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Summary

Dollar-cost averaging (DCA) versus lump sum investing (LSI) is often a difficult decision fraught with emotion.
The historical and theoretical evidence contradicts the notion that DCA leads to better results from a return perspective, and only some measures of risk point to benefits in DCA.
Rather than holding cash while implementing DCA, employing a risk managed strategy can lead to better DCA performance even in a muted growth environment.
Ultimately, the best solution is the one that gets an investor into an appropriate portfolio, encourages them to stay on track for their long term financial goals, and appropriately manages any behavioral consequences along the way.

Dollar-cost averaging (DCA) is the process of investing equal amounts into an asset or a portfolio over a period of time at regular intervals. It is commonly thought of as a way to reduce the risk of investing at the worst possible time and seeing your investment immediately decline in value.

The most familiar form of dollar-cost averaging is regular investment directed toward retirement accounts. A fixed amount is deducted from each paycheck and typically invested within a 401(k) or IRA. When the securities in the account decline in value, more shares are purchased with the cash, and over the long run, the expectation is to invest at a favorable average price.

For this type of dollar-cost averaging, there is not a lot of input on the investor’s part; the cash is invested as it arrives. The process is involuntary once it is initiated.

A slightly different scenario for dollar-cost averaging happens when an investor has a lump sum to invest: the choice is to either invest it at once (“lump-sum investing”; LSI) or spread the investment over a specified time horizon using DCA.

In this case, the investor has options, and in this commentary we will explore some of the arguments for and against DCA with a lump sum with the intention of reducing timing risk in the market.

The Historical Case Against Dollar-Cost Averaging

Despite the conventional wisdom that DCA is a prudent idea, investors certainly have sacrificed a fair amount of return potential by doing it historically.

In their 2012 paper entitle Dollar-Cost Averaging Just Means Taking Risk Later[1], Vanguard looked at LSI versus DCA in the U.S., U.K., and Australia over rolling 10-year periods and found that for a 60/40 portfolio, LSI outperformed DCA about 2/3 of the time in each market.

If we assume that a lump sum is invested in the S&P 500 in equal monthly amounts over 12-months with the remaining balance held in cash earning the risk-free interest rate, we see a similar result over the period from 1926 to 2017.

Why does dollar-cost averaging look so bad?

In our previous commentary on Misattributing Bad Behavior[2], we discussed how the difference between investment return – equivalent to LSI – and investor return – equivalent to DCA – is partly due to the fact that investors are often making contributions in times of positive market returns. Over this 92 year period from 1926 to 2017, the market has had positive returns over 74% of the rolling 12-month periods. Holding cash and investing at a later date means forgoing some of these positive returns. From a theoretical basis, this opportunity cost is the equity risk premium: the expected excess return of equities over cash.

In our current example where investors voluntarily choose to dollar-cost average, the same effect is experienced.

Source: Kenneth French Data Library and Robert Shiller Data Library. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

The average outperformance of the LSI strategy was 4.1%, and as expected, there is a strong correlation between how well the market does over the year and the benefit of LSI.

Source: Kenneth French Data Library and Robert Shiller Data Library. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

Surely DCA Worked Somewhere

If the high equity market returns in the U.S., and as the Vanguard piece showed in the U.K. and Australia, were the force behind the attractiveness of lump sum investing, let’s turn to a market where returns were not so strong: Japan. As of the end of 2017, the MSCI Japan index was nearing its high water mark set at the end of 1989: a drawdown of 38 years.

Under the same analysis, using the International Monetary Fund’s (IMF) Japanese discount rate as a proxy for the risk-free rate in Japan, DCA only outperforms LSI slightly more than half of the time over the period from 1970 to 2017.

Source: MSCI and Federal Reserve of St. Louis. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

Truncating the time frame to begin in 1989 penalizes DCA even more – perhaps surprisingly, given the negligible average return – with it now outperforming slightly under 50% of the time.

Over the entire time period, there is a similar relationship to the outperformance of LSI versus the performance of the Japanese equity index.

Source: MSCI and Federal Reserve of St. Louis. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

The Truth About Dollar-Cost Averaging

Given this empirical evidence, why is dollar-cost averaging still frequently touted as a superior investing strategy?

