# Rate of Return

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).

At its simplest, ROR is the money you put up versus the money you get back between the time you open and close an investment. Since we are currently interested in risk and return, we will concentrate specifically on the ROR of risky investments – let’s say a stock in a portfolio. The actual return in this example is the proceeds from selling the stock, plus any dividends received, less the initial purchase cost and any brokerage or margin fees. The time-span from purchase to sale is known as the holding period.  The ROR is the return divided by the outlay.

A simple example will suffice: you buy a 100 shares of XYZ Corporation on April 1 for \$.95 a share plus \$.01/share commission.  You receive a dividend of \$.03/share on May 15, and then on July 1 sell the shares at  \$1.02/share less \$.01/share commission.

Outflow: 100 * (.95 +.01) = \$96.

Inflow: 100 * (1.02 – .01 + .03) = \$104.

Return: 104 – 96 = \$8.

Actual ROR: 8 / 96 = 8.33%

Annualized ROR = 8.33% * (12 months per year / 3 month holding period) = 33.33%

The actual ROR in this example is fairly easy to compute – in reality, one needs to look at the effect of multiple purchases and sales on the stock’s cost basis, the effect of dividend reinvestments, compounding, and the cost of interest for stock bought on margin. For our current discussion here, we can just use the simple model.

A Capital Asset Pricing Model (CAPM) is a set of calculations whose purpose is to estimate the expected rate of return of an investment within a portfolio. CAPM is a model that calculates the expected ROR of an investment, normalized for the perceived riskiness of the investment. The actual ROR can be compared to the estimated ROR (after the fact) to ascertain how well the model performed. We’ll have much more to say about CAPM in future blogs.

The risk-free rate of return (Rf) is the return on liquid short term government bonds, such as 3-month T-Bills.  As a risk-free investment, it has a beta of zero (although not all investments with a beta of zero are risk-free). Rf plays an important role in Modern Portfolio Theory, which will be our next topic.