Important facts on risk & returns


The return from an investment is the change n market price, plus any cash payments received due to ownership, divided by the beginning.

The risk of a security can be viewed as the variability of returns from those that are expected. The expected return is simply a weigh-tage average of the possible returns, with the weights being the probabilities of occurrence.

The conventional measure of dispersion, or variability around an expected value is the standard deviation, the square of the standard deviation is known as variance.
The standard deviation can sometimes be misleading in comparing the risk, or uncertainty, surrounding alternative investments if they differ in size. To adjust for the size, or scale, problem, the standard deviation can be divided by the expected return to compute the coefficient of variation (CV)—a measure of “risk per unit of expected return.�

Investors are, by and large, risk averse. This implies that they demand a higher expected return, the higher the risk. The expected return from a portfolio (or group) of investments is simply a weighted average of the expected returns of the securities comprising that portfolio. The weights are equal to the proportion of total funds invested in each security. The weights must sum to 100 percent.
The covariance of the possible returns of two securities is a measure of the extent to which they are expected to vary together rather than independently of each other. For a large portfolio, total variance and hence, standard deviation depend primarily on the weighted covariance among securities.

Meaningful diversification involves combining securities in a way that will reduce risk. Risk reduction occurs as long as the securities combined are not perfectly, positively correlated.

Total security (or portfolio) risk is comprised of two components—systematic risk and unsystematic risk. The first component, sometimes known as unavoidable or non-diversifiable risk, is systematic in the sense that it affects all securities although to different degrees.

Unsystematic risk is company specific in that it does not depend on general market movements. This risk is avoidable through proper diversification of one’s portfolio.

In market equilibrium, a security is supposed to provide an expected return commensurate with its systematic risk, the risk that cannot be avoided with diversification. The capital-asset pricing model (CAPM) formally describes this relationship between risk and return.

The degree of systematic risk that a security possesses can be determined by drawing a characteristic line. This line depicts the relationship between a stock’s excess expected returns (returns in excess of the risk-free rate) and the market’s excess expected returns. The slope (rise over run) of this line, known as beta, is an index of systematic risk. The greater the beta, the greater the unavoidable risk pf the security involved.

The relationship between the required rate of return for a security and its beta is known as the security market line. This line reflects the linear, positive relationship between the return investors requires and systematic risk. The required returns is the risk-free rate plus a risk premium for systematic risk that is proportional to beta.

Although the CAPM has proved useful in estimating rates of return in capital markets, it has been seriously challenged in recent years. Anomalies such as the small-firm effect, price / earnings ratio effect. A firm’s market capitalization (size) and the Market-to-book-value ratio are better predictors of average stock returns than is beta. Still, CAPM serves as a useful theoretical framework for understanding risk and leads naturally to multiple factor models and the arbitrage pricing theory. Financial markets are said to be efficient when security prices fully reflect all available information. In such a market, security prices adjust very rapidly to new information.