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 use VFINX as a dollar-cost avaraging example 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.

Date Dividend Close Shares
purchased
Appreciation
on 01/03/07
26-Dec-06 $0.65 $130.43 0.049 6.43
1-Dec-06 $0 $130.59 0.765 -0.58
1-Nov-06 $0 $129.43 0.772 -17.26
2-Oct-06 $0 $127.04 0.787 2.18
22-Sep-06 $0.52 $121.08 0.032 4.23
1-Sep-06 $0 $123.04 0.812 5.51
1-Aug-06 $0 $120.48 0.830 7.75
3-Jul-06 $0 $117.7 0.849 10.29
23-Jun-06 $0.48 $114.6 0.021 2.76
1-Jun-06 $0 $116.99 0.854 10.96
1-May-06 $0 $117.33 0.852 10.64
3-Apr-06 $0 $120.83 0.827 7.44
17-Mar-06 $0.49 $120.35 0.010 1.33
1-Mar-06 $0 $119.24 0.838 8.87
1-Feb-06 $0 $118.26 0.845 9.77
3-Jan-06 $0 $117.96 0.847 10.05

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.

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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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13 Responses to “Dollar-Cost Averaging: For Higher Return or for Lower Risk?”

  1. Jeremy |  Jan 12, 2007 at 11:54 am

    As always, great visual representation.

    The only argument I have is that while monthly DCA may lag slightly behind in total returns and risk, it is still simply the easiest way to save. If you don’t use some form of DCA, how do you invest?

    If you contribute 4k to your IRA every year and don’t make small systematic purchases how do you invest this money? Do you save what would be a monthly contribution in a savings account until the end of the year and make that lump deposit? What happens if you make your 4k deposit on December 31 each year for 5 years. What if the market reaches a peak each of those years right around when you make your deposit and then subsequently pulls back? In this case you will be worse off than if you made monthly contributions.

    Then it all comes down to emotional investment decisions. When you make small regular contributions you likely don’t even think twice about market conditions. But when you’ve been saving up money for a whole year and suddenly have to invest this larger chunk of cash, you will undoubtedly be a little more focused on your decision.

    Clearly we would all like to be given a very large sum of money to throw into the market all at once and let time and compounding do its thing, but unfortunately that isn’t life. If you do have a large chunk of money to invest, obviously it wouldn’t make sense to use DCA, but most people are not faced with that scenario.

    Anyway, sorry I’m just throwing this out there for the sake of generating discussion. I know that DCA is commonly advertised as a great way to reduce risk, but like your results show it may not actually be the case. My argument for DCA is that most people have to use this method to invest anyway, and those who don’t and rely on waiting to make less frequent larger sum investments will have an emotional or market timing factor that can’t be shown in raw data.

    Oh, and your site tells me I’m not using firefox, but I am :)

  2. Jonathan |  Jan 12, 2007 at 3:29 pm

    I’m also using Firefox and it’s telling me I’m not :)

    Hmm… those std dev numbers look really different between 1-month and 1-year. Once/If I find time this weekend I will do this too and we can compare numbers. Thanks for doing this by the way.

  3. mikealao |  Jan 12, 2007 at 4:52 pm

    John R. Knight and Lewis Mandell, “Nobody Gains from Dollar Cost Averaging: Analytical, Numerical, and Empirical Results,” Financial Services Review, 2(1) 1993, pp. 51-61. “Our results strongly imply that the additional cost and effort associated with Dollar Cost Averaging cannot be justified for any investor, regardless of degree of risk aversion. With the possible exception of its promoters, nobody gains from Dollar Cost Averaging.”

  4. Liz |  Jan 14, 2007 at 11:10 am

    Dovetailing on Jeremy’s comment: For most people, the true comparison is between DCA and LS at the end of the year, not DCA and LS at the beginning of the year. Assuming I intend to put aside 30% of my income towards investments, I do not have these funds available on January 1st, or even January 31st. In order to contribute LS, I would have to wait until 4th quarter to accrue the necessary funds. In this scenario, I am better served with DCA. However, if a significant portion of my income comes from a bonus paid early in the year, your analysis illustrates that I am best served by putting my bonus towards the 30% investment goal.

  5. The Sun |  Jan 15, 2007 at 4:18 pm

    Liz: First about the time to do the comparison. The data I used were from January 1988 to January 2007 and returns I calculated were from January 1989 to January 2007, one year after the investments (1-month and 1-year plan) began. Since I only downloaded weekly data instead of daily (that would be too much to process), the first day of the current year is almost the same as the last day of the previous year. And because every plan used the same time frame, there shouldn’t be a difference as far as the results are concerned.

