Question

A portfolio is invested 20 percent in stock A, 50 percent in stock B, and 30 percent in stock C. Assuming the returns are normally distributed, what is the 68 percent probability range of returns for any given year?

State of Economy. Probability of State of Economy. Stock A. Stock B. Stock C
Boom .15 .18 .13 .15
Normal .75 .13 .09 .12
Recession .10 -.25 .02 -.20
A.) -3.89 percent to 15.77 percent
B.) -3.89 percent to 22.32 percent
C.) 2.66 percent to 15.77 percent
D.) 2.66 percent to 22.32 percent
E.) 6.55 percent to 15.77 percent

Answer 1

The 68% probability range of returns for the given portfolio is approximately -0.72% to 7.38%.

Step-by-step explanation:

To find the range of returns for a portfolio, we need to consider the range of returns for each individual stock and their respective weights in the portfolio. The returns for each stock are normally distributed.

1. For stock A, the 68% probability range of returns is -3.89% to 15.77%.
2. For stock B, the 68% probability range of returns is -25% to 0.13%.
3. For stock C, the 68% probability range of returns is -0.20% to 0.02%.

Now, we can calculate the overall range of returns for the portfolio. Using the portfolio weights (20% for stock A, 50% for stock B, and 30% for stock C), we can combine the individual ranges to find the overall range.

20% * (-3.89%) + 50% * (-25%) + 30% * (-0.20%) = -0.72%

20% * 15.77% + 50% * 0.13% + 30% * 0.02% = 7.38%

Therefore, the 68% probability range of returns for the portfolio is approximately -0.72% to 7.38%. The closest option is A) -3.89 percent to 15.77 percent.

Answer 2

To determine the 68 percent probability range of returns for the portfolio, one must calculate the expected return for each stock, weight these by the portfolio allocation, and sum them up. The normal distribution properties are then used to calculate the standard deviation and establish the confidence interval.

Step-by-step explanation:

The question pertains to finding the expected return of a portfolio invested in three different stocks, with each stock having a different percentage of investment and different rates of return based on the state of the economy. It involves using probability theory to calculate the weighted average expected return, and then applying the properties of a normal distribution to find the 68 percent probability range of returns for a given year.

To calculate the expected return (E[R]) of the portfolio:

1. Calculate the expected return for each stock by multiplying the returns by their respective probabilities and summing them up.
2. Multiply each stock's expected return by the percentage of the portfolio it represents.
3. Sum up the products from step 2 to get the overall portfolio expected return.

The next step is to apply the standard deviation of the portfolio returns to establish the 68% confidence interval, assuming a normal distribution of returns.A