This post is available as a PDF download here.

Summary­

  • The choice to lump sum invest (“LSI”) or dollar-cost average (“DCA”) is one fraught with emotion.
  • Intuition tells us that LSI likely offers the best bet for long-term investors as markets, in general, tend to go up. However, can signals derived from simple trend models offer an edge?
  • We find that over longer-term periods (e.g. 6- and 12-months), LSI largely dominates DCA.However, in the short-term, where trend signals may have more predictive power, results are largely mixed.
  • Average results, however, are often of little use to investors looking to make a one-off decision about LSI and DCA. In light of this, we explore a framework of regret minimization that looks at downside exposure over a variety of time-frames and based upon a number of signals.
  • We find that downside risk tends to increase with negative trend signals, indicating that investors looking to put a significant amount of money to work at once may favor a DCA approach during negatively trending markets if their goal is to avoid the risk of immediate loss.

A question that we are often asked about is lump sum investing (“LSI”) versus dollar-cost averaging (“DCA”).  While we wrote about the topic quite extensively not too long ago (see Should You Dollar-Cost Average?), several advisors have asked us whether the trend following approach, of which we are strong advocates, can be a useful guide as to which approach they should take at a given time.

For example, if we believe in trend following, it would seem obvious that we should LSI when trends are up (i.e. when delayed purchases will only lead to higher prices), and in a down trend we should DCA.

But is it true?  This commentary aims to explore the idea.

Before we even begin this analysis, we can speculate as to what the results might be using our knowledge of how history has unfolded.

First, we know that the U.S. equity market has historically exhibited a significant equity risk premium.  Therefore, time spent out of the market – i.e. choosing to DCA instead of LSI – can be seen as an expected opportunity cost or an expected negative cost of carry.

Secondly, the evidence supporting trend following requires the systematic application of trend following.  In fact, the majority of trades, taken individually, will actually be losers. We see this when evaluating naïve long/flat equity trend following strategies against simple buy-and-hold equity exposure: the median rolling 1-year performance is often negative, only offset by massive “winners” during periods like the dot-com crash and the credit crisis.

Frequently the question of LSI vs DCA is in the context of putting new, and often large sums of, client money to work.  In this case, we are not afforded the opportunity to take the trend bet repeatedly over time.  Our success will be determined by a single trial.  And, as with most things in the market, there is little edge found in a single trial.  Indeed, this is the crux of the argument we outlined in A Case Against Overweighting International Equity, where a single, large bet made only once requires a massive degree of accuracy to garner any confidence.

Therefore, before we bother with any data, our expectation is thus: on average, LSI is probably going to dominate DCA, particularly using historical U.S. equity data, regardless of whether it is guided by a trend following policy or not.

The Design of the Test

We will explore LSI vs DCA using a variety of signals, including those capturing both trend and mean-reversionary effects:

  • Moving Average:A positive or negative signal determined by whether U.S. equity prices are above or below their 200-day moving average.
  • Momentum: 12-1 month total return of U.S. equity prices.
  • Slope: The percentage change in the 200-day moving average of U.S. equity prices.
  • Moving Average Ratio: The ratio of a 21-day moving average to a 200-day moving average. 
  • Z-Score:A z-score based upon the distance of price and its 200-day moving average using a rolling 200-day period to estimate mean and volatility.
  • RSI: Relative Strength Index measured over a 14-day period. 
  • Volatility: 63-day exponentially weighted estimates of realized volatility.

Capital invested is assumed to grow at the rate of a broad U.S. equity index and capital not invested is assumed to grow at the U.S. risk-free rate (source: Kenneth French Data Library).

At each point in time, the total return for an LSI approach is compared against that of a DCA approach.  The DCA approach is defined over a frequency with which new money is invested and a horizon over how long the strategy will average.  For example, an assumption of four weeks would assume that 1/4thof the money is invested at the beginning of the next four weeks, while the LSI approach invests everything at the beginning of the first week.[1]

Total returns are then compared at the date both strategies are fully invested, as both strategies will exhibit identical returns thereafter.

Specifically, we explore six different time-frames: four weeks (“4W”), three months (“3M”), six months (“6M”), twelve months (“12M”), and four quarters (“4Q”).

