A brokerage statement serves as a ledger for transactions but possesses no capacity to record the profound costs of inaction or interrupted compounding. Long-term wealth is a function of Ergodicity, necessitating a psychological framework that prioritizes staying in the game over the illusory comfort of frequent activity.
The most significant drawdowns are often the invisible ones where time was traded for the false promise of market timing.
The drawdown approach to opportunity cost is interesting. It might actually have been a more intuitive way to frame it.
That said, I disagree on brokers. I do the calculation myself using my statements and an API, so I have little doubt they could do it as well. They could even show clients an annual opportunity cost estimate by comparing actual results to a simple buy-and-hold of the portfolio from the start of the previous year (essentially a “do-nothing” benchmark).
But from a business standpoint, that would probably be close to economic suicide.
That’s true. But I don’t see it as a pure counterexample.
First, that -90% drawdown happened during the dot-com bubble. Many tech companies (and even some non-tech ones) fell well beyond -90%, and that does not imply Amazon would automatically have been sold.
And even if it was sold, other compounders from the eventual winner bucket could still have been held while Amazon was not. That kind of scenario is inherently captured in the simulation and partly contributes to the results (I actually mention that specific case.)
That said, the simulation only looks at the numbers in hindsight. It completely ignores the psychological skill required to apply such a rule over time, which is precisely what makes investing so difficult. In my view, that is the main limitation of the result.
It quantifies a simple and intuitive idea, but beyond giving one more reason to apply it, it does nothing to reduce how hard it is to execute consistently over time.
Excellent work! I loved how quantitative this was! This is exactly why I think rebalancing can be a poor investing decision: rebalancing is all about selling what's doing well which, as you show so elegantly, is one of the worst things you can do.
“Rebalancing can be a poor investing decision.” Honestly, I didn’t have your level of wisdom before running this simulation. Like many investors, I tended to justify every sale and purchase based on what I believed were sound fundamentals.
But the results are clear: on average and over time, the reasons I came up with were often poor ones that led to poor decisions. That is why I need to adapt my system.
I’m speaking in the past tense, but this realization is actually very recent. I have no doubt I will still struggle not to systematically sell a position I believe is overvalued, or not to reallocate capital toward what I see as a major opportunity.
As always, simple, but not easy.
If you’ve already managed to get past that stage, then honestly, well done!
I think I've honestly just lucked into my current mentality. One of the earlier books on investing I read almost a decade ago was Michael Covel's "Trend Following." And trend following is all about buying and holding what's going up and avoiding/selling what's going down
you define a winner as one above its purchase price.
in theory (and probably in practice too) you could buy a stick that goes up significantly in year 1, and stays at same range for 19 years.
had the investor sold it/ trimmed the position - he might be able to find another winner.
i realize that this case might be solved by other winners eventually catching up to it, passing it and perhaps eventually pushing it to a sell. but even at that case - we let some stock fester while other catch up to it - thus paying an opportunity cost too.
i'd suggest checking winners of the past year - but i'm not gonna - as you could easily find a great long term winner stopping to breath before it's next climb.
maybe take winners of the past 5 years? maybe finding the optimal number is the subject of the next simulation :)
2/
for the non-random sells, it feels like selling at year 1 differs from selling at year 15 - as at year 15 you have far more data points.
technically - both are selling a loser/ winner - but in one case it's almost a coin-toss, and in the other probability is on your side.
Thanks for your relevant remarks. In your point 1, I see two separate points:
On 1 year vs 5 years, you're very likely right: over that time frame, the mistake of not selling a "fake" winner (one that will end up winning in the long run) is probably much less likely than over 1 year. Tbh, I even think that's a time scale better suited to the strategy overall. I went with 1 year because, on one hand, there were real-world parameters I couldn't model (or it would have multiplied the complexity tenfold). So I tried to get as close to reality as I systematically could whenever the variables allowed it, hence the 1 year. Few investors have a minimum 5-year time horizon (this isn't a criticism), and the average stock holding period figures prove it (even adjusted for special activities like market making, quantitative trading, etc.).
However, you use an example to show the strategy's limits with not selling a "fake" winner that could have let you hold a real winner if you'd sold it. But in my opinion, that's actually the real value of this simulation: the sheer amount of data. Every counter-example the mind can come up with is already included in these results. And as I say in the analysis, to get this kind of result you have to accept making this kind of mistake, because they will happen, mathematically. And that's exactly the trap every investor needs to avoid, one I wasn't able to avoid myself: overfitting. My dataset is limited. If I'd wanted a longer time frame, I would have had to pay for it (and stock data isn’t cheap). Even the one I used has certain flaws that, in principle, pull it away from reality. And it's quite likely that the AI revolution underway will make the data somewhat different from what we've seen so far. It's a trade-off between optimizing the strategy and making it generalizable. From a more "theoretical" standpoint, if I had exhaustive data going back 100 years, I think you'd be right. A 5-year window would bring better performance to the don't-sell-winner strategy. But conversely, I'm not ready to bet that a 5-year window will outperform a 1-year one in the years ahead.
