Even God Couldn’t Beat Dollar-Cost Averaging

The Problem with Buying the Dip

Photo: Fabrizio Verrecchia on Unsplash

This is the last article you will ever need to read on market timing.  It’s a bold claim, but I’m not messing around.  So strap in, because the training wheels are off on this one.  To start, let’s play a game:

Imagine you are dropped somewhere in history between 1920 and 1979 and you have to invest in the U.S. stock market for the next 40 years.  You have 2 investment strategies to choose from.

  1. Dollar-cost averaging (DCA):  You invest $100 (inflation-adjusted) every month for all 40 years.
  2. Buy the Dip: You save $100 (inflation-adjusted) each month and only buy when the market is in a dip.  A “dip” is defined as anytime when the market is not at an all-time high.  But, I am going to make this second strategy even better.  Not only will you buy the dip, but I am going to make you omniscient (i.e. “God”) about when you buy.  You will know exactly when the market is at the absolute bottom between any two all-time highs.  This will ensure that when you do buy the dip, it is always at the lowest possible price.

The only other rule in this game is that you cannot move in and out of stocks.  Once you make a purchase, you hold those stocks until the end of the time period.

So, which strategy would you choose: DCA or Buy the Dip?

Logically, it seems like Buy the Dip can’t lose.  If you know when you are at a bottom, you can always buy at the cheapest price relative to the all-time highs in that period.  However, if you actually run this strategy you will see that Buy the Dip underperforms DCA over 70% of the time.  This is true despite the fact that you know exactly when the market will hit a bottom.  Even God couldn’t beat dollar-cost averaging. 

Why is this true?  Because buying the dip only works when you know that a severe decline is coming and you can time it perfectly.  Since dips, especially big ones, haven’t happened too often in U.S. market history (i.e. 1930s, 1970s, 2000s), this strategy rarely beats DCA.  And the times where it does beat DCA require impeccable timing.  Missing the bottom by just 2 months lowers the chance of outperforming DCA from 30% to 3%.

Instead of taking my word for it, let’s dig into the details to see why this is true.

To start, let’s consider the U.S. stock market from January 1995 to December 2018 to familiarize ourselves with this strategy.  Below I have plotted the S&P 500 (with dividends and adjusted for inflation) over this time period with the all-time highs colored green:

Now, I am going to show the exact same plot as above, but I am going to add a red dot for every “dip” in the market (the biggest decline between a pair of all-time highs).  These dips are the points at which the “Buy the Dip” strategy would make purchases.

As you can see, the dips (red dots) occur at the lowest point between any two all-time highs (green dots).  The most prominent “dip” over this time period occurred in March 2009 (the lone red dot before 2010), which was the lowest point after the market high in August 2000.  However, you will also notice that there are many less prominent dips that are nested between all time highs.  These dips cluster during bull markets (i.e. mid-to-late 1990s, mid 2010s).

If we wanted to visualize how the Buy the Dip strategy works, I have plotted the amount the strategy has invested in the market and its cash balance over this time period:

Every time the strategy buys into the market (the red dots), the cash balance goes to zero and the invested amount moves upward accordingly.  This is most obvious when we look at March 2009 when, after nearly 9 years of cash savings, $10,600 is put into the market.  If we compare the portfolio value of Buy the Dip and DCA, you will see that the Buy the Dip strategy starts outperforming around the March 2009 purchase:

If you want to understand why this one purchase is so important, let’s consider how much each individual purchase for the DCA strategy grows to by the end of the time period.  Each black bar in the chart below represents how much a $100 purchase grew to by December 2018.  For example, the $100 purchase in January 1995 grew to over $500.  The red dots (once again) represent when the Buy the Dip strategy makes purchases:

This chart illustrates the power of buying the dip as every $100 invested in March 2009 (that single red dot towering near 2010) would grow to ~$350 by December 2018.  This one purchase (and its growth) accounts for 52% of the final portfolio value for the Buy the Dip strategy in December 2018.  In addition, there are two things to notice about this plot:

  1. The earlier payments, on average, grow to more (Yay for compounding!!)
  2. There are a handful of big dips (i.e. February 2003, March 2009) where some payments grow to a lot more than others.

