Question

Financial Managers, Inc., buys and sells a large number of stocks routinely for the various accounts that it manages. Portfolio manager Andrea Colson has asked for your assistance in the analysis of the Johnson Fund. A portion of this portfolio consists of 10 shares of stock A and 8 shares of stock B. The price of A has a mean of 10 and a variance of 16, while the price of B has a mean of 12 and a variance of 9. The correlation between prices is 0.3. a. What are the mean and variance of the portfolio value? b. Andrea has been asked to reduce the variance (risk) of the portfolio. She offers to trade the 10 shares of stock A and receives two offers, from which she can select one: 10 shares of stock 1 with a mean price of 10, a variance of 25, and a correlation with the price of stock B equal to -0.2; or 10 shares of stock 2 with a mean price of 10, a variance of 9, and a correlation with the price of stock B equal to +0.5. Which offer should she select?

          Financial Managers, Inc., buys and sells a large number of stocks routinely for the various accounts that it manages. Portfolio manager Andrea Colson has asked for your assistance in the analysis of the Johnson Fund. A portion of this portfolio consists of 10 shares of stock A and 8 shares of stock B. The price of A has a mean of 10 and a variance of 16, while the price of B has a mean of 12 and a variance of 9. The correlation between prices is 0.3.

a. What are the mean and variance of the portfolio value?
b. Andrea has been asked to reduce the variance (risk) of the portfolio. She offers to trade the 10 shares of stock A and receives two offers, from which she can select one: 10 shares of stock 1 with a mean price of 10, a variance of 25, and a correlation with the price of stock B equal to -0.2; or 10 shares of stock 2 with a mean price of 10, a variance of 9, and a correlation with the price of stock B equal to +0.5. Which offer should she select?

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Financial Managers, Inc., buys and sells a large number of stocks routinely for the various accounts that it manages. Portfolio manager Andrea Colson has asked for your assistance in the analysis of the Johnson Fund. A portion of this portfolio consists of 10 shares of stock A and 8 shares of stock B. The price of A has a mean of 10 and a variance of 16, while the price of B has a mean of 12 and a variance of 9. The correlation between prices is 0.3.

a. What are the mean and variance of the portfolio value?
b. Andrea has been asked to reduce the variance (risk) of the portfolio. She offers to trade the 10 shares of stock A and receives two offers, from which she can select one: 10 shares of stock 1 with a mean price of 10, a variance of 25, and a correlation with the price of stock B equal to -0.2; or 10 shares of stock 2 with a mean price of 10, a variance of 9, and a correlation with the price of stock B equal to +0.5. Which offer should she select?

Added by Frank M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jon Southam

10/21/2022

Step 1

- Mean of stock A = 10, number of shares = 10 - Mean of stock B = 12, number of shares = 8 \[ \text{Mean of portfolio} = (10 \times 10) + (12 \times 8) = 100 + 96 = 196 \] Show more…

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Financial Managers, Inc., buys and sells a large number of stocks routinely for the various accounts that it manages. Portfolio manager Andrea Colson has asked for your assistance in the analysis of the Johnson Fund. A portion of this portfolio consists of 10 shares of stock A and 8 shares of stock B. The price of A has a mean of 10 and a variance of 16, while the price of B has a mean of 12 and a variance of 9. The correlation between prices is 0.3. a. What are the mean and variance of the portfolio value? b. Andrea has been asked to reduce the variance (risk) of the portfolio. She offers to trade the 10 shares of stock A and receives two offers, from which she can select one: 10 shares of stock 1 with a mean price of 10, a variance of 25, and a correlation with the price of stock B equal to -0.2; or 10 shares of stock 2 with a mean price of 10, a variance of 9, and a correlation with the price of stock B equal to +0.5. Which offer should she select?

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Transcript

00:01 So we have a fund manager who is managing a portfolio.

00:06 That consists of 10 shares of stock a, 10 shares of stock a and eight shares of stock b.

00:13 And the price of a is a mean of 10 and a variance of 16.

00:18 And stock b is a mean of 12 and a variance of nine.

00:22 And the correlation between those prices is 0 .3.

00:26 So we're going to find the mean and variance of the portfolio.

00:29 So let's first find the total.

00:32 The portfolio.

00:34 Well, that's going to be the number of shares times the mean.

00:37 So, because generally need to get a value.

00:39 So if the means 10, we have 10 of them.

00:42 It's going to be 100 plus 8 times 12, which is 96.

00:48 So the total value of our portfolio is $196, we'll say.

00:57 And then let's see, we need to find the weights.

01:03 So the weight of each stock is going to be by the total value of the stock divided by the value of the portfolio.

01:09 So the weight will be for the for a will be 100 over 186 and then to figure out this value would just do one minus 100 one 86 or you could do 96 over 196.

01:25 So the same thing with that.

01:27 Those are weights so because the mean of the portfolio is given as the the weight of a plus or time excuse me the the the mean of the of a and we're going to add to it the weight of b times the mean of b and we get the we do the appropriate multiplications and we get this 10 .979 and the variance is equal to the weight of a times the standard deviation or the square well sorry it's variance you should say of a we're told the variance so the weight is just you literally square the weight right here, take that number and you square it.

02:18 So it would be 0 .51 squared times 16 in this case.

02:24 And then we add to it the weight of b squared times the variance of b squared.

02:29 And then we're going to add to this two times the correlation r between a and b times the standard deviation of a times the standard deviation of b.

02:40 And the way you get the standard deviation is you take the square root of the variance...

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