February 25, 2016

Dual Momentum and Dollar Cost Averaging

Last month a millennial emailed me saying he liked my book. But he wondered if the outperformance of dual momentum would disappear if he used dollar cost averaging (DCA) because he would not be able to buy cheaply during bear markets. This is because dual momentum reduces bear market drawdowns. I showed him logically that he would actually end up with more shares at a lower average cost by using dual momentum along with DCA. [1] I promised to post a more complete analysis using actual monthly returns.

DCA Benefits

Meanwhile, there was an internet article last week called “How Great Is Dollar Cost Averaging? You Don't Know the Half  of  It” by Eric D Nelson. The point of the article was that lackluster returns provide an opportunity to buy more shares at depressed prices.  Nelson gave an example of how the S&P 500 returned only 4.1% per year since 2000, but a DCA approach during these same years returned 8.5%. This is because you could buy more shares in the weak market years of 2001, 2002, 2008, and 2011. This turned volatility into a benefit.  Nelson concluded by saying DCA works well with stocks and not as well with portfolios containing both stocks and bonds.

Josh Brown (The Reformed Broker) in his post, "How to Make Volatility Your Bitch," used Nelson’s logic to make the point that a portfolio dropping in half twice during a 15 year period would outperform a portfolio having the same return but with zero drawdowns. This is due to the rebalancing profits of DCA. Our friend Jake (EconompicData) in his "Combining Momentum and Dollar Cost Averaging for Smoother Results," showed that regardless of volatility, a trend following moving average overlay applied to DCA could outperform DCA alone over the long run.

Relative Momentum

I will move this discussion forward and show how momentum and DCA reinforce and complement each other. Let us first look at a simple two asset relative strength momentum portfolio. We will use the S&P 500 and the MSCI All Country World ex-U.S. (MSCI World ex-U.S. before 1988) indices from January 1971 through January 2016. Every month we buy or hold whichever index had the higher total return over the past year.

Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our Disclaimer page for more information.

An initial $1000 investment would have grown to $265,176 for our relative momentum portfolio versus $86,443 for just the S&P 500 and $98,055 for a benchmark made up of the S&P 500 and MSCI indices in the same 55% to 45% ratio as the amount of their use in the relative momentum model over those 45 years [2]. The compound annual growth rate of the relative momentum portfolio was 13.2% versus 10.7% for benchmark portfolio and 10.4% for the S&P 500. The average number of transactions per year with relative momentum was less than one, so relative momentum did not suffer from high trading costs or scalability issues, as can happen with momentum using individual stocks. There is an annual 250 basis point advantage here over the benchmark portfolio by using relative momentum.

There is a mountain of academic research supporting the use of relative momentum. Geczy and Samonov (2015) showed that relative momentum has outperformed buy-and-hold all the way back to the year 1800, and momentum using stock indices has outperformed individual stock momentum. This was before  transaction costs. After transaction costs, the contest wasn’t even close.

We should take note that the world is now more globally connected than it once was. Many large U.S. corporations derive a large part of their revenue from international operations. Portfolio diversification using h U.S. and non-U.S. stocks now has more to do with the strength or weakness of the U.S. dollar than it does with stock market returns.

Since it is counterproductive to be both long and short the U.S. dollar, it makes more sense to invest in only U.S. stocks or non-U.S. stocks depending on which is stronger, rather than in both together. Adaptive diversification based on market condition is the key to momentum investing.

DCA with Relative Momentum

Let us see now how relative momentum does when combined with DCA. We start with $1000 and this time add $100 every month. The ending value of a DCA relative strength portfolio after 45 years is $2,844,126 compared to $1,073,465 for a DCA benchmark portfolio without the use of momentum. The internal rate of return (IRR) for the DCA relative momentum portfolio is 13.4% versus 10.4% for the DCA benchmark portfolio that does not use momentum. We get a 300 basis point annual increase in return by adding relative momentum to our DCA benchmark portfolio.  

Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our Disclaimer page for more information.

DCA with Dual Momentum

We will now extend our earlier logic where we said you cannot be both long and short the U.S. dollar, and we used relative momentum to select the better scenario. We can also say that the stock market cannot be going both up and down at the same time. Following the same logic as before, we will be in stocks when they are in an uptrend and move to the safety of bonds when stocks are in a downtrend. This is absolute momentum. When in stocks, we will use relative momentum to see whether we should be in U.S. or non-U.S. stocks. We will use DCA with this dual momentum and see what it does to our DCA profits. The dual momentum DCA benchmark will be 45% S&P 500, 25% MSCI All World ex-U.S., and 30% Barclays Capital U.S. Aggregate Bond (Ibbotson Intermediate Government Bond before 1976) index. This  is the allocation to each of these assets over the 45 year period using dual momentum.

Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our Performance and Disclaimer pages for more information.
As with relative momentum DCA, the dual momentum DCA strategy has an initial $1000 investment with $100 per month additions. The dual momentum DCA strategy gives an ending value of $9,467,595. During this same period, the non-momentum DCA benchmark portfolio grew to $882,763. The IRR of the DCA portfolio with dual momentum was 17.0%, versus 9.8% for the DCA non-momentum benchmark portfolio. We get an increase in return of  over 700 basis points per year by adding dual momentum to DCA.We also get downside protection from being largely in bonds during bear markets in stocks.

When Bonds Are Good

The non-momentum DCA benchmark portfolio that is without bonds has a higher IRR than the non-momentum DCA  benchmark portfolio that uses bonds (10.4% versus 9.8%). The IRR of the dual momentum DCA portfolio that uses bonds adaptively to reduce bear market risk is substantially higher then the IRR of the relative momentum DCA portfolio that does not include bonds (17.09% versus 13.4%). But better returns is only half the story. The worst drawdown of the DCA dual momentum portfolio is less than half the worst drawdown of its non-momentum benchmark DCA portfolio.


Rules-based approaches are a good thing. They can provide a disciplined framework to help us overcome self-defeating behavioral biases. DCA is a worthwhile approach since it can counteract our natural tendency to buy as we become greedy and sell when we become fearful. This is the opposite of what we should do, according to Warren Buffett.

Adding relative momentum to DCA more than doubles DCA’s ending capital after 45 years. Adding dual momentum instead of relative momentum to DCA gives more than a ten-fold increase in ending wealth, and it does so with considerably less downside risk exposure.

DCA and dual momentum complement each other well. DCA converts volatility into higher returns, while dual momentum converts differential returns into higher  returns and provides important downside portfolio protection. Both DCA and dual momentum make it easier for investors to accept the volatility of their investments. For those who have to accumulate investment capital over time rather than go all in at once, DCA with dual momentum can be a great combination.

[1] DCA works well assuming you have periodic inflows of capital to invest. With lump sum amounts of capital to invest, DCA is not optimal.
[2] This is about the same allocation as the capitalization weighted MSCI All Country World Index (57% S&P500 and 43% MSCI) that includes both U.S. stocks and non-U.S. stocks.