As for point 2, I admit I don't get it. Each year has just as many data points. If you could give me a bit more detail, I'd appreciate it.
in software engineering there's a similar deadly sin called "premature optimization" :)
on the other hand how do you know if you've not just threw out a really good tweak to the strategy? you feel the strategy results are good enough?
i'll give an example. you probably heard of magic-formula-investing. basically buy a beaten down stock of a business that generates good results. it is almost the opposite of this strategy, to be honest. they too had to make a decision on when to stop waiting for the market to align. they also made the arbitrary choice of 1 year.
when i ran some tests it turns out that waiting longer might provide better results.
one could claim that by trying longer periods - i was overfitting.
regarding point no 2:
you've chosen to ignore data points inside the year - as they produce noise that is not helping in any way.
I am completely ok with this.
but once you've introduced rotation into the strategy - you'll need to choose between assets that had short time to compound vs ones that had much longer.
e.g.
at year 0 you bought asset A1...A10. then at year 9 you sell A10 and buy A11.
in year 10 - you'd need to make a decision between A1 (that had 10 years to compound) with A11 (that had just 1).
if A1 survived for 9 years - it probably had good compounding already.
for A11 to win - its current year return would have to be better than A1's 9 + current year.
this makes the sell-relative-losers strategy biased towards old assets. maybe that's a feature, not a bug 🤔
I think your question 1 and all of point 2 come down to a question of definition.
My starting point was to check what great investors (Buffett, Lynch, Lu, etc.) generally say: a handful of winners do all the work. To check that, I had to define what a "winner" actually was.
Initially I leaned toward something more faithful to reality (which also handles your point 2): best annualized return over a 3-year window (or less if the stock was added to the portfolio more recently). But that choice forced a bunch of other decisions I wasn't comfortable with. Tbh, I don't remember which ones anymore, I just remember deciding it wasn't worth it. So I needed something simple enough while still staying reasonably close to how readers actually experience this. Hence the psychological winner/loser definition.
To answer your "on the other hand, how do you know you haven't just thrown out a really good tweak to the strategy? Do you feel the strategy's results are good enough?", that's exactly the point: it's not the goal. The goal was never to optimize a strategy or squeeze out the best possible performance. It was to measure the opportunity cost in a simulation that behaves roughly the way the average investor would.
I'm 100% sure the strategy isn't optimized. I played around with the parameters a bit, and, without remembering the exact configurations, some choices clearly produced better results, at the cost of lower fidelity/simplicity.
Your point 2 is actually a great illustration of one of the costs of that performance-vs-simplicity/fidelity trade-off. I could, for example, have overweighted the positive performance of a stock that had already run for a long time, so it wouldn't get kicked out of the portfolio over one bad year (in a way, that's arguably pretty faithful to actual human bias), but that would have complicated the simulation, and my explanation of it, for the one point I was simply trying to make: the massive cost of selling your winners and holding onto your losers.
At one point my great grandfather, who was a high-conviction, small-portfolio guy, had $7 million in Motorola stock. It was a massive “winner”, and he held it until it was nearly worthless.
Wow! What a study! Thank you. This study proves WHY one should not have more than 10 or 12 positions in a portfolio. But let's be honest. Most portfolios have way more than 10 or 12 holdings.
So even the brightest investors do not consider opportunity cost to be a real factor.
Personally, I would keep my portfolio down to around ten holdings (or less).
Simply because I don't have that much cash to be holding dozens of ticker symbols.
Amazing study, tho.
We have always been advised to keep a low number of holdings in a portfolio. It is maintained that a portfolio of 12 holdings can equal the diversification of dozens or even hundreds of holdings.
We never really understood why, tho. This study explains why. And it is counter intuitive. If a portfolio of 12 holdings is good diversification, holding 24, or 36 holdings should be a lot better diversification, right?
This is one of the probs with holding index funds. The index funds typically hold hundreds of securities. The bad performing securities bring down the funds over all performance to average at best.
Thanks for the feedback and for the thoughtful response!
I think my simulation is too limited to draw conclusions on the merits of diversification.
The main issue: I assumed equal weights throughout (5 stocks at 20% each, 50 stocks at 2% each).
The second problem is that I only looked at number-based diversification.
