Dollar Cost Averaging

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Overview

As a method of investing money into the market, dollar cost averaging (DCA) is often proposed. Dollar cost averaging involves investing a fixed proportion of your capital in each of n periods. These periods can be monthly, quarterly, etc. The premise of dollar cost averaging is that the investor wants to guard against the market losing value shortly after making his investment. Therefore, he chooses to spread his investment over a number of periods

Since the market has a positive mean rate of return, dollar cost averaging usually requires the investor to give up some expected return for the benefit of reduced variance in their eventual outcome.

The purpose of this analysis is to better understand quantitatively the trade-off between the loss in expected return versus the downside reduction provided. Further, we will explore the idea of how the decision is different depending on the relative valuation of the market at the point of entry.

Analysis

To find answers to these issues, we have collected historical data on the monthly value of the S&P 500 from the period of 70 years (from Jan-1936 to Dec-2005) from Global Financial Data. Against this data, we have applied 6 different investing strategies: Lump Sum, DCA over 2 quarters, DCA over 4 quarters, DCA over 8 quarters, DCA over 12 quarters, and DCA over 16 quarters. The table below shows when the investor will make investments in each strategy.

Table 1: When investors make investments in each strategy
Strategy Investment Periods
Lump Sum Month 1
2 Quarters Month 1, 4
4 Quarters Month 1, 4, 7, 10
8 Quarters Month 1, 4, 7, 10, ..., 22
12 Quarters Month 1, 4, 7, 10, ..., 34
16 Quarters Month 1, 4, 7, 10, ..., 46

We have assumed that the investor is investing $1,000 and will invest an amount of cash at each investment period that is equivalent to (1/n) of his $1,000 where n is the number of quarters over which he is dollar cost averaging. We have chosen to make investments on a quarterly basis (every 3 months) since this is probably easier to manage for an individual investor. Our guess would be that the results based on a monthly investment schedule would be similar.

As a general method for comparing the effectiveness of each strategy, we have examined the investor’s position at the end of a 4 year horizon. Since all strategies will be fully invested at the 4 year mark and will earn the same future rates of return, this allows for a fair comparison amongst the strategies.

Bill Jones performed an analysis in 1996 (see below for a link to it) of the dollar cost averaging problem using monthly investment periods. We like some of his analysis but he fails to compare strategies over the same time horizon which we think is a major flaw in his analysis. However, he does pose the problem in an interesting way: he views the option of using dollar cost averaging as an insurance problem where the investor can buy downside insurance by giving up expected returns.

Jones uses some interesting metrics to demonstrate the value of the insurance (in terms of reduced variance and downside risk) that the investor is buying. We will employ similar metrics to illustrate the differences in the strategies.

Metrics

  • Average Gain – over the 4 year investing horizon (this is the cumulative gain)
  • Standard Deviation – calculated from the average 4 year gain
  • Down Periods – percent of periods where the investment value at the end of 4 years is less than the original $1,000
  • 10% Down Periods – percent of periods where the investment value at the end of 4 years is down at least 10%
  • Average Loss – average of all 4 year losses (when their is a loss)
  • 5% Improvement – percent of periods where the Lump Sum strategy produces a 10% down outcome where the DCA strategy would improve the outcome by at least 5%

Assumptions

  • The un-invested money earns interest at an annual rate of 5%

General Results

Our dataset provides 792 periods with a 4 year horizon of returns. The table below shows the results from this historical data.

  Lump Sum 2 Qrts 4 Qrts 8 Qrts 12 Qrts 16 Qrts
Average Gain (over 4 years) 36% 36% 35% 33% 31% 30%
Standard Deviation 40% 39% 37% 32% 27% 23%
Down Periods 19% 18% 16% 15% 12% 9%
10% Down Periods 11% 10% 10% 9% 7% 4%
Average Loss -16% -16% -16% -14% -13% -10%
5% Improvement NA 0% 7% 28% 43% 59%

As you can see from the results, the investor can reduce the average gain and standard deviation of the gain over the 4 year investing horizon by increasing the period of time over which he employs a DCA strategy. Dollar cost averaging over 16 quarters will reduce the number of down periods from 19% to 9% but will cost the investor 6% in expected return. The reduction in average gain is equivalent to 1.2% on an annual basis. The number of 10% down periods is also substantially reduced from 11% of the periods to 4% of the periods. Additionally, in 59% of the periods where the lump sum strategy will produce a loss of more than 10%, this would be alleviated by at least 5% if the 16 quarter DCA strategy was employed.

It doesn’t seem like any strategy is clearly dominant in this case. The risk preferences of the investor should lead him to choose a strategy that is appropriate.

Smart Dollar Cost Averaging

We think that it is inappropriate to make a decision on whether to DCA (and over what time frame) without at least having a general view on the overall valuation of the market. While incorporating this information does take one into market timing strategies, we think that recognizing periods when the market is sufficiently under-valued or over-valued by historical standards can lead to better decisions.

