Determining mean and Standard Deviation of Returns

What is the approximate standard deviation of returns if over the past four years an investment returned 8.0%, -12.0%, -12% and 15.0%?

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Because you did not specify, I assume that this is the entire population of returns. If it is, see parts A, B. C. If it is only a sample, see parts A, D, and E.

The standard deviation is computed by taking the square root after dividing the total of the ...

Solution Summary

This solution takes you step by step through computing the mean and standard deviation of a set of investment returns.

Consider the use of probability analysis in estimating returnsanddetermining the standard deviation. You may use a hypothetical situation and do the calculations or just describe the steps in the process.

Calculate the expected return and standard deviation of returns for asset A are (See below.)
Possible Outcomes Probability Returns (%)
Pessimistic 0.25 5
Most likely 0.55 10
Optimistic 0.20 13

Two stocks with actual returns as follows are being considered by me as an investor. Assist me by calculating the standard deviationand the coefficient of variation and avise me based on a comparison of risk and return.
Stock X - Actual Returns: 6%, 12%, 8%, 10%
Stock Z - Actual Returns: 9.5%, 9.25%, 8%, 9%

The following table shows the nominal returns on U. S. stocks and the rate of inflation.
a. What was the standard deviation of the market returns?
b. Calculate the average real return.
Year Nominal Return (%) Inflation (%)
2004 12.5 3.3
2005 6.4

Suppose the expected returnsand standard deviations of stocks A and B are E(R^A)=0.15, E(r^B)=0.25, s^a=0.1, and s^b=0.2, respectively.
a.Calculate the expested return and standard deviation portfolio that is composed of 40 percent A and 60 percent B when the correlation between returns on A and B is 0.5.
b. Calculate the

What is the standard deviation of the returns on a stock given the following information?
State of Economy Probability Rate of Return if State Occurs
Boom 10% 16%
Normal 60% 11%

An investor is considering two investments, an office building and bonds. The possible returns from each investment and their probabilities are listed as follows. Using expected value and standard deviation as a basis for comparison, discuss which of the two investments should be selected.
Office Building

You are considering a security with the following possible rates of return:
Probability Return (%)
0.30 9.5
0.15 12.0
0.25 15.0
0.30 16.0
Calculate the expected rate of return and the standard deviation of the returns.
Probability Return (%)
0.15 6