True diversification is measured by covariance between assets. The number of stocks in the portfolio is just a proxy, it doesn't necessarily imply diversification. As you said, 10 assets with low covariance are far more diversified than 50 with high covariance.
Indexes like the S&P 500 are actually poorly diversified in covariance terms, but they have one huge advantage: they're market-cap weighted. The more a company wins, the bigger its weight in the index; the more it loses, the more its weight shrinks. A solid proxy for selling losers and holding winners.
Imho, market-cap weighted indexes are an excellent compromise between performance, risk, and time spent. Equal-weighted, by contrast, falls right into everything you described. In a way, it's great news (and probably no coincidence) that market-cap weighted is the market norm over equal-weighted.
That said, I do share your view, for anyone with the time and skill to stock pick, a concentrated low-covariance portfolio beats a 40-stock one.
I think in pratical terms, rules such as "selling a high conviction holding which importantly has the ability to compound at high rates for 10+ years should be avoided on the basis of valuation" are likely good.
As for some small pratical critics:
- This assume that an investor sells a whole position to buy a new one. If they had a position which has done well (ie has gained 4x), in a 10 stock (if all 10% sized cost basis) this postion could be 30-40% of the portfolio. Nobody is going to sell 30% and put it all into a new position. In reality, investors would generally trim this position to fund a purchase.
- I dislike the distinction between selling winners vs losers (although realise it needed to follow these rules for modeling). I myself tend to sell my lowest conviction position to fund a new position, which doesn't mean the position hasn't made money, and could well be that higher conviction positions have lost money vs my cost basis. The gain or loss since you've invested in a company doesn't / shouldn't match with your conviction rating of the company/range of returns forward.
- If an investor never sold a strong returning investment in a concentrated portfolio, it could easily get to 50-80% of the portfolio's value. Depending on if various things like if you are drawing an income from the portfolio or not, and your risk appetite (you need to know yourself well as an investor), you should make trim / partial sell decisions around the concentration risk when a winner gets too big, even though it has a chance on meaning you don't maximise your eventual wealth.
The goal isn't maximum wealth strategy (if it were, leverage would be involved), (in my opinion) it's a strong return with a high chance of happening and being able to stick to your plans.
All of these criticisms are extremely well-founded. I have almost nothing to add, given that you cover both the critique and the meta-critique.
As you point out, some are deliberate choices: converting qualitative data into numerical values in order to apply mathematical tools. Others are inherent limitations of the simulation itself, some made in the name of simplicity, others simply unavoidable.
Thank you for taking the time to add all of this. Very sharp analysis, genuinely appreciated.
I want to be a critic on the post, what you will do in a war like scenario and you just find out a gem from micro cap universe, yet the stock corrected more than 50%, however there are no change in fundamentals and the going is intact, what changes is liquidity, liquidity matters a lot in such case , but saying that compounding happens when a stock moves higher and higher, this is just the partial truth.
I gladly accept the criticism, and it actually points to a limitation I explicitly acknowledged in the methodology: this is only a simulation of broad statistical tendencies. It is too far removed from specific real-life situations to be applied directly or mechanically. That limitation is intrinsic to the exercise, if only because of the computing power and modeling scope available to me.
Your example of a war-like scenario and a 50% drawdown in a micro-cap highlights the psychological dimension of investing, which is probably its most central one. And that is precisely what this simulation does not capture. But I think criticizing it on those grounds approaches the problem from the wrong direction. The point of having data, and of understanding what the data implies, is precisely to reduce the influence of our biases and emotions, so as to avoid value-destructive actions such as panic selling.
That was the initial purpose of this simulation: to give me concrete data points I can bring back to mind at the right moments, in order to reduce the probability of making mistakes such as selling a winner too early.
Put differently, the goal of the simulation is to provide data that can help improve decision-making, not to prescribe the right decision in every specific situation.
And on the last point, I think reducing the post to “saying that compounding happens when a stock moves higher and higher” misses several of its core arguments: the impact of portfolio size, the role of turnover, the relevance of buy-and-hold, and the quantification of these effects and how they evolve over time.
Love this! I posted a Substack on this topic using Keynes’ art collection as a heuristic: “To Build Wealth, Don’t Sell Your Cezanne Stocks”. Your data is invaluable.
Great methodology and a well-written post as usual.
Identifying losers early and consistently is a challenge especially when there are weeds that looked like flowers at one point. That said, difficult doesn't mean impossible. I believe over time, one gets better at making these decisions.
Ideally, running a concentrated portfolio should be an advantage to the investor here. The opportunity cost of preventing capital from searching from a true winner is greater here and that should motivate the investor to act decisively.
