Investing Strategy: Averaging Up or Down

How do you work out whether you should average in or not?

Every so often, I find myself working out again from 1st principles how many shares I would need to buy to achieve a certain average price, based on my current average and the current share price.

So I thought a post might be helpful and would save me (and maybe you) time in the future. As usual, I thought this would be quick, but it wasn’t!

There is probably a deeper discussion here about whether you should care about average price at all - surely a stock is either attractively priced right now, or it isn't. If it isn't, why buy at all? And if it is, surely you should buy as many shares as your capital allocation / portfolio strategy allows?

I get the 'pennies look after the pounds' argument here - if every one of your purchases is well considered and profitable, you WILL make money. But by only ever buying when prices are depressed (in your view), you may miss out on getting money into the market when prices appear high. This is obviously a risk if you over-pay and prices fall back, but I think we all know time in the market beats timing the market as a general rule.

So for me, average price is important. I don't really care whether one particular transaction was more or less profitable than another, I care whether - on average - I am making money by holding a stock. Sometimes I am willing to pay a premium above what I personally consider to be fair value in order to increase my exposure to a stock, as I know I tend to be more conservative than other investors, which can lead me to miss out on growth stocks that look expensive unless you assume more optimistic future growth rates than I generally do. But I still want to protect my margin of safety, even in this case.

Conversely, for averaging down, as you add to your holding, it gets progressively harder to bring your average down further if the price keeps dipping. I find it valuable to work out how many more shares I would have to buy to achieve a certain average at different price points, to decide if I am comfortable having that much capital exposed to any one stock, especially one that is in distress for one reason or another. Perhaps I would prefer to hold 1% of my portfolio in a stock which is 50% down, on average, than 10% of my portfolio in a stock which is 5% down on average.

So, before you buy, how do you calculate your future average price or calculate how many shares are required to achieve a certain average?

The information required is the same in both cases:

🔹️your current average price

🔹️your current number of shares held

🔹️the current or target share price at which you are considering buying more shares (this logic would also work if you wanted to sell shares to achieve a certain average, but I think that is a more unusual scenario, so I won't discuss that topic here)

Your average share price is always going to be the total amount you have paid for all shares you hold in a particular stock, divided by the total number of shares you hold in that stock.

New Average Price = (total capital currently invested + new capital to be invested) / (Total shares held after new investment)

To make this easier (honestly), let's introduce a bit of maths here.

🔹️current average price = A

🔹️current share count = n

🔹️target purchase price = P

🔹️additional share count to be purchased = c

🔹️new average price after new investment (the target) = T

This means:

🔹️Total capital currently invested = A × n

🔹️New capital to be invested = P × c

🔹️Total shares held after new investment = n + c

Therefore:

T = (A × n + P × c) / (n + c)

And if you are targeting a specific average price, you can set a value for T and calculate how many shares that will take to achieve (c):

T × (n + c) = A × n + P × c

T × c - P × c = A × n - T × n

c × (T - P) = n × (A - T)

leading to:

c = n × ( (A - T) / (T - P) )

In other words, the number of new shares you would need to buy is equal to your current share count, multiplied by the difference between your current average and your target average, divided by the difference between your target average and the target purchase price.

To help avoid working with negative numbers, I like to re-write the above equation in two forms:

If looking to average up:

c = n × ( (T - A) / (P - T) )

If looking to average down:

c = n × ( (A - T) / (T - P) )

and before pushing the button, you can confirm your calculations by re-using the Average Target calculation with your value for 'c':

T = (A × n + P × c) / (n + c)

(Thanks to MiguelSoares for catching my copy/paste error on the averaging up / down calcs, now corrected)

Great. How is this valuable to me?

🔹️ as n increases, c must also increase in the future to have the same overall effect on your average, allowing you to calculate how much additional capital you would need to invest under different future price assumptions

🔹️The closer your current average is to your target average, either the more shares you need to buy to hit your target, or the greater your price differential between target purchase price and target average must be. You can then assess how likely it is that the share price will reach your target price, or how many shares you would need to buy to achieve your target. You may choose you are not willing to buy that many, or that you want additional exposure and you are willing to adjust your targets to achieve that.

🔹️ your new average will never be exactly the same as your target price, as there will always have to be a differential between target average price and target purchase price without buying an infinite number of additional shares (which is obviously impossible).

🔹️ By understanding the above, you can understand your risk exposure better, in terms of both capital at risk and margin of safety.

In my own case, this approach has led me NOT to invest further in ALB or AAL at this time, because i am not prepared to put more capital at risk to achieve substantially lower averages. I am willing to accept no return on investment or wait for the prices to come to me, at least until the relative weight of these stocks in my portfolio has dropped further. However, I did average down a little on Arcadium, because it is a much smaller holding, meaning the same level of capital investment can have a much more pronounced effect on that stock, and I perceive its risk profile to be similar to that of ALB.