Module: 2 - Skill Development Risk/Return Analysis - Portfolio Risk
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In order to estimate the total risk of a portfolio of assets, several estimates are needed, the variance of each individual asset under consideration for inclusion in the portfolio and the covariance, or correlation co-efficient, of each asset with each of the other assets. The risk of a portfolio depends not only on the risk of its securities, considered in isolation, but also on the extent to which they are affected similarly by underlying events. The variance is simply a weighted average of such products, using the probabilities of the events as weights. A positive value for the covariance indicates that the securities returns tend to go together - for example, a better-than- expected return for one is likely to occur along with a better-than-expected return for the other. A negative covariance indicates a tendency for the returns to offset the another - for example, a better-than-expected return for one is likely to occur along with a worse-than- expected return for the other. A small or zero value for the covariance indicates that there is a little or no relationship between the two returns. Correlation coefficients always lie between +10 and 1.0, inclusive. The relationship between the covariance and the correlation coefficient can be represented as follow:

Cxy= rxy Sx Sy

Or

rxy = Cxy
       Sx Sy

Where:

Cxy = covariance between return on X and return on Y.
Rxy = coefficient of correlation between return on X and return on Y
Sx = standard deviation of return for X
Sy = standard deviation of return for Y

Much time and effort has been expended on developing a measure of risk and a system for using this measure in assessing returns. The two key components of that have emerged from this theoretical effort are beta, which is a statistical measure of risk, and the capital asset pricing model (CAPM), which links (beta) to the level of required return.

Much time and effort has been expended on developing a measure of risk and a system for using this measure in assessing returns. The two key components of that have emerged from this theoretical effort are beta, which is a statistical measure of risk, and the capital asset pricing model (CAPM), which links (beta) to the level of required return.

The total risk of an investment consists of two components;

• diversifiable and

• non-diversifiable risk.

Diversifiable, or unsystematic, risk represents the portion of an investment's risk that can be eliminated by holding enough stocks. This risk results from uncontrollable or even random events that tend to be unique to an industry and/or a company such as management changes, labor changes, labor strikes, lawsuits, and regulatory actions.

Nondiversifiable or systematic, risk is external to an industry and/or business and is attributed to broad forces, such as war, inflation, and political and even sociological events. Such forces impact all investments and therefore not unique to a given vehicle. The relationship between total risk, diversifiable risk and nondiversifiable risk is given by the equation.

Total risk = Diversifiable risk + Nondiversifiable risk

Because any knowledgeable investor can eliminate diversifiable risk by holding a large enough portfolio of securities, the only relevant risk to be concerned about is non-diversifiable risk. Studies have shown that by carefully selecting as few as fifteen securities for a portfolio diversifiable risk can be almost entirely eliminated. Nondiversfiable risk is unavoidable, and each security possesses its own level of nondiversifiable risk measured using the beta coefficient.

Beta measures nondiversifiable risk. Beta shows how the price of a security responds to market forces. In effect, the more responsive the price of a security is to changes in the market, the higher will be its beta. Beta is calculated by relating the returns on a security with the returns for the market. The beta for the overall market is equal to 1.00 and other betas are viewed in relation to this value.

Betas can be positive or negative. However, nearly all betas are positive and most betas lie somewhere between 4 and 1.9.

CAPM (Capital Asset Pricing Model) uses beta to link formally the notions of the risk and return. CAPM was developed to provide a system whereby investors are able to assess the impact of an investment in a proposed security on the risk and return of their portfolio. We can use CAPM to understand the basic risk-return tradeoffs involved in various types of investment decisions. CAPM can be viewed both as a mathematical equation and, graphically, as the security market line (SML).

When the CAPM is depicted graphically, it is called the Security Market Line (SML). Plotting CAPM, we would find that the SML is a straight line. It tells us the required return an investor should earn in the marketplace for any level of unsystematic (beta) risk.

Detailed Process of calculating BETA, CAPM & SML are explained in Annexure: 4

Risk evaluation based on the above concepts to be arrived at by investors. It must relate the risk perceived in a given security not only to return but also to their own attitudes toward risk. Thus, the evaluation process is not one in which we simply calculate risk and compare it to a maximum risk level associated with an investment offering a given return.