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Comment by Nursie | Hacker News Reader

Can you point me to some of this mathematical proof? Because I'm seeing advice all over the net that it can help iron out short-term volatility.

Your point that "If you think it will go down over several months, you shouldn't be buying in" is fine, but I'm not sure it's equivalent to "I don't know what it's going to do anytime soon I'm buying this for long-term prospects".

Imagine a stock with a sinusoidal price fluctuation at a frequency of just under a week, but which you expect to rise significantly over a 5 year period. Investing in that weekly over 5 weeks will net you a more locally average price than going all in today, particularly if you don't have good information about that sine pattern. Going all-in right now might net you a low price, but you may also be buying at a local maximum.

(Think of discrete waveform sampling)

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I believe your intuition is correct, and it just straightforwardly does help iron out short term volatility. What it de-risks is the likelihood the bottom arrives some time in the next year, at a point lower than today, and that you could have achieved a significantly lower average entry price by waiting. The risk it exposes you to is that it's already the bottom, and you're going to keep buying in on the recovery. So if you're long term optimistic but short term bearish, but lacking high confidence in your ability to call the bottom, DCA makes sense imho.

I don't know what the conjecture is that would make it not de-risking that, or what a proof would be, maybe GP will clarify.

It should be noted that many analyses of DCA versus lump sum are around the S&P 500 overall. In the case of highly volatile growth stocks or just single stock investing like Fred is discussing in the article, market timing risk is more acute, since the drawdowns are more severe (it is quite rare for the S&P 500 to drop 70-80%).

Shameless plus, I am the owner of a DCA investing app + a simulator tool to backtest DCA with different stocks, over different time periods

https://simulator.tryshare.app/

The intuitive leap which is hard and important is how "not knowing" works.

Presumably you are choosing to invest in an asset because over the long term you believe it will go up. But you know nothing about what it will do in any defined timeframe.

Choosing to DCA with a fixed strategy is choosing x prices at which to enter, of which (x-1) are unknown. But they are fixed, and based on your above assumptions you know nothing about them except that they're generally trending upwards (and thus your entry price is averaging up by DCAing). Knowing nothing means knowing nothing, it's as likely to vary upwards as down.

You can express the above as a summation with a positive (but unknown) dv/dt and a canceling-out e if you think better in notation, but I can't figure out how to make that legible in a HN comment.

If you have any reason to believe that there is more downside risk than upside risk over the DCA period, then you should delay investing until that is no longer true, and go 100% at that time.

DCA is essentially the same intuitive leap as the Monty Hall problem, but backwards.

I don’t know that the prices during the DCA period are trending upwards, I have no information about short term fluctuations other than they exist.

I have no reason to believe that over the relatively short period of DCA that there is specific upside or downside coming along immediately, but I know that there is noise in the pricing. The rising trend I’m betting on is further down the line and very slow.

You’re adding assumptions that support your view, rather than addressing the problem as stated.

I'm adding no assumptions, and my view is math.

The only thing we know is that we're choosing an asset which we believe will trend upwards.

Over the relatively short period of DCA, it will trend upwards.

If you're saying you know that the rising trend won't begin until a future date, then that's an assumption you're adding, and it probably indicates you should wait until the rising trend begins until increasing.

> Over the relatively short period of DCA, it will trend upwards.

But this is an assumption!

> If you're saying you know that the rising trend won't begin until a future date, then that's an assumption you're adding

I'm saying I have no idea what's going to happen during the DCA period.

I think at this point its safe to say your view that DCA doesn't work to denoise a signal is predicated on assumptions about what the price trend is doing over the DCA timescale. If the stock is trending up over that period, then you're likely better off buying now regardless of local fluctuation. OK!

I've seen this advice all over too, but it's never accompanied by anything approximating a mathematical proof. IMO, the burden of proof is on showing DCA works, not the other way around. In any case, the problem with your analogy is that if you have no information about that sin wave, you're equally likely to be investing at a local minimum.

> you're equally likely to be investing at a local minimum.

If you invest at a few different times, whether fixed interval or random, is this not increasing the probability of approach an average value over the period you're investing?

I'm not asserting it's a good idea, I'm not using it as a strategy myself (or in fact making investment choices myself at all really), I'm just interested from the technical perspective.

> If you invest at a few different times, whether fixed interval or random, is this not increasing the probability of approach an average value over the period you're investing?

It does indeed increase the probability that you will approach the average value over that period.

But there's no reason to believe that average will be lower than the current value.

> But there's no reason to believe that average will be lower than the current value.

100%, not disagreeing. But it does reduce the risk that you're buying at an outlier price.

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