The problem with "averaging in"

A popular approach to buying shares is set "buy" thresholds.  It's a fairly simple approach - when the share prices falls to reach the threshold price, you buy some shares.  Often, there are multiple buy point thresholds, such that as the share price falls through each of the threshold, you buy more shares.  The theory is that if you thought that the share price was cheap at say $5, then when it hits $4.50, it must be even better value, and so a better buying opportunity.

The theory is not wrong, it is just not optimal.




After all, why buy any shares at $5 when they are going to become available at $4.50.  Clearly, if you've got $10,000 to invest, there is no combination of thresholds that will beat putting all $10,000 once the price hits $4.50, and not a penny until then.  That's how you'll end up with the highest number of shares for your $10,000, which is the best outcome.

"Ah but you can't pick the bottom" I hear you say.


The case for the optimal extreme 


Let's say that you are considering purchasing shares in a company.  The quoted market price per share is approaching your buy threshold price.  Let's consider the "average-in" approach compared to the "all-in" approach.  In the average-in approach, you define 3 prices which you consider "cheap", "very cheap" and "unbelievably cheap", and say that you'll allocate 1/3 of your funds at each threshold.  In the all-in approach, you simply wait for the "unbelievably cheap" price, then allocate 100% of your funds.

Oops.  I forgot to mention that the company only has 3 shares.  But that shouldn't change anything, should it?

So, now, in the average-in scenario, you'll end up owning either 0/3, 1/3, 2/3 or 3/3 of the company, depending on offers that you receive, and you'll end up paying somewhere between "cheap" and "very cheap" for the company, but you'll never get it for an "unbelievably cheap" price, because you started averaging-in at higher prices.

In the all-in scenario, there are only 2 outcomes.  You will either own 0/3 of the company, or you will own 3/3 of the company, purchased at an "unbelievably cheap" price.

So, in the case where the price ultimately drops to "unbelievably cheap", then you would have been better off waiting, then going "all-in", rather than averaging in. 

What about if the price never reaches "unbelievably cheap"  though?  Are you not better off owning 1/3 of the company at a "cheap" price than none at all?

I don't think so, and here's why.   There isn't just a single opportunity for you to consider, there are many.  In fact, every day, you get many quotes for each and every company on the stock market.  In hour lots, that's (6 hrs x 2000 companies = ) 12000 opportunities every day, and over the course of a year, let's say around (x 180 days =) 2,000,000 opportunities.

Above, I had labeled these opportunities as "unbelievable cheap", "really cheap",  "cheap",  and there are obviously any number of labels that could be applied.  There is also a corresponding numerical value for each opportunity that will be easy to work with going forward.  Let's just call the the net return on equity.  Unbelievably cheap might be an opportunity that represents a return on equity of 40%, "cheap" might be 15%, and so on.

We can create a frequency distribution graph of all the opportunities, to determine how often these types of opportunities come up.  Not only that, we can calculate whether or not it is worth waiting for the 40% opportunity, given it's likelihood, verses grabbing any other opportunity, given it's likelihood and outcome, including those opportunities being presented to us today.  It's about maximizing expectation value.


With a 10 year timeframe, it is worth waiting up to 3 years to get the difference between 10% and 15%.  Similarly, it is worth waiting up to 3 years to get the difference between 20% and 30%.

The frequency distribution of the opportunities should show us how often the 20% comes up in comparison to the 30% in comparison to the 40%, therefore we should be able to calculate the optimal extreme threshold for investing in these opportunities.

So, it's not about "picking the bottom", it's about picking an "all-in" threshold that maximizes returns based on the likelihood of the opportunity occurring and the expected outcome when it does.