How to Invest a Lump Sum

A Deep Dive Into Investing Large Amounts of Money

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So, it happened.  You just received a lot of money.  Maybe a relative passed away and left you a nest egg.  Maybe you sold your business.  Maybe you hit the lottery.  Regardless of how you got the chunk of change you are currently sitting on, you now have to ask yourself:

Should I invest this money immediately or over time?

This question comes up a lot when we are chatting with clients.  I understand the fear they (and you) may have around investing this money.  There is a lot at stake.  Hundreds of thousands, maybe millions, of dollars.  What if the market crashes right after you invest?  Wouldn’t it be better to average-in over time (i.e. dollar-cost averaging/DCA) to smooth out any unlucky timing on your part?

Statistically, the answer is no.  In a paper from 2012, Vanguard found that 66% of the time it is better to invest your money right away (“Lump Sum”) rather than buying in over 12 months (“DCA”).  I don’t disagree with Vanguard’s results (my results were strikingly similar), but I don’t think they went deep enough in explaining why this is true.

The main reason Lump Sum outperforms DCA is because most markets generally rise over time.  Because of this positive long-term trend, DCA typically buys at higher average prices than Lump Sum.  Additionally, in those rare instances where DCA does outperforms Lump Sum (i.e. in falling markets), it is difficult to stick to DCA.  So the times where DCA has the largest advantage are also the times where it can be the hardest for investors to stick to their plan.

By putting these two points together I hope you come to the conclusion that you should just invest your cash now and move on with your life, because you are very likely to lose more money (in missed growth) if you don’t.  I may not have convinced you yet, but I plan to.  Let’s begin.

To compare Lump Sum and DCA, all you have to do is compare what a Lump Sum payment grows to and what each individual DCA payment grows to over the same buying period.  When I say “buying period” I mean the amount of time you take to average-in to the market (i.e. 6 months, 12 months, etc.).  Once the buying period is over, whichever strategy has more money is the winner.  Why?

Because once DCA is fully invested, any subsequent returns between the two strategies will be identical going forward.  This means that if over a 12-month buying period DCA has 10% more money than Lump Sum at the end of month 12, it will also have 10% more at the end of month 13, 10% more at the end of month 14, and so on.

Therefore, to compare Lump Sum and DCA, I looked at how much each strategy grew to in a 60/40 (stock/bond) portfolio over various buying periods from 1960-2018.  The buying periods varied from as short as 2 months to as long as 60 months (5 years).

For example, below is a chart illustrating how DCA performed against Lump Sum in a 60/40 portfolio (using a 12-month DCA buying period) for each month from 1960-2018.  The first point in January 1960 represents how much money the DCA strategy grew to (by averaging-in over 12 months) compared to how much the Lump Sum payment in January 1960 grew to over the same 12 months.  I then did this for February 1960, March 1960, and so on:

lump sum vs dollar cost averaging outperformance over time for a 12 month dollar cost averaging window

What you will notice is that DCA underperforms Lump Sum 80% of the time, but there are still a handful of periods where DCA outperforms.  The most notable outperformance occurred 12 months before the bottom in March 2009.  This makes sense because DCA beats Lump Sum when buying into a falling market (as I mentioned above).

However, you will also notice that immediately after the March 2009 bottom, Lump Sum immediately starts outperforming DCA again.  This occurs because the market changes from a falling market to a rising market at the exact bottom (March 2009).  It is at this exact inflection point that Lump Sum regains its advantage over DCA.

If we look at a distribution of DCA’s outperformance you can see the relative performance more clearly:

lump sum vs dollar cost averaging outperformance distribution for a 12 month dollar cost averaging window

While 3.7% is the average underperformance of DCA, 5%-10% underperformance is far more common.  More importantly, the distribution is quite symmetric, meaning that DCA has roughly the same amount of underperformance as outperformance at the tails of the distribution.  So your fear of a market crash needs to be balanced out by the fear of being left behind as the market shoots upward.

But, it gets worse.  Let’s say you think 12 months is far too short of a period over which to invest your money.  You want to try something longer.  Well, as you lengthen the buying period, the chance of you outperforming doesn’t change much, but the chance of you underperforming starts to go up quickly.  Specifically, as you average-in over 24 months (or more) the relative performance starts to drop precipitously.  Below is an animated plot showing the DCA outperformance over time in a 60/40 portfolio for buying periods ranging from 2 to 60 months:

lump sum vs dollar cost averaging outperformance over time for varying time windows

As you can see, DCA underperformance increases as the length of the buying period increases.  By the time you get to a 5-year DCA buying period, the chance of underperforming a Lump Sum is 95% and the average underperformance is 17%!  You can see this more directly by observing the leftward shift of the relative performance distribution as the buying period increases:

lump sum vs dollar cost averaging outperformance distribution for varying time windows

If this doesn’t illustrate the problem of waiting long periods of time to average-in your wealth, I don’t know what will.

