This issue is as old as personal finance itself: What should an investor do with a large windfall, say, a bonus, gift, inheritance, etc.? Invest it all at once as one big lump sum or should we “ease into the market” and invest the cash in multiple installments? The latter is called Dollar Cost Averaging (DCA). This is a popular topic in the personal finance world and many of you might have read about it. JL Collins had a blog post on why he doesn’t like DCA and Vanguard has a nice study with extensive simulations showing that, on average, the lump sum investment pretty handily beats DCA. The intuition for that result is pretty straightforward: equities go up on average, so if you sit on your hands and voluntarily delay your investments you will have lower returns on average.
End of story! End of story? Not so fast! Even if you’re familiar with the subject already, please keep reading because we’ll have a new spin on this old topic. Spoiler alert: we propose a way dollar cost averaging will reduce risk and have the same average return as the lump-sum investment!
Dollar Cost Averaging:
As Wikipedia explains it:
“By dividing the total sum to be invested in the market […] into equal amounts put into the market at regular intervals […], DCA hopes to reduce the risk of incurring a substantial loss resulting from investing the entire “lump sum” just before a fall in the market.
So, instead of investing a large lump sum, say $10,000 all in month 1, we could alternatively spread the investment over 2 months ($5,000 each), over 3 months ($3,333.33 each) or over 4 months ($2,500 each). The total investments are the same but DCA could potentially spread out the risk of investing one large amount all in one month.
Side note 1: There is some confusion about the meaning of DCA. The regular monthly investments of a fixed dollar amount (into a 401(k) plan, for example) over many years will imply that when the market is down you buy more shares, and when the market is up you buy fewer shares. Some people call this dollar cost averaging as well. But the periodic investments into a 401(k) plan are more or less mandatory; ten years ago I couldn’t have funded my 401(k) with a lump sum of ten years’ worth of contributions. Dollar Cost Averaging in the context of today’s post means having the funds available and voluntarily spreading out and thus delaying the investment.
Side note 2: Speaking of 401(k) accounts, some personal finance bloggers advocate “front loading” your retirement account contributions, i.e., investing a big chunk or potentially all of your maximum annual 401(k) contribution in January. Physician on FIRE and MadFIentist had blog posts on this recently. The rationale is the same as with lump sum vs. DCA: Since the equity market goes up on average you want to have the maximum equity exposure as early as possible. But keep in mind that the regular periodic 401(k) contributions are not really the same as DCA because your investments occur when you get your income. In contrast, DCA means you voluntarily delay investing while holding on to cash, waiting to deploy the investments over time.
To see whether lump sum investments beat DCA, let’s run some simulations. We use monthly equity returns (S&P500 total return) since January 1871 minus a short-term, risk-free return (3-month T-Bill after 1926, 1-year T-bill before 1926, due to data availability). We calculate how a lump sum investment would have performed over 12-month windows relative to spreading out the investment. Vanguard’s study uses DCA spread out over 12 months and then also performs the same analysis over 6, 18, 24, 30 and 36 months, but we are more interested in shorter DCA horizons and use 2, 3, 4, 5, 6, 8, 10, and 12 months instead. Below are the results for the entire sample since 1871 and also for the more recent period since 1980.
We pretty much replicate the results from the Vanguard study: DCA indeed reduces risk but lags behind the lump sum investment in every other conceivable measure: returns are lower and Sharpe Ratios (excess return divided by risk, i.e., a measure of risk-adjusted mean return) are lower. Over the earlier period, there were a few DCA simulations that yielded marginally higher probabilities of positive returns, but that’s been reversed since 1980. Also, DCA’s probability of beating the lump sum investment is always below 50% and it declines the more we spread out the investments. Bummer!
So we confirmed the well-known result for all DCA horizons between 2 and 12 months: The peace of mind of investing in several installments over time comes at a high price. Some would argue that Dollar Cost Averaging is only for jittery chicken-little investors. But in the FIRE community, we are all cool and rational investors so there is no place for Dollar Cost Averaging around here, right? Or, maybe there is?!