The claims – many of which come from media outlets – that dollar-cost averaging is predominantly beneficial from a return perspective are false. It nearly always sacrifices returns, and many examples highlighted in these articles paint pictures of hypothetical scenarios that, while grim, are very isolated and/or unrealistic given the historical data.

Moving beyond the empirical evidence, dollar-cost averaging is theoretically sub-optimal to lump sum investing in terms of expected return.

This was shown to be the case in a mean-variance framework in 1979 by George Constantinides.[6]

His argument was that rather than committing to a set investment schedule based on the initial information in the market, adopting a more flexible approach that adjusts the investment amount based on subsequent market information will outperform DCA.

In the years since, many other hypotheses have been put forward for why DCA should be beneficial – different investor utility functions, prospect theory, and mean reversion in equity returns, among others – and most have been shown to be inadequate to justify DCA.

More recently, Hayley (2012)[7] explains the flaw in many of the DCA arguments based on a cognitive error in assuming that the purchase at a lower average price increases the expected returns.

His argument is that since purchasing at the average price requires buying equal share amounts each period, you can only invest the total capital at the true average price of a security or portfolio with perfect foreknowledge of how the price will move. This leads to a lower average purchase price for DCA compared to this equal share investing strategy.

But if you had perfect foreknowledge of the future prices, you would not choose to invest equal share amounts in the first place!

Thus, the equal share investing plan is a straw man comparison for DCA.

We can see this more clearly when we actually dive into examples that are similar to ones generally presented in favor of DCA.

We will call the equal share strategy that invests the entire capital amount, ES Hypothetical. This is the strategy that uses the knowledge of the price evolution. The more realistic equal share investing strategy assumes that prices will remain fixed and purchases the same shares in each period as the DCA strategy purchases in the first period. The strategy is called ES Actual. Any remaining capital is invested in the final period regardless of whether it purchases more or fewer shares than desired, but the results would still hold if this amount were considered to still be held as cash (possibly borrowed if need be) since the analysis ends at this time step.

The following tables show the final account values for 4 simple market scenarios:

Downtrend
Uptrend
Down then up
Up then down

In every scenario, the DCA strategy purchases shares at a lower average cost than the ES Hypothetical strategy and ends up better off, but the true comparison is less clear cut.

The ES Actual and LSI strategies’ average purchase prices and final values may be higher or lower than DCA.

A Comparison of DCA to Equal Share Investing and LSI

Calculations by Newfound Research. All examples are hypothetical.

A More General Comparison of LSI and DCA

In these examples, DCA does outperform LSI half the time, but these examples are extremely contrived.

We can turn to simulations to get a better feel for how often LSI will outperform DCA and by how much under more realistic assumptions of asset price movements.

Using Monte Carlo, we can see how often LSI outperforms DCA for a variety of expected excess returns and volatilities over 12-month periods. Using expected excess returns allows us to neglect the return on cash.

For any positive expected return, LSI is expected to outperform more frequently at all volatility levels. The frequency increases as volatility decreases for a given expected return.

If the expected annual return is negative, then DCA outperforms more frequently.

Calculations by Newfound Research. Results assume Geometric Brownian Motion using the given parameters and compare investing all capital at the beginning of 12 months to investing capital equally at the beginning of each month.

Turning now to the actual amount of outperformance, we see a worse picture for DCA.

For more volatile assets, the expected outperformance is in LSI’s favor even at negative expected returns. This is the case despite what we saw before about DCA outperforming more frequently for these scenarios.

As interest rates increase, DCA will benefit assuming that the expected return on equities remains the same (i.e. the expected excess return decreases). However, even if we assume that the cash account could generate an extra 200 bps, which is generous given that this would imply that cash rates were near 4%, for the 15% volatility and 5% expected excess return case, this would still mean that LSI would be expected to outperform DCA by 100 bps.

What About Risk?

It is clear that DCA does not generally outperform LSI from a pure return point-of-view, but what about when risk is factored in? After all, part of the reason DCA is so popular is because it is said to reduce the risk of investing at the worst possible time.

Under the same Monte Carlo setup, we can use the ulcer index to quantify this risk. The ulcer index measures the duration and severity of the drawdowns experienced in an investment, where a lower ulcer index value implies fewer and less severe drawdowns.

The chart below shows the median ratio of the LSI ulcer index and the DCA ulcer index. We plot the ratio to better compare the relative riskiness of each strategy.

