# Portfolio expected return & risk analysis using crystal Ball

Solve the following exercise using Crystall Ball. Please refer to the attached word document for the instructions.

Erin Jones has $100,000 and, to diversify, she wants to invest equal amounts of $50,000 each in two mutual funds selected from a list of four possible mutual funds. She wants to invest for a three-year period. She has used historical data from the four funds plus data from the market to determine the mean and standard deviation (normally distributed) of the annual return for each fund, as follows:

Fund µ σ

1. Internet .20 .09

2. Index .12 .04

3. Entertainment .16 .10

4. Growth .14 .06

The possible combinations of two investments are (1,2),(1,3),(1,4),(2,3),(2,4), and (3,4).

a. Use Crystal Ball to simulate each of the investment combinations to determine the expected return in 3 years. (Note that the formula for the future value, FV, of a current investment, P, with return, r, for n years in the future is FVn = Pr (1 + r)n . Indicate which investment combination has the highest expected return.

b. Erin wants to reduce her risk as much as possible. She knows that if she invests her $100,000 in a CD at the bank she is guaranteed a return of $20,000 after 3 years. Using the frequency charts for the simulation runs in Crystal Ball determine which combination of investments would result in the greatest probability of receiving return of $120,000 or greater.

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https://brainmass.com/statistics/percentile/portfolio-expected-return-risk-analysis-using-crystal-ball-64976

#### Solution Preview

See the attached file. The text here may not print correctly for tables and symbols. Thanks

There are two ways to do this, either we simulate the return for each year to calculate the overall return for the 3-year period. Else, we can simulate it for just one year and use the same return for the three years. The formula shown above

FVn=Pr(1+r)n indicates that we are looking for one year simulation.

If we are looking for 3 ...

#### Solution Summary

This post illustrates how simulation analysis can be used to build the portfolios with required expected return and risk. Crystal ball software is used for the simulation process. Thus this post provides an opportunity to learn the financial modeling using crystal ball along with the risk return basics for finance.