If we put these two points together, this means that Buy the Dip will outperform DCA when big dips happen earlier in the time period.  The best example of this is the period 1928-1957, which contains the largest dip in U.S. stock market history (June 1932):

Buy the Dip works incredibly well over this period because it buys the biggest dip ever (June 1932) early on.  Every $100 you invested at the bottom in June 1932 would have grown to $4,000 in real terms!  There is no other time period in U.S. market history that even comes close to this.

I know it might sound like I am trying to sell the Buy the Dip strategy, but the 1995-2018 and the 1928-1957 periods just happen to be two where there were prolonged, severe bear markets.

If we look over longer time frames, historically, Buy the Dip doesn’t outperform most of the time.  The chart below shows the amount of outperformance from Buy the Dip (as compared to DCA) over every 40-year period over time.  Outperformance is defined as the final Buy the Dip portfolio value divided by the final DCA portfolio value.  When Buy the Dip ends with more money than DCA it is above the 0% line, and when it ends with less money than DCA it is below the 0% line.  To be precise, over 70% of the time, Buy the Dip underperforms DCA (i.e. it is below the 0% line):

What you will notice is that Buy the Dip does well starting in the 1920s (due to the severe 1930s bear market) with an ending value up to 20% higher than DCA.  However, it stops doing as well after the 1930s bear market and does continually worse.  Its worst year of performance (relative to DCA) occurs immediately after the 1974 bear market (starting in 1975).

This 1975-2014 period is particularly bad for Buy the Dip because it misses the bottom that occurred in 1974.  Starting in 1975, the next all-time high in the market doesn’t occur until 1985, meaning there is no dip to buy until after 1985.  Due to this unfortunate timing for Buy the Dip, DCA is easily able to outperform:

You can see this more clearly if we look at the purchase growth plot for this period:

As you can see, unlike the 1928-1957 or 1995-2018 plots, Buy the Dip does not get to buy large dips early.  It does get to buy the March 2009 dip, but it happens so late in the simulation that it doesn’t provide enough benefit to outperform.

My point in all of this is that Buy the Dip, even with perfect information, typically underperforms DCA.  So if you attempt to build up cash and buy at the next bottom, you will likely be worse off than if you had bought every month.  Why?  Because while you wait for the next dip, the market is likely to keep rising and leave you behind.

What makes the Buy the Dip strategy even more problematic is that we have always assumed that you would know when you were at every bottom (you won’t).  I ran a variation of Buy the Dip where the strategy misses the bottom by 2 months, and guess what?  Missing the bottom by just 2 months leads to underperforming DCA 97% of the time!  So, even if you are somewhat decent at calling bottoms, you would still lose in the long run.

I wrote this post because sometimes I hear about friends who save up cash to “buy the dip” when they would be far better off if they just kept buyingMy friends do not realize that their beloved dip may never come.  And while they wait, they can miss out on months (or more) of continued compound growth.  Because if God can’t beat dollar cost averaging, what chance do you have?


God Still Has the Last Laugh

One of the most important things I re-learned from crunching all the numbers for this post is how dependent we are on timing luck (formally known as sequence of return risk).  This is something that is completely out of our control.

For example, the best 40-year period between 1920 and 1979 was from 1922-1961, where your $48,000 (40 years * 12 months * $100) in total purchases grew to over $500,000.  Compare this to the worst period 1942-1981, where your $48,000 in total purchases only grew to $153,000.  That is a difference of 226%, which is much larger than any divergences we saw between the DCA and Buy the Dip timing strategies!  Your strategy is less important than what the market does.  God still has the last laugh.

If you made it this far, congratulations on finishing this monster post.  I hope it makes you re-consider having “cash on the sidelines” ever again.  Lastly, special thanks to this Alpha Architect article for inspiring the post title and thank you for reading.

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This is post 110. 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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59 Responses

  1. Anonymous commented on Feb 05

    Now do Japan, or China – markets that haven’t gone up in perpetuity over decades.

  2. Anonymous commented on Feb 05

    Your points are well taken and while I don’t think steelmanning the BTD strategy is necessary, it would be interesting to compare the sharpe ratio and max drawdowns of the comparisons. Return is just one side of the equation. If the risk metrics of BTD were significantly better than it probably should have been levered (this strategy was endowed with foresight to start with take its actions to their logical conclusions). Again, I don’t think this additional comparison dilutes your point if your talking about personal finance and behavior. Your posts are always top notch, thanks for sharing your efforts

  3. Anonymous commented on Feb 06

    🙂 Epic article.. But there is an irony which makes this article kind of redundant… People who actually understand the math behind the power of compounding..have not been waiting for this article to open their eyes… They have been doing DCA anyway.. And people who needed to read this to open their eyes are the ones who in all likely hood do not fully grasp compounding… In which case they will also not fully grasp the calculations the author explains.. They will keep waiting with their crystal balls trying to time the markets😋.. But great article. Thanks

    • Nick Maggiulli commented on Feb 06

      I appreciate the comment and partially agree. I don’t think this idea is necessarily that intuitive. I didn’t know I would get this results when I started this. I was just interested in seeing what would happen. The thinking behind why DCA > Buy the Dip most of the time is what was most intriguing to me.

