Читать книгу Risk Management and Financial Institutions - Hull John C. - Страница 17

15. Suppose that one investment has a mean return of 8 % and a standard deviation of return of 14 %. Another investment has a mean return of 12 % and a standard deviation of return of 20 %. The correlation between the returns is 0.3. Produce a chart similar to Figure 1.2 showing alternative risk-return combinations from the two investments.

16. The expected return on the market is 12 % and the risk-free rate is 7 %. The standard deviation of the return on the market is 15 %. One investor creates a portfolio on the efficient frontier with an expected return of 10 %. Another creates a portfolio on the efficient frontier with an expected return of 20 %. What is the standard deviation of the return on each of the two portfolios?

17. A bank estimates that its profit next year is normally distributed with a mean of 0.8 % of assets and the standard deviation of 2 % of assets. How much equity (as a percentage of assets) does the company need to be (a) 99 % sure that it will have a positive equity at the end of the year and (b) 99.9 % sure that it will have positive equity at the end of the year? Ignore taxes.

18. A portfolio manager has maintained an actively managed portfolio with a beta of 0.2. During the last year, the risk-free rate was 5 % and major equity indices performed very badly, providing returns of about −30 %. The portfolio manager produced a return of −10 % and claims that in the circumstances it was good. Discuss this claim.