Finally, the results are binned into deciles based upon the raw scores.  Note that this step explicitly assumes look-ahead bias and therefore any conclusions drawn from the following results should be considered an upper limit.

For each approach, we report the average performance difference, whether the result is statistically significant at a 95% confidence (**), and the number of observations.  We also report the frequency with which LSI outperformed DCA.

LSI vs DCA Test Results Conditioned on Signal Values

For all the results reported below, we see much of the same trends (our apologies for the pun):

  • LSI holds a statistically significant edge over DCA for 6- and 12-month periods, particularly when trends are positive.
  • Few signals offer any significance in the short-run.Those that do are more likely to continue rather than reverse.  However, there is little stability in these figures.  For example, while one decile may be statistically significant, those around it are not.  Given that these figures explicitly incorporate foresight bias, this does not bode well for any application of these results.

Broadly speaking, the results align with expectations.

We know, ex-ante, that trend is a short-lived signal.  In other words, a measure like 12-1 month momentum might provide us a forecasting edge over the next 1-to-3 months, but likely tells us little about returns over the next 12-36 months.  Therefore, using it to guide longer-term DCA decisions (e.g. over 12-month periods) means you are using a short-term signal to make long-term decisions.  Expectedly, trend offers little conditional information for longer-term DCA decisions and, broadly speaking, LSI tends to have an edge on DCA since markets appreciated over the historical period examined.

Unfortunately, despite being a short-term signal, the evidence supporting utilizing the beginning trend signal to drive the LSI versus DCA decision over shorter horizons (e.g. four weeks) is tenuous at best.

 

Moving Average

As an example on how to read this table, we can see that LSI has, on average, outperformed a DCA approach applied over four-week periods (“4W”) when starting trend signals are positive by 0.09%.  The result is statistically significant. 

On the other hand, we can see that LSI only outperforms DCA on average by 0.02% when DCA is applied over a 6-month (“6M”) period and the beginning trend signal is negative.  The result, however, is not statistically significant, meaning that we cannot reject the null hypothesis that there is no meaningful difference between the two approaches.

4W3M6M12M4Q
Negative-0.10% (1298)-0.20% (307)0.02% (307)0.57% (307)0.01% (103)
Positive0.09%** (3415)0.04% (776)0.84%** (773)2.78%** (767)0.58%** (255)

 

4W3M6M12M4Q
Negative52.00%47.90%51.50%55.70%53.40%
Positive58.60%57.70%62.60%70.10%61.60%

 

Momentum

4W3M6M12M4Q
[-0.642, -0.141]-0.07% (456)-0.33% (100)-0.49% (100)0.11% (100)-0.03% (32)
(-0.141, -0.0476]-0.18%** (457)-0.29% (110)-0.18% (110)2.27%** (110)-0.47% (44)
(-0.0476, 0.0254]0.11% (473)0.07% (115)1.08%** (115)3.22%** (115)0.86% (33)
(0.0254, 0.0879]-0.01% (475)0.04% (105)0.98%** (105)2.65%** (105)1.10% (35)
(0.0879, 0.132]0.12%** (493)0.06% (112)0.23% (112)0.95% (112)0.06% (41)
(0.132, 0.17]0.08% (470)-0.03% (110)0.59% (110)1.51%** (109)0.02% (34)
(0.17, 0.216]0.08% (483)0.23% (115)1.40%** (114)3.56%** (109)0.67% (29)
(0.216, 0.271]0.08% (480)0.05% (106)1.09%** (104)2.24%** (104)0.55% (37)
(0.271, 0.342]0.03% (453)-0.17% (96)1.08%** (96)3.50%** (96)1.63% (35)
(0.342, 1.183]0.10% (473)0.03% (114)0.25% (114)1.50%** (114)0.07% (38)

 

