Wednesday, March 14, 2007

Examples of "Dollar Cost Averaging on Steroids"

From comments it sounds like a couple of examples might serve to further explain my previous post about taking advantage of volatility.

Let's take a simple example. Say you have $2000 and want to allocate it 50% to bonds and 50% to stocks. Using index funds, you buy 100 shares of each at $10/share. Now, apply a long term average return. I use 0.7% per month, or about 8.5% per year. That means, on average, you would expect after one month each fund would appreciate 0.7% to $10.07share. But because of volatility ( and assuming they are completely correlated) in the market the price goes to $9/share after one month. You would purchase the difference for each fund, buying 11.19 shares at $9/share. You now own 111.19 shares(100+11.19) of each fund. Now, assume after another month the share prices return to $10/share. Each fund would now be worth $1111.90 (111.19 x 10), but you would have invested only $1100.7 in each, and the market is exactly where it was when you started. Voila, you make about 1% in a flat market by taking advantage of the volatility. Since you make this in 2 months, your annualized return in this flat market is over 6%. And, it works the same way for upside volatility.

Let's take an example for the upside. Assume the same starting point, but then assume after the first month the market is up 10% . You would sell the difference between your assumed value($1007) and the actual value($1100), ie 8.45 shares at $11/share. You now have 91.55 shares. Again, assume the price goes back to $10/share after the second month. You now have $915.5 and have invested only $907 . Again, a return of almost 1% in a flat market. And , this is with perfectly correlated investments, which would eliminate the advantage for normal rebalancing. To the extent markets are not correlated, the returns would improve, as with the usual rebalancing methods.

This will always improve your returns if the market is up less than your money market rate, as well as when the market is up more than the money market, assuming there is significant volatility. The only conditions in which your returns will be less than the market are when the market goes up steeply with little volatility. I have been using this method for over ten years and tracking the results. Only 2 of those years have I underperformed the average of the markets I'm in, and on average I've beat the market averages by 1-2% per year.

Now about the spreadsheet. My spreadsheet is fairly complex, as I've added features over the years to allow me to track the performance of each fund, the average of all funds and my actual results, both numerically and graphically. All the above seems a little complicated, but with a spreadsheet it is easy. All you need to do is start with your allocations across the top row and write a formula on the row below which multiplies the balance above by (1 + your long term assumed return) for the period. For the example above, that would be 1.007. Now, on the next sheet, enter your actual values each period. On a third sheet, write a formula which calculates the difference between the two. This is the amount you would buy and sell each period. Then, all you have to do each period is enter the actual values of each fund and buy or sell the amounts automatically calculated on the third sheet.

I should mention that I do this in my 401K, so there are no tax implications. And, I use no load index funds, so there are no transaction costs.

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