Subject 2. Pricing of Risk and Computation of Expected Return

Systematic Risk and Unsystematic Risk

Total risk is measured as the standard deviation of security returns. It has two components:

  • Systematic risk is the risk that is inherent in the market that cannot be diversified away. The systematic risk of an asset is the relevant risk for constructing portfolios. Examples of systematic risk or market risk include macroeconomic factors that affect everything (such as the growth in U.S. GNP, inflation, etc.).

    Note that different securities may respond differently to market changes, and thus may have different systematic risks. For example, automobile manufacturers are much more sensitive to market changes than discount retailers (e.g., Wal-Mart). As a result, automobile manufacturers have higher systematic risk.

  • Unique, diversifiable, or unsystematic risk (or nonsystematic risk) is risk that can be diversified away. This risk is offset by the unique variability of the other assets in a portfolio. An investor should not expect to receive additional return for assuming unsystematic risk.

Systematic risk is priced, and investors are compensated for holding assets or portfolios based only on that investment's systematic risk. Investors do not receive any return for accepting unsystematic risk.

Return-Generating Models

A return-generating model tries to estimate the expected return of a security based on certain parameters. Both the market model and CAPM are single-factor models. The common, single factor is the return on the market portfolio. Multifactor models describe the return on an asset in terms of the risk of the asset with respect to a set of factors. Such models generally include systematic factors, which explain the average returns of a large number of risky assets. Such factors represent priced risk, risk which investors require an additional return for bearing.

According to the type of factors used, there are three categories of multifactor models:

  • In macroeconomic factor models, the factors are surprises in macroeconomic variables that significantly explain equity returns. Surprise is defined as actual minus forecast value and has an expected value of zero. The factors, such as GDP, interest rates, and inflation, can be understood as affecting either the expected future cash flows of companies or the interest rate used to discount these cash flows back to the present.

  • In fundamental factor models, the factors are attributes of stocks or companies that are important in explaining cross-sectional differences in stock prices. Among the fundamental factors are book-value-to-price ratio, market cap, P/E ratio, financial leverage, and earnings growth rate.

  • In statistical factor models, statistical methods are applied to a set of historical returns to determine portfolios that explain historical returns in one of two senses. In factor analysis models, the factors are the portfolios that best explain (reproduce) historical return covariances. In principal-components models, the factors are portfolios that best explain (reproduce) the historical return variances.

Here is a two-factor macroeconomic model.

Ri = ai + bi1 FGDP + bi2 FINT + εi

where

  • Ri = the return for asset i.
  • ai = expected return for asset i in the absence of any surprises.
  • bi1 = GDP surprise sensitivity of asset i. This is a slope coefficient which is interpreted as the GDP factor sensitivity of asset i.
  • FGDP = surprise in GDP growth. This is the GDP factor surprise, the difference between the expected value and the actual value of the GDP.
  • bi2 = interest rate surprise sensitivity of asset i. This is the interest rate factor sensitivity of asset i.
  • FINT = surprise in interest rates. This is the interest rate factor surprise.
  • εi = firm-specific surprises (the portion of the return to asset i not explained by the factor model).

The model says stock returns are explained by surprises in GDP growth and interest rates. The regression analysis is usually used to estimate assets' sensitivities to these factors.

Calculation and Interpretation of Beta

Beta (β) is the standardized measure of systematic risk.

Since all investors want to hold the market portfolio, a security's covariance with the market portfolio (Covi,M) is the appropriate risk measure. Covi,M is an absolute measure of the security's systematic risk. Its magnitude is affected by the variability of both the security and the market portfolio (recall that Covi,j = pi,j x σi,j x σi,j). To standardize the measure of systematic risk, divide Covi,M by the covariance of the market portfolio with itself (CovM,M). Therefore, the standardized measure of systematic risk (beta) is defined as β = Covi,M / CovM,M = Covi,M / σM2 = ρi,M σiM.

  • The market portfolio has a β of 1.
  • If β > 1, the security is more volatile than the market.
  • If β < 1, the security is less volatile than the market.

User Contributed Comments 6

You need to log in first to add your comment.
GeorgeC: unsystematic risk is also called idiosyncratic risk (remember you'd have to be an idiot to have idiosyncratic risk in your portfolio!!).
jgraham6: "Investors can reduce systematic risk by diversifying globally rather than in the U.S. only."

Is this still true?
scancubus: If you are a professor, yes.
dmfcrowe: Yep, all nice little theories on paper, in practical terms not particularly usefull. All based on past performance for a start, and almost completely unworkable in real life. Try working out the the covariances and correlations in a 50 security portfolio each time its changed. Efficient frontier? I think not.
johntan1979: Well, well... quite obviously, we still have living specimens of primitive humans, because it has been estimated that the value of non-U.S. assets exceeds 60% of the world total. Furthermore, U.S. equities make up only about 10% of total world assets.
RamaG: the key is to find the asset classes that will be -very correlated in the near future.. Adding T bills (kindda risk free) , Gold during 2008-12 period and then adding Japan stocks between 3rd quarter 2012 - 2nd quarter 2013 are sound examples of implementation of this sound theory in real world.. Of course the theory will not tell you what the ideal asset classes are going to be