4W3M6M12M4Q
[-0.642, -0.141]51.50%52.00%50.00%55.00%56.20%
(-0.141, -0.0476]49.70%46.40%51.80%66.40%54.50%
(-0.0476, 0.0254]58.40%58.30%62.60%70.40%57.60%
(0.0254, 0.0879]54.30%53.30%55.20%64.80%54.30%
(0.0879, 0.132]58.80%54.50%57.10%65.20%61.00%
(0.132, 0.17]60.20%56.40%60.90%67.90%58.80%
(0.17, 0.216]60.00%63.50%70.20%71.60%65.50%
(0.216, 0.271]61.70%59.40%67.30%63.50%59.50%
(0.271, 0.342]55.60%49.00%66.70%72.90%71.40%
(0.342, 1.183]57.10%55.30%52.60%62.30%55.30%

 

Slope

4W3M6M12M4Q
[-0.00418, -0.000717]-0.09% (448)-0.21% (104)-0.38% (104)0.86% (104)-0.67% (39)
(-0.000717, -0.000238]-0.04% (471)-0.33% (109)-0.37% (109)-0.20% (109)-0.75% (34)
(-0.000238, 9.56e-05]-0.14%** (467)-0.20% (105)0.26% (105)1.77% (105)0.53% (32)
(9.56e-05, 0.000317]0.13%** (486)0.07% (119)0.69% (119)2.50%** (119)1.32% (39)
(0.000317, 0.0005]0.11%** (482)0.01% (112)0.27% (112)0.69% (112)-0.89% (43)
(0.0005, 0.00065]0.00% (478)-0.02% (112)0.90%** (112)2.64%** (110)1.20%** (33)
(0.00065, 0.000815]0.18%** (477)0.21% (107)1.70%** (104)4.11%** (101)1.29% (32)
(0.000815, 0.000998]0.07% (453)0.05% (107)1.25%** (107)3.76%** (106)0.95% (37)
(0.000998, 0.00125]0.08% (486)0.08% (102)1.18%** (102)3.32%** (102)0.49% (31)
(0.00125, 0.00397]0.04% (465)0.05% (106)0.60% (106)2.23%** (106)1.00% (38)

 

4W3M6M12M4Q
[-0.00418, -0.000717]51.80%49.00%45.20%55.80%51.30%
(-0.000717, -0.000238]50.70%50.50%56.00%58.70%52.90%
(-0.000238, 9.56e-05]53.70%45.70%53.30%61.90%56.20%
(9.56e-05, 0.000317]59.10%58.00%59.70%68.90%64.10%
(0.000317, 0.0005]56.60%58.90%60.70%58.00%51.20%
(0.0005, 0.00065]55.90%56.20%61.60%75.50%63.60%
(0.00065, 0.000815]63.70%62.60%68.30%78.20%68.80%
(0.000815, 0.000998]58.10%52.30%65.40%67.00%64.90%
(0.000998, 0.00125]60.50%56.90%65.70%73.50%61.30%
(0.00125, 0.00397]57.40%58.50%58.50%63.20%60.50%

 

Moving Average Ratio

4W3M6M12M4Q
[0.668, 0.925]0.00% (459)-0.06% (105)0.21% (105)1.39% (105)0.52% (41)
(0.925, 0.975]0.00% (470)-0.21% (107)0.01% (107)0.15% (107)-1.47% (28)
(0.975, 1.0045]-0.14%** (484)-0.30% (113)-0.04% (113)0.59% (113)0.55% (42)
(1.0045, 1.0283]0.01% (472)-0.05% (109)0.47% (109)2.38%** (109)0.23% (32)
(1.0283, 1.0457]0.06% (489)0.16% (113)1.07%** (113)3.17%** (112)0.29% (37)
(1.0457, 1.0617]0.08% (473)-0.06% (111)0.70%** (111)2.12%** (110)0.54% (34)
(1.0617, 1.0792]0.12%** (480)-0.04% (107)0.62% (105)1.86%** (101)-0.47% (41)
(1.0792, 1.0996]0.14%** (474)0.23% (113)1.48%** (112)4.56%** (112)2.24%** (34)
(1.0996, 1.126]0.06% (477)0.05% (103)0.90% (103)2.70%** (103)0.96% (41)
(1.126, 1.505]0.04% (470)0.01% (109)0.82%** (109)2.95%** (109)0.84% (31)

 

