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 andeach of the first two is 20.8.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 20.8. But explain intuitively why this makes no sense. Try to run thesimulation with these negative correlations and see what happens.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Suppose you are going to invest equal amounts in three stocks. The annual return from each stock is
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
each of the first two is 20.8.
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 20.8. But explain intuitively why this makes no sense. Try to run the
simulation with these negative
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