WFU Law School
Law & Valuation
2.5.1 CAPM Basics

2.5.2 Theoretical Basis of CAPM

Valuation of assets, like any art, has its techniques. And the techniques all have hidden secrets, sometimes skeletons in the closet. The CAPM is a case in point. To appreciate the CAPM's pitfalls, it is important to know how the model is derived. Here are the steps:

  • Investors are rational. They prefer portfolios that combine greater returns and less risk.
  • There exists an optimal portfolio. At some point, portfolios cannot be constructed that offer a better mix of return and risk.
  • The optimal portfolio can be improved. Once this optimal portfolio is constructed, it can be made to have --
    • less risk by lending portfolio assets, substituting them with risk-free assets.
    • more risk by borrowing additional funds at risk-free rates and acquiring even more portfolio assets.
  • The market risk-return line is linear. In a market with fully-informed pricing, these portfolios all lie on a straight line -- thus establishing a linear relationship between return and risk.

 

Investors want more return/less risk

The first assumption is that investors are risk-averse. They will want to be compensated with higher returns if they take on greater risk. This leads to a conclusion that each investor will value certain investments identically: a low-return, low-risk asset is just as good as a medium-return, medium-risk asset, which is just as good as a high-return, high-risk asset. Not all investors will be equally risk-averse, but we predict they will always prefer more return for the same risk, and less risk for the same return. Their investment desires (or utility curves) can be shown graphically:

[chart] xxx / black at 108


An "optimal portfolio" best matches return and risk.

The second assumption is that, although there will be many ways to construct portfolios that combine return and risk, there will be an optimal portfolio. At some point, you cannot do better.
This analysis begins by constructing a series of portfolios for which you cannot reconstitute the portfolios to provide more return with the same risk, or less risk with the same returns. That is, there is a "frontier" to the set of "efficient" portfolio possibilities.

[chart] xxx / black at 108

Is one of these "efficient" portfolios optimal? The answer is yes -- wherever the investor's investment demand curves touches the portfolio supply curve. (Or in the language of financial economists, this is where the "indifference" curve is tangent to the "efficient frontier.")

[chart] xxx / black at 109

But is there a way to improve this portfolio, so it satisfies an even higher "utility curve" -- is even more desirable to an investor?


Even more "optimal" portfolio can be constructed using risk-free assets.

The third assumption is that you can construct new portfolios, that lie above the "efficiency frontier," by adding or subtracting risk-free assets to the "optimal portfolio."

This can be done in one of two ways:

  • Lending at risk-free rates. You can lend some of the assets in your "optimal" portfolio and invest these funds in risk-free assets. Your portfolio now has a different return-risk profile. You have increased the proportion of risk-free assets and decreased the proportion of risky assets. With this lending, your portfolio's return and risk decrease along a straight line -- proportional to the risk-free rate and the "optimal" portfolio rate.
  • Borrowing at risk-free rates. You can borrow funds at risk-free rates (assuming this possible) and invest these funds in additional "optimal" assets. This has the effect of leveraging your portfolio's return-risk characteristics. You decrease the proportion of risk-free assets and increase the proportion of risky assets. With this borrowing, your return and risk increase along a straight line -- again proportional to the risk-free rate and the "optimal" portfolio rate.

See Black at 110.


Risk and return lie on a straight "capital market line."

The fourth assumption is that market participants have homogeneous risk-return expectations. This means that the "optimal" portfolio in terms of combining risk and return is the portfolio of all securities available in the market, weighted by their market values. This weighted portfolio is, by definition, the market portfolio.

As we have seen, it is possible to reconstruct the risk-return characteristics of the market portfolio along a straight line. By lending at the risk-free rate, you can construct a portfolio that moves down the line. By borrowing at the risk-free rate, your portfolio moves up the line.

[Chart Black at 112 ]

The slope of the capital market line represents the additional return the market assigns to taking additional risk. Notice that this line lies above and beyond the regular reward (or rate of return) assigned to simply waiting -- the time value of a risk-free investment. The capital market line tells us the amount of additional expected return that market participants require for assuming additional risk -- or volatility.

Different investors, with different risk preferences, can create portfolios with different risk profiles. But they cannot create a portfolio that lies above the capital market line. If any investment is offered with returns that the risk-adjusted returns predicted by the capital market line, investors will seek the investment and its price will rise. And if its price rises, its returns fall -- until they reach the capital market line!

 

 

 

2.5.1 CAPM Basics

©2003 Professor Alan R. Palmiter

This page was last updated on: August 4, 2003