A new spin on DCA: Why wait for the windfall to arrive?
If the risk reduction in DCA is for real but the opportunity cost messes up our returns, why not simply spread out the investments to reduce risk, but start investing before the windfall arrives. Could that be the best of both worlds? Avoid the opportunity cost and still get the risk reduction, see below!
I try the DCA over 3 months starting 1 month before the windfall and the DCA over 5 months starting 2 months before the windfall, see the chart above. Notice the beauty of this assumption: We now invest 1/3 of the equity portfolio for 11, 12 and 13 months each. So the average length of the equity investment is indeed 12 months, the same as in the lump sum case! And analogously, invest one-fifth for 10, 11, 12, 13 and 14 months, also for an average of 12 months.
As the baseline, let’s assume that we are able to borrow the funds prior to the windfall date at the risk-free rate. That might be a bit of a stretch, but for folks who have an emergency fund, why not just “borrow” from that account for one or two months? The opportunity cost is exactly the risk-free rate! And what if a big expense shows up just during that one or two-month window? Come on, everybody, be creative. Use the credit card float or put the charge on a new card with introductory zero percent interest. I don’t have to tell you how to hack that, right?
Of course, as many of you may know, we don’t even have an emergency fund. But we could access a Home Equity Line of Credit (HELOC) to borrow the funds, though at a higher interest rate; the “Prime Rate” in our case (roughly the risk-free rate plus 3% p.a.). So, let’s assume that when borrowing the pre-windfall investment we have to pay that higher interest. But likewise, we also use the excess cash we have when the windfall arrives to pay down our existing HELOC balance (normally around $20,000-$25,000) until we’re done with the DCA. So, how would we implement a DCA of a $10,000 investment over 5 months with an assumed $20,000 initial HELOC balance?
- 2 months before windfall, borrow $2,000 from HELOC to invest. Balance $22,000
- 1 month before windfall, borrow $2,000 from HELOC to invest. Balance $24,000
- Windfall: Receive $10,000, invest $2,000 and use the remaining $8,000 to pay down the HELOC. New Balance: $16,000
- 1 month after the windfall: Take $2,000 out of HELOC and invest. Balance: $18,000
- 2 months after the windfall: Take $2,000 out of HELOC and invest. Balance: $20,000
This scheme generates an average HELOC balance of exactly $20,000, no different than our “normal” HELOC balance. So, don’t be surprised if even with borrowing costs the DCA results will look very similar to the baseline!
If you have no sizable emergency fund and no HELOC either you could still buy equities on margin at an extremely low cost: equity index futures deliver exactly what we want: the index total return (incl. dividends) minus risk-free rate. See our other posts on futures trading: general info here and the post on the Synthetic Roth IRA. Unfortunately, futures contracts are also very lumpy: One single S&P500 futures contract is worth 50x the index level, currently just under $120,000. You’d need a really nice size inheritance to make it worthwhile implementing DCA with equity index futures. Better be nice to your Aunt Betty!
In any case, here are the simulation results, see table below:
- There is essentially no difference in average returns between the lump sum investment and the DCA. That’s not a surprise because the average investment length in the equity market is now the same for both the lump sum and the DCA.
- Amazingly, there is no sizable deterioration in the average return even when factoring in borrowing costs. But again, that’s due to having an existing HELOC balance. The borrowing cost before the windfall is exactly offset by using some of the windfall money to temporarily pay down the HELOC until the conclusion of the DCA.
- The Sharpe Ratio under DCA is higher than with the lump sum. You get a higher probability of positive returns than with the lump sum investment and there is higher than 50% chance of beating the lump sum investment with DCA. How cool is that?!
Of course, the DCA with borrowing will not be feasible all the time. Here are some important limitations:
- Uncertainty about the timing of the windfall: If we don’t even know if or when the windfall arrives it might not be so prudent to put borrowed money in the stock market!
