# CAPM and the Sharpe ratio

William Sharpe, an American academic and consultant, is one of the founders of what is known universally as the Capital Asset Pricing Model (CAPM) and also of a ratio that bears his name that is used to measure the riskiness of an investment relative to the returns it generates.

We can deal with the CAPM first by noting that Sharpe's main contribution to portfolio theory was the insight that an individual investment contained two types of risk: specific risk, unique to that investment; and market risk, sometimes called systemic risk. Specific risk can be removed through diversification.

Coping with systemic risk is what really plagues investors, according to Sharpe.

The CAPM evolved as a way of quantifying this risk. Sharpe found that the return on an individual investment or portfolio of investments should equate to the risk free rate of return plus the excess return that the market provided over that risk-free rate multiplied by a factor, which Sharpe called beta. Beta is the measure of an individual investment's (or portfolio's) sensitivity to the movement in the market.

Each individual investment has a beta, which varies over time and for the time-period chosen over which to measure it. A beta for a stock with measurements taken hourly over the course of a week, for example, might be different to one calculated daily over a period of three months.   In both cases, though, beta means the same thing. A stock with a beta of 1.5 could, for example, be expected to rise 15% if the market rose 10% and fall 15% if the market fell 10%.

Beta is found by statistical analysis of share price returns compared with the market's returns over precisely the same period. Betas of individual stocks can be combined together to give a portfolio beta.   The importance of Sharpe's model is that it allows one to predict the expected return from a portfolio given its beta, the market rate of return and the risk free rate.

Say the portfolio beta was 2.0, the risk free rate 3% and the market rate of return 7%.  Then the market's excess return is 4% (7-3) the portfolio's excess return is 8% (2 x 4, multiplying market excess return by beta) and the portfolio's total expected return is 11% (8+3, the portfolio's excess return plus the risk free rate).  What this means is that it is possible, by knowing these individual components of the CAPM, to establish whether or the current price of an investment is consistent with it or not, in other words whether or not the investment is cheap or dear.

One other offshoot of Sharpe's work is a ratio for standardising the measuring of the performance of funds, notably hedge funds. Known as the Sharpe Ratio, this compares the excess return that a fund earns, over and above the risk-free rate, with the volatility of those returns. The argument underlying this is that any investment manager can earn higher returns by assuming more risk.

Risk is equated with volatility of returns. The trick is to capture high returns without taking on too much risk.

By comparing excess return with volatility, investments can be ranked on the basis of degree of return provided per unit of risk. The higher is the Sharpe Ratio the more favourable are the risk-return characteristics of the individual investment or fund. Just as funds can have Sharpe ratios, so too can markets.

Peter says

This might all sound rather dry and academic, but the work of Sharpe and others led directly to the creation of index-tracking investments.

Sharpe, for example, by devising the concept of beta, demonstrated that it would not be necessary for an index-tracking portfolio to hold all of the constituents of an index in the exact proportions they represented of it to produce a performance that matched the index. All one needed to do was construct a portfolio that had, over time, a consistent beta of 1 and it would mimic the performance of the index.

It is perhaps significant that among the firms that used Sharpe's services as a consultant was Wells Fargo. Back in the mists of time, Wells Fargo Nikko Investment Advisors was a predecessor firm of Barclays Global Investors, creator of the iShares concept and now the biggest providers of exchange traded index funds for investors.   If you hold an index-tracking investment, you have Sharpe to thank for the fact that the product is available for you to invest in.