    I agree with your conclusion one will be better served to start investing right away using DCA instead of saving the money and making a LS investment at the end of the year and that’s the conclusion from my previous post where I compared 1-month DCA at the beginning of the year and 1-year LS at the end of the year and the 1-year LS scheme lagged quite significantly. Actually, in addition to the comparison between DCA and LS, one main conclusion I got is that we shouldn’t delay investing for whatever reason, including “don’t have enough fund for a lump sum investment.” If that’s the case, just use DCA.

  6. Duane Gran |  Jan 16, 2007 at 12:55 pm

    My impression of DCA is that it is better thought of as a useful habit than an optimal investment strategy. Consider for a moment the alternative. We all know the advice from Buffet and his cohorts to be a contrary investor — which means to buy when others are selling — but it is emotionally taxing to throw a lump sum into the market when the popular press and your neighbor are all gloomy about investing.

  7. The Sun |  Jan 18, 2007 at 10:57 pm

    Duane: I agree with you that for small investors, DCA makes more sense emotionally than financially as we all don’t want to lose money in the short term. Though 20 or 30 years from now our worry may prove to be unnecessary, it’s hard to see what it will be that far away. As you said, with DCA, we can develop a good habit of investing a small amount continuously without even trying to figure out what the market will be tomorrow. With that alone, we can sleep well in the evening.

  8. mike |  Feb 28, 2007 at 4:39 pm

    Excellent analysis. But isn’t the conclusion simply the result of investing as early as possible in a fund that rose in value 80% of the time (16 years out of 20)? DCA allows people with jobs and regular pay checks to do just that. Unless you can find some trust-fund baby to lend you all the money interest-free at the beginning of each year…

  9. The Sun |  Feb 28, 2007 at 5:28 pm

    Actually, as you said, the conclusion is to start investing as early as possible. The amount I used in the analysis is quite small ($100 a month, or $1200 a year), so it won’t become a problem for people who want to invest. And in this case, $1200 shouldn’t an amount that too difficult to come up with. If the fund is available, then making a lump sum investment at the beginning is better than putting $100 every month. On the other hand, if the money isn’t available, then using DCA is a better choice than saving the money to invest. Of course, a lump sum at the beginning of the year works better in up markets, as we saw in the past 20 years. For the long-term, we should invest as early as we can and as much as we can.

  10. Inclement |  Mar 14, 2007 at 11:00 pm

    This quote from the footnote of the Knight, Mandell, 1993 paper cited above helped me:

    Thus, we take care not to confuse Dollar Cost Averaging with periodic investing where the
    investor puts aside a regular amount of savings each period to invest in risky securities. Periodic
    investment of savings as funds become available is a Buy and Hold strategy and has the
    additional positive attribute of encouraging habitual savings, a characteristic not shared by
    Dollar Cost Averaging.

    They define and analyze DCA as having all assets (say $100K) in a risk-less investment (T-bills) up front, and investing only small amounts each month for a holding period of 10 years until they reach their asset allocation target.

    That’s not the same as NOT having all $100K up front and buying as you go. The paper says that Optimal Rebalancing produces the best results. You can achieve this with periodic investment by buying each month enough stocks, bonds, and cash so as to maintain your desired asset allocation (which is based on the risk you can tolerate). Since stocks will (most of the time) outpace bonds and cash, you may end up buying more of the latter each month.

    That’s periodic investing + rebalancing in the real world.

  11. The Dividend Guy |  Oct 05, 2007 at 8:59 am

    Sun – thanks for the analysis. I appreciate seeing this and learned some things from it.

    The only other comment I would make is that often, we as investors try to over-analyze things and complicate things. At the end of the day, what will matter is that people are invested in a diversified portfolio and make regular contributions as money comes available. If faced with the choice of LS vs. DCA, then LS wins, but to keep things simple and easy, often a regular investment plan is just easier to do.

    Thanks again for the analysis!

    The Dividend Guy

  12. Chad @ Sentient Money |  Jun 10, 2008 at 9:33 am

    I couldn’t agree more. I don’t use DCA and never will. I also don’t use index funs or many funds at all. DCA and index funds are fine if you want to retire when you are 65, but I would prefer to have some real health left and shot for 10-15 years earlier.

  13. Sun |  Jun 10, 2008 at 9:38 pm

    Chad: Right, DCA and index funds are slow, steady ways to build up investments. Though it seems DCA may not be such a good idea in the long-term, I am still using it to buy most of my funds. Then again, I also have a lot of active funds that I hope can generate better returns :)