As we would expect, since the DCA strategy linearly moves from cash to an investment, the LSI scheme takes on about twice the drawdown risk in many markets.

When the lump sum is invested, the whole investment is subject to the mercy of the market, but if DCA is used, the market exposure is only at its maximum in the last month.[8]

The illustration of this risk alone may be enough to convince investors that DCA meets its objective of smoothing out investment returns. However, at what cost?

Combining the expected outperformance and the risk embodied in the ulcer index shows that LSI is still expected to outperform on a risk adjusted basis between about 35% and 45% of the time.

While this is lower than it was from a pure return perspective, it should be taken with a grain of salt.

First, we know from the start that LSI will be more exposed to drawdowns. One possible solution would be treat a ratio of ulcer indices of 2 (instead of 1) as the base case.

Second, for an investor who is not checking their account monthly, the ulcer index may not mean much. If you only looked at the account value at the beginning and end of the year regardless of whether you did DCA or LSI, then LSI is generally expected to leave the account better off; the intermediate noise does not get “experienced.”

When Can DCA Work?

So now that we have shown that DCA is empirically and theoretically suboptimal to LSI , why might you still want to do it?

First, we believe there is still a risk reduction argument that makes sense when accounting for investor behavior. Most research has focused on risk in the form of volatility. We showed previously that focusing more on drawdown risk can lead to better risk-adjusted performance of DCA.

We could also look at the gain-to-pain ratio, defined here as the average outperformance divided by the average underperformance of the LSI strategy.

The following chart shows a sampling of asset classes expected returns and volatilities from Research Affiliates with indifference boundaries for different gain-to-pain ratios. Indifferences boundaries show the returns and volatilities with constant gain-to-pain ratios. For a given gain-to-pain ratio (e.g. 1.5 means that you will only accept the risk in LSI if its outperformance over DCA is 50% higher, on average), any asset class points that fall below that line are good candidates for DCA.

The table below shows which asset classes correspond to each region on the chart.

Source: Research Affiliates. Calculations by Newfound Research. Results assume Geometric Brownian Motion using the given parameters and compare investing all capital at the beginning of 12 months to investing capital equally at the beginning of each month.

As the indifference coefficient increases, the benefit of DCA from a gain-to-pain perspective becomes less. For volatile asset classes with lower expected returns (e.g. U.S. equities and long-term U.S. Treasuries), DCA may make sense. For less volatile assets like income focused funds and assets with higher expected growth like EM equities, LSI may be the route to pursue.

A second reason for using DCA is that there are also some market environments that are actually favorable to DCA. As we saw previously, down-trending markets lead to better absolute performance for DCA and volatility makes DCA more attractive from a drawdown risk perspective even in markets with positive expected returns.

Sideways markets are also good for DCA. So are markets that have a set final return.[9] The more volatility the better for DCA in these scenarios.

The chart below shows the return level below which DCA is favored. If you are convinced that the market will return less than -0.6% this year, then DCA is expected to outperform LSI.

Calculations by Newfound Research. Results assume Brownian Bridges using the given parameters and compare investing all capital at the beginning of 12 months to investing capital equally at the beginning of each month.

While a set final return may be an unrealistic hope – who knows where the market will be a year from now? – it allows us to translate beliefs for market returns into an investing plan with DCA or LSI.

However, even though the current high-valuation environment has historically low expected returns for stocks and bonds, the returns over the next year may vary widely. The appeal of DCA may be stronger in this environment even though it is sub-optimal to LSI.

Instead of using DCA on its own as a risk management tool – one that may sacrifice too much of the return to be had – we can pair it with other risk management techniques to improve its odds of outperforming LSI.

Finding a DCA Middle Ground

One of the primary drags on DCA performance is the fact that much of the capital is sitting in cash for most of the time.

Is there a way to reduce this cost of waiting to invest?

One initial alternative to cash is to hold the capital in bonds. This is in line with the intuitive notion of beginning in a low risk profile and moving gradually to a higher one. While this improves the frequency of outperformance of DCA historically, it does little to improve the expected outperformance.

Another option is to utilize a risk managed sleeve that is designed to protect capital during market declines and participate in market growth. Using a simple tactical strategy that holds stocks when they are above their 10-month SMA and bonds otherwise illustrates this point, boosting the frequency of outperformance for DCA from 32% to 71%.

