Fama&MacBeth Presentation

Risk, Return, and

Equilibrium: Empirical Test

by Eugene Fama

and James MacBeth

Antonio Fernós and Miguel Ruiz

LA VII PhD Finance Program

February 24, 2012

BUSN 8510

Prof. Yufeng Han

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Risk, Return, and Equilibrium: Empirical Test The Journal of Political Economy, Vol.

81, No. 3. (May - Jun., 1973) by Eugene Fama and James MacBeth

Methodology

Test relationship between average return and risk

Testing for two parameter model

Cannot reject H0 : pricing of common stocks reflects the attempts of risk-averse investors to hold portfolios that are “efficient” in terms of expected value and dispersion returns

“Fair game” properties of the coefficients

Residuals of the risk-return regressions are consistent with an “efficient capital market” (i.e.: market where prices of securities fully reflect available information)

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Literature Review:

Tobin (1958): Liquidity Preference as Behavior toward Risk

Markowitz (1959): Portfolio Selection: Efficient Diversification of Investments

Fama (1965): Portfolio Analysis in a Stable Pareto State

Cass and Stiglitz (1970): The Structure of Investor Preferences and Asset Returns, and Separability in Portfolio Allocation: A Contribution to the Pure Theory of Mutual Funds

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Literature Review

Tobin (1958)

– Believed the theory of liquidity preference was essentially a Keynesian explanation.

– Under certain conditions the investor’s portfolio allocation decision could be considered as a 2-stage process:

- Investor first decides in what proportions to purchase the available risky assets

- Then decides how to divide his total investment between risky and safe assets

– This 2-stage process is called “separation” and is a special case of a more general property of the investor’s portfolio allocation

– A set of “m” linear combinations with weights adding to one (1) of the available assets



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Literature Review

Markowitz (1959)

– Separation

– An investor selects a portfolio at time t -1 that produces a stochastic return at t. The model assumes investors are risk averse and, when choosing among portfolios, they care only about the mean and variance of their one-period investment return.

– As a result, investors choose “mean variance-efficient” portfolios, in the sense that the portfolios:

- minimize the variance of portfolio return, given expected return, and

- maximize expected return, given variance.

– Thus, the Markowitz approach is often called a “mean-variance model.”



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Literature Review

Fama (1965)

– Using earlier work from Sharpe developed portfolio analysis model for a stable Paretian market

– Empirical probability distributions of returns of securities conform better to Paretian distributions with infinite variances than the normal distribution

– Established the conditions under which diversification is a meaningful economic activity, even though probability distributions of returns on individual securities have finite variances



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Literature Review

Cass & Stiglitz (1970)

– Separation process properties derives four (4) sources:

1. Keynesian macro-economic models conventionally assume that such a separation property obtains

2. When such a separation property does obtain, achieving a pure exchange Pareto optimum may not require a full complement of Arrow-Debreu securities. And, of course, there are good reasons (i.e.: transaction costs) for believing Arrow-Debreu markets will not exist

3. Many of the results in modern portfolio theory depend crucially on the existence of a safe and just one risky asset or, equivalently, a single mutual fund composed of risky assets

4. The separation property represents a particular extension of an aggregation property which has long interested economists



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Theoretical Background/Assumptions

Capital markets are perfect in the sense that investors are prices takers and there are neither transaction sense or transaction costs

Distributions of percentage returns are assumed normal

Investors are risk averse

Optimal portfolio for any investor must be efficient in the sense that no other portfolio with the same or higher expected return has lower dispersion on returns

The difference between the expected return on the asset and the expected return on the portfolio is proportional to the difference between the risk of the asset and the risk of the portfolio



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Hypothesis

A stochastic two-parameter model for expected returns

With testable implications:

– C1: Linearity

– C2: No systemic effects on non beta risk.

– C3: Positive expected return-risk tradeoff/Capital market efficiency

- Sharpe – Lintner Hypothesis



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Conclusion

Results support the important testable implications of the two-parameter model

Market portfolio efficiency hypothesis at least cannot be rejected: NYSE common stocks reflect the attempts of risk averse investor to hold efficient portfolios

On average, there seems to be a positive tradeoff between return and risk, with risk measured from the portfolio viewpoint

There are “stochastic non-linearities” form period to periods, nonlinearity (C1) cannot be rejected

Hypothesis on two-parameter model being no measure of risk, in addition to portfolio risk, systematically affects average returns, cannot be rejected

“fair game” properties of the coefficients and residual of the risk-return regressions are consistent with an efficient capital market



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Appendix

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Documents

Fama&MacBeth Presentation