lump sum or dollar cost average investing

Lump Sum or Dollar Cost Average Investing? Part 2

Do you prefer to drip-feed your investments into the market rather than invest in one single “big-bang”? Part 1 compared Lump Sum (LS) and Dollar Cost Averaging (DCA) strategies. If you haven’t read it and you don’t want a spoiler then look away now – the LS strategy wins hands-down! In most past scenarios a LS strategy will result in a larger ending value than adopting a DCA strategy. This is also what Vanguard found in a paper they wrote on the subject.

Before going any further you need to read the important notes.

Dollar Cost Average Investing

In part 1 we looked at how often the LS strategy beat the DCA strategy, and in this part we will look at the magnitude of the outperformance.

We saw the following results from part 1 where we plotted the outperformance of the LS strategy by starting year for a ten year horizon. This compares a LS strategy of a single investment on day one, with spreading the investment out over the next ten years. You can see that most of the periods (in fact 88% of them) resulted in the LS strategy winning. There were a couple of big exceptions like the Great Depression and the period of Stagflation in the 1970’s that we examined in part 1.

100pc Equity 10yr
Outperformance of Lump Sum versus Dollar Cost Averaging strategy

The average out performance of the LS strategy over a ten year period was in fact 2.6%, but you can see that there were a number of historical periods with outperformance way in excess of that. In other words it has paid to be invested in the market, and that’s why I don’t have an emergency fund in cash and don’t keep any “dry powder”.

But what happens when we reduce the period of investment to five years?

Changing the Investment Period

In the next chart I have overlaid the outperformance figures for a five year period to compare with the ten year period.

5y and 10y

You can see it follows the same sort of pattern but more exaggerated highs and lows, and there are more periods where the LS strategy actually under-performed the DCA strategy. For a five year period the LS strategy won 78% of the time and the outperformance reduced to 2.4%.

So reducing the time period makes the LS strategy slightly less effective, but let’s be honest it’s still far superior to the DCA strategy in the majority of cases.

Now let’s lengthen the investment period to 30 years.

Do you want a fat pipe of information rich content with an actuarial slant? Sign up for emails. You won’t get many emails from me, I’m too busy to be honest. Or follow me on Twitter yeah! @actuaryonfire

Lump Sum or Dollar Cost Average investing – which way to go?

 Long Investment Periods

If we now consider a 30 year investment period we get some interesting results. The following chart overlays the 30 year period on top of the five year and ten year periods.

5y 10y 30y

The black line shows the outperformance of the LS strategy over a 30 year period. It outperforms the DCA strategy in 100% (yes 100%!) of scenarios, and the average outperformance was 2.3%.

It’s also a fascinating chart in that we can see that the outperformance is clearly mean reverting. It’s converging on a sort of long term average. When I reflect on these blog posts I think they actually have nothing to do with the efficacy of a LS strategy versus a DCA strategy, but instead they are a homage to the amazingly robust mean reversion of real equity returns over two centuries!

Another feature that changes is the highs and lows get less “spiky” as we increase the investment horizon. This is simply due to the fact that we are averaging over a much longer period and so any one, or two bad years of investment performance can’t have too large an impact. Even major market upheavals like the Great Depression and 70’s Stagflation are no match for decades of cumulative investment performance.

This is pretty interesting, but we need to put it together into a coherent format.

Putting It All Together

I looked at all periods of investment from two to 30 years using the market data from 1802 onwards. In the last post we looked at how successful the LS strategy was and now we are going to quantify that success with the average outperformance.

avg outperformance

The chart above shows the average outperformance of the LS strategy for different projection periods; it has a pretty pleasing shape doesn’t it? The clear takeaway is that whatever the asset allocation and time period the LS strategy results in a healthy outperformance against the DCA strategy.

You can see how my results diverge from Vanguard’s result and this reflects the fact that under short time periods of a year or two there is a much greater sensitivity to the idiosyncrasies of short periods of returns that get averaged away when you extend the projection period.

