There is an ongoing discussion in the investment community about the proper number of stocks one should hold in their stock portfolio. This article will suggest a formula that investors can use to estimate that number. I will first describe what led me to this formula, then I will briefly discuss the typical arguments used for highly concentrated or highly diversified portfolios. I will finish with a description of the formula.
Multiple Model Portfolio
Over the past six months, I have been in the process of building a model portfolio using the stock ideas I've written about on Seeking Alpha. As part of the process of building the portfolio, I put a lot of thought into just how many stocks the MMP should, on average, hold. This led me to putting a lot of thought into weightings, and what role weightings would play in determining the number of stocks to hold. Obviously, the number of stocks one holds and their weightings are related, and both are very important. For example, imagine two portfolios. One portfolio has 10 stocks and the other has 50 stocks. On the surface, the portfolio with 50 stocks appears more diversified. But what if three stocks make up 90% of the value of the 50-stock portfolio while the 10-stock portfolio was evenly weighted at about 10% per stock? In a very important way, the portfolio with less holdings may be more diversified.
To further complicate the issue, what if the initial weighting of the portfolio with 50 stocks was evenly weighted at 2% each, but over time, three of the stocks dramatically outperformed the rest of the portfolio and that is why they currently make up 90% of the portfolio's value?
I'll save the full discussion of weighting for a different article, but what I have decided to do with my portfolio is to focus on two things: The initial weighting, and value of the stock relative to price. This means that my initial weighting is determined by my confidence level in the value of the stock. A stock with a higher percentage of confidence and higher future return probability will receive a higher initial weighting. After that, whether or not I sell the stock will have nothing to do with weighting. Selling is determined purely on how I value the prospects of the stock in relation to my initial thesis, not by how much the stock is weighted relative to the rest of the portfolio.
For example, I thought Duluth Holdings (NASDAQ:DLTH) was a classic example of a Peter Lynch-style stock with multi-bagger potential when I wrote about it back in January. I suggested a 1% weighting at the time. Since then, the price has risen nicely:
DLTH data by YCharts
Now Duluth has approximately a 1.4% weighting. As far as I'm concerned, it could grow to a 10% weighting and I still wouldn't sell it simply because the weighting had grown. I will only sell when the thesis has played out. In short, I only pay attention to the initial weighting.
(For the Multiple Model Portfolio, I assume a starting value of $100,000, but in real life people usually are dollar-cost averaging. In that case, I use an estimated five-year contribution total to determine weightings. So, if one was just getting started investing, and contributed $2,000 per year to their stock portfolio, then I would use $10,000 ($2,000 x 5 years) as the baseline for weightings. In this case, a $500 investment would be considered a 5% weighting).
Weightings are important, and going forward, while I recognize that each investor has their own weighting preferences, I'll assume that one's initial weighting in a stock is the only weighting factor that would limit the number of stocks one owns, and not the notion that a position could potentially grow "too big", and compel one to sell for that reason alone.
With that said, let's now move on to the typical justifications put forth for both concentrated and diversified portfolios, so that we can see where my thinking fits in with conventional thinking.
The Case For Holding A Large Number Of Stocks
The basic argument for holding a large number of stocks is that there is safety in doing so. For example, if someone owns 100 stocks, and two of them go bankrupt, then they have only lost approximately 2% of their portfolio's value, everything else being equal. This holds true for dividend investors as well. Provided no stock produces a disproportionate amount of income, if two companies out of 100 went bankrupt, only about 2% of income would be lost, all other things being equal.
This, of course, is essentially the same argument for owning index funds. The downside is that you can't outperform an index by owning an index fund. Owning a large number of stocks is likely to produce average returns. In addition to this downside, owning an index fund doesn't prevent someone from selling the index near the bottom or at a loss. In fact, I think owning an index makes someone more likely to sell out during a market crash because buyers of indexes rarely have individual theses for the stocks in the index. Whether or not one stays in an index is largely determined by how much they believe that historical macro trends will hold. This faith tends to get shaken more when things are going poorly. It's much easier to click a button and sell an entire index than it is to individually go through a large portfolio and sell each stock one by one. So, it may make some sense to build a large portfolio of stocks from the ground up if it means the investor actually knows why they are purchasing them and it makes the investor less likely to sell their whole portfolio near the bottom of a market decline. With a large, individually selected portfolio, they would get the benefit of diversification and at least somewhat limit the natural propensity to sell everything when things get scary.
