Beyond DCA

In the last chapter, we learned how to exploit volatility in order to get a lower price with the strategy known as dollar-cost averaging (DCA). To explain it simply, we invest the same amount of money in a particular stock regularly at a certain time interval, and that way, we are buying more when the price is low and less when the price is high, ending up with a lower average price. Here's the formula for DCA:

But it's sometimes better to use a different formula. Maybe you want to try to exploit volatility even more than DCA permits. Suppose a stock is trading in the 8 to $12 range. Instead of using DCA, we can just as easily buy a number of shares proportional to how far the price is from 12, so we end up buying considerably more when the price is closer to $8.

The threshhold you set will determine how much you can exploit the volatility. A closer threshhold will try to exploit volatility more, but you run the risk of the price going over the threshold, meaning you won't be able to finish buying the intended amount.

Choosing a good multiplier requires a bit more careful math. Suppose we want to invest $1000 in this particular stock over a course of five days, and we see the current price is around $10, so we estimate that we want 100 shares. We set the threshhold to $12, and the distance of the threshhold from the current price of $10 is $2. So our multiplier will be 100/2/5=10.

Though DCA helps when buying, you should avoid using DCA when selling because it gives a lower price, but it's ok to come up with a different formula that's more suitable. Suppose we reverse the math of the previous formula for selling, so we sell more when the price is higher and sell less when the price is lower. This way, we maximize the price in selling similar to the way DCA minimizes the price for buying.

Getting the best prices possible when buying and selling is a beautiful thing.

So far, we've explored ways to exploit volatility even more than DCA, but suppose we want to see what we can do in the other direction. How about a compromise between DCA and upfront lump-sum investing?

Instead of investing $500 per day for five consecutive days, you might decide to invest 600, 550, 500, 450, and $400 on those days, which would be the same total amount, but it would mean having more invested into the stock faster. You still benefit from dollar-cost averaging to some extent by dividing the purchase across five days, but you get %20 more invested on the first day than otherwise, and you get 15% more invested in the first two days than with normal dollar-cost averaging. This sort of strategy is in essence a compromise between upfront lump-sum investing and the normal dollar-cost averaging, as such it might perform better than the other strategies when there is both volatility and steady growth, which probably describes most of the stocks out there.

I came up with that sequence, 600, 550, 500, 450, and $400, off the top of my head, but if you want a more mathematical methodology, you could use this formula that I've come up with:

i=m*(1+(2*(d-x-1)/(d-1)-1)*k)

i=dollar amount to invest today
m=average desired amount to invest per day
d=total number of days to invest
x=today, as a number from 0 to d-1
k=0 to 1 constant, use 0 for flat, 1 for max slope

For the best results, k should be approximately inversely proportional to the volatility of the stock. Use k=0 for perfectly volatile and k=1 for steady growth with very little volatility. It does still spread the purchase of stocks out a bit more than upfront lump-sum investing even with k=1, so it wouldn't be the best choice for steady growth with zero volatility.

This page is intended as educational and informative and is not to be taken as personalized financial advice. Strong efforts are made to ensure these documents are correct, but there could be mistakes, especially when first uploaded. Please verify important facts before making investing decisions.