So over the last couple of posts we’ve looked at the benefits of investing  a lump sum rather than dollar cost averaging. It’s hard to overcome the cognitive bias of fearing an immediate loss in capital from an event like the Great Financial Crisis, but these are extremely rare and the equity markets have shown extraordinary boucebackability (technical actuary term) over the last two centuries.

What d’ya think? Are you all-in on the lump sum strategy or still nervous about the markets and want to dollar cost average your investment? I can understand it, but the weight of analysis is compelling. If you believe in long term real equity returns then you need to get invested now. Oh yeah, also get that emergency cash fund invested too!

Technical Notes

We can’t blindly accept these results without considering whether they are reasonable. Is there some quick quality-control we can use to check the veracity of these claims?

A simplistic model would be to look at a portfolio of 100% equities. Over any particular projection period the DCA strategy is a bit like investing the total amount at the half-way point. In reality, we have invested under half of our total sum in the first half of the period and then invested over half in the latter half of the projection period. But on average it is roughly like investing everything in at the halfway point. So the DCA strategy is a bit like a LS strategy for only half the time.

If we assume that equities have a real return of 5%, then half the return is 2.5%. I would therefore assume that the LS outperformance to be of the order of 2.5% per year, and if you look at the chart above – it is! Hurrah! And the Vanguard result was 2.6%. So I’m pretty confident that this is all hanging together.

15 thoughts on “Lump Sum or Dollar Cost Average Investing? Part 2”

  1. Great post! I really like the details & charts.
    In all cases, you compared a single sum to the same sum spread out over the time period with annual investments?

    1. Mike, that’s right, compared initial lump sum versus spread out over annual payments. I’ll make that clearer in the post. Thanks for swinging by!

  2. It’s interesting 100% stock outperform 100% bonds only by about 1% while the risk between the 2 is far greater.

    I wonder if DCA is simply reflecting increased SORR on the accumulation side.

    1. This is a bit of a head scratcher, and I don’t have a good answer. Given real equity returns of 5% say, then I show in the last paragraph why LS outperforms DCA by 2.5% (i.e. half the amount). So give an equity risk premium of 4% I might expect the all bond portfolio to show a 2% lower performance than the all equity portfolio (half the amount). But bonds are only 1% lower performance than the equities.
      So like you say, there must be other forces at work. I’m just struggling to come up with a good way to show that it is due to SORR, but that’s a good starting hypothesis.
      I think SORR on the accumulation side would be really interesting to look at.

  3. Really excellent post, AOF. I like the cross-checking. 2.5 percent per year would really add up over time. Your analysis certainly persuades me that lump sum is the correct approach for a long term investor. In the articles I have read on this topic, the consensus is that DCA actually does reduce risk, but that your reward for reduced risk is…you guessed it, a lower return. Time in the market really is everything, I guess.

    1. You’re right, Time in the market is everything. But you raise a good point about quantifying the risk reduction. I think LS wins so conclusively that no amount of risk reduction benefits could compensate you for the loss of a DCA strategy. Thanks for visiting and commenting.

  4. You and the math have convinced me of LS. But one thing confuses me when doing these comparisons. You’re assuming that nothing in the portfolio itself changes when you look at the market over time periods, correct?

    None of us exist in a vacuum. With DCA, what happens if you stop investing for a few months before your new baby arrives or you switch jobs? With LS, what happens when you pull money out of the market for a down payment on a house? Or a health emergency?

    It seems to me that none of us can predict our true investment behavior over our lifetimes. Aren’t we looking at it all in hindsight when we do comparisons? Or am I missing something?

    1. Yay for math! I *knew* I would convince you!
      I’m assuming that the asset allocation gets re-balanced back to the target each year, but you’re right I’m not including any other cashflows that you describe. Things get really complicated with sequence of returns risk when you have money coming in and out. If you want me to model a particular scenario that you have in mind then let me know.
      But you’re right, this is all done in a testube. It’s not real life, but it gives a good guide as to what to do.

  5. Have you considered analyzing the impact of tax-loss harvesting on LS vs DCA? I am thinking about TLH available through robo-advisors like Betterment as opposed to doing it manually. Thanks.

Leave a Reply