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William F. Sharpe: The ivory tower meets the real world

Today's investment landscape would be very different without the Capital Asset Pricing Model and the Sharpe ratio, both developed by this Nobel Prize-winning economist.

William F. Sharpe, the American economist and Stanford University professor, didn't just develop groundbreaking theories about investing. He put them into practice as a consultant to large institutional investors, and by co-founding the Financial Engines company in the 1990s, which provides automated advice on retirement planning to individuals.

Sharpe, a Boston native, was awarded the Nobel Prize in Economics in 1990, together with Harry Markowitz and Merton Miller, for pioneering work on the theory of financial economics. Sharpe's contribution was the development of the Capital Asset Pricing Model (CAPM). This model makes it possible to judge a portfolio's performance by the risk inherent in its investments, and helps managers decide when a potential return is worth the investment risk.

Sharpe's combination of intellectual prowess and practical real-world involvement is unusual in the rarefied world of Nobel theoreticians. This was nurtured at influential US think-tank RAND in the 1950s and 1960s, where Sharpe not only met his mentor, Markowitz, but was exposed to the new fields of computer programming, game theory, and applied economics. Markowitz had developed a theory for portfolios under conditions of uncertainty, which is now considered the foundation of financial economics as a respectable research area.

Sharpe distilled Markowitz's model, extending it from microanalysis to market analysis of price formation for financial assets. CAPM describes the relationship between systemic risk, in other words the general risks associated with investing, and the expected return on an asset, such as a stock. In its first version, set out by Sharpe in a 1962 paper, the model established a linear relationship between risk and return. Risk here has two parts: first a stock's beta or risk-free rate (typically a government bond rate), and the equity risk premium, or the market return less beta.

CAPM has evolved over time, just as markets have also changed thanks to the development of new financial instruments and computing power. CAPM helps determine if a security or portfolio is fairly valued. Today, however, it is seen as just one element of a multifaceted approach to investing. That's because a CAPM calculation, whether for a security or a portfolio, rests on several assumptions that rarely, if ever, are present in reality. For example, CAPM assumes that all investors are risk-averse by nature; that investors have the same time-period to evaluate information; that there is unlimited capital available to borrow at a risk-free rate; and perhaps most importantly, that risk and return are linearly related.

As financial economics has developed, models like CAPM are routinely pulled apart and updated. But CAPM's simplicity and elegance means that it continues to be used to understand portfolio risk and expected returns, although often together with other ideas, such as the efficient frontier and modern portfolio theory. For instance, the model can be used to research the cost of capital associated with takeover decisions, or as the basis for pricing decisions in regulated industries.

Sharpe was responsible for developing a simple measure of investment risk.

Sharpe spent much of the 1960s and 1970s teaching, first at the University of Washington, then the University of California at Irvine, before moving to Stanford in 1973. During this period, his research focused on issues connected with equilibrium in capital markets and the implications for investor portfolio choices. He was extending his original CAPM theory, developing new ideas, and using empirical analyses to examine how theory translates into the real world.

In 1966, Sharpe proposed what he called a reward-to-variability ratio, later known as the Sharpe ratio. (He claims that the well-known financial economist Eugene Fama came up with the name.) Yet again, Sharpe was responsible for developing an easy - perhaps too easy - measure of investment risk.

The Sharpe ratio measures the excess return earned over the risk-free rate per unit of volatility. While two portfolios may have similar returns, the Sharpe ratio shows which portfolio is taking more risk to achieve that return, called the risk-adjusted return.

A very simple single stock example shows how the Sharpe ratio works. Assume that:

- The risk-free rate is 3 per cent
- Stock X has returned 12 per cent over the past year, with a volatility of 5 per cent
- Calculating (12-3)/5 gives a Sharpe ratio of 1.8 for Stock X
- Stock Y, on the other hand, also returned 12 per cent, but had a volatility of 8 per cent
- Calculating (12-3)/8 gives a Sharpe ratio of 1.125 for Stock Y

So the higher Sharpe ratio of Stock X indicates that it offers a lower risk for the same return.

Of course, the Sharpe ratio is another model that uses a range of assumptions that are not always consistent with reality. It assumes that what has happened before will happen again, and that the risk-free rate will stay stable over time.

Is the Sharpe ratio a (too) simple model?

The volatility measure, or the standard deviation of returns, is based on a statistically normal probability distribution, the well-known Bell curve. However, market variations often move outside normal distributions in what is called tail risk, and this part of volatility risk will be underestimated in a standard Sharpe ratio calculation.

Perhaps the most important criticism of the Sharpe ratio is that it is just too simple. Even Sharpe himself suggests that with today's enormous computational power, investors don't need just one number. The Sharpe ratio has its place, but a more sophisticated approach than just using it to compare managers or portfolios would be to consider the time periods covered by the returns, as well as the accuracy of the market values used, for instance.

Sharpe may be best known for his theoretical contributions, but from the 1970s onward, he complemented his academic work with consultancy to financial institutions, helping to develop the first passive index funds at Wells Fargo, and advising Merrill Lynch Pierce Fenner Smith. Through Sharpe-Russell Research, a firm he started in partnership with the Frank Russell Company in 1986, and later at William F. Sharpe Associates, he developed and deployed new ideas about dynamic asset allocation, models for evaluating manager performance, and liability hedging for pension funds and foundations.

In the 1990s, as defined contribution pension plans became the dominant method of retirement provision for American workers, Sharpe realised that there were millions of individual investors who needed tailored investment advice. This was because unlike defined benefit plans, where investment decisions are made centrally and workers receive pension payments based on salary, in a defined contribution plan each worker has their own investment portfolio and makes their own investment decisions. Financial Engines, the company Sharpe co-founded in 1996, offered a "robo-advisor," an online engine that helps plan participants take investment decisions to match their specific circumstances. Although Sharpe is no longer involved, the company is still in business today.

Sharpe remains STANCO 25 Professor of Finance, Emeritus at the Graduate School of Business at Stanford University.

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