- Borrowing limits: If you have a net worth of $1,000,000 and the windfall is $30,000 you’ll likely find it easy to come up with $10,000 for one month before the windfall actually arrives. If it’s the other way around and you expect a $1,000,000 windfall and your current net worth is only $30,000 you will probably not get a $300k+ loan to invest the month before the windfall!
- Legal and tax constraints: If you want to invest a lump sum in a retirement account for a specific calendar year you can do that as early as January of that year. But you can’t invest the 2018 contribution before January 1, 2018, at least not in the retirement account. Back to the Front Loading technique mentioned above: Investing one large lump sum in January might be advantageous to the periodic investments. Investing three equal amounts in December, January and February (or five equal amounts in November-March) might be even more advantageous but it’s not allowed in the retirement account because of restrictions on how much you can invest in each calendar year.
Is this all a fluke? Where is the mathematical proof?
We are getting beyond 2,000 words so I don’t want to push this too much more. But the superior performance of DCA with borrowing vis-a-vis the lump sum investing is not a fluke. Quite the opposite, in addition to the empirical evidence, I can prove this mathematically. It has to do with the fact that returns and risk in a multi-period investment problem are aggregated very differently. You don’t aggregate risk linearly.
Here’s a simple example (please skip if you don’t like statistics and mathematics): Imagine there are three consecutive (monthly) returns X1, X2, X3. They have some joint distribution and all I require is that they have the same expected returns, the same variance/risk, but there could be some non-zero correlation between the returns.
Lump sum investment: If you invest a lump sum of $1 after X1 has been realized, you would be exposed to returns X2 and X3 only and the variance of the lump sum return is:
V_LumpSum = Var(X2) + Var(X3) + 2∙Cov(X2,X3)
The risk (=standard deviation) would be the square root of that.
Dollar Cost Averaging: If you invest $0.50 before X1 has been realized and another $0.50 before X3 has been realized, then this would be a form of DCA. You invest half the amount one month before the windfall and the other half in the month after the windfall. Slightly different from the 1/3, 1/3, 1/3 setup above but the intuition is the same. $0.50 would be exposed to X1 and X2 and $1.00 would be exposed to X3. The variance of the DCA portfolio return is:
V_DCA = 0.25∙Var(X1) + 0.25∙Var(X2) + Var(X3) + 0.5∙Cov(X1,X2) + Cov(X1,X3) + Cov(X2,X3)
Unless all returns are perfectly correlated, i.e., Cov(Xi,Xj) = Var(Xi) = Var(Xj), the DCA variance is smaller than the lump sum investment variance. That’s because with DCA you spread out the risk more evenly between X1 and X2. In the most basic case where the covariances are all zero (returns are uncorrelated, not a bad assumption for equity returns!), the lump sum investment has a variance that’s 1/3 higher than the DCA portfolio: 2.0∙Var(Xi) vs. 1.5∙Var(Xi). This translates into 15.5% higher risk in the lump sum investment! Despite having the same mean returns the two portfolios have very different risk profiles!
Side note 1: Yes, yes, yes, I know that returns are not additive but they compound. One would define the X=log(1+return) to fix that!
Side note 2: We clearly took today’s post from geeky to super-geeky with this, but there are some of us in the FIRE community who wouldn’t have it any other way!
Dollar Cost Averaging is getting a bad reputation. But before you ridicule the proponents of DCA, keep in mind that, if done properly, DCA delivers exactly what it promises: Risk reduction without the opportunity cost. It will not beat the average return but it delivers the same expected return with less risk. Of course, it involves a little bit of financial hacking. Specifically, it requires leverage (gasp!) and not everybody has an appetite for that. But we do! We wrote a post a while ago on the seven benefits of debt and leverage. And we might mark this one as benefit number eight: Use leverage to reduce risk. Who would have thought?