Question

Hello tutor! Just these three, please!

1)Calculate the standard deviation for the following company based on the forecasts given.

Economic condition	Probability	Return forecast
Expansion	20%	13%
Normal	60%	5%
Recession	20%	-14%

Provide your answer in percent, rounded to two decimals, omitting the % sign.

2) As a financial adviser, you are recommending a well-diversified fund with an expected rate of return of 17% and a standard deviation of 39% to your clients. A client would like to split her investment between your fund and T-bills so that her standard deviation is no more than 27%. What will be her expected return? T-bill's yield 3%. Provide your answer in percent rounded to two digits, omitting the % sign.

3)

Assume that you manage a risky portfolio with an expected rate of return of 15% and a standard deviation of 25%. The T-bill rate is 3% . Suppose your risky portfolio includes the following investments in the given proportions.

Dell	50%
Apple	30%
HP	20%

What are the investment proportions of your client’s overall portfolio, including the position in T-bills, if your client's risk aversion coefficient is 3?

-       A.       B.       C.       D.    Dell       -       A.       B.       C.       D.    Apple       -       A.       B.       C.       D.    HP       -       A.       B.       C.       D.    T-Bill

A. 32% B. 19.2% C. 12.8% D. 36%

Answer 1

Since, multiple questions have been posted and each question is independent of another, I have answered the first question.

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Question 1:

Step 1: Calculate Expected Return

The expected return is calculated as below:

Expected Return = Probability of Expansion*Return Forecast Under Expansion + Probability of Normal*Return Forecast Under Normal + Probability of Recession*Return Forecast Under Recession

Substituting values in the above formula, we get,

Expected Return = 20%*13% + 60%*5% + 20%*(-14%) = 2.80%

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Step 2: Calculate Variance

The value of variance is arrived as below:

Variance = Probability of Expansion*(Return Forecast Under Expansion - Expected Return)^2 + Probability of Normal*(Return Forecast Under Normal - Expected Return)^2 + Probability of Recession*(Return Forecast Under Recession - Expected Return)^2

Substituting values in the above formula, we get,

Variance = 20%*(13% - 2.80%)^2 + 60%*(5% - 2.80%)^2 + 20%*(-14% - 2.80%)^2 = 0.008016

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Step 3: Calculate Standard Deviation

The value of standard deviation is determined as follows:

Standard Deviation = (Variance)^(1/2) = (0.008016)^(1/2) = 8.95% (answer)