Question

Risk and Rates of Return: Stand-Alone Risk Stand-alone risk is the risk an investor would face if he or she held only _________________ . No investment should be undertaken unless its expected rate of return is high enough to compensate for its perceived _________________ . The expected rate of return is the return expected to be realized from an investment; it is calculated as the _________________ of the probability distribution of possible results as shown below: The _________________ an asset's probability distribution, the lower its risk. Two useful measures of stand-alone risk are standard deviation and coefficient of variation. Standard deviation is a statistical measure of the variability of a set of observations as shown below: If you have a sample of actual historical data, then the standard deviation calculation would be changed as follows: The coefficient of variation is a better measure of stand-alone risk than standard deviation because it is a standardized measure of risk per unit; it is calculated as the _________________ divided by the expected return. The coefficient of variation shows the risk per unit of return, so it provides a more meaningful risk measure when the expected returns on two alternatives are not _________________ . Quantitative Problem: You are given the following probability distribution for CHC Enterprises:

State of Economy	Probability	Rate of return
Strong	0.25	18%
Normal	0.5	8%
Weak	0.25	-6%

What is the stock's expected return? Round your answer to 2 decimal places. Do not round intermediate calculations. ________ %

What is the stock's standard deviation? Round your answer to two decimal places. Do not round intermediate calculations. ________ %

What is the stock's coefficient of variation? Round your answer to two decimal places. Do not round intermediate calculations. ________

Answer 1

Stand-Alone Risk Stand-alone risk is the risk an investor would face if he or she held only one asset.
No investment should be undertaken unless its expected rate of return is high enough to compensate for its perceived risk.
The expected rate of return is the return expected to be realized from an investment; it is calculated as the weighted average of the probability distribution of possible results as shown below:
The tighter/narrower an asset's probability distribution, the lower its risk.
Two useful measures of stand-alone risk are standard deviation and coefficient of variation. Standard deviation is a statistical measure of the variability of a set of observations as shown below:
If you have a sample of actual historical data, then the standard deviation calculation would be changed as follows:
The coefficient of variation is a better measure of stand-alone risk than standard deviation because it is a standardized measure of risk per unit; it is calculated as the standard deviation divided by the expected return.
The coefficient of variation shows the risk per unit of return, so it provides a more meaningful risk measure when the expected returns on two alternatives are not same/equal.

What is the stock's expected return?
=Sum(probability*returns)
=0.25*18%+0.5*8%+0.25*(-6%)
=7.00%

What is the stock's standard deviation?
=sqrt(Sum(probability*(returns-expected returns)^2))
=sqrt(0.25*(18%-7.00%)^2+0.5*(8%-7.00%)^2+0.25*(-6%-7.00%)^2)
=8.54%

What is the stock's coefficient of variation?
=standard deviation/expected returns
=8.54%/7.00%
=1.22