4W3M6M12M4Q
[0.668, 0.925]54.50%58.10%54.30%60.00%53.70%
(0.925, 0.975]53.80%45.80%47.70%52.30%42.90%
(0.975, 1.0045]49.80%46.00%54.90%60.20%64.30%
(1.0045, 1.0283]57.80%57.80%57.80%63.30%56.20%
(1.0283, 1.0457]58.10%58.40%62.80%70.50%56.80%
(1.0457, 1.0617]59.20%48.60%58.60%68.20%61.80%
(1.0617, 1.0792]61.30%58.90%63.80%70.30%56.10%
(1.0792, 1.0996]60.10%58.40%68.80%76.80%76.50%
(1.0996, 1.126]59.10%62.10%63.10%69.90%61.00%
(1.126, 1.505]55.30%56.00%65.10%70.60%64.50%

 

Z-Score

4W3M6M12M4Q
[-8.307, -1.855]0.02% (456)-0.08% (100)0.91% (100)2.19%** (100)1.25% (31)
(-1.855, -1.272]-0.07% (470)0.11% (116)0.54% (116)1.29% (115)-0.59% (41)
(-1.272, -0.768]-0.01% (472)-0.23% (115)0.50% (115)1.46% (115)0.10% (40)
(-0.768, -0.316]-0.05% (462)-0.22% (109)-0.03% (109)1.12% (109)-1.57% (29)
(-0.316, 0.13]0.06% (461)0.14% (109)1.36%** (109)2.76%** (106)1.53% (41)
(0.13, 0.528]0.03% (475)-0.41%** (120)-1.36%** (120)-0.67% (118)0.32% (38)
(0.528, 0.902]0.03% (473)-0.01% (104)0.55% (103)2.29%** (103)0.18% (32)
(0.902, 1.28]0.02% (486)-0.01% (108)0.70% (108)2.44%** (108)-0.20% (44)
(1.28, 1.723]0.15%** (471)0.09% (100)1.35%** (100)4.18%** (100)0.81% (35)
(1.723, 3.987]0.18%** (487)0.41%** (102)1.95%** (100)5.18%** (100)2.76%** (27)

 

4W3M6M12M4Q
[-8.307, -1.855]57.20%53.00%60.00%61.00%67.70%
(-1.855, -1.272]52.60%58.60%55.20%55.70%46.30%
(-1.272, -0.768]53.80%50.40%55.70%60.00%50.00%
(-0.768, -0.316]55.60%52.30%53.20%60.60%44.80%
(-0.316, 0.13]62.90%59.60%65.10%68.90%73.20%
(0.13, 0.528]54.90%45.80%48.30%60.20%63.20%
(0.528, 0.902]56.90%54.80%60.20%69.90%56.20%
(0.902, 1.28]57.40%49.10%54.60%72.20%54.50%
(1.28, 1.723]56.90%60.00%69.00%73.00%62.90%
(1.723, 3.987]59.80%67.60%77.00%82.00%77.80%

 

Relative Strength Index

4W3M6M12M4Q
[2.696, 35.504]-0.00% (451)-0.02% (125)0.89% (125)2.45%** (125)1.99% (33)
(35.504, 40.614]-0.05% (476)-0.18% (121)0.31% (120)1.51% (120)-0.81% (44)
(40.614, 44.699]0.05% (469)-0.20% (93)0.22% (93)0.61% (92)-1.30% (29)
(44.699, 48.274]0.07% (448)-0.06% (115)0.28% (115)1.62%** (114)-0.70% (38)
(48.274, 51.588]-0.01% (512)0.03% (114)0.60% (114)2.63%** (114)1.40%** (37)
(51.588, 54.862]-0.06% (480)-0.03% (103)0.56% (103)1.42% (102)0.61% (29)
(54.862, 58.123]0.06% (464)-0.02% (97)1.07%** (96)2.88%** (96)-0.59% (34)
(58.123, 62.144]0.08% (468)0.07% (98)0.86% (98)2.69%** (97)0.61% (36)
(62.144, 67.815]0.14%** (487)0.17% (125)1.09%** (124)3.42%** (123)1.52%** (47)
(67.815, 98.408]0.09% (458)-0.07% (92)0.07% (92)1.94% (91)1.27% (31)

 

