If your portfolio is invested 40 percent each in A and B and 20 percent in C, wh

Question

If your portfolio is invested 40 percent each in A and B and 20 percent in C, what is the portfolio expected return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

What is the variance? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.)

What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

If the expected T-bill rate is 4.00 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

If the expected inflation rate is 3.60 percent, what are the approximate and exact expected real returns on the portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

What are the approximate and exact expected real risk premiums on the portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Explanation / Answer

Since, there are multiple parts to the question, the first four have been answered.

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Part a-1)

We need to calculate expected return under each scenario to determine the portfolio return. The formula for calculating expected return is given below:

Expected Return (Boom/Normal/Bust) = Percentage Investment in Stock A*Expected Return on Stock A under Boom/Normal/Bust + Percentage Investment in Stock B*Expected Return on Stock B under Boom/Normal/Bust + Percentage Investment in Stock C*Expected Return on Stock C under Boom/Normal/Bust

The expected return on the portfolio is calculated as follows:

Expected Return (Portfolio) = Probability of Boom*Expected Return under Boom + Probability of Normal*Expected Return under Normal + Probability of Bust*Expected Return under Bust

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Using the values provided in the question, we get,

Expected Return under Boom = 40%*.24 + 40%*.36 + 20%*.58 = 35.60%

Expected Return under Normal = 40%*.20 + 40%*.18 + 20%*.16 = 18.40%

Expected Return under Bust = 40%*.04 + 40%*-.36 + 20%*-.45 = -21.80%

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Now, we can calculate expected return of the portfolio as follows,

Expected Return of Portfolio = .20*35.60% + .50*18.40% + .30*-21.80% = 9.78%

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Part a-2)

The formula for calculating variance is given below:

Variance = Probability of Boom*(Expected Return under Boom - Expected Return of the Portfolio)^2 + Probability of Normal*(Expected Return under Normal - Expected Return of the Portfolio)^2 + Probability of Bust*(Expected Return under Bust - Expected Return of the Portfolio)^2

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Using the values calculated in Part a-1), we get,

Variance = .20*(35.60% - 9.78%)^2 + .50*(18.40% - 9.78%)^2 + .30*(-21.80% - 9.78%)^2 = .04697

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Part a-3)

The formula for calculating standard deviation is given below:

Standard Deviation = (Variance)^(1/2)

Using the value of variance calculated in Part a-2), we get,

Standard Deviation = (.04697)^(1/2) = 21.67%

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Part b)

The risk premium is calculated as follows

Risk Premium = Expected Return of the Portfolio - Risk Free Rate (T-Bill Rate) = 9.78% - 4% = 5.78%

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