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QuestionCalculate the expected return rpr_{p} for a portfolio of stocks L (40\%) and M (60\%) over 2013-2018, then find rˉp\bar{r}_{p} and σrp\sigma_{r_{p}}. Discuss 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 stock for each year are given in the table4. The portfolio return for a year is the weighted sum of the returns of the stocks, with the weights being their respective portfolio shares5. The expected value of portfolio returns over the6-year period is the average of the yearly portfolio returns6. The standard deviation of expected portfolio returns over the6-year period is calculated using the standard deviation formula for a sample7. The correlation of returns of the two stocks is characterized qualitatively by observing the trend in their returns over the years

STEP 2

First, we need to calculate the portfolio return for each year. This is done by multiplying the return of each stock by its weight in the portfolio and adding these products.
rp,year=weightL×return,year+weightM×returnM,yearr_{p, year} = weight_L \times return_{, year} + weight_M \times return_{M, year}

STEP 3

Now, plug in the given values for the weights and returns for the year2013 to calculate the portfolio return for that year.
rp,2013=0.×14%+0.6×20%r_{p,2013} =0. \times14\% +0.6 \times20\%

STEP 4

Repeat this calculation for each of the remaining years.

STEP 5

Now that we have the portfolio return for each year, we can calculate the expected value of portfolio returns over the-year period. This is done by adding up the yearly portfolio returns and dividing by the number of years.
rˉp=1∑year=20132018rp,year\bar{r}_{p} = \frac{1}{} \sum_{year=2013}^{2018} r_{p, year}

STEP 6

Now, plug in the calculated values for the yearly portfolio returns to calculate the expected value of portfolio returns.

STEP 7

Now that we have the expected value of portfolio returns, we can calculate the standard deviation of expected portfolio returns over the6-year period. This is done by subtracting the expected value from each yearly return, squaring the result, adding up these squares, dividing by the number of years minus1, and taking the square root.
σrp=15∑year=2013201(rp,year−rˉp)2\sigma_{r_{p}} = \sqrt{\frac{1}{5} \sum_{year=2013}^{201} (r_{p, year} - \bar{r}_{p})^2}

STEP 8

Now, plug in the calculated values for the yearly portfolio returns and the expected value of portfolio returns to calculate the standard deviation of portfolio returns.

STEP 9

To characterize the correlation of returns of the two stocks L and M, observe the trend in their returns over the years. If both stocks tend to go up and down together, they are positively correlated. If one goes up when the other goes down, they are negatively correlated. If there is no clear pattern, they are uncorrelated.

STEP 10

To discuss the benefits of diversification achieved by Jamie through creation of the portfolio, consider the standard deviation of portfolio returns. If this is lower than the standard deviations of the returns of the individual stocks, Jamie has achieved diversification benefits, as his portfolio risk is lower than the risk of the individual stocks.

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