This article is the ninth in a ten-part series loosely based on Michael J. Mauboussin’s white paper “Thirty Years: Reflections on the Ten Attributes of Great Investors.” See “Part One: Be Numerate,” “Part Two: Understand Value,” “Part Three: Properly Assess Strategy,” “Part Four: Compare Effectively,” “Part Five: Think Probabilistically,” “Part Six: Update Your Views Effectively,” “Part Seven: Beware of Behavioral Biases,” and “Part Eight: Know the Difference Between Information and Influence” for previous installments. And please keep in mind that although I’m basing my work on Mauboussin’s, I am departing from his ideas on occasion.
Mauboussin writes, “success in investing has two parts: finding edge and fully taking advantage of it through proper position sizing. Almost all investment firms focus on edge, while position sizing generally gets much less attention.”
This is because position sizing is a forbidding concept. If you try mean-variance portfolio optimization or using the Kelly criterion to decide how much to put into each stock you own, you’re likely to get bogged down in remarkably complex computations with results that are indefinite at best.
Position sizing has to answer two main questions: how many positions should you hold? and how much of your portfolio should you allocate to each position? The answers are complicated by the following considerations:
- If you have a very good stock-picking strategy, the fewer positions you’re in, the higher the returns will be.
- If you have a mediocre stock-picking strategy, the fewer positions you’re in, the lower your returns will be.
- If you invest in low-liquidity stocks, the fewer positions you take, the more market impact your buys and sells are going to have.
- The fewer positions you’re in, the greater the variance of your returns will be.
Given this, it might seem more sensible to invest in a hundred stocks than ten. But practically every backtest will show you otherwise. So what do you do?
I can’t answer that question for everyone. There’s no one-size-fits-all approach to position sizing. Instead, I’ll give you my approach, even though I’m sure it’s not suitable for everyone.
In my personal accounts, I currently own shares in 24 companies, with weights ranging from 8.2% to 0.7%. My top ten stocks account for 59% of my holdings.
Many great investors take an even more concentrated approach. I’ll quote from Excess Returns by Frederik Vanhaverbeke:
Joel Greenblatt usually put about 80% of his funds in no more than eight stocks. Eddie Lampert holds about eight major positions at a time. And Glenn Greenberg has a rule that he will not buy a stock if he is not willing to put at least 5% of his assets in it. . . . Warren Buffett states that for relatively small portfolios (< $200 million), he would put about 80% of his portfolio in five stocks. . . . In his private portfolio he is even willing to go up to 75% in one single stock.
But Vanhaverbeke also notes, “[High] portfolio concentration obviously only makes sense for true stock pickers. It does not make sense, for instance, for quantitatively driven investors.” And I’m one of the latter. I view my portfolio concentration as moderate; many investors I know have a very low portfolio concentration, owning fifty to a hundred stocks at any one time.
My position-sizing formula has three components.
- Rank. Because I use a ranking system to decide what stocks to buy and sell, one component is based on rank: the higher the rank, the more I put into the stock. Since stocks change rank positions over time, I gradually increase or decrease my investment in a stock as it moves.
- Liquidity. To diminish market impact, I invest less in stocks with very low liquidity.
- Industry concentration. If I’m invested in more than a certain number of stocks in any one industry, I’ll lower the weights of those stocks.
Here’s how I came up with the number of stocks to invest in and how much to invest in each one. I ran out-of-sample backtests over the last three or four years on various ranking systems that I formulated back in 2015, 2016, and early 2017, adjusting the costs per transaction higher for fewer positions taken. I then looked at the position-sizing approach that would have given me the highest out-of-sample alpha for each system and averaged them all. Some of them would have performed best with very high concentrations, others would have performed best with lower concentrations. The average gave me a formula that I’m pretty pleased with.
Here’s the nitty-gritty of the formula I use. I first give each stock a number of points based on its rank. The actual formula is 47 * (4.7 – ln (rank + 12)), but if you simplify that to 101 – rank, there’s not much difference. Either way, if a stock is ranked #1 it gets 100 points, and if a stock is ranked #100, it gets close to 0. The major difference is that with the log-based formula, the ranking goes down more steeply for highly ranked stocks. So when a stock is ranked, say, #35, using my formula, it gets 40 points, but with the 101 – rank formula, it gets 66.
I then adjust these numbers for liquidity—if a stock has low liquidity, the number of points may go down by 20. I also adjust them lower if I own more than four stocks in one industry: in that case, the total number of points for those stocks are diminished so that they add up to what they would if I only owned four companies in that industry. Once I’ve settled on the final number of points for each stock, I apportion my total investment accordingly, and if there is a major difference between the ideal apportionment and my current apportionment, I buy and sell to rebalance my positions. If a stock I don’t own turns up in my top ten or top twelve, I sell bottom-ranked and overweight positions in order to free up enough money to buy the new stock. If there’s nothing for me to buy, I don’t sell, no matter how low a stock ranks.
Obviously, this technique is not for everyone. You may do better with a modified Kelly criterion or a mean-variance optimization formula. Or you may have an entirely different approach that works well for you. (If so, I’d love to learn about it in the comments below.) At any rate, many people put too little thought into position sizing. It can make a huge difference in one’s returns.
Here’s an example. I’m going to use an eleven-factor ranking system that I designed back in December 2015 and backtest it, using Portfolio123, on the Russell 3000 since then (starting in January 2016).
If I bought the top 20 stocks in equal weight and sold them when the rank went below 50, buying and selling monthly without rebalancing, I would have made an annualized return of 13.47%. If I’d bought the top 25 stocks instead, the return goes up to 15.88%, and if I’d bought the top 40 stocks, the return goes down to 11.38%. That gives me a good range to start with.
Now what if I had used my ranking formula to determine the portfolio weight? The top 20 return goes up 195 basis points to 16.32%, the top 25 goes up 165 basis points to 17.53%, and the top 40 goes up 240 basis points to 13.78%. In each case, the return is higher than for equal weights.
Why is this? Well, consider that four out of my eleven factors are value factors. Thus, when a stock falls in price relative to other stocks, it gets a higher rank, and when it increases in price relative to other stocks, the rank falls. But if you don’t resize your portfolio, when a stock falls in price, it has a lower weight, and when it rises in price, it has a higher weight. So rebalancing by rank, if you use value factors, does exactly the opposite of what the portfolio would do naturally.
With rank-based position sizing, your biggest bets are always on the stocks with your highest expectations. If you use a multi-factor ranking system to lower risk, this can produce significantly better returns than other methods would.