The Security Market Line

Let us pause for thought:

- Total risk comprises unsystematic and systematic risk.

- Unsystematic risk, unique to each company, can be eliminated by portfolio diversification.

- Systematic risk is undiversifiable and depends on the market as a whole.

These distinctions between total, unsystematic and systematic risk are vital to our understanding of the development of Modern Portfolio Theory (MPT). Not only do they validate beta factors as a measure of the only risk that investors will pay a premium to avoid. As we shall discover, they also explain the rationale for the Capital Asset Pricing Model (CAPM) whereby investors can assess the portfolio returns that satisfy their risk-return requirements. So, before we consider the CAPM in detail, let us contrast systemic beta analysis with basic portfolio theory that only considers total risk.

The linear relationship between total portfolio risk and expected returns, the Capital Market Line (CML) based on Markowitz efficiency and Tobin's Theorem, graphed in Chapter Four does not hold for individual risky investments. Conversely, all the characteristics of systemic beta risk apply to portfolios and individual securities. The beta of a portfolio is simply the weighted average of the beta factors of its constituents.

This new relationship becomes clear if we reconstruct the CML (Figures 4.2 and 4.1 from Chapter Four of our Theory and Exercise texts, respectively) to form what is termed the Security Market Line (SML). As Figure 5.3 illustrates, the expected return is still calibrated on the vertical axis but the SML substitutes systemic risk (b) for total risk (ap) on the horizontal axis of our earlier CML diagrams.

Once beta factors are calculated (not a problem) the SML provides a universal measure of risk that still adheres to Markowitz efficiency and his criteria for portfolio selection, namely:

Maximise return for a given level of risk Minimise risk for a given level of return

Like the CML, the SML still confirms that the optimum portfolio is the market portfolio. Because the return on a portfolio (or security) depends on whether it follows market prices as a whole, the closer the correlation between a portfolio (security) and the market index, then the greater will be its expected return. Finally, the SML predicts that both portfolios and securities with higher beta values will have higher returns and vice versa.

The Security Market Line

Figure 5.3: The Security Market Line

As Figure 5.3 illustrates, the expected risk-rate return of rm from a balanced market portfolio (M) will correspond to a beta value of one, since the portfolio cannot be more or less risky than the market as a whole. The expected return on risk-free investment (rf) obviously exhibits a beta value of zero.

Portfolio A (or anywhere on the line rf -M) represents a lending portfolio with a mixture of risk and risk-free securities. Portfolio B is a borrowing or leveraged portfolio, because beyond (M) additional securities are purchased by borrowing at the risk-free rate of interest.

Review Activity

Given your knowledge of perfect capital markets, Fisher's Separation Theorem, stock market efficiency, mean-variance analysis, utility theory, Markowitz efficiency and Tobin's Capital Market Line (CML):

Briefly summarise what the Security Market Line (SML) offers rational, risk-averse individuals seeking a well-diversified portfolio of investments?

Summary and Conclusions

Throughout our analyses (including the background SFM and SFME texts) we have observed how rational, risk-averse individuals and companies operating in perfect markets with no "barriers to trade" can rank individual investments by interpreting their expected returns and standard deviations using the concept of expected utility to calibrate their risk-return attitudes. In this book (and its Exercise companion) we began with the same mean-variance efficiency criteria to derive optimum portfolio investments that can reduce risk (standard deviation) without impairing return. In Part Two this culminated with Tobin's Theorem and the CML that incorporates borrowing and lending opportunities to define optimum "efficient" portfolio investment opportunities.

Unfortunately, the CML only calibrates total risk (cp) not all of which is diversifiable. Fortunately, the SML offers investors a lifeline, by discriminating between non-systemic and systemic risk. The latter is defined by a beta factor that measures relative (systematic) risk, which explains how rational investors with different utility (risk-return) requirements can choose an optimum portfolio by borrowing or lending at the risk-free rate.

We shall return to this topic in Chapter Six when risk is related to the expected return from an investment or portfolio using the CAPM.

Selected References

1. Markowitz, H.M., "Portfolio Selection", The Journal of Finance, Vol. 13, No. 1, March 1952.

2. Tobin, J., "Liquidity Preferences as Behaviour Towards Risk", Review of Economic Studies, February 1958.

3. Fisher, I., The Theory of Interest, Macmillan (London), 1930.

4. Modigliani, F. and Miller, M.H., "The Cost of Capital, Corporation Finance and the Theory of Investment", American Economic Review, Vol. XLVIII, No. 4, September 1958.

5. Miller, M.H. and Modigliani, F., "Dividend Policy, Growth and the Valuation of Shares", Journal of Business of the University of Chicago, Vol. 34, No. 4, October 1961.

6. Black, F., Jensen, M.L. and Scholes, M., "The Capital Asset Pricing Model: Some Empirical Tests", reprinted in Jensen, M.L. ed, Studies in the Theory of Capital Markets, Praeger (New York), 1972.

7. Hill, R.A.,

- Strategic Financial Management, 2009.

- Strategic Financial Management; Exercises, 2009.

- Portfolio Theory and Financial Analyses; Exercises, 2010.

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