  4. Anonymous commented on Feb 06

    What about a “lump sum”? Say you receive an inheritance, a large tax refund, or something else that is large and all at once. Obviously, putting the cash into a savings account and DCA every month over 40 years doesn’t work either. Great article for savers though!

  5. Anonymous commented on Feb 06

    For a lump sum or windfall investor, sitting on a pile of cash, it sounds like combing the two strategies would work well. Commit to a DCA strategy while also setting up a rule where additional lump sums get invested as the market drops.

  6. Anonymous commented on Feb 06

    Thanks for the post, Nick. One quick follow-up question- did you consider the yields on cash (via 6-month T-bills, historical CD rates, or any other metric) over the years?

    Clearly yields are very low today, but in the 80s 6-month CD rates were 7%+ for the majority of the decade and in the 90s were often above 4%, which would improve the BTD results (would have higher cash balances to purchase more stock on the dips.) I would assume many investors who build up cash to buy on dips would attempt to get some yield on their cash in the meantime.

    • Nick Maggiulli commented on Feb 06

      I assumed inflation-adjusted cash over time (i.e. invest in TIPS). I did not look at using other forms of fixed income, but my prior suggests that they would not change the results that much. And even if they did, remember that Buy the Dip still requires perfect timing, which is the most ridiculous assumption I made. By Buying the Dip a little later than the bottom and all the outperformance would likely fade once again. So, on balance, I don’t think the cash yield was that wild of a thing to ignore.

  7. Anonymous commented on Feb 06

    I posted harsher comments on Marketwatch.com, but in fact, you did a really good work. I just want to hear from you about the comments that I made. Most people read stuffs online without any critical thinking, and I’d love to hear your feedback on my comments.

    Because all of the invesment dollars are never sold in your comparison, the “market timing” that you are trying to compare is in fact relatively minor. Or I shall say that you didn’t give “God” the chance to sell and time the market perfectly, because it is not allowed in your comparison.

    Therefore, you are really just comparing the market timing of the initial investment. I don’t know the exact criterion for you to determine the “dip”, but what you have definitely shown here is that stocks tend to go up more than go down, and it doesn’t really pay to sit and wait around for the next correction dip.

    If you did add the selling, I believe the results will be very different. My personal belief is that market timing (for either buy/sell) doesn’t work possibly 95% of the time, but towards the end of the bubble peak, it would become obvious. If one just catches that 5%, maybe the results would be different. But obviously, that’s just my conjecture.

    • Nick Maggiulli commented on Feb 07

      I am trying to compare a market timing strategy that actual investors do. Frequently people build up cash to buy dips and don’t necessarily move completely out of stocks. This is far more common than selling out completely and buying back in completely (which would change the results dramatically as you suggest). My point in this article is to suggest that building cash on the sidelines (while a good portion of your assets are invested) is usually suboptimal to a DCA strategy, especially if you can’t time which no one can consistently.

      As for the “it would become obvious” near a bubble peak. This is wishful thinking. It was obviously a DotCom bubble in 96 and 97, but it didn’t burst for 3 years. That is 3 years of you shorting or sitting on the sidelines while watching your friends get rich. Good luck timing that. Few did successfully.

  8. Anonymous commented on Feb 07

    Nice post. Thanks a lot!

  9. Anonymous commented on Feb 07

    Nick,

    Thanks for your thoughtful analysis. I’m always jealous of people like you that have the programming skills to back-test interesting ideas.

    Have you considered that the results are largely driven by how you’ve chosen to frame the question (i.e. you’ve defined market timing as buying the dip)?

    My post on Sharpe’s classic market timing paper illustrates the issues this creates:

    https://marketfox.org/2017/11/16/i3-insights-quants-and-market-timing-part-ii/

    No market timer or asset allocator I know would ever do this. They would either use trend (just like the Ritholtz’ “Goaltender”) or valuation (which isn’t necessarily the same as buying a dip).

