Suppose you are going to invest equal amounts in three stocks. The annual return from each stock is normally distributed with mean 0.01 (1%) and standard deviation 0.06. The annual return on your portfolio, the output variable of interest, is the average of the three stock returns. Run @RISK, using 1000 iterations, on each of the following scenarios.

a. The three stock returns are highly correlated. The correlation between each pair is 0.9.

b. The three stock returns are practically independent.

The correlation between each pair is 0.1.

c. The first two stocks are moderately correlated. The correlation between their returns is 0.4. The third stock’s return is negatively correlated with the other two. The correlation between its return and each of the first two is – 0.8.

d. Compare the portfolio distributions from @RISK for these three scenarios. What do you conclude?

e. You might think of a fourth scenario, where the correlation between each pair of returns is a large negative number such as –0.8. But explain intuitively why this makes no sense. Try running the simulation with these negative correlations to see what happens.