So let’s ignore those longer periods and focus on the relative performance over a 2-year buying window:

lump sum vs dollar cost averaging outperformance over time for a 24 month dollar cost averaging window

Do you really think you are going to be one of the lucky ones to start averaging-in during the handful of months above the 0% line?  Or do you think it is far more likely that you will average-in during the months below the 0% line?  Better yet, instead of the difference in performance between these strategies, consider the absolute performance of each for the same buying period (Note: Lump Sum = blue line, DCA = black line):
lump sum vs dollar cost averaging performance over time for a 24 month dollar cost averaging windowHow much clearer can it get?  Do you really want to choose the black line over the blue line?  If you are still not convinced of the absolute dominance of Lump Sum investing over DCA, then maybe I haven’t learned my lesson from Jeremy Siegel:

Fear has a greater grasp on human action than does the impressive weight of historical evidence.


The More Important Question

If I still haven’t convinced you of the power of Lump Sum investing over DCA, then maybe YOU are not asking yourself an even more important question:  What is my risk tolerance?

Anytime someone has fear about a market crash, my immediate response is that maybe their balance of risky and less risky assets is not appropriate for them.  Everything I did here was for a 60/40 portfolio, but this could be done for any portfolio (with a generally positive long-term trend) and my conclusions would remain unchanged.  So, what is the largest amount of underperformance you could stomach?  Once you know this, you can find a portfolio that fits you AND still do a Lump Sum investment.

Lastly, you only get one life to live.  Time is your most important asset as a person and as an investor.  Don’t waste it on the sidelines.  I hope this post was useful to you (or your clients, if you’re an advisor).  Special thanks to Alex Palumbo and Matt Lohrius for lots of useful insights for this post based on their client experiences.  Thank you for reading!

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This is post 112. Any code I have related to this post can be found here with the same numbering: https://github.com/nmaggiulli/of-dollars-and-data

 
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51 Responses

  1. Anonymous commented on Feb 19

    Great post Nick. I really enjoyed it.

  2. Anonymous commented on Feb 19

    Great article. I appreciate the data.

    A couple of questions that I had after reading are:

    How would this analysis work when not examining the US Equity or Debt market, but looking at a different asset class? For example, a commodity/currency like Silver.

    If the performance of lump sum investing involves a component of market timing (better performance in rising, vs falling markets), could you look back with trend-investing technical analysis signals to create a hybrid approach (DCA and LSI) to achieve optimal returns?

    Did averaging the DCA buy periods between 2 months to 5 years, marginalize the return performance of DCA? As I understand DCA, the more regular buying intervals, the lower the effect of price on the underlying asset.

    How does this analysis answer the question any different than saying, “most markets generally rise over time”, which is a supported, yet overtly generalized statement?

    I understand the theory behind DCA to be; reduce emotions/fear when investing, reduce price impact, and reduce odds of incorrectly timing the market (which most all investors understand to be nearly impossible on a consistent basis). The same advantages of what you have stated LSI offers based on historical return.

    Thank you.
    Alex

  3. Anonymous commented on Feb 19

    Great article with great data, however if DCA helps you sleep at night, do that.

    Also, rather than comparing lump sum to DCA, I’d be curious to see how it would look to compare lump sum to value averaging.

  4. Anonymous commented on Feb 19

    Hi,
    Just a few comments.. when the rest of the money was not invested in the DCA models compared to fully investing the block of money, was the unused portion included in gaining bank interest income or was that part excluded?

    Also, with the DCA model, when markets drop, the increase of the next months contributions could go up, buying more at a lower price, and then again so if the market drops further. Once the markets go back up to the break even level, the remaining amount of money can be invested as if the entire block was invested first and then all purchases before that break even point will beat the lump sum model for the life of the comparison.

    Thanks!

  5. Anonymous commented on Feb 19

    Thank you for another great write up and addressing this important topic. Out of curiosity, I wonder what the results would be if DCA were used when the SP500’s fwd PE is above its trailing 10-year avg vs lump sum when fwd PE is below its 10-year average. I’d imagine lump sum would still outperform as historically ‘expensive’ markets can get a lot more ‘expensive’. In any case, keep up the great writing and analysis!