Holding onto winners for long enough is a whole other level of difficulty. In most cases, this means holding overvalued stocks where market value far exceeds intrinsic value. Still, that's not an excuse. Many 20-, 50-, 100-baggers would have been overvalued at different periods of the holding period. The upside of one of these great investments far exceeds the downside.
As always, thank you for sharing posts that provide an "intellectual itch" for lack of a better term!
Thanks for the feedback, Seyi, really appreciate it.
As always, you’re dead right, especially this part: “this means holding overvalued stocks where market value far exceeds intrinsic value.”
From my perspective, not selling when you know it’s overvalued is probably the hardest things in investing. And yet, in the median case, not doing it is value-destructive.
All I/we can do now is hope, and make sure, this becomes true: “over time, one gets better at making these decisions.”
The data on psychological winners will be a gut punch to many. We’re wired to lock in gains to feel successful, but your simulation suggests that playing it safe by selling winners is actually the most aggressive way to destroy future wealth.
Given that the biggest winners often have the scariest valuations, it's likely many readers have difficulty distinguishing between letting a winner run and being blind to a genuine bubble. Are you considering a future post on specific frameworks or 'red flags' you use to hold onto winners even when the valuation feels stretched?
I’m still digesting the data and coming to terms with the fact that the “fundamental” reasons that, in theory, and sometimes in practice, seem to justify my approach are very likely destroying value over time.
Honestly, I don’t have a framework or red flags that survive these results + a precautionary principle yet. But I’m working on it right now!
My own personal framework around strategies for letting winners run includes labelling some holdings as "Permanent holdings" (very high conviction and runway which can stretch >10 years at teens+ growth), which I've held for 2+ years (to better understand the company). When marked, I then don't trim/sell on valuation, until conviction changes, growth rate trends below mid-teens and/or visable likely runway for growth shortens under 10 years.
The whole backtest is based on one 25-year window (2001–2025), and that happens to be a stretch dominated by a handful of mega-cap tech compounders. So a rule like "never sell your top 5" is built on a single historical regime - it could just as easily be a pattern specific to this period rather than something universal.
The same reasoning applies to the 1990s-2000 dot-com bubble. And to the Nifty Fifty in the 70s. The pattern isn't as specific to the period you're describing as you make it sound.
If anything, it's an intrinsic feature of markets. Even more so now, with market-cap-weighted passive flows.
That said, your sampling-bias point still holds. It always does the moment you study long-term trends in a field as young as finance.
Full disclosure: I picked this window because it was the widest dataset I could get with free price data on individual stocks. Anything longer and I'd have had to pay.
Here a contrary thought: In Benjamin Graham's universe, where I practice, one can identify a fair value for a company and can buy its stock when the undervaluation is significant. You don't sell something just because it is a "loser", but you do sell it if the investing thesis breaks. You also sell it when it reaches fair value, perhaps letting it run some to take advantage of the momentum investors who are acting like the stock market is a casino. You do need to understand and pay attention to the company. This has proven successful for many investors including myself. But the kind of analysis discussed here can never hope to identify such success.
That Buffett line is a perfect bridge into his own evolution: he went from classic Graham-style deep value to something much closer to GARP (the implicit style of my analysis), largely under Charlie Munger’s guidance and pressure.
You framed your answer as a “contrary thought” to my point. But it isn’t, at least not to me.
I put numbers on the table and interpreted them. The only real rebuttals are: my numbers are wrong, there are better numbers that contradict them, or the interpretation is flawed.
Saying “other strategies work without holding onto winners” doesn’t contradict any of that. Those numbers may still hold inside those strategies. The opportunity cost isn’t “winning vs. losing.” It’s how much you fail to win, sometimes to the point of turning a win into a loss.
So it’s hard for me to validate or contest your “counterargument,” because I don’t see it as one. Deep value can work, I’m not arguing otherwise, but it’s not the path I’ve chosen. If it works for you, I’m genuinely glad.
Likewise if your approach works for you and your subscribers, I am glad for you and them. And certainly doing deep value requires having the necessary temperament. I do think there is a fourth response to your list, though I don’t see it as a rebuttal. In my view, your methodology will be unable to detect winning value investments as distinct from other investments that happen to win. But value investing does take investors to distinct places.
A brokerage statement serves as a ledger for transactions but possesses no capacity to record the profound costs of inaction or interrupted compounding. Long-term wealth is a function of Ergodicity, necessitating a psychological framework that prioritizes staying in the game over the illusory comfort of frequent activity.
The most significant drawdowns are often the invisible ones where time was traded for the false promise of market timing.
The drawdown approach to opportunity cost is interesting. It might actually have been a more intuitive way to frame it.
