This is why you Dollar Cost Average though. You do the same thing the 3rd and 4th time it happens. It's extremely unlikely there will be a 5th, 6th, etc (if there is, we probably have more important things to worry about like 25% of the world dying)
>Risk-averse investors who prefer dollar-averaging can accomplish the aim of risk reduction more effectively by lowering the fraction of funds invested in the risky asset and investing them all at once.
If you invest the same total amount of money for a constant exposure to the market measured in funds*time in the market, you have higher risk choosing to rely more strongly on the later years (which is DCA) than evenly spreading out the exposure over time (which is lump-sum investing). Theory is very simple. Lump sum is diversification and DCA is the opposite - diversification is a "free lunch" producing lower risk with higher returns.
The study you cite shows this is only true for when there is a positive expected risk premium, hence the evidence only supports cherry picked cases.
Additionally, if you read it, the paper admits the DA is inherently less risky than LS, so it attempted to even out risk by adjusting the investment amounts between the two methodologies until expected returns were even, and then compared. This method is arguably flawed for fairly evaluating total risk, since the total invested amounts at risk are different - that is, it relies on the reward to balance out the risk (ie. a positive risk premium). As so it's mostly tautological evidence...
If there's no expected risk premium, then buying stocks has a 0 expected return, and it clearly doesn't matter how you buy them.
> the total invested amounts at risk are different
Obviously, you need to invest the same amount in total to have a valid comparison. If your argument is that DCA is investing a lower amount, and is therefore lower risk, then the answer is that a lump-sum strategy investing the same amount as DCA is both lower risk and higher return, and therefore strictly better.