How to boost your earnings from stocks and ETFs: my research on modified dollar-cost averaging

[joyfulboy]

UPDATES (17-09-2020):

Instead of replying to each of you individually, here are my comments and corrections (thank you for valuable comments):

• From your comments I see the post turned out to be a bit misleading: the DCA and modified DCA do indeed perform better than lump sum investing, but in terms of % return (it can't be different since with the modified DCA you make purchases at ever lower prices). So in a bullish market, investing $100 a month would result in similar % gains with lump sum and DCA, with the difference that absolute amount invested with lump sum is bigger, therefore also absolute gains (in dollars, not %) are incomparably higher than with the modified DCA (not to mention the regular DCA, in which you would keep buying at ever growing prices). So this. overall, does not contradict previous research, I believe. For instance, one of you mentioned this: https://static.twentyoverten.com/59...ing-Just-Means-Taking-Risk-Later-Vanguard.pdf , which, however, compares the final values of hypothetical portfolios from lump sum and DCA. I should have better stressed the metrics used to compare the three strategies.
• In reference to previous point that in bullish market the modified DCA performs similar to lump sum investing in terms of % return but underperforms in terms of absolute return: this is because smaller amounts are invested. In order to (partly) solve this issue, look for other investment opportunities, as mentioned in the post, to make your money work for you. This makes the strategy a bit more complicated but at the sime time helps diversify your portfolio. Also, since you're buying at equal intervals, spreading your purchases of additional assets in time helps you to further even out the market volatility.
• Lump sum definition: removed the part about "buying at best possible price", which of course is not required in this strategy, though in times of market downturns this is how it could be played out
• costs: DCA and modified DCA mean more purchases than lump sum, hence higher commision paid to your broker. In general, however, more and more brokers offer commision-free trading or at least extremely low fees. Also, if you invest higher amount, the commissions are negligible By the way, you might like the link provided by one of you: https://money.stackexchange.com/que...stments-to-maximise-returns-and-minimise-fees

(as I couldn't load images to this post, I'm using links from a post in my profile - not to be understood as self promotion, it's just a solution)

Hi Guys,

As you might already know the idea behind dollar-cost averaging (DCA) is to divide up the total amount to be invested into purchases done in regular intervals. For instance, having $10,000 to invest in AAPL, one could either try to time the market, executing a single purchase (this is the so called lump sum investing) or split it into smaller (let’s say $500) purchases executed monthly (DCA), which reduces the impact of price volatility on the overall performance of one’s portfolio and, generally speaking, often helps gaining higher yields.

The advantages of dollar-cost averaging are as follows:

• it eliminates or at least reduces the need to time the market – which we know is hard to do – and uses time to minimize the effect of price volatility
• it’s an attractive option for those who want to contribute to their portfolios on a regular basis, such as those who begin to invest or those who can’t afford investing large sums but wish to enter the market; for these reasons, DCA fits retirement plans like IRA and 401(k) quite well
• it reduces – but certainly does not eliminate – the overall investing-related stress. Look at this: if the share’s price drops, you buy at a discount If the price skyrockets, the value of your portfolio is rising, so you’re happy as well

If you would like to read more about dollar-cost averaging, here is a couple of readings, which might deserve your attention:

• https://www.investopedia.com/terms/d/dollarcostaveraging.asp
• https://investinganswers.com/dictionary/d/dollar-cost-averaging
• https://www.forbes.com/advisor/investing/dollar-cost-averaging/

Here is a practical example.

Assuming you wish to spend $4000 to buy shares of Some Nice Company Ltd., the purchases will be distributed across four months:

• Month 1: share price is $50; you can purchase 20 shares for $1000
• Month 2: share price reaches $62.5: you can purchase only 16 shares for $1000
• Month 3: share price is down to $40: you can now buy 25 shares for $1000
• Month 4: the price is still $40, so again you get 25 shares for $1000

After four months you own 86 shares of Some Nice Company Inc. But if you never heard of DCA and decided to invest the whole sum on day one instead, you would only own 80 shares (80 shares x $50 = $4000). That’s a HUGE difference, isn’t it?

So while the DCA approach is fine, why actually bother and try to change anything in it? Simply becaue it’s good but far from being perfect. What I mean is that you can modify this very simple approach a bit to get substantially better results in the long term, as I’m going to show you below. Today, I’ll only focus on randomly generated stock data that simulates both bear and bull markets, with varying volatilities. In one of the following posts we will look further on how the modified DCA behaves when applied to real life share prices.