  6. Anonymous commented on Feb 19

    I disagree, and no amount of simulation addresses my concerns. If you lump sum invest and have extraordinary luck, you may get a self-confidence that causes you ruin later in life. If you lump sum invest and have bad luck, you may be unable to invest properly due to the trauma of a fast and (in hindsight) poor decision. You may second-guess everything for the rest of your investing life and not have the minimum confidence to do the basics.. If you DCA you realize that there were more optimum strategies but the process you followed allows you to follow other processes required to be successful. DCA avoids either extreme and is worth the cost. Love your blog, but I think you are too young to have the correct perspective here. I’m 51 and am lucky to have had the lump-sum problem more than once.

    • Nick Maggiulli commented on Feb 20

      You make some valid points about behavior that I agree with. Sounds like you are talking about someone who is taking far too much risk. If someone is having issues sticking to a plan, then they should probably be taking less risk in their portfolio and Lump Sum with THAT less risky portfolio. Remember that there are other levels you can pull to fix bad behavior besides timing.

  7. Anonymous commented on Feb 19

    Nick – I have had a similar question which is, if you can max out 401k, IRA, kids 529s, etc in January each year (rather than equally throughout the year), wouldn’t it make sense to do so (because to you’re point the market on average is going up throughout the year). Basically follows the same logic, do you agree?

  8. Anonymous commented on Feb 20

    Very insightful post. How does the data behave over a 6 month DCA period? Will the risk reward ratio then prefer DCA over lumpsum? Thanks in advance?

  9. Anonymous commented on Feb 20

    Hi Nick, compelling argument but I suppose it works only if you receive a windfall?

    If an investor only had a regular monthly salary, given the above, would you say it’s better to save up and invest lumpsum once a year rather than DCA?

  10. Anonymous commented on Feb 20

    Very interesting, thank you Nick
    Nicolas

  11. Anonymous commented on Feb 20

    Did the uninvested cash earn T-Bill rates during the DCA period?

  12. Anonymous commented on Feb 20

    I am struck by a couple questions when reading this analysis.
    The first question is that by the same logic of achieving the higher return by lump sum investing, we should revisit why one is investing in a 60/40 mix and not 100% in equities assuming one’s investing horizon is not short term (particularly when interest rates are perceived to be relatively low). I tend to agree with some of the other comments that point out that loss aversion needs to acknowledged and one’s risk tolerance can be managed either by the asset mix or with the time dimension of DCA.
    I would also suggest that your argument is much more convincing for a situation where the “large amount of money” represents a more modest percent of one’s overall net worth or portfolio, say 10%, as opposed to a very large percent, say 80%, where loss aversion will be more prevalent.
    My second observation is that I do not consider the investable universe to be limited to equities and fixed income, and that there are other asset classes and other investment opportunities that are not immediately available or that may require time and dry-powder to take advantage of. Such opportunities would theoretically have the additional benefit of providing additional diversification to one’s portfolio.

  13. Anonymous commented on Feb 20

    Is there any significant difference in the results if the asset mix is 100/0? That is, 100% into an index fund?

    • Nick Maggiulli commented on Feb 21

      They are all index funds (stock/bond). The 60/40 is the split between stocks and bonds not whether something is in an index fund.

  14. Anonymous commented on Feb 22

    Great post! Thank you.

  15. Anonymous commented on Feb 22

    Most people DCA into equity. Why would anyone DCA into bonds!

  16. Anonymous commented on Feb 22

    Great article Nick, with excellent supporting illustrations. In your opinion, would it be reasonable to assume DCA will provide a higher likelihood of positive results in the converse situation, i.e., the investor has a chunk of dollars invested and is looking to liquidate for cash, but does not need it immediately? It would be interesting to see the same supporting illustrations for the opposite scenario. Thanks for taking the time to share your expertise.

    • Nick Maggiulli commented on Feb 22

      You are correct. If you assume the market will have a long-term positive trend, then DCA out of the market is better than selling all at once, in most cases. If you are worried about market crashes, then you should change your asset allocation to have fewer risky assets and then DCA out. Hope this helps.

  17. Anonymous commented on Feb 24

    Hi Nick, Just wondering if it would be a nominal or significant difference going 80/20 instead of 60/40 in your models? Maybe 80/20 makes sense on your age up to a point, then converting to 60/40 when you hit a certain age for a steadier rider would make more sense. Thanks!

  18. Anonymous commented on Mar 16

    Excellent post, and helpful follow up on the impact of uninvested cash earning T-Bill returns. Thank you Nick.