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Chapter B.2, Problem 16AYU

Investment Risk Investors not only desire a high return on their money, but they would also like the rate of return to be stable from year to year. An investment manager invests with the goal of reducing volatility (year-to-year fluctuations in the rate of return). The following data represent the rate of return (in percent) for his mutual fund for the past 12 years.

Chapter B.2, Problem 16AYU, Investment Risk Investors not only desire a high return on their money, but they would also like the

  1. (a) Verify that the data are normally distributed by constructing a normal probability plot.
  2. (b) Determine the sample standard deviation.
  3. (c) Construct a 95% confidence interval for the population standard deviation of the rate of return.
  4. (d) The investment manager wants to have a population standard deviation for the rate of return below 6%. Does the confidence interval validate this desire?
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8 (Correlation and Diversification) Assume we have two stocks, A and B, show that a particular combination of the two stocks produce a risk-free portfolio when the correlation between the return of A and B is -1.
9 (Portfolio allocation) Suppose R₁ and R2 are returns of 2 assets and with expected return and variance respectively r₁ and 72 and variance-covariance σ2, 0%½ and σ12. Find −∞ ≤ w ≤ ∞ such that the portfolio wR₁ + (1 - w) R₂ has the smallest risk.
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