Saturday, 24 October 2015

Scientific method vs. dollar cost averaging

Being curious, I wanted to study the cumulative expected holding period return for a passive buy and hold strategy over time.

I've mentioned numerous times that there is nothing wrong with indexing in equal dollar increments at regular intervals.  The drawbacks to indexing:

  1. It's lazy, auto-pilot investing, but for some (or most), it may be the approach that results in the least amount of worry, and most success (capital growth) over time.
  2. It's not exciting.
  3. You will not hit home runs indexing.  Instead, indexers should experience steady, methodical growth over time (barring financial catastrophe).
  4. On the subject of financial catastrophe, indexers will very likely experience capital drawdowns of more than 30% peak to trough once per cycle (more on this shortly).
  5. Indexing requires discipline to stick with the plan.
  6. Indexers should take fixed income and cash allocations into the overall index equation 

I started with the following question:

If an investor were to have bought SPY in equal $400 monthly increments starting at a previous market high (I used July 1998), and continued to keep buying at the end of each month on auto-pilot, what expected return would an investor likely realize (compound, holding period return, not including dividends)?  I wanted to start my study at a previous market high to demonstrate the effect on compound annualized returns on buying at a "sub-optimal" (i.e., buying a market high).

So, I ran the #'s, and here's what I came up with:

The chart above demonstrates the actual compound annual return by month, between July 1998 and December 2014 of dollar cost averaging into SPY at the end of each month in equal $400 increments. The compound return is holding period return on cumulative units purchased only over time.  It does not include any dividends

The return works out to around 4.263%.  Add in expected annual dividend yield of say, 2.5%, and we can possibly expect a return of 6.76%.

My next question:

What happens if an investor chooses to buy SPY in equal $400 monthly increments, but only adds to holdings if the current month's close in SPY is lower than the previous month's?

Here are the results:

The return improves by about 25 bps over time, to 4.54%.  This may not sound significant, but 25 bps on $1M compounded over 15 years works out to an additional $38,163 at the end of the 15th year (enough to pay for a child's university tuition for a couple of years) just by altering the frequency of purchases to included additions to cumulative units of SPY only when monthly price is lower than the previous month.

However, this comparison is simplistic because in return for earning $38,163 by reducing purchases of SPY, an indexer gives up excess growth on an additional units invested under a regular monthly program. The difference in contributed capital under a regular monthly program vs. a negative monthly close program is $90K in invested capital at the end of the 15th year.  More capital at work under the first program, earning additional dividends which get reinvested into additional units...

My next question:

What happens if an investor chooses to buy SPY in equal $400 monthly increments only at lower monthly closes, and chooses to dollar cost average into long bonds in $100 monthly increments (this is an 80% equities, 20% fixed income allocation)?

Here are the results:

Here, there's an additional 55 bps improvement in compound return over time by adding fixed income to the equation at 20%.  PS, this is before interest and before dividends, having bought at a previous market high.  Add in expected dividend yield of say 2.5% x 80% of cumulative capital at work, and expected yield on long bonds of somewhere between 3% and 5% x 20% of cumulative capital at work, and the expected return doesn't look all that bad.

Finally, my last question:

What happens if an investor chooses to increase the frequency of purchases from monthly to weekly, but again, uses the negative weekly close rule and allocates 20% to fixed income?

Here are the results:

The results: a .07 bps improvement on monthly purchases.  Not great, but not terrible.

A few comments on study inception:

You can see that initially, there's a huge spike and then a drop in compound annualized return.  This is a function of a) a small number of inputs in the initial year leading to nonsensical compound annualized return data, and b) the effect of drawdown on capital at risk in the initial years buying at a previous market high on a small base of capital.

A few further comments on expected drawdowns:

I mentioned previously that indexers should likely prepare themselves for capital drawdowns of 30% (or more) once a cycle.  I believe this is an honest and realistic expectation, and one of the real caveats of indexing.  Cumulative capital started in July 1998 experienced three significant drops between inception and December 2014, once in summer 1998, once again 1999/2000, and then again in 2008/2009.

Although cumulative capital rebounded in all three cases, at times towards the trough period, cumulative capital got down to -20% and -30% (on an absolute basis).

The reality is, indexers are subject to the vagaries of the market, and to think that the market won't correct or experience another significant move going forward is a delusion.  Over time, the compound return seems to right itself, but my arbitrary study is in no way shape or form a guarantee of 4.5% + returns going forward.


  1. Daniel,

    So in case 2 the $400 just never gets invested if it gets skipped that month? You say that there's $90k less capital invested so that's how I read it. How would it look if the capital was just pooled until it met the lower monthly close and all saved capital was then invested? Thanks for the look at DCA and indexing. I think it's a solid option for most investors.

  2. Hey JC, thanks for commenting. Yes, in case 2, I took the "hypothetical" approach that if a passive investor wants to buy an asset over time (in my study's case, the asset is the S&P500 = SPY), he/she would be preferential to only adding more of the asset if it was cheaper than the previous month's purchase. This is obviously an oversimplification, because SPY could rally 10% over 12 months, and then have two or three consecutive months of lower closes. In this case, the investor buys incremental units if he/she gets a lower monthly close, but he/she is still averaging up into a rising market.

    And yes, the $400 stays in cash until the first monthly lower close vs. the previous month.

    I should post my spreadsheet showing the scenarios (which are arbitrary), but yes, cumulatively, not adding $400 automatically and waiting for a lower monthly close ended up working out to about $90K less in cumulative capital invested by my calculations.

    The study raises additional questions:

    1) How does compound annual return change if an investor began their first purchase on January 1, 2000 through now. What about from June 2008 through now?
    2) How does compound annual change if the study period is longer than 1998 through current?
    3) Just because 1998 return through current ended up being somewhere between 4.25% and 5% on a weekly/monthly systematic basis before dividends and interest , should investors expect similar returns using today as their start date?

    One more thought, and I forgot to post this, the data I used for bonds was TLT per yahoo finance. This data only went back to July 2002, so in order to be comparable, I had to alter the study period for SPY from July 1998 to July 2002. The two periods in history were completely different, so I hope I'm not comparing apples to oranges.