Position Sizing: Optimizing for Better Returns
Position Sizing: Optimizing for Better Returns
Knowing how much to invest behind each holding is a critical but under-discussed component of portfolio returns.
“There ain’t only three things to gambling. Knowin’ the 60-40 end of a proposition, money management, and knowin’ yourself.” – Puggy Pearson, poker legend
If you’re an active investor, your objective is to outperform the market. Otherwise, you should index. And that’s not a knock – it’s a valid and respectable option.
Assuming you’re still with me, stock selection and position sizing are the two key drivers of your portfolio returns.
One of the ways investors can become overconfident is by having some success with stock selection and mistakenly thinking that it means they will be good at running a portfolio.
To be sure, good stock selection is a prerequisite for successful portfolio management. You can’t turn a group of underperforming stocks into an outperforming portfolio. That said, decent stock selection and poor position sizing can produce sub-par performance.
Consider two 10-stock portfolios. In both situations, 70% of the picks were “winners” in that they generated positive returns, but the portfolio returns were vastly different because of position sizing.
An equal weight would have produced a 6.2% return in the above scenario. How you position size can indeed augment or diminish portfolio-level returns.
One way to visualize position sizing is playing multiple poker games at once (representing individual positions) and having 100 chips (representing 100% of the portfolio) to allocate across those hands. What’s the best way to do that?
Some investors look to the Kelly Criterion to answer this question. The Kelly Criterion was initially applied to gambling by betters who wanted to understand optimal bet sizes given specific odds. If this were a giant poker game, you could use Kelly to figure out how the chips should be distributed based on the expected value of each hand.
But unlike card games, the odds of a given outcome in investing are unknown, so the application of Kelly needs to be modified. Still, Kelly’s core principle that you should place more money behind your highest expected return (probability times payoff) remains relevant and valuable.
A Kelly-type approach requires investors to consider their conviction in the thesis and their estimated discount to fair value to arrive at a position size. The benefit of this approach is that you can augment the position’s contribution to portfolio returns by being correct in your probability and payoff estimate. The risk of this approach is that your perceived probability was wrong and you either bet too much or too little.
Another approach to position sizing is to place more emphasis on security selection by equal-weighting the portfolio. It’s simple to figure out. Determine how many stocks you want to own (more on that in a moment) and divide 100 by that number. If you want to own 40 stocks, for example, equal weight would be 2.5% in each position.
The downside to equal weighting is keeping it simple over time. Some positions will do well, others not, and weights naturally become unbalanced. Depending on how you rebalance and how often, you may cut your flowers and water the weeds.
A third approach I’ve seen used is to have a small set of concentrated holdings (e.g., top 10 names account for 80% of the portfolio) and a more extensive group of holdings (e.g., 40 stocks account for the remaining 20% of the portfolio) that might be newer ideas or downgraded holdings from the concentrated section of the portfolio. The upside to this approach is that you have skin in more games, so you’ll keep closer tabs on companies you might have forgotten about otherwise.
The downside to this approach is stretched attention and less time to focus on the largest holdings that drive the bulk of your returns.
If you’re going to actively weight your portfolio, weighting the top of your portfolio is critical to get right. It’s tempting to put your highest upside potential returns at the top, but the potential downside must also be considered.
Howard Marks tells a story about someone who bet his rent money on a one-horse race only to have the horse jump over the rails and run away. Joel Greenblatt once shared how, before a “sure thing” deal for a Florida property was about to close, a sinkhole appeared and much of the property fell into it.
He added:
“It just tells you, things can happen that you don’t anticipate, that it’s not really your fault. I’d never even heard of a sinkhole before I read about this happening, so it’s a risk that I… When you’re doing a merger deal, you’re not really saying risk of sinkhole is in your checklist of things to look for, so stuff happens, less kind words for that.”
No matter how confident we are in our business assessments or valuation work, strange things can happen, and we must be prepared for that. Rory Sutherland recently told Rick Rubin that “Everybody when they look for a reason for something serious is looking for a serious reason…but actually great things happen for stupid reasons.” Great things happening in this context can be positive or adverse events.
Be in a position for luck to help your returns but not break your returns.