    Also, how does the analysis look if you risk-adjust the return? You could compare the two strategies in terms of Sharpe ratio.

    Thanks

    Daniel

    • Nick Maggiulli commented on Feb 07

      I agree that this article does not answer every market timing question. My quip about being the “last article you will ever need to read on market timing” was more for theatrics. However, I don’t think how I have framed it is controversial. I know many individuals that build cash piles in hopes of buying a dip. This is the exact behavior I am trying to get people to stop undertaking.

      Lastly, of course Buy the Dip would have a better Sharpe ratio than DCA (cash is less volatile than the market), but this misses the point. The only reason that it is less volatile is that I have given you PERFECT information. You KNOW when the dips will occur so you can avoid market volatility while you wait. This is so unfair and unrealistic that comparing Sharpe ratios is all but meaningless in this scenario.

  10. Anonymous commented on Feb 07

    How about digging into the retirement version of the same question. Assume the retiree needs $3000/mth on a $1,000,000 60/40 portfolio. Would it be better to “sell the dips,” sell every month, or just sell once a year?

  11. Anonymous commented on Feb 07

    Can you open source your code for this? I’m curious to see what would happen if you set a rule to invest all your cash at the end of each month if there was no dip by then.

  12. Anonymous commented on Feb 08

    Go to Greece, Italy or any other European market and try this… Luckily US has been most successful market in last century so it seems ok on hindsight. What happened on past 80 years need not to be repeated in next 10-15 or another 80 years. World is changing so fast so no body knows how next century look like. The only way to perform is to focus on growth and valuation and respect it to avoid any catastrophic…

  13. Anonymous commented on Feb 08

    Absolutely love your study, but I guess the results would have been better for the market timer had he parked his savings at money market rates (t-Bills) or in medium term notes rather than staying in cash

  14. Anonymous commented on Feb 09

    I too am curious about how this works for retirees that are exiting their 60/40 portfolio for cash flows in retirement. Assuming a 4.5% withdrawal rate including dividends and income being withdrawn/distributed. How would selling at the highs extend the life of the portfolio when liquidating on a quarterly basis versus systematically “dollar-cost-averaging” out of their positions also quarterly. Applying the video-game “God” mode, perfectly timing the high of the each quarter when they liquidate-how much further their portfolio would sustain their income.

  15. Anonymous commented on Feb 11

    Hi nice post. Why didn’t buy in the dip of around 2001/02?

  16. Anonymous commented on Feb 13

    Nick,

    Great post! Really thought provoking. Here’s my question for you and the community.

    Do you think its best to max your 401k as quickly as possible or spread that 19k contribution across the 12 months of the year? I’ve argued for and against this and have done both. Would be interested in everyone’s thoughts.

    • Nick Maggiulli commented on Feb 13

      I am writing a post on this now (Lump Sum vs. DCA). Lump Sum is almost always better than DCA and the performance differences won’t be that large over shorter time periods. Also, given you have the ability to max earlier in the year without any affect on your need for cash is good. Don’t know if everyone could do this.

  17. Anonymous commented on Feb 13

    Yes, what you call buying the dip is not a good strategy. However it makes sense to do a little timing when your whole position looks to be in jeopardy. I sold all October 2018 and got back in January 2019. Saved me 10% loss. Moving on.

  18. Anonymous commented on Feb 14

    Nice post with more analysis than most. I may try to look at it myself if I ever get time free from kids etc but rather than building up cash and “perfectly timing major bottoms” which can take many years to play out e.g. the big gap from 2000 to 2009 I would look at a scenario of build up cash and buy x% below peak. Much easier to implement since you don’t need to verify God. If x is 10 then you will not have to wait as long to buy. Be interesting to optimise for x. It all relies on the market going up over time and not sitting on the sidelines too long.

  19. Anonymous commented on Feb 15

    Wonderful analysis & post. Although, embarrassed that I have mixed DCA and lump summing in during my accumulation phase — obviously, my nest egg is smaller because I have been well-short of God-like.

    Thank you Nick, I have shared this with my adult children in hopes they don’t walk in my lump sum footsteps.

  20. Anonymous commented on Feb 16

    What interst rate was assumed for the cash that sat waiting for the next dip in the buy-the-dip case?

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