The Case For Concentration
The arguments for holding a smaller number of stocks are (1) the benefits of diversification are front-loaded, so that the first half-dozen stocks or so can capture most of the benefits of diversification, (2) you have more upside potential owning fewer stocks, and (3) you tend to have more knowledge about the stocks you own the fewer of them you follow.
I think all of these arguments have merit, but I wish to propose an entirely different approach.
Formula For Determining How Many Stocks One Should Hold
The first thing I think an investor has to determine is how many undervalued stocks they can find in an average year (over the course of, say, 10 years). Charlie Munger has said that he and Warren Buffett generally find only about one or two stocks per year that they consider good values. This isn't necessarily because there are only two undervalued stocks that fit what they are looking for in any given year. It is because they are only capable of finding that many. Charlie is very much aware that he and Warren have missed many opportunities over the years. My view is that each investor has to determine just how many undervalued stocks in any given year they will actually be able to find and invest in with confidence. That's step one.
One might think that selecting only two stocks per year on average means that a Buffett/Munger portfolio would naturally be fairly concentrated. But that is not necessarily the case. The next part of the formula is determining one's average holding period for each stock. As many people have pointed out, Berkshire (NYSE:BRK.A) (NYSE:BRK.B) holds stock in dozens of companies, and owns several more outright. All things considered, Buffett and Munger have not built a concentrated portfolio (though there are times in the past when it has been concentrated).
The reason for this phenomenon is that Berkshire's average holding period is very long, quite often over 10 years. Taking this into account, buying two stocks per year for 50 years and never selling them would create a portfolio with around 100 stocks. Berkshire doesn't have a portfolio that numerous because sometimes Buffett does indeed sell. But you get the point. One's average holding period is an important factor in determining how many stocks should be in a portfolio.
So, here is how I think one should estimate how many stocks should be in a stock portfolio: Determine how many undervalued or mispriced stocks you can find on average in a year, then multiply that number by how long you usually hold those stocks on average. The answer you get is about how many stocks you should hold in your portfolio on average (At times when the market is overvalued, you should find yourself holding less, and when it is undervalued, holding more. But this formula should give you a solid idea of what you should hold on average).
This is how I've been approaching the issue both in the Multiple Model Portfolio, and in my personal portfolio, which closely mirrors the MMP: Since I have a strong focus on the medium term, I figure that my average holding period is probably around two years. While I usually plan to hold stocks for as long as 3-5 years, usually whatever thesis I have plays out before then and the market recognizes its pricing mistake in fairly short order, which results in a shorter actual holding period. I feel fairly confident I'm in the ballpark using two years as my average holding period, though it's something I'll monitor as time goes on. After a decade has passed, and my strategies have been used in multiple economic conditions, I should have more confidence in this number.
The second number is trickier. Currently, I spend probably 20 hours per week on research, and I've been finding about one or two investments per month while putting in that amount of time. Using that number, I'll estimate that I can find about 20 investments per year if the market conditions are similar going forward, and less if the market moves significantly higher. If I were able to only spend 10 hours per week researching, then the number would likely drop to something around 10, everything else being equal. If I were to gain more skill and efficiency in my research, then the number would go up.
Using the estimates of being able to find 20 undervalued stocks per year with an average holding period of two years, my portfolio, over the long term, should probably average about 40 stocks. And if my research time was cut in half, then that number would likely be cut in half as well, down to 20 stocks.
The key takeaway of this exercise is that we should be thinking differently about how to determine the proper number of stocks in our portfolio. Our ability to find undervalued investments and our holding period should be what determines how many stocks we hold, not volatility, or risk of individual stock underperformance. And since our ability to find undervalued and mispriced investments is highly correlated to the amount of time one can spend looking for said investments, we should expect that some combination of time and skill, combined with our average holding period, is what ultimately determines the number of stocks in our portfolio.
Disclosure: I am/we are long DLTH, BRK.B.
I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.