QuestionJamie Wong's portfolio has stocks L (40%) and M (60%). Calculate expected return, average return, std. dev., correlation, and diversification benefits.

Studdy Solution

STEP 1

Assumptions1. Stock L represents40% of the portfolio's value. Stock M represents60% of the portfolio's value3. The expected returns for each year and for each stock are given in the table4. We assume that the returns are independent from year to year5. We assume that the portfolio is rebalanced each year to maintain the40%-60% split

STEP 2

First, we need to calculate the expected portfolio return, $r_{p}$ , for each of the6 years. The expected portfolio return is a weighted average of the returns of the individual stocks, where the weights are the proportions of the portfolio's value that each stock represents.
$r_{p} = w_{} \cdot r_{} + w_{M} \cdot r_{M}$ where $w_{}$ and $w_{M}$ are the weights of stocks L and M respectively, and $r_{}$ and $r_{M}$ are the returns of stocks L and M respectively.

STEP 3

Now, plug in the given values for the weights and returns for each year to calculate the portfolio return for each year.
For example, for the year2013 $r_{p,2013} =0. \cdot0.14 +0.6 \cdot0.20$ Repeat this calculation for each of the6 years.

STEP 4

Next, we need to calculate the expected value of portfolio returns, $\bar{r}_{p}$ , over the6-year period. This is simply the average of the portfolio returns for each year.
$\bar{r}_{p} = \frac{1}{n} \sum_{i=1}^{n} r_{p,i}$ where $n$ is the number of years (6 in this case), and $r_{p,i}$ is the portfolio return for year $i$ .

STEP 5

Now, plug in the calculated portfolio returns for each year to calculate the expected value of portfolio returns.
For example $\bar{r}_{p} = \frac{1}{} (r_{p,2013} + r_{p,2014} + r_{p,2015} + r_{p,201} + r_{p,2017} + r_{p,2018})$

STEP 6

Next, we need to calculate the standard deviation of expected portfolio returns, $\sigma_{r_{p}}$ , over the6-year period. The standard deviation is a measure of the variability or dispersion of a set of values.
$\sigma_{r_{p}} = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (r_{p,i} - \bar{r}_{p})^2}$ where $n$ is the number of years (6 in this case), $r_{p,i}$ is the portfolio return for year $i$ , and $\bar{r}_{p}$ is the expected value of portfolio returns.

STEP 7

Now, plug in the calculated portfolio returns and expected value of portfolio returns for each year to calculate the standard deviation of expected portfolio returns.
For example $\sigma_{r_{p}} = \sqrt{\frac{1}{5} ((r_{p,2013} - \bar{r}_{p})^2 + (r_{p,2014} - \bar{r}_{p})^2 + (r_{p,2015} - \bar{r}_{p})^2 + (r_{p,2016} - \bar{r}_{p})^2 + (r_{p,2017} - \bar{r}_{p})^2 + (r_{p,201} - \bar{r}_{p})^2)}$

STEP 8

To characterize the correlation of returns of the two stocks L and M, we need to look at how the returns of the two stocks move in relation to each other. If the returns move in the same direction, they are positively correlated. If they move in opposite directions, they are negatively correlated. If there is no consistent pattern, they are uncorrelated.

STEP 9

The benefits of diversification achieved by Jamie through creation of the portfolio can be discussed in terms of the reduction in risk. By investing in two stocks that are not perfectly correlated, Jamie is able to reduce the portfolio's risk compared to investing in a single stock. This is because the returns of the two stocks do not move perfectly together, so a poor return from one stock may be offset by a good return from the other.

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