Dollar cost averaging involves investing a fixed amount at fixed intervals of time. It is different from investing at fixed intervals based on your income (such as committing yourself to investing a fixed amount of your salary every month toward your retirement). With dollar cost averaging, you invest a lump sum that you currently have over a fixed time interval, as opposed to, investing everything at once. For example, if you had $12,000 that you wanted to invest in a stock index fund, you would invest $1000 per month over a year, rather than investing the whole amount immediately. The rationale is that market volatility should then work in your favor, because you will automatically be purchasing more shares when the price is low, and fewer shares when the price is high.

0. Malkiel and French argue that dollar cost averaging may reduce risk during downturns and reduce regret that the investor may experience. We will empirically assess these claims in the following questions:

   5. 5) Suppose you have $1200 to invest. You can invest the full amount ($1200) at the beginning of each year, or invest $100 beginning of each month over the same year. Compute what your returns would have been under the two strategies for each year from 1927 to 2012. You can transform the data in Excel using PIVOT tables. Plot the differences in returns between the lump-sum and dollar cost averaging strategies over time. Are there particular years when the dollar cost averaging strategy does better?

   6. 6) In the previous question, we have examined the historical record which only provides 85 unique non-overlapping one year observations. To assess the argument that dollar cost averaging reduces risk in downturns and investor regret, we need a distribution of one year returns. We can simulate returns as described in Chapter 5 of BKM. First, simulate a series of monthly returns for the stock market assuming a normal distribution. You can use NORMINV and RAND functions in Excel. NORMINV(RAND(),historical mean, historical std deviation) would provide a simulated return drawn from a normal distribution with the specified mean and std deviation. Cumulative 1 year return on a $1200 lump-sum investment would be $1200*(1+simulated rate1)*(1+simulated rate2)*.....*(1+simulated rate12) -$1200 . For the dollar cost averaging strategy, the return would be: $100*(1+simulated rate1) + ($100 + $100*(1+simulated rate1) )* (1+simulated rate2) + .... -$1200. Compute 5,000 of these 1 year returns for the two strategies.