Part 1: Market Timing This question explores uncertainty in investing. Assume you plan to invest in a broad-based equity index. You start with a zero balance account. Each year, you plan to contribute an extra $10,000 at year-end. (Assume annual compounding and uncorrelated market returns from year to year.) a. If you invest (and contribute) for 30 years and the equity index return each year is normally distributed with expected return of 10% and standard deviation 20% (i.e., a different realized return each year), what is the expected value of your investment account in 30 years (just after your last payment)? b. What is the likelihood that you end up with less than $600,000 in 30 years (i.e., twice what you contributed)? c. How does the expected balance and likelihood change if you move your money to cash in years where the realized index return in the previous year was negative? (Note: You still make a contribution to your account every year, but your allocation to the market is zero in years where the prior year realized market return was negative.) d. Let's explore the assumption of uncorrelated market returns. The accompanying spreadsheet provides annual realized market excess returns. Run the following regression of current year returns on last-year returns (you'll need to lag the returns one year to form the x-variable): Rmkt=a+PR+ E