FINA 385 Study Guide - Final Guide: Risk Premium, Expected Return, Risk Aversion

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14 Dec 2017

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Formulas for the final: an estimate of expected return, variance and covariance of returns based on historical data. !t=1 (rxt rx )(ry t ry : variance of portfolio with two risky assets a and b p = w2. B + 2wawb a b ab: equation for the capital allocation line. E(rc) = rf + y[e(rp ) rf : standard deviation of complete portfolio. C = y p: optimal fraction of complete portfolio allocated to portfolio p in the market with t-bills and portfolio. P: utility of an investor when his capital allocation is optimal. P: optimal weight of risky asset 2 in the risky portfolio with two risky assets 1 and 2 in the market with no t-bills w . 2 2cov(r1, r2): optimal weight of risky asset 2 in the risky portfolio with two risky assets 1 and 2 in the market with. M where a is an average coe cient of risk aversion.

Related Questions

You are on the board of the Springfield College Endowment Fund (SCEF), which is evaluating two potential managers for its investments: Mr. Monty Burns (MB) and Mr. Waylon Smithers (W S). The expected returns on portfolios MB and W S are 11% and 14%, respectively. The beta of MB is 0.8 while that of W S is 1.5. The T-Bill rate is 7%, while the expected return of the market index is 12%. The standard deviation of portfolio MB is 10%, while that of W S is 31%, and that of the index is 20%. 1. Suppose SCEF currently holds a market index portfolio. Based on the data, would you add portfolios MB and/or W S to SCEFâs mix of holdings? (Hint: check for under/overpricing.) 2. If SCEF were ordered to invest only in T-Bills and one of the portfolios MB or W S, which portfolio should SCEF invest? Why?

Question 1.

Consider a portfolio that has equal amounts of $10 invested in two assets. Suppose returns on the two assets are jointly normally distributed. The annual expected returns and variance or return on the first asset are given by

m₁ = 0.10 s₁^2 = 0.04

And those on the second asset are given by

m₂ = 0.05 s₂^2 = 0.03

Consider three cases:

The correlation between the return is r = 0

The correlation between the return is r = +0.50

The correlation between the return is r = -0.50

For each case, identify the 99% Value-at-Risk of the portfolio. Explain the pattern of dependence of VaR on the correlation.

Question 2.

You are given a portfolio of three assets whose returns are jointly normally distributed with the following mean vector and covariance matrix:

0.20 0.08 0.02 0.02

0.10 0.02 0.06 0.03

0.15 0.02 0.03 0.07

a. Compute the 95% VaR for the portfolio if we invest $1 in the first asset. $2 in the second asset, and $3 in the third asset.

b. How much does each assetâs holding contribute to the overall VaR risk?

Question 3.

You are given a portfolio of two assets whose returns are jointly distributed with the following vector and covariance matrix.

0.20 0.08 0.04

0.10 0.04 0.06

a. Compute the 95% VaR of the portfolio if $1 is invested in the first asset and $1 is invested in the second.

b. Compute the risk-contribution of each asset to the VaR.

c. Is the current portfolio weighting optimal? If not, suggest a better one.

sapphireduck935

1. You own a stock portfolio invested 15 percent in Stock Q, 20 percent in Stock R, 35 percent in Stock S, and 30 percent in Stock T. The betas for these four stocks are 1.1, 0.8, 1.2, and 0.9, respectively. What is the portfolio beta? (Round your answer to 3 decimal places.)

2. You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.95, and the total portfolio is exactly as risky as the market, what must the beta be for the other stock in your portfolio? (Round your answer to 2 decimal places.)

Beta
3. A share of stock sells for $38 today. The beta of the stock is 1, and the expected return on the market is 17 percent. The stock is expected to pay a dividend of $1.10 in one year. If the risk-free rate is 3.7 percent, what should the share price be in one year? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Share price

4. A stock has a beta of 0.7 and an expected return of 9 percent. A risk-free asset currently earns 4 percent.

a.	What is the expected return on a portfolio that is equally invested in the two assets? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Expected return

b.	If a portfolio of the two assets has a beta of 0.6, what are the portfolio weights?(Round your answers to 2 decimal places. Omit the "%" sign in your response.)

	Weight
x_S	%
x_rf	%

c.	If a portfolio of the two assets has an expected return of 8 percent, what is its beta? (Round your answer to 2 decimal places.)

Beta

d.	If a portfolio of the two assets has a beta of 2.80, what are the portfolio weights? (Negative amounts should be indicated by a minus sign. Omit the "%" sign in your response.)

	Weight
x_S	%
x_rf	%

5. Asset W has an expected return of 8 percent and a beta of 2. If the risk-free rate is 5.5 percent, what is the market risk premium? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Market risk premium

6. Stock Y has a beta of 1.5 and an expected return of 12 percent. Stock Z has a beta of 0.8 and an expected return of 8 percent. What would the risk-free rate have to be for the two stocks to be correctly priced relative to each other? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Risk-free rate

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FINA 385 Study Guide - Final Guide: Risk Premium, Expected Return, Risk Aversion

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