Amanda is a recent college graduate, and has just started her first job. She would like to know if she saves 5,000 per year out of her salary over the next 30 years what the distribution of the value of her retirement fund after 30 years. She has decided that she will invest all her money in the stock market that she estimates has a return that is normally distributed with mean 12 per year and standard deviation 25.
Simulate Amandas portfolio over the next 30 years and determine how much she can expect to have in her account at the end of that period. At the beginning of each year, compute the beginning balance in Amandas account. Note that this balance is either 0 (for year 1) or equal to the ending balance of the previous year. The contribution of 5,000 is then added to calculate the new balance. The market return for each year is given by a normal random variable with the parameters above (assume the market returns in each year are independent of the other years). The ending balance for each year is then equal to the beginning balance, augmented by the contribution, and multiplied by (1+Market return).
Next, suppose Amandas broker thinks the stock market may be too risky and has advised her to diversity by investing some of her money in money market funds and bonds. He estimates that this will lower her expected annual return to 10 per year, but will also lower the standard deviation to 10. What is the standard deviation of the ending balance? What does the distribution look like now? What should Amanda infer from this?
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