As a proxy for the relative value of the S&P 500, let’s use the overall index’s P/E ratio at the beginning of each 4 year period. There are plenty of value metrics to use and P/E ratio is definitely not ideal but it does serve to help make decisions in this case. The table below divides the value of the P/E ratio into four intervals and displays the percentage of our total 792 investing periods which had P/E ratios in each interval at the start of the period.

S&P 500 P/E Ratio Percent of Periods
Less than 10 21%
Between 10 and 15 29%
Between 15 and 20 32%
More than 20 18%

Now, let’s look at the results of our general analysis when we filter by the P/E ratio of the S&P 500 at the time of making our initial investment.

Low P/E Ratio (Less than 10) – this occurred in 176 periods

  Lump Sum 2 Qrts 4 Qrts 8 Qrts 12 Qrts 16 Qrts
Average Gain (over 4 years) 58% 58% 56% 51% 46% 41%
Standard Deviation 27% 26% 24% 21% 20% 17%
Down Periods 1% 0% 0% 0% 0% 0%
10% Down Periods 0% 0% 0% 0% 0% 0%
Average Loss -2% NA NA NA NA NA
5% Improvement NA NA NA NA NA NA

In this case, it is clear that the investor would want to move his money into the market quickly. The risk of a negative return on your initial stake over the 4 years is very low. The decision to DCA over 16 quarters rather than invest lump sum would cost the investor 3% in expected annual return. That’s pretty expensive!

Medium-Low P/E Ratio (Between 10 and 15) – this occurred in 248 periods

  Lump Sum 2 Qrts 4 Qrts 8 Qrts 12 Qrts 16 Qrts
Average Gain (over 4 years) 36% 35% 34% 33% 32% 30%
Standard Deviation 37% 35% 32% 29% 25% 20%
Down Periods 17% 17% 12% 12% 11% 8%
10% Down Periods 8% 7% 7% 6% 5% 2%
Average Loss -17% -16% -17% -12% -9% -7%
5% Improvement NA 0% 24% 57% 76% 86%

Here, it is less clear which strategy the investor should adopt. These values are similar to the overall analysis above. The annual lost expected return between the lump sum case and the 16 quarter DCA strategy is 1.2%.

Medium-High P/E Ratio (Between 15 and 20) – this occurred in 249 periods

  Lump Sum 2 Qrts 4 Qrts 8 Qrts 12 Qrts 16 Qrts
Average Gain (over 4 years) 29% 28% 26% 25% 24% 24%
Standard Deviation 43% 42% 40% 33% 28% 22%
Down Periods 24% 23% 24% 19% 15% 10%
10% Down Periods 13% 10% 12% 12% 8% 5%
Average Loss -13% -13% -13% -13% -13% -11%
5% Improvement NA 0% 3% 22% 28% 38%

In this scenario, the options of dollar cost averaging are more appealing. The annual lost expected return between the lump sum case and the 16 quarter DCA strategy is 1.0%. That price does buy significant reduction in standard deviation and the number of down periods are reduced from 24% to 10%. It seems like dollar cost averaging over 16 quarters would be preferable to DCA over 4, 8, or 12 quarters. Therefore, the decision can be reduced to investing quickly (lump sum or 2 quarters) versus long term DCA.

High P/E Ratio (More than 20) – this occurred in 119 periods

  Lump Sum 2 Qrts 4 Qrts 8 Qrts 12 Qrts 16 Qrts
Average Gain (over 4 years) 20% 20% 22% 25% 25% 25%
Standard Deviation 39% 39% 40% 38% 34% 28%
Down Periods 40% 38% 33% 34% 26% 23%
10% Down Periods 29% 28% 29% 20% 18% 13%
Average Loss -18% -19% -21% -18% -17% -12%
5% Improvement NA 0% 0% 17% 37% 63%

Again, we have clarity. The market is most likely over-valued. Thus, the longer horizon DCA strategies will actually boost returns and reduce risk of down periods. It could make sense to DCA for a period longer than 4 years in these situations.

Conclusions

Dollar cost averaging clearly offers investors the ability to limit downside and reduce variance of their returns at the cost of giving up expected returns. When making the decision of whether or over how many periods to DCA, you should ideally form an opinion (based on data) on the relative valuation of the market.

At the time of writing (July 31, 2006), the S&P 500 has an P/E ratio of about 17.5 according to Global Financial Data. Thus, the market seems relatively fairly valued to slightly over-valued according to historical averages. In these types of periods, you should probably consider either moving quickly into the market or dollar cost averaging over a longer horizon.

Useful Links

Do Not Dollar Cost Average for More than 12 Months
An article by Bill Jones found in the Efficient Frontier which poses the dollar cost averaging problem as an insurance option

Lump Sum Beats Dollar Cost Averaging
An analysis published in the Journal of Financial Planning