That said, I disagree on brokers. I do the calculation myself using my statements and an API, so I have little doubt they could do it as well. They could even show clients an annual opportunity cost estimate by comparing actual results to a simple buy-and-hold of the portfolio from the start of the previous year (essentially a “do-nothing” benchmark).
But from a business standpoint, that would probably be close to economic suicide.
Still the absolute best compounders usually have also brutal drawdowns, for example Amazon -90%. Pretty easy to become the worst loser on some point
That’s true. But I don’t see it as a pure counterexample.
First, that -90% drawdown happened during the dot-com bubble. Many tech companies (and even some non-tech ones) fell well beyond -90%, and that does not imply Amazon would automatically have been sold.
And even if it was sold, other compounders from the eventual winner bucket could still have been held while Amazon was not. That kind of scenario is inherently captured in the simulation and partly contributes to the results (I actually mention that specific case.)
That said, the simulation only looks at the numbers in hindsight. It completely ignores the psychological skill required to apply such a rule over time, which is precisely what makes investing so difficult. In my view, that is the main limitation of the result.
It quantifies a simple and intuitive idea, but beyond giving one more reason to apply it, it does nothing to reduce how hard it is to execute consistently over time.
Excellent work! I loved how quantitative this was! This is exactly why I think rebalancing can be a poor investing decision: rebalancing is all about selling what's doing well which, as you show so elegantly, is one of the worst things you can do.
Thanks for the feedback, I really appreciate it.
“Rebalancing can be a poor investing decision.” Honestly, I didn’t have your level of wisdom before running this simulation. Like many investors, I tended to justify every sale and purchase based on what I believed were sound fundamentals.
But the results are clear: on average and over time, the reasons I came up with were often poor ones that led to poor decisions. That is why I need to adapt my system.
I’m speaking in the past tense, but this realization is actually very recent. I have no doubt I will still struggle not to systematically sell a position I believe is overvalued, or not to reallocate capital toward what I see as a major opportunity.
As always, simple, but not easy.
If you’ve already managed to get past that stage, then honestly, well done!
I think I've honestly just lucked into my current mentality. One of the earlier books on investing I read almost a decade ago was Michael Covel's "Trend Following." And trend following is all about buying and holding what's going up and avoiding/selling what's going down
insightful!
1/
i do have some internal debate about winners.
you define a winner as one above its purchase price.
in theory (and probably in practice too) you could buy a stick that goes up significantly in year 1, and stays at same range for 19 years.
had the investor sold it/ trimmed the position - he might be able to find another winner.
i realize that this case might be solved by other winners eventually catching up to it, passing it and perhaps eventually pushing it to a sell. but even at that case - we let some stock fester while other catch up to it - thus paying an opportunity cost too.
i'd suggest checking winners of the past year - but i'm not gonna - as you could easily find a great long term winner stopping to breath before it's next climb.
maybe take winners of the past 5 years? maybe finding the optimal number is the subject of the next simulation :)
2/
for the non-random sells, it feels like selling at year 1 differs from selling at year 15 - as at year 15 you have far more data points.
technically - both are selling a loser/ winner - but in one case it's almost a coin-toss, and in the other probability is on your side.
Thanks for your relevant remarks. In your point 1, I see two separate points:
On 1 year vs 5 years, you're very likely right: over that time frame, the mistake of not selling a "fake" winner (one that will end up winning in the long run) is probably much less likely than over 1 year. Tbh, I even think that's a time scale better suited to the strategy overall. I went with 1 year because, on one hand, there were real-world parameters I couldn't model (or it would have multiplied the complexity tenfold). So I tried to get as close to reality as I systematically could whenever the variables allowed it, hence the 1 year. Few investors have a minimum 5-year time horizon (this isn't a criticism), and the average stock holding period figures prove it (even adjusted for special activities like market making, quantitative trading, etc.).
However, you use an example to show the strategy's limits with not selling a "fake" winner that could have let you hold a real winner if you'd sold it. But in my opinion, that's actually the real value of this simulation: the sheer amount of data. Every counter-example the mind can come up with is already included in these results. And as I say in the analysis, to get this kind of result you have to accept making this kind of mistake, because they will happen, mathematically. And that's exactly the trap every investor needs to avoid, one I wasn't able to avoid myself: overfitting. My dataset is limited. If I'd wanted a longer time frame, I would have had to pay for it (and stock data isn’t cheap). Even the one I used has certain flaws that, in principle, pull it away from reality. And it's quite likely that the AI revolution underway will make the data somewhat different from what we've seen so far. It's a trade-off between optimizing the strategy and making it generalizable. From a more "theoretical" standpoint, if I had exhaustive data going back 100 years, I think you'd be right. A 5-year window would bring better performance to the don't-sell-winner strategy. But conversely, I'm not ready to bet that a 5-year window will outperform a 1-year one in the years ahead.
