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

question 47

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 can she expect to have in her account after thirty years under this investing strategy?

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Definitions:

Periodic Interest Rate

The rate of interest charged on a loan or earned by an investment for a duration that is less than one year.

Annuity

An economic scheme that delivers a constant payment stream to a recipient, predominantly utilized in preparing for retirement.

Payment Interval

The frequency with which a recurring payment is made, such as monthly or annually.

Ordinary General Annuity

An annuity where payments are made at the end of each period, such as monthly or annually, in contrast to at the beginning.