# William Sharpe and the Breakthrough of Diversifiable and Un-Diversifiable Risk

Sharpe was just a few years out of his undergraduate program when he accepted a position at RAND. While at RAND he was looking for a Ph.D. dissertation topic when Fred Weston suggested he talk to Harry Markowitz. The path that ensued changed investment management forever. The idea was that Sharpe could build on the work of Markowitz extending the concepts of the efficient frontier and mean-variance optimization.

From Markowitz's work, with the following extensions:

- The market is in equilibrium.
- We add a risk free asset (Tobin 1958.)
- Investors don't buy inferior portfolios.

We can conclude that one portfolio has the best risk/return ratio and that specific portfolio is leveraged up or down to meet an investor's risk preference. This single superior portfolio that has been equilibrated to us is the total market portfolio of all investable assets.

Is this a big deal? yes! Why?

Because as we add the equilibrium concept noted above, any deviation from the market portfolio is a bet that you know something that markets do not. We also can now understand what we should get (return) for a particular level of risk - Risk Premiums.

###### Tom Owens, Garde Capital Principal

## Asset Pricing, Systematic Risk, and Non-Systematic Risk

The next leap of logic is the idea that since investors have equilibrated the best portfolio, any portfolio that is not this best market portfolio

entails additional risk. If the investor chooses the portfolio with extra risk, investors should not be compensated for that extra risk, because if they wanted to, they could better diversify the poorly diversified portfolio. The perfectly diversified portfolio possesses only systematic risk, and the poorly diversified portfolio possesses some systematic and some non-systematic risk. Investors should not expect a return for bearing risk that could be diversified away.

## Hold on, what did you just say, in English please:

- Markowitz Developed a framework for measuring risk by combining risky assets to formulate optimal risk adjusted portfolios.
- A guy named Tobin said if you add in a risk-free asset like treasury bills, investors would be smart to buy a combination of the best risk-adjusted portfolio blended with the risk-free asset to meet their risk target.
- Sharpe took this framework and added the idea that if a market is in equilibrium, the best risk adjusted portfolio is the portfolio of all investable assets.
- And therefore, Sharpe continued, portfolios or assets that are not this total market portfolio possess risk that could be better diversified and that you shouldn't expect any extra return for taking the risk that could be better diversified, and we call this type of risk non-systematic risk. Sharpe then tidied this up into a simple elegant equation and graphed the results of the CAPM, this is known as the Securities Market Line or SML.

## Effects on Asset Prices

We now can now conclude several points:

- The Slope of the SML tells us how much of a return premium we should receive for the systematic risk of a security.
- The Beta of a security tells us what level of systematic risk a particular security possesses.
- We can find the Beta of a particular security by regressing the security against the market. We can also find the Beta by dividing a security's co-variance by the variance of the market.
- We should not be paid a return premium for risk that could be diversified away when we've chosen not to diversify the risk.

## The CAPM Equation

## The CAPM Equation in Graph

## Summary

Many market professionals argue that the CAPM is dead and that Beta is dead and have criticized this model. However, these same individuals use the CAPM to measure themselves in terms of Alpha and other portfolio metrics.

At Garde Capital we are most interested in the equilibrium portfolio of all investable assets and feel that for all of the CAPM's faults, from over simplifying to problematic assumptions, it's still one of the most applicable fundamental theories to all investment markets around the world and that it should not be overlooked in its importance.

Lastly, in the 1960's several people were working on ideas that eventually became the CAPM and although William Sharpe' 1963 publishing has received the most credit, Jack Treynor, John Lintner, and Jan Mossin, also published and added to this work in what has now become widely known as the Capital Asset Pricing Model.

## Beyond the CAPM

After Sharpe's 1963 publishing of A Simplified Model for Portfolio Analysis

## Since the CAPM and Extensions

Most asset allocation and asset pricing models have some relation to the CAPM whether it be an extension of a variant, or through additional factors or input strategies.

Stephen Ross proposed Arbitrage Pricing Theory (APT) that generally uses a multi-factor model to generate betas for specific asset exposures. There's wide acceptance of this idea.

Eugene Fama and Kenneth French criticized the CAPM for its simplicity in a single factor and expanded this into a three factor model using Size, Price to Book, and the Market, as the key factors with some success. This is known as the Fama French Three Factor Model. Some criticize this model for the time period used as well as the potential downside in difficult periods.

Fama French Carhart is another well know four factor model, with Carhart adding momentum as the fourth factor. This model has had some success but more recently has proved challenging when momentum changed.

And even the mortgage industry of securitization is about diversifying risk that can be diversified, such as borrower specific risk, and paying lenders on the risk that can't be diversified, the entire economy risk. This has led to the power of allowing homeowners to borrow at more attractive rates than what would otherwise be possible.

In a 1993 Dow Jones interview of William Sharpe, he points out that the CAPM has plenty of faults, and that there's likely to be more than one factor, but the problem is finding the right factors, and argued that there are an infinite number of factors, and the infinite number of factors in a general sense, roll up to a single general factor, and that may just be the CAPM?

Thoughts or comments, please let us know.