As for point 2, I admit I don't get it. Each year has just as many data points. If you could give me a bit more detail, I'd appreciate it.
regarding point no 1:
i like your point about overfitting.
in software engineering there's a similar deadly sin called "premature optimization" :)
on the other hand how do you know if you've not just threw out a really good tweak to the strategy? you feel the strategy results are good enough?
i'll give an example. you probably heard of magic-formula-investing. basically buy a beaten down stock of a business that generates good results. it is almost the opposite of this strategy, to be honest. they too had to make a decision on when to stop waiting for the market to align. they also made the arbitrary choice of 1 year.
when i ran some tests it turns out that waiting longer might provide better results.
one could claim that by trying longer periods - i was overfitting.
regarding point no 2:
you've chosen to ignore data points inside the year - as they produce noise that is not helping in any way.
I am completely ok with this.
but once you've introduced rotation into the strategy - you'll need to choose between assets that had short time to compound vs ones that had much longer.
e.g.
at year 0 you bought asset A1...A10. then at year 9 you sell A10 and buy A11.
in year 10 - you'd need to make a decision between A1 (that had 10 years to compound) with A11 (that had just 1).
if A1 survived for 9 years - it probably had good compounding already.
for A11 to win - its current year return would have to be better than A1's 9 + current year.
this makes the sell-relative-losers strategy biased towards old assets. maybe that's a feature, not a bug 🤔
I think your question 1 and all of point 2 come down to a question of definition.
My starting point was to check what great investors (Buffett, Lynch, Lu, etc.) generally say: a handful of winners do all the work. To check that, I had to define what a "winner" actually was.
Initially I leaned toward something more faithful to reality (which also handles your point 2): best annualized return over a 3-year window (or less if the stock was added to the portfolio more recently). But that choice forced a bunch of other decisions I wasn't comfortable with. Tbh, I don't remember which ones anymore, I just remember deciding it wasn't worth it. So I needed something simple enough while still staying reasonably close to how readers actually experience this. Hence the psychological winner/loser definition.
To answer your "on the other hand, how do you know you haven't just thrown out a really good tweak to the strategy? Do you feel the strategy's results are good enough?", that's exactly the point: it's not the goal. The goal was never to optimize a strategy or squeeze out the best possible performance. It was to measure the opportunity cost in a simulation that behaves roughly the way the average investor would.
I'm 100% sure the strategy isn't optimized. I played around with the parameters a bit, and, without remembering the exact configurations, some choices clearly produced better results, at the cost of lower fidelity/simplicity.
Your point 2 is actually a great illustration of one of the costs of that performance-vs-simplicity/fidelity trade-off. I could, for example, have overweighted the positive performance of a stock that had already run for a long time, so it wouldn't get kicked out of the portfolio over one bad year (in a way, that's arguably pretty faithful to actual human bias), but that would have complicated the simulation, and my explanation of it, for the one point I was simply trying to make: the massive cost of selling your winners and holding onto your losers.
cool.
thanks for taking the time.
i kind get the impression that you really love what you're doing :)
if you ever want to enhance it - i'd love to help.
At one point my great grandfather, who was a high-conviction, small-portfolio guy, had $7 million in Motorola stock. It was a massive “winner”, and he held it until it was nearly worthless.
Wow! What a study! Thank you. This study proves WHY one should not have more than 10 or 12 positions in a portfolio. But let's be honest. Most portfolios have way more than 10 or 12 holdings.
So even the brightest investors do not consider opportunity cost to be a real factor.
Personally, I would keep my portfolio down to around ten holdings (or less).
Simply because I don't have that much cash to be holding dozens of ticker symbols.
Amazing study, tho.
We have always been advised to keep a low number of holdings in a portfolio. It is maintained that a portfolio of 12 holdings can equal the diversification of dozens or even hundreds of holdings.
We never really understood why, tho. This study explains why. And it is counter intuitive. If a portfolio of 12 holdings is good diversification, holding 24, or 36 holdings should be a lot better diversification, right?
This is one of the probs with holding index funds. The index funds typically hold hundreds of securities. The bad performing securities bring down the funds over all performance to average at best.
Thanks for the feedback and for the thoughtful response!
I think my simulation is too limited to draw conclusions on the merits of diversification.
The main issue: I assumed equal weights throughout (5 stocks at 20% each, 50 stocks at 2% each).
The second problem is that I only looked at number-based diversification.
True diversification is measured by covariance between assets. The number of stocks in the portfolio is just a proxy, it doesn't necessarily imply diversification. As you said, 10 assets with low covariance are far more diversified than 50 with high covariance.