4W3M6M12M4Q
[2.696, 35.504]57.90%55.20%58.40%61.60%63.60%
(35.504, 40.614]55.50%49.60%57.50%66.70%52.30%
(40.614, 44.699]56.50%58.10%52.70%57.60%48.30%
(44.699, 48.274]57.10%51.30%57.40%60.50%55.30%
(48.274, 51.588]54.50%55.30%59.60%69.30%73.00%
(51.588, 54.862]51.90%53.40%59.20%66.70%55.20%
(54.862, 58.123]55.60%53.60%63.50%66.70%52.90%
(58.123, 62.144]56.60%67.30%70.40%72.20%55.60%
(62.144, 67.815]61.60%57.60%59.70%71.50%72.30%
(67.815, 98.408]61.10%48.90%56.50%67.00%58.10%

 

Volatility

4W3M6M12M4Q
[0.0458, 0.0805]-0.01% (487)0.02% (105)0.63% (102)2.17%** (100)0.17% (32)
(0.0805, 0.0909]0.08%** (480)0.08% (116)1.07%** (116)3.31%** (112)0.90% (40)
(0.0909, 0.1]0.07% (484)-0.19% (114)0.50% (114)2.71%** (114)0.54% (41)
(0.1, 0.111]0.04% (474)0.18% (106)1.35%** (106)3.44%** (106)1.44%** (32)
(0.111, 0.122]0.11%** (480)0.04% (113)0.67% (113)2.64%** (113)0.41% (38)
(0.122, 0.136]-0.04% (465)-0.21% (109)-0.01% (109)1.44% (109)0.10% (36)
(0.136, 0.156]0.14%** (468)0.01% (104)0.51% (104)1.99%** (104)0.67% (34)
(0.156, 0.189]0.07% (468)0.02% (109)1.02%** (109)2.53%** (109)-0.01% (37)
(0.189, 0.25]-0.22%** (466)-0.14% (104)-0.27% (104)-0.94% (104)-0.40% (33)
(0.25, 0.583]0.12% (441)-0.10% (103)0.54% (103)2.00% (103)0.26% (35)

 

4W3M6M12M4Q
[0.0458, 0.0805]55.90%49.50%59.80%65.00%59.40%
(0.0805, 0.0909]58.50%58.60%63.80%68.80%60.00%
(0.0909, 0.1]59.10%50.00%60.50%74.60%58.50%
(0.1, 0.111]57.40%59.40%67.00%77.40%75.00%
(0.111, 0.122]60.00%58.40%58.40%69.00%65.80%
(0.122, 0.136]52.70%55.00%56.90%63.30%55.60%
(0.136, 0.156]60.30%56.70%62.50%61.50%58.80%
(0.156, 0.189]56.80%55.00%60.60%64.20%51.40%
(0.189, 0.25]51.70%52.90%54.80%57.70%51.50%
(0.25, 0.583]55.30%53.40%49.50%57.30%57.10% 


Minimizing Regret

The tests above all assume we care about the long-term, average edge.  In reality, with most advisors we speak to, LSI versus DCA is a one-off decision (e.g. investing a new client’s capital).  Thus, the long-term average is hardly applicable. Rather, we might consider a framework that seeks to minimize our regret.  In other words, we may be willing to forego some upside if it means we avoid the greater risk of downside.

To explore this idea, we re-run the above analysis but now report the 95% conditional value-at-risk for U.S. equity markets over each period.  For those unfamiliar with this figure, the easiest way to think about it is, “what happens, on average, in the worst 5% of cases?”

Here we see an interesting pattern emerge: periods identified by negative trends tend to exhibit higher average downsides.  The periods of the strongest trends alsotend to exhibit an increased risk of downside relative to shallower positive trends, potentially indicating a higher risk of reversal. This latter effect is not nearly as pronounced, however, as the former.