So what’s the strategy? Assume you decided to invest in our favorite Some Nice Company Inc. and you want to purchase a $100 worth of its stock each month. After a month from the first purchase, the share price may have dropped, gone up or be essentially unchanged. With the modified DCA we’re only going to purchase more shares if the price is down compared with previous purchase, meaning buying at a discount. The exact amount we are about to purchase is specified with the following formula:

• the price is down by less than 2% ⇒ buy 1 share
• the discount is in between 2% and 4% ⇒ buy 2 shares
• the price drops by more than 4% ⇒ buy 3 shares

In other words, we’re trying to buy the shares at a discounted price, while with a regular DCA we would be purchasing a $100 worth of stock each month.

Importantly, we are also setting up a Stop Loss at -50% and Take Profit at 50%.

Using these settings with simulated stock prices in 100,000 simulations of 24 monthly intervals, we get the following:

1. Moderate volatility, assuming no trend in price change, i.e. the price fluctuates randomly up and down

https://preview.redd.it/w2fmufnojcn51.png?width=298&format=png&auto=webp&s=01c8dbd7e09df08d2a5a3e3e096de20e913551f7

When the price fluctuates randomly and there is no clear UP or DOWN trend (let’s say, the price consolidates), an investor using lump sum strategy will earn nothing (here: 0.01%). However, DCA allows one to get a minimal profit of 1.5% under those circumstances, while the modified DCA grants as much as 6.68% on average. Noteworthy, with the modified DCA Take Profit was triggered 18,810 times and Stop Loss only 667 times (less than 0.7% of investments).

2. High volatility, assuming no trend in price change, i.e. the price fluctuates randomly up and down

https://preview.redd.it/ybvskyqqjcn51.png?width=291&format=png&auto=webp&s=6c388134d40c41b9cb7a612ef4464f6337834dd0

This is similar to the above scenario but volatility is increased substantially. Now, both the regular and modified DCA grant higher yields, with the latter being significantly more effective (6.23% vs 14.6%). For the modified DCA Take profit was triggered 44,639 times (almost half of cases) and Stop Loss 15,216 times.

3. Moderate volatility, moderate trend UP

https://preview.redd.it/02hl95zsjcn51.png?width=293&format=png&auto=webp&s=bb1615654f95f92c6bc6707682e191078141c6fc

Now let’s look what happens if there is a tendency for share prices to rise. Well, lump sum and the modified DCA perform equally good, with the regular DCA being a runner-up.

4. Moderate volatility, moderate trend DOWN

https://preview.redd.it/sraaiydujcn51.png?width=299&format=png&auto=webp&s=3cb2c66601b101cfcd212da1e76bd31d7ca9f2b9

And what if the prices are going down? This shows one of the greatest advantages of the modified DCA: with a loss of -14.62% it is marginally better than the regular DCA but amazingly outperforms lump sum strategy. In other words, the strategy may serve as a cushion against unexpected market downturns and helps to preserve value of your investment portfolio.

5. Moderate volatility, strong trend UP

https://preview.redd.it/p5tokgwvjcn51.png?width=293&format=png&auto=webp&s=ca87f76eeb4402b8604066c59d8d354d902ba20b

When the share prices rise strong and fast, it is the lump sum that performs best. Still, however, the modified DCA is a runner-up, with an average profit of 44.85%, Take Profit was triggered 71,330 times and Stop Loss used only 54 times.

6. Moderate volatility, strong trend DOWN

https://preview.redd.it/w5cmwj5xjcn51.png?width=294&format=png&auto=webp&s=389eb414c564b6be5eacd0d8f0d8db9f591ecc48

Finally, what if the share prices go wildly down? Previously, with a moderate trend DOWN we saw the modified DCA to reduce losses by half compared to lump sum strategy. Here, the situation is quite similar but it’s worth noting that Stop Loss was triggered 11.379 times (over 11% of cases).