Source: Kenneth French Data Library and Robert Shiller Data Library. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

The tactical strategy narrows the distribution of expected outperformance much more than bonds.

Since we know that the tactical strategy did well over this historical period with the benefit of hindsight, we can also look at how it would have done if returns on stocks and bonds were scaled down to match the current expectations from Research Affiliates.[10]

Source: Kenneth French Data Library and Robert Shiller Data Library. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

The frequency of outperformance is still in favor of the tactical strategy, and the distribution of outperformance exhibits trends similar to using the actual historical data.

Going back to the Japanese market example, we also see improvement in DCA using the tactical strategy. The benefit was smaller than in the U.S, but it was enough to make both the frequency and expected outperformance swing in favor of DCA, even for the period from 1989 to 2017.

Source: MSCI and Federal Reserve of St. Louis. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results. Data from 1970 to 2017.

Deploying cash immediately into a risk-managed solution does not destroy the risk of DCA underperforming if it uses cash. The cost of using this method is that a tactical strategy can be exposed to whipsaw.

One way to mitigate the cost of whipsaw is to use a more diversified (in terms of process and assets) risk management sleeve.

Conclusion

Dollar-cost averaging verses lump sum investing is often a difficult decision fraught with emotion. Losing 10% of an investment right off the bat can be a hard pill to swallow. However, the case against DCA is backed up by empirical evidence and many theoretical arguments.

If a portfolio is deemed optimal based on an investor’s risk preferences and tolerances, then anything else would be suboptimal. But what is optimal on paper is not always the best for an investor who cannot stick with the plan.

Because of this, there are times when DCA can be beneficial. Certain measures of risk that account for drawdowns or the asymmetric psychological impacts of gains and losses point to some benefits for DCA over LSI.

Given that even in this low expected return market environment, the expected return on cash is still less than that on equities and bonds, deploying cash in a risk-managed solution or a strategy that has higher expected returns for the amount of risk it takes may be a better holding place for cash while implementing a DCA scheme.

It is important to move beyond a myopic view, commonly witnessed in the market, that DCA is best for every situation. Even though LSI may feel like market timing, DCA is simply another form of market timing. With relatively small balances, DCA can also increase commission costs and possibly requires more oversight or leads to higher temptation to check in on a portfolio, resulting in rash decisions.

Ultimately, the best solution is the one that gets an investor into an appropriate portfolio, encourages them to stay on track for their long term financial goals, and appropriately manages any behavioral consequences along the way.

[1] https://personal.vanguard.com/pdf/s315.pdf

[2] https://blog.thinknewfound.com/2017/02/misattributing-bad-behavior/

[3] A Note on the Suboptimality of Dollar-Cost Averaging as an Investment Policy, https://faculty.chicagobooth.edu/george.constantinides/documents/JFQA_1979.pdf

[4] Dollar-Cost Averaging: The Role of Cognitive Error, https://www.cass.city.ac.uk/__data/assets/pdf_file/0008/128384/Dollar-Cost-Averaging-09052012.pdf

[5] This is a form of sequence risk. In DCA, the initial returns on the investment do not have the same impact as the final period returns.

[6] Milevsky, Moshe A. and Posner, Steven E., A Continuous-Time Re-Examination of the Inefficiency of Dollar-Cost Averaging (January 1999). SSBFIN-9901. Available at SSRN: https://ssrn.com/abstract=148754

[7] Specifically, we use the “Yield & Growth” capital market assumptions from Research Affiliates. These capital market assumptions account assume that there is no valuation mean reversion (i.e. valuations stay the same going forward). The adjusted average nominal returns for U.S. equities and 10-year U.S. Treasuries are 5.3% and 3.3%, respectively.

Nathan Faber

Nathan is a Portfolio Manager at Newfound Research. At Newfound, Nathan is responsible for investment research, strategy development, and supporting the portfolio management team. Prior to joining Newfound, he was a chemical engineer at URS, a global engineering firm in the oil, natural gas, and biofuels industry where he was responsible for process simulation development, project economic analysis, and the creation of in-house software. Nathan holds a Master of Science in Computational Finance from Carnegie Mellon University and graduated summa cum laude from Case Western Reserve University with a Bachelor of Science in Chemical Engineering and a minor in Mathematics.

The Research Library of Newfound Research

Should You Dollar-Cost Average?

Summary