One popular way to measure risk is to examine the variability of return over time by computing a standard deviation or variance of an annual rate of return for an asset class. Another intriguing measure of risk is the probability of not meeting investment return objectives.
One of the best known measures of risk is the variance or standard deviation of expected return. It is a statistical measure of the dispersion of returns around the expected value whereby a larger variance or standard deviation indicates greater dispersion. The idea is that the more disperse the expected returns, the greater the uncertainty of future returns.
Population variance = Σ (Xi – Χ)/ n
Population standard deviation
= (Population variance) 1/2
Another measure of risk is the range of returns. It is assumed that a larger range of expected return, from the lowest to the highest expected return, means greater uncertainty and risk regarding future expected return.
Range = maximum value of return – minimum value of return
In practice, risk may be measured in absolute terms or in relative terms with reference to various risk concepts.
Examples of absolute risks measurement are a specified level of standard deviation or variance of total return such as standard deviation below 15% is an example of absolute risk.
Relative risks measurement are a specified level of standard deviation relative to a reference. Tracking risk is an example of relative risk measurement where it specified the standard deviation of the different between a portfolio’s and the benchmark’s total return.
Risk aversion
Portfolio theory assumes that investors are basically risk adverse, meaning that, given a choice between two assets with equal rate of return, they will select the asset with the lowest level of risk or given the same level of risk, investor will select the asset with higher level of return.
Evidence that most investors are risk averse is that they purchase various type of insurance, including life insurance, car insurance and health insurance. Buying insurance basically involves an outlay of a given known amount to guard against an uncertain, possibly larger, outlay in the future.
Further evidence of risk aversion is that investor required higher return for investment which expected with higher risk. Investor requested different yield (rate of return) for different class of bond with different degree of credit risk. Promise yield (rate of return) on corporate bonds increase from AAA (the lowest risk class) to AA to A and so on, indicating that investors require a higher rate of return to accept higher risk.
This does not imply that everybody is risk averse, or that investors are completely risk averse regarding all financial commitments. The fact is, not everybody buy insurance for everything. Some people have no insurance against anything, either by choice or because they cannot afford it.
In addition , some individuals buy insurance related to some risks such as auto accidents or illness, but they also buy lottery tickets and gamble at race tracks or in casinos , where it is known that the expected returns are negative ( which means that participants are willing to pay for the excitement of the risk involved). This combination of risk preference and risk aversion can be explained by an attitude towards risk that depends on the amount of money involved where people who like to gamble for small amounts (in lottery or slot machines) but buy insurance to protect themselves against large losses such as fire or accident.
While recognizing such attitudes, the basis assumption is that most investors committed large sums of money developing an investment portfolio is risk averse. Therefore, we expect a positive relationship between expected return and expected risk.