Here's an example of what I mean by that. The idea for Amazon Prime began when an Amazon engineer dropped a note into an employee suggestion box. Jeff Bezos may have eventually figured out Prime independently, but shareholders greatly benefitted from that engineer taking the initiative to write up a note during a break.
A creative investor may have similarly thought a membership model would work at Amazon before this event. Still, it would have been unreasonable to assume such a game-changing idea would occur when determining position sizing.
A good check on the probability of an outcome is to look at base rates for companies of similar sizes and growth rates to the one you’re forecasting. Michael Mauboussin and Dan Callahan have published historical base rates for sales growth, gross profits, and earnings growth, which you can find here. Note that when thinking about base rates, companies with mostly intangible assets tend to have different base rates from the larger set, which includes tangible asset-heavy companies.
Let’s say you are forecasting a certain level of sales growth for a company and the base rates suggest that the outcome you expect happened in just 1% of cases for its relevant reference class. You may be highly confident in the forecast, and it may prove to be the correct call, but it’s reasonable to make that a smaller position size than if the outcome happened in 50% of historical results.
There’s no one-size-fits-all approach to position sizing, but some general principles are useful when considering your approach.
Live to fight another day. Position sizing is a dance between playing to win and playing not to lose. Ultimately, you must have capital to compound capital.
Know yourself. Whatever position sizing strategy you employ must match your personality, or it won’t work. Some investors can sleep fine at night having a 30% position; others panic at the idea of a 10% position. The more you understand your behavioral tendencies, the better you’ll stick with your position-sizing framework.
Understand your research capacity. Think about this on two axes – research depth and time. The deeper you want to go on a handful of names and the more time you can dedicate to that research, the more concentrated your portfolio can be, all else equal. And vice versa. Yes, Peter Lynch beat the market with over 1,000 stocks in the Magellan portfolio, but he also had the entire Fidelity research team at his disposal. In my experience, a single, experienced investor doing it full-time can keep track of about 20-25 companies at a good level of research depth at a given time.
Position sizing is an essential but under-discussed topic. How do you think about position sizing? Please let me know in the comments below.
Stay patient, stay focused.
Todd
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Position Sizing: Optimizing for Better Returns
The generalization of Kelly is (for the quants) essentially to maximize the expected logarithmic returns over the subperiods. One implication of this approach is that it seeks to avoid large drawdowns (as larger and larger drawdowns have unbounded negative logarithms).
So even a full-Kelly approach will tend to keep a substantial cash allocation or perhaps allocate some to puts (about the only strictly defensible 100% equity full-Kelly portfolio would treat conservative estimates of the price that would ensure a PE bid as cash equivalent: something like positive net-net (more current assets than total liabilities) might approximate that). Kelly bettors in games where there are definable odds generally practice half-Kelly which is exactly equivalent to 50% in cash and 50% in a full-Kelly portfolio (which itself will have some cash allocation!), if nothing else to help account for uncertainty around whether you've correctly figured out the payouts and probabilities.
The key point is not only to think about the odds and payout of success, but to consider the odds and payout in the worst-case scenario (and consider those at least as much as the success case). This is pretty easy to analogize to the Graham & Dodd "margin of safety" (and there's at least some research indicating that Buffett sizes bets in a Kelly-esque manner: he also endorsed Ed Thorp as a good manager for his limited partners who didn't follow him into Berkshire (someone who took their money from Buffett and put it into Thorp's fund and then bought BRK when Thorp stopped managing other people's money may actually have done better than someone who stayed with Buffett)).
I've toyed with the idea of an equal-weight portfolio that sells flowers and waters weeds but when the sales (plus dividends, covered call premiums, etc.) of a flower exceed what you put in by enough to have gotten an acceptable annual return, you exempt it from equal-weighting and only sell enough to keep that realized return profile (until you decide it doesn't deserve any weight).
There is a time element to it. I started my portfolio in 2012 more or less, I bought some stocks, and I still find new ideas in 2023, so I could not have started my portfolio with 15 equal weights Ideas. I did not even have 15 ideas when I started! So new ideas get added progressively, and their weight depends not only on confidence, but also on available funds and saving rates, and things to sell.
On top of that I am willing to add less weight on a new idea if I just discovered the company. I like to have followed it for two years to really feel confident to concentrate more.
Very complicated.