The variance is the average squared difference between which of the following? Multiple Choice Actual return and average return Actual return and (average return + N - 1) Actual return and the real return
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It is calculated by taking the average of the squared differences from the mean. Show more…
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Akash M.
The last four years of returns for a stock are as follows: 1 2 3 4 -4% +28% +12% +4% What is the average annual return? What is the variance of the stock's returns? (Answer: 0.018667) What is the standard deviation of the stock's returns?
The rate of return of an asset is the change in price divided by the initial price (denoted as $r$ ). Suppose that $\$ 10,000$ is used to purchase shares in three stocks with rates of returns $X_{1}, X_{2}, X_{3}$. Initially, $\$ 2500, \$ 3000,$ and $\$ 4500$ are allocated to each one, respectively. After one year, the distribution of the rate of return for each is normally distributed with the following parameters: $\mu_{1}=0.12, \sigma_{1}=0.14, \mu_{2}=0.04, \sigma_{2}=0.02, \mu_{3}=0.07, \sigma_{3}=0.08$ (a) Assume that these rates of return are independent. Determine the mean and variance of the rate of return after one year for the entire investment of $\$ 10,000$. (b) Assume that $X_{1}$ is independent of $X_{2}$ and $X_{3}$ but that the covariance between $X_{2}$ and $X_{3}$ is $-0.005 .$ Repeat part (a). (c) Compare the means and variances obtained in parts (a) and (b) and comment on any benefits from negative covariances between the assets.
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