 

Moving Average

4W3M6M12M4Q
Negative-13.82%-22.36%-33.59%-46.39%-43.80%
Positive-8.01%-13.93%-18.37%-22.95%-21.03%

 

Momentum

4W3M6M12M4Q
[-0.642, -0.141]-16.16%-27.15%-38.55%-56.89%-49.07%
(-0.141, -0.0476]-12.76%-18.88%-31.39%-32.35%-33.99%
(-0.0476, 0.0254]-7.70%-12.14%-16.55%-35.74%-26.20%
(0.0254, 0.0879]-8.34%-8.89%-17.56%-24.47%-13.81%
(0.0879, 0.132]-6.69%-14.80%-21.00%-21.26%-19.08%
(0.132, 0.17]-7.14%-13.58%-16.63%-21.97%-18.27%
(0.17, 0.216]-8.23%-9.32%-17.77%-26.47%-13.60%
(0.216, 0.271]-8.82%-10.38%-13.00%-30.30%-17.48%
(0.271, 0.342]-10.00%-18.68%-19.90%-17.88%-19.27%
(0.342, 1.183]-9.05%-18.72%-21.79%-27.44%-34.57%

 

Slope

4W3M6M12M4Q
[-0.00418, -0.000717]-16.68%-26.18%-36.98%-49.62%-49.07%
(-0.000717, -0.000238]-11.06%-19.33%-33.34%-48.88%-41.60%
(-0.000238, 9.56e-05]-10.95%-13.86%-25.88%-29.60%-34.65%
(9.56e-05, 0.000317]-6.64%-13.64%-17.35%-24.90%-15.83%
(0.0005, 0.00065]-9.10%-10.17%-10.84%-11.88%-9.98%
(0.00065, 0.000815]-6.64%-12.11%-16.08%-21.59%-34.57%
(0.000815, 0.000998]-7.70%-12.49%-15.93%-20.39%-16.67%
(0.000998, 0.00125]-8.46%-12.07%-15.86%-22.44%-11.69%
(0.00125, 0.00397]-9.57%-16.77%-22.72%-23.17%-17.90%

 

Moving Average Ratio

4W3M6M12M4Q
[0.668, 0.925]-16.13%-26.02%-37.82%-54.43%-43.46%
(0.925, 0.975]-11.24%-18.40%-30.63%-39.40%-40.75%
(0.975, 1.0045]-9.61%-17.37%-28.96%-39.23%-34.32%
(1.0045, 1.0283]-9.95%-16.14%-18.39%-22.90%-18.97%
(1.0283, 1.0457]-8.15%-11.49%-16.25%-20.31%-17.22%
(1.0457, 1.0617]-6.25%-10.08%-14.27%-15.74%-16.43%
(1.0617, 1.0792]-8.40%-13.39%-15.40%-21.11%-24.73%
(1.0792, 1.0996]-7.14%-8.04%-12.01%-13.31%-0.42%
(1.0996, 1.126]-8.60%-15.23%-23.45%-32.80%-22.59%
(1.126, 1.505]-9.34%-16.12%-16.51%-16.61%-13.23%

 

Z-Score

4W3M6M12M4Q
[-8.307, -1.855]-12.81%-14.70%-19.77%-38.35%-45.50%
(-1.855, -1.272]-10.42%-16.10%-22.24%-34.42%-23.20%
(-1.272, -0.768]-10.49%-17.32%-31.75%-27.12%-36.46%
(-0.768, -0.316]-10.66%-22.12%-27.40%-28.09%-26.96%
(-0.316, 0.13]-10.85%-11.67%-18.33%-30.12%-26.13%
(0.13, 0.528]-11.47%-26.61%-34.57%-47.07%-28.21%
(0.528, 0.902]-9.40%-11.57%-15.11%-23.84%-17.01%
(0.902, 1.28]-9.37%-16.05%-23.67%-40.54%-38.17%
(1.28, 1.723]-6.91%-11.54%-17.30%-20.60%-24.42%
(1.723, 3.987]-7.99%-12.63%-17.65%-26.49%-11.74%

 

