Risk Management Midterm
Solutions to Exam 1
1. (Chapter 1, slides, Q3) Suppose there are two investments.The expected returns from the investments are 10% and 15%, the standard deviation of the returns are 16% and 24%, and the correlation between returns is 0.2.Let w1 be the proportion of wealth put into the first investment. (a). Calculate the expected return and the standard deviation for portfolio w1=0,0.2,0.4,0.6. (b). Draw a picture of these risk and returns for w1. (c). What is it called? (d). Draw the picture of (c) when there is a riskless asset. (e). How should an investor choose the optimal investment? Solutions: (a)
(b)
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(c) It is called Efficient Frontier. An efficient frontier represents the limit of how far we can move in a northwest direction and is illustrated in the following figure. There is no investment that dominates a point on the efficient frontier, in the sense that it has both a higher expected return and a lower standard deviation of return. (d)
(e) Every possible combination of the risky assets, without including any holdings of the risk-free asset, can be plotted in risk-expected return space, and the collection of all such possible portfolios defines a region in this space. The left boundary of this region is a hyperbola, and the upper edge of this region is the efficient frontier in the absence of a risk-free asset.
2. (Chapter 1, Practice Questions 14) The return from the market last year was 10% and the risk-free rate was 5%. A hedge fund manager with a beta of 0.6 has an alpha of 4%. What return did the hedge fund manager earn? Solutions:
3. (Chapter 2, Q3)
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(a). How many banks are there in the United States? (b). What is the size of the assets held by these banks? Solutions: (a)&(b)
4. (Chapter 2, slides, Q8) Suppose that there is a severe recession and as a result the bank's loan losses rise by 3.2%of assets, to 4% next year. We assume that other items on the income statement in Table 2.3 are unaffected.
1. (Chapter 1, slides, Q3) Suppose there are two investments.The expected returns from the investments are 10% and 15%, the standard deviation of the returns are 16% and 24%, and the correlation between returns is 0.2.Let w1 be the proportion of wealth put into the first investment. (a). Calculate the expected return and the standard deviation for portfolio w1=0,0.2,0.4,0.6. (b). Draw a picture of these risk and returns for w1. (c). What is it called? (d). Draw the picture of (c) when there is a riskless asset. (e). How should an investor choose the optimal investment? Solutions: (a)
(b)
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(c) It is called Efficient Frontier. An efficient frontier represents the limit of how far we can move in a northwest direction and is illustrated in the following figure. There is no investment that dominates a point on the efficient frontier, in the sense that it has both a higher expected return and a lower standard deviation of return. (d)
(e) Every possible combination of the risky assets, without including any holdings of the risk-free asset, can be plotted in risk-expected return space, and the collection of all such possible portfolios defines a region in this space. The left boundary of this region is a hyperbola, and the upper edge of this region is the efficient frontier in the absence of a risk-free asset.
2. (Chapter 1, Practice Questions 14) The return from the market last year was 10% and the risk-free rate was 5%. A hedge fund manager with a beta of 0.6 has an alpha of 4%. What return did the hedge fund manager earn? Solutions:
3. (Chapter 2, Q3)
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(a). How many banks are there in the United States? (b). What is the size of the assets held by these banks? Solutions: (a)&(b)
4. (Chapter 2, slides, Q8) Suppose that there is a severe recession and as a result the bank's loan losses rise by 3.2%of assets, to 4% next year. We assume that other items on the income statement in Table 2.3 are unaffected.