Dollar-Cost Averaging: For Higher Return or for Lower Risk?

In the past couple of days, I did some further study on VFINX after I took a look at the market value and shares owned at the beginning of 2007 if I started investment in January 1988 with four different investment schemes (here’s the previous post). In this study, I want to find out the annual return for each investment plans from January 1988 to January 2007 and consider the risk of each plan by comparing the annual performance against S&P 500 during the same period.

One argument I heard about using dollar-cost-averaging (DCA) instead of lump sum (LS) is that DCA can buy you peace of mind. Since you are investing a fixed small amount of money regularly, you are not trying to figure out when is a good time to buy (i.e., you are not trying to time the market). By investing regularly, you effectively ignore the short-term market fluctuation. Over long-term, DCA can reduce your risk. According to Investopedia.com, risk is defined as

The chance that an investment’s actual return will be different than expected. This includes the possibility of losing some or all of the original investment. It is usually measured by calculating the standard deviation of the historical returns or average returns of a specific investment.

When investing in funds like VFINX, which tracks S&P 500, we expect our returns to be close to the performance of S&P 500. However, with the four investment plans as I used in the previous post, the performances are different as compared to S&P 500. The question is how different are they?

Return

Here I still use the four investment schemes as I used in the last study and make first purchase of the year for all plans on the first trading day of January. For 2006, the 1-month DCA plan made the following purchases on the first trading day of each month.

All dividends are reinvested and the number of shares purchased with each distribution is calculated as

No. of shares = (Current no. of shares) * (Dividend per share) / (Close price)

For example, on March 17, 2006, there was dividend distribution of $0.49/share. At that time, the total number of shares I owned were (0.847+0.845+0.838) = 2.53 shares. Thus, the number of shares I added from this distribution was 2.53 * 0.49 / 120.35 = 0.0103 shares. For other distributions throughout the year, as I accumulated more shares, the number of shares I obtained from dividend distribution became bigger, and the last dividend distribution on December 26, 2006 was the largest of the year.

The close price of VFINX on January 3, 2007 is $129.82 and this is the price that I use to calculate the appreciation of each purchase I made. For example, I bought 0.847 shares on January 3, 2006 at $117.96. On January 3, 2007, these 0.847 shares appreciated 0.847 * (129.82 - 117.96) = 10.0454 dollars. Those shares purchased from dividend distribution will add net gains to the return since I didn’t spend money to make the purchases. Thus, the 0.0103 shares from March 17, 2006 dividend distribution will add a net gain of 0.0103 * 129.82 = 1.3371 dollars.

The summation of last column (Appreciation on 01/03/07) of the above table is the net market value appreciation of $80.37 for 2006 and I paid $1,200 to get the gain. Therefore, for 2006, the annual return of my 1-month DCA investment plan is 80.37 / 1200 * 100% = 6.70%. That’s right. If I buy $100 of VFINX on the first day of every month, I only have an annual return of 6.70%.

Using the same method, I calculated the annual returns for four different investment schemes from 1988 to 2007, which are shown in the following plot.

The annual returns of S&P 500 from 1998 to 2007 are calculated as

S&P annual return = ((S&P on the 1st day of this year) - (S&P on the 1st day of last year)) / (S&P on the 1st day of last year)

From my calculation, only the 1-year investment scheme has performance that matches S&P 500 over the past 19 years (the slight higher return is due to dividend reinvestment). The plan that I am using right now for all my mutual funds investments, 1-month DCA, actually has the worst performance among the four DCA plans that I considered in the study. For 1-month DCA, it only beat others when there was a year-over-year decline of S&P, but that only happened four times from 1988 to 2007.

Risk

So instead of giving a return that matches the broad market (even though I invested in a fund that tracks the market), I got far inferior performance by investing $100 every month. Then, what about risk? People always say that to get a higher return, you have to take a greater risk. Since I got lowest return with 1-month DCA, the risk should also be the lowest among the four plans. To measure the risk involved in each plan, I calculated the standard deviation of each of them using the annual returns of S&P 500 from 1988 to 2007 as the expected returns. Standard deviation, according to Morningstar,

is a statistical measure of the range of a fund’s performance. When a fund has a high standard deviation, its range of performance has been very wide, indicating that there is a greater potential for volatility.

Thus, with the standard deviation, I can tell how much each investment scheme is away from the expected return that we can get by investing in an index fund such as VFINX. A higher standard deviation means higher volatility and, thus, higher risk.

Well, when I saw the results of my calculation, it didn’t really surprise that the 1-month DCA plan, which is supposed to help me reduce risk, came out with the highest standard deviation. This can be clearly observed from the return picture as the performance of the 1-month DCA plan is usually far away from the index. The above figure shows that the longer the investment frequency (12 months is the longest investment period), the lower the standard deviation.

Conclusions

The main conclusion from my study is that one widely used investment plan, monthly DCA, may not be as good as we have thought. It seems that it neither can provide higher return, no can it reduce risk. Though my study with this single fund may not be thorough and the way I calculated the returns and risk may be flawed (please do let me know if you find something that’s not right so this post won’t be misleading), it is at least indicative. What causes the lackluster performance of the 1-month DCA plan is not just that the shares we purchased later in the year became more and more expensive in a up market as we have experienced most of the time of the past 19 years, the returns from dividend distribution were also much lower than what we could otherwise receive with a LS purchase at the beginning of the year as only a small portion of the annual investment earns the full year dividend.

Maybe it’s time for a change.

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