Relative Strength Index

4W3M6M12M4Q
[2.696, 35.504]-13.03%-17.22%-29.69%-41.61%-26.77%
(35.504, 40.614]-12.32%-20.85%-29.34%-38.30%-29.83%
(40.614, 44.699]-9.66%-14.44%-32.24%-38.89%-31.68%
(44.699, 48.274]-10.43%-21.45%-24.19%-29.81%-41.82%
(48.274, 51.588]-9.95%-14.80%-18.40%-27.87%-10.14%
(51.588, 54.862]-9.95%-13.39%-23.98%-33.15%-42.95%
(54.862, 58.123]-9.01%-15.65%-20.10%-21.50%-30.60%
(58.123, 62.144]-9.21%-18.95%-23.01%-38.22%-31.80%
(62.144, 67.815]-8.50%-11.93%-16.62%-21.97%-12.81%
(67.815, 98.408]-9.12%-19.23%-24.97%-34.38%-30.72%

 

Volatility

4W3M6M12M4Q
[0.0458, 0.0805]-5.80%-8.43%-16.20%-15.01%-17.46%
(0.0805, 0.0909]-5.43%-9.54%-12.95%-18.46%-16.43%
(0.0909, 0.1]-6.53%-8.81%-11.51%-10.64%-6.17%
(0.1, 0.111]-7.91%-11.99%-10.01%-12.84%-13.76%
(0.111, 0.122]-7.16%-12.10%-16.65%-23.26%-17.48%
(0.122, 0.136]-8.83%-17.44%-20.11%-31.48%-29.58%
(0.136, 0.156]-9.32%-20.49%-27.62%-26.33%-21.06%
(0.156, 0.189]-9.40%-13.18%-24.33%-34.87%-34.40%
(0.189, 0.25]-14.68%-19.38%-31.24%-48.10%-42.58%
(0.25, 0.583]-16.78%-26.44%-38.09%-48.66%-48.09% 


Conclusion

With everything we know about how U.S. equity markets have performed over the last century, it really should come as no surprise that lump sum investing outperforms dollar-cost averaging.  Quite simply, the equity risk premium has been so large that it requires a very accurate signal to justify sitting on the sidelines, particularly for extended periods.

We see this evidence in comparing the performance of lump sum investing versus dollar-cost averaging over 6- and 12-month periods.  Trend following, which is a fast decaying signal by nature, does not offer a tremendous amount of predictive help in these areas.

Over shorter horizons, the evidence is less pronounced in either direction.  There are cases where trend direction appears to offer some signal over a 4-week period, but the strength is tenuous at best when we consider that the conditional figures calculated within this commentary explicitly incorporate foresight bias.

All said, however, the long-term edge offered by LSI versus DCA is not often the important question.  Rather, for many, the choice to LSI or DCA is a one-off decision.  In this case, employing a framework of regret minimization may be more prudent.  As such, we can look at the conditional value-at-risk as a measure of downside loss potential.  In this framework, we see that the periods subsequent to the identification of strong, negative trends tend to be periods of increased downside risk.

A second, albeit less powerful, effect we notice is that downside risk tends to increase in periods after a very strong trend, likely indicating a greater potential of mean-reversion.

Taken all together, we come to this conclusion: if you seek to maximize your returns, you’re probably better off taking an LSI approach unless you have very strong conviction why the equity risk premium will be negative over the period you would DCA.  However, if you are worried about suffering short-term losses, trend signals may be able to provide some guidance.

 


 

[1]Technically, 1/4thof available capital would be invested the first week.  At the second week, 1/3rd of the remaining capital would be invested after accounting for growth at the risk-free rate.  At the third week, ½ of the remaining capital would be invested, again after accounting for growth at the risk-free rate.


Information on Newfound’s trend equity strategies is available here.  Specific research and educational materials are available below:


Corey is co-founder and Chief Investment Officer of Newfound Research, a quantitative asset manager offering a suite of separately managed accounts and mutual funds. At Newfound, Corey is responsible for portfolio management, investment research, strategy development, and communication of the firm's views to clients.

Prior to offering asset management services, Newfound licensed research from the quantitative investment models developed by Corey. At peak, this research helped steer the tactical allocation decisions for upwards of $10bn.

Corey is a frequent speaker on industry panels and contributes to ETF.com, ETF Trends, and Forbes.com’s Great Speculations blog. He was named a 2014 ETF All Star by ETF.com.

Corey holds a Master of Science in Computational Finance from Carnegie Mellon University and a Bachelor of Science in Computer Science, cum laude, from Cornell University.

You can connect with Corey on LinkedIn or Twitter.

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