Indexes like the S&P 500 are actually poorly diversified in covariance terms, but they have one huge advantage: they're market-cap weighted. The more a company wins, the bigger its weight in the index; the more it loses, the more its weight shrinks. A solid proxy for selling losers and holding winners.
Imho, market-cap weighted indexes are an excellent compromise between performance, risk, and time spent. Equal-weighted, by contrast, falls right into everything you described. In a way, it's great news (and probably no coincidence) that market-cap weighted is the market norm over equal-weighted.
That said, I do share your view, for anyone with the time and skill to stock pick, a concentrated low-covariance portfolio beats a 40-stock one.
An interesting analysis and read, thank you.
I think in pratical terms, rules such as "selling a high conviction holding which importantly has the ability to compound at high rates for 10+ years should be avoided on the basis of valuation" are likely good.
As for some small pratical critics:
- This assume that an investor sells a whole position to buy a new one. If they had a position which has done well (ie has gained 4x), in a 10 stock (if all 10% sized cost basis) this postion could be 30-40% of the portfolio. Nobody is going to sell 30% and put it all into a new position. In reality, investors would generally trim this position to fund a purchase.
- I dislike the distinction between selling winners vs losers (although realise it needed to follow these rules for modeling). I myself tend to sell my lowest conviction position to fund a new position, which doesn't mean the position hasn't made money, and could well be that higher conviction positions have lost money vs my cost basis. The gain or loss since you've invested in a company doesn't / shouldn't match with your conviction rating of the company/range of returns forward.
- If an investor never sold a strong returning investment in a concentrated portfolio, it could easily get to 50-80% of the portfolio's value. Depending on if various things like if you are drawing an income from the portfolio or not, and your risk appetite (you need to know yourself well as an investor), you should make trim / partial sell decisions around the concentration risk when a winner gets too big, even though it has a chance on meaning you don't maximise your eventual wealth.
The goal isn't maximum wealth strategy (if it were, leverage would be involved), (in my opinion) it's a strong return with a high chance of happening and being able to stick to your plans.
Best regards
Jack
All of these criticisms are extremely well-founded. I have almost nothing to add, given that you cover both the critique and the meta-critique.
As you point out, some are deliberate choices: converting qualitative data into numerical values in order to apply mathematical tools. Others are inherent limitations of the simulation itself, some made in the name of simplicity, others simply unavoidable.
Thank you for taking the time to add all of this. Very sharp analysis, genuinely appreciated.
A sharp articulation of a cost that compounds quietly in most portfolios.
The asymmetry is clear - the damage from a few premature sells far outweighs the benefit of most reallocation decisions.
In practice, the edge is less in finding winners and more in not interrupting them.
Great writeup
Thanks!
I want to be a critic on the post, what you will do in a war like scenario and you just find out a gem from micro cap universe, yet the stock corrected more than 50%, however there are no change in fundamentals and the going is intact, what changes is liquidity, liquidity matters a lot in such case , but saying that compounding happens when a stock moves higher and higher, this is just the partial truth.
I gladly accept the criticism, and it actually points to a limitation I explicitly acknowledged in the methodology: this is only a simulation of broad statistical tendencies. It is too far removed from specific real-life situations to be applied directly or mechanically. That limitation is intrinsic to the exercise, if only because of the computing power and modeling scope available to me.
Your example of a war-like scenario and a 50% drawdown in a micro-cap highlights the psychological dimension of investing, which is probably its most central one. And that is precisely what this simulation does not capture. But I think criticizing it on those grounds approaches the problem from the wrong direction. The point of having data, and of understanding what the data implies, is precisely to reduce the influence of our biases and emotions, so as to avoid value-destructive actions such as panic selling.
That was the initial purpose of this simulation: to give me concrete data points I can bring back to mind at the right moments, in order to reduce the probability of making mistakes such as selling a winner too early.
Put differently, the goal of the simulation is to provide data that can help improve decision-making, not to prescribe the right decision in every specific situation.
And on the last point, I think reducing the post to “saying that compounding happens when a stock moves higher and higher” misses several of its core arguments: the impact of portfolio size, the role of turnover, the relevance of buy-and-hold, and the quantification of these effects and how they evolve over time.
I acknowledge it and understand your point.
Love this! I posted a Substack on this topic using Keynes’ art collection as a heuristic: “To Build Wealth, Don’t Sell Your Cezanne Stocks”. Your data is invaluable.
Great methodology and a well-written post as usual.
Identifying losers early and consistently is a challenge especially when there are weeds that looked like flowers at one point. That said, difficult doesn't mean impossible. I believe over time, one gets better at making these decisions.
