there would be no return either, except for the slow drain of commissions, fees, etc.

If you have been following our recent blogs, you are by now familiar with the concepts of alpha, beta, and the Efficient Market Hypothesis. Our final goal is to evaluate the role of alpha in hedge fund investing, and to look at trading strategies that do not rely on alpha. Before we can discuss these topics, we need to better understand financial asset pricing models, the role of alpha and beta within these models, and how the models apply specifically to hedge funds. In this installment, we’ll review the concept of rate of return (ROR).

In our previous blog, we discussed the concept of beta as it applies to the risk and return of an investment. Recall that beta is the price movement in an individual investment that can be accounted for by the price movement of the general market. If your investment has a beta of 1.0 and the market returns 10%, your investment should also return 10%. If your investment returns over 10%, the excess return is called alpha. Alpha is derived from a in the formula R_{i} = a + bR_{m} which measures the return on a security (R_{i}) for a given return on the market (R_{m}) where b is beta.

Hedge funds use an array of strategies to guide trading. Most of these strategies seek to decouple returns from those of the overall market, as measured by a statistic called “beta” (β). Beta is calculated by dividing the covariance of an investment’s return by the variance of a portfolio or market return:

β_{i} = Cov (r_{i}, r_{m}) / Var(r_{m}) where i = an investment, m = market portfolio, and r = return