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.