Define the standard deviation and coefficient of variation, and explain which one is a better measure for performance.
Standard deviation a statistical measure of the variability of a set of observations, the symbol for which is “σ(sigma)”.
Coefficient
of variation standard
measure of the risk per unit of return, and it provides a more
meaningful basis for comparison when the expected returns on two
alternatives are not the same; calculated as standard deviation
divided by the expected return. CV=
The standard deviation can sometimes be misleading in comparing the risk. Because the coefficient of variation captures the effects of both risk and return, it is a better measure for evaluating risk in situations where investments have substantially different expected returns.
Explain the following statement: “most investors are risk averse”. Explain the relationship between risk aversion and rates of return.
First of all, we must understand what does risk aversion mean? Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. Risk averse- A description of an investor who, when faced with two investments with a similar expected return (but different risks), will prefer the one with the lower risk. Consequently, he or she will demand a greater rate of return for a risky investment to compensate themselves for this risk element. Therefore, in summary, riskier investments will attract greater rate of returns.
Determine Security Market Line and construction of this line.
The security market line (SML) is the line that reflects an investment's risk versus its return. The measure of risk used for the security market line is beta. The security market line is a useful tool in determining whether an asset being considered for a portfolio offers a reasonable expected return for risk. Individual securities are plotted on the SML graph. If the security's risk versus expected return is plotted above the SML, it is undervalued because the investor can expect a greater return for the inherent risk. A security plotted below the SML is overvalued because the investor would be accepting less return for the amount of risk assumed. The line begins with the risk-free rate (with zero risk) and moves upward and to the right. As the risk of an investment increases, it is expected that the return on an investment would increase. An investor with a low risk profile would choose an investment at the beginning of the security market line. An investor with a higher risk profile would thus choose an investment higher along the security market line.
SML: k =k +(k –k )b= Risk-free return+ (Market risk premium)(Stock I’s beta)
Explain Market Risk Premium and calculation.
Market Risk Premium is additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk. The size of premium depends on perceived risk of the stock market and investors’ degree of risk aversion. The market risk premium can be calculated as follows:
Market Risk Premium = Expected Return of the Market – Risk-Free Rate= k -k
Market risk premium is equal to the slope of the security market line (SML), a capital asset pricing model. MRM shows the difference between the expected return on an investment and and the risk-free rate of return.