Below is a typical situation for share’s price with high volatility and with its value dropping: the value of portfolio of someone who invested with lump sum would be decreased by 24%, while both regular and modified DCA help reduce the losses (notably, the modified DCA performs beter than the regular DCA):

https://preview.redd.it/cdb0mivyjcn...bp&s=2450da7d12f34adf71f29fe5d06a9392c0bda4dd

In case of a strong uptrend, however, both DCA’s perform slightly worse than the lump sum, as shown above in the statistics and examplified in the following figure:

https://preview.redd.it/4clhwt80kcn...bp&s=264015d6f9e51d52a0906a1d4d56fd3d79c9295a

Finally, it sometimes happens that the regular DCA outperforms the modified DCA: this only occurs occasionally:

https://preview.redd.it/khxg3de1kcn...bp&s=cdaf00ce9ae2d5c91338bce2e412720315eb1504

BOTTOM LINE

In most cases, dollar-cost averaging outperforms lump sum purchasing, as demonstrated in a couple of tests for different market circumatsnces using 100,000 simulations. Notably, a modified version of DCA typically performs significantly better than the regular DCA. The main difference between them is that purchases in the modified version are conditional upon the price change of the asset: they are only executed at the beginning of investment and then only if the current price is lower than the mean price of purchases. This means that, technically speaking, the modified DCA is not really a DCA, because purchases are not performed in equal time intervals: by calling it the moified DCA I only mean to show that the strategy originates from the DCA approach. Please also note that we are applying Stop Loss and Take Profit thresholds, because I believe one should always be doing so, even though the regular DCA is typically described and (maybe) used without those parameters.

The advantages of dollar-cost averaging were already laid down above. The added value of modified DCA is that, generally speaking, it grants higher yields from investments than the regular DCA. How about its drawbacks? Well, it promotes byuing assets whose value drops, which is generally OK but there is a danger of sticking in bad investments: sometimes the value drops for a good reason and it might be a batter idea to exit the investment, rather than ever increasing your exposure to it. It is important that you do your due diligance and make sure you invest youm money in an advised way. This is also why I’m setting the Stop Loss value. Another issue I have to mention is that in prolonged bull markets you might be stopped from further purchases for a while, but remember this means you made a good investment since the value of your shares is rising. What can you do about it? Simply find another opportunity, there are always some undervalued assets worth investing. Finally, in bearish markets you might have to invest more than you originally wanted to (the number of shares to be bought is multiplied by the factor of 1, 2 or 3, depending on size of the discount, as mentioned above); if you’re not happy with that, you may stick to the smallest amount you feel comfotable with but remember this will also reduce your potential gains when the price recovers.

Last but not least, these were just simulations with random data. In one of the upcoming posts I’ll show you how the modified DCA performs using historical stock data. Sign in to my newsletter if you wouldn’t like to miss it.

I hope you enjoyed this post. Feel free to leave your comment below.

Thank you,

Michael

Disclosures:

• What you see here is my personal opinion, my own investments and should not be treated as investing advice
• I’m an amateur investor
• no promotional content; I'm not affiliated to any of the linked entities and am not paid by them; this is my personal research

 

[jalp2016]

@joyfulboy There a couple of things wrong with this post, and it starts with a fundamental misunderstanding of lump sum investing.

one could either try to time the market, executing a single purchase at the best possible price (this is the so called lump sum investing)

When discussing DCA vs Lump sum, we are generally talking about investing an large-ish amount that was acquired rapidly or before we started investing (e.g, a windfall, or savings as a teen/young adult). Lump sum is not "to time the market", but simply to commit it all to the stock market as quickly as possible.

It gets confusing because DCA is often also used to describe monthly/weekly investments from new money (for example, Bogleheads split the terms into "DCA" for a large sum, and "periodic automatic investments" for new money)

The other main thing you got wrong, is that you compared your strategies on random data, without accounting for the fact that in the real world, over the time it takes for DCA to be fully invested (several months), uptrends are far more common than downtrends. You mention this in your closing statement (and I'd be curious to see your historical data), but the start of your conclusion:

In most cases, dollar-cost averaging outperforms lump sum purchasing

Is already flipped compared to most studies. DCA is widely seen as a strategy to decrease volatility at the cost of lower returns and this is backed by historical data. And it makes sense; Lump Sum is riskier.

 

[joyfulboy]

@jalp2016 I clarified a couple of things in the post to answer your comments. Thank you for valueble remarks.

Here I used random data just to show the idea but of course historical stock data would be much, much better. I'm working on that.

