Simulate Amanda's Portfolio Over the Next 30 Years and Determine

Essay

Simulate Amanda's 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 Amanda's 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).
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Next, suppose Amanda's 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?