Ideally, running a concentrated portfolio should be an advantage to the investor here. The opportunity cost of preventing capital from searching from a true winner is greater here and that should motivate the investor to act decisively.
Holding onto winners for long enough is a whole other level of difficulty. In most cases, this means holding overvalued stocks where market value far exceeds intrinsic value. Still, that's not an excuse. Many 20-, 50-, 100-baggers would have been overvalued at different periods of the holding period. The upside of one of these great investments far exceeds the downside.
As always, thank you for sharing posts that provide an "intellectual itch" for lack of a better term!
Thanks for the feedback, Seyi, really appreciate it.
As always, you’re dead right, especially this part: “this means holding overvalued stocks where market value far exceeds intrinsic value.”
From my perspective, not selling when you know it’s overvalued is probably the hardest things in investing. And yet, in the median case, not doing it is value-destructive.
All I/we can do now is hope, and make sure, this becomes true: “over time, one gets better at making these decisions.”
The data on psychological winners will be a gut punch to many. We’re wired to lock in gains to feel successful, but your simulation suggests that playing it safe by selling winners is actually the most aggressive way to destroy future wealth.
Given that the biggest winners often have the scariest valuations, it's likely many readers have difficulty distinguishing between letting a winner run and being blind to a genuine bubble. Are you considering a future post on specific frameworks or 'red flags' you use to hold onto winners even when the valuation feels stretched?
Your diagnosis is spot on in my case.
I’m still digesting the data and coming to terms with the fact that the “fundamental” reasons that, in theory, and sometimes in practice, seem to justify my approach are very likely destroying value over time.
Honestly, I don’t have a framework or red flags that survive these results + a precautionary principle yet. But I’m working on it right now!
My own personal framework around strategies for letting winners run includes labelling some holdings as "Permanent holdings" (very high conviction and runway which can stretch >10 years at teens+ growth), which I've held for 2+ years (to better understand the company). When marked, I then don't trim/sell on valuation, until conviction changes, growth rate trends below mid-teens and/or visable likely runway for growth shortens under 10 years.
The whole backtest is based on one 25-year window (2001–2025), and that happens to be a stretch dominated by a handful of mega-cap tech compounders. So a rule like "never sell your top 5" is built on a single historical regime - it could just as easily be a pattern specific to this period rather than something universal.
The same reasoning applies to the 1990s-2000 dot-com bubble. And to the Nifty Fifty in the 70s. The pattern isn't as specific to the period you're describing as you make it sound.
If anything, it's an intrinsic feature of markets. Even more so now, with market-cap-weighted passive flows.
That said, your sampling-bias point still holds. It always does the moment you study long-term trends in a field as young as finance.
Full disclosure: I picked this window because it was the widest dataset I could get with free price data on individual stocks. Anything longer and I'd have had to pay.
Magic Formula Strategy is based on the Opportunity Cost.
.
Literally, Opportunity Cost is a ratio:
.
Opportunity Cost
= P/E ÷ Intrinsic Multiple
.
Intrinsic Multiple
= G, Return on Capital or their combinations
Here a contrary thought: In Benjamin Graham's universe, where I practice, one can identify a fair value for a company and can buy its stock when the undervaluation is significant. You don't sell something just because it is a "loser", but you do sell it if the investing thesis breaks. You also sell it when it reaches fair value, perhaps letting it run some to take advantage of the momentum investors who are acting like the stock market is a casino. You do need to understand and pay attention to the company. This has proven successful for many investors including myself. But the kind of analysis discussed here can never hope to identify such success.
"There are many roads to the investment heaven"
That Buffett line is a perfect bridge into his own evolution: he went from classic Graham-style deep value to something much closer to GARP (the implicit style of my analysis), largely under Charlie Munger’s guidance and pressure.
You framed your answer as a “contrary thought” to my point. But it isn’t, at least not to me.
I put numbers on the table and interpreted them. The only real rebuttals are: my numbers are wrong, there are better numbers that contradict them, or the interpretation is flawed.
Saying “other strategies work without holding onto winners” doesn’t contradict any of that. Those numbers may still hold inside those strategies. The opportunity cost isn’t “winning vs. losing.” It’s how much you fail to win, sometimes to the point of turning a win into a loss.
So it’s hard for me to validate or contest your “counterargument,” because I don’t see it as one. Deep value can work, I’m not arguing otherwise, but it’s not the path I’ve chosen. If it works for you, I’m genuinely glad.
Likewise if your approach works for you and your subscribers, I am glad for you and them. And certainly doing deep value requires having the necessary temperament. I do think there is a fourth response to your list, though I don’t see it as a rebuttal. In my view, your methodology will be unable to detect winning value investments as distinct from other investments that happen to win. But value investing does take investors to distinct places.