 

[how2101]

@joyfulboy I like the time and effort you spent on this piece. Well researched and thanks for sharing. My thoughts are below:

The main difference between them is that purchases in the modified version are conditional upon the price change of the asset: they are only executed at the beginning of investment and then only if the current price is lower than the mean price of purchases.

This requires tracking price movements and waiting until a drop exceeds the thresholds. This may lead to investors waiting in cash or encourage delaying their investment plans until the right opportunity arises.

Your conclusion of DCA leading to superior returns goes against most academic research. Vanguard has found that lump sum beats DCA in the US about 67% of the time.

 

[joyfulboy]

@how2101 Thank you.

I wrote an update to answer your remarks.

 

[hummel2]

@joyfulboy Interesting. What bothers me, as "investor" from Germany, my bank/broker charges me only 0.5 Euros if I have Sparplan set up (re-occurring ETF buying every month at same day), and if I want to lump sum it, it's 10 Euros per transaction, that makes equation little bit different.

Good to read about different approach nevertheless.

 

[jalp2016]

@hummel2 Generally speaking, lump sum vs DCA should only occur a few times in your life (when you first start investing, then windfalls such as inheritance, large severance packages, lottery wins...), and usually with sums that make the fees pretty meaningless.

For monthly savings, it is not a question of DCA vs Lump Sum. There isn't really a reason to let monthly saving accumulate before investing, especially if it leads to higher fees. Most people have the opposite problem where flat fees make small monthly investments more expensive. In that case, you refer to this calculation.

 

[marissavchon61]

@hummel2 You could just lump sum everything with one saving plan execution and stop it afterwards.

 

[hummel2]

@marissavchon61 I actually thought about it but never looked into it. Seems like legit way to do, thanks!

 

[joyfulboy]

@hummel2 Good point, I forgot about that. I have account with several brokers so that I can minimise or even almost eliminate the commission paid, depending on what I'm buying. In the US the commissions are lower, but in Germany you could have access e.g. to eToro, DeGiro or Firstrade (US broker)

 

[ianamol]

@joyfulboy This blog will help

https://ofdollarsanddata.com/even-god-couldnt-beat-dollar-cost-averaging/

 

[davidconley947]

@ianamol I was going to post that!
Also there are other methods that can be pretty effective if you can handle it, like "follow the money".
Nick talks about that in one post.

 

[ianamol]

@davidconley947 Yea, the idea of following the trend.

 

[joyfulboy]

@ianamol Buying the dip is not my cup of tea, it's interesting though

 

[resjudicata]

@ianamol It's not the same question as in this post though.. It compares DCA with lump sum at a later time (buy the dip).

OP compares DCA with lump sum at an EARLIER time. In both cases, it is usually best to get your money in as early as you can.

 

[jeepneytravel]

@joyfulboy You can achieve something similar by coupling DCA with rebalancing a portfolio to fixed allocations.

 

[exsoldier]

@joyfulboy Hello I find the analysis interesting even though contrariant to my own simulations.

What distributions did you use for the random data sampling?

Also which measure do you use for yields? IRR or ttwror?

 

[joyfulboy]

@exsoldier No particular distribution was used, just pseudorandom % change in assets value from within a given range, e.g. -5% to +7%. So each value from that range is equally probable. This was not meant to be academic research but please let me know what distribution could best mimic stock prices.

The profit is ROI (%) defined as total profit divided by total amount invested.

 

[exsoldier]

@joyfulboy I will get back to you with what I had used but your current simulation overweight considerably rare events. Having a +7 daily return is just as likely as having a - 7% which is unlikely.

I took sp data from 1871. What I used was a non central student's t distribution for sp500. In your case though you would need intraday values. Since you're emulating stop loss behaviors within a day to trigger or not buts and sells. If you use just daily data your missing all the flash crashes.

Another aspect to note is that you have cash inflows and outflows. I would suggest to look into time weighted returns and internal rate of return. For your simulation since you attribute much importance to inflows and outflows IRR would be more appropriate.

 

[katlinja99]

@joyfulboy Nice research and well written, enjoyed reading! However it's mathematically proven "the earlier you are in the market the better", so lump sum ASAP beats DCA long-term in the real world. You are reaching a different conclusion, which is correct for random data, but in reality downtrends are very rare compared to uptrends; and this provides a significant advantage for lump sum investing.

Very interested in your next post using actual historical stock data. Thanks for sharing!