Diversification Is Not About Counting Stocks

"Put all your eggs in one basket, and then watch that basket."

Diversification is one of the most misunderstood ideas in finance.

Should I diversify my portfolio? Should I concentrate? If I diversify, how many companies do I need to be protected?

One side of the debate quotes Munger on the virtues of concentrated portfolios. The other quotes studies on the benefits of diversification. But very often they are not talking about the same thing.

The question "how many stocks should I own?" is badly framed. Two portfolios with 10 positions can have completely different risks: one may be genuinely diversified, while the other may be a single bet in disguise.

What matters is not the number of positions, but which risks you are repeating, how much capital you are putting into each one, and what opportunity cost you accept by not putting more money into your best ideas.

To keep the thread clear, the central point of this article is simple: good diversification is not about adding positions. It is about reducing your dependence on the same negative scenario without giving up too much expected value.

More specifically, I am going to separate three things that are often mixed together:

1. A portfolio with more stocks is not always more diversified.
2. A good idea does not always deserve a huge position.
3. The best portfolio is not necessarily the sum of your best individual ideas.

My concern comes mainly from a chart many of you will know, and that I have seen repeated endlessly:

This chart is often presented as the "holy grail" of diversification: definitive proof that you should own 20 to 25 companies.

The chart is not wrong. The problem is using it to prove something it does not prove.

Many value investors reject beta and volatility as complete measures of risk, and then defend diversification with a chart that measures precisely volatility.

That chart does not measure risk of permanent loss. It does not measure the risk of overpaying. It does not measure fraud, competitive deterioration, poor capital allocation, or analytical error. It measures the standard deviation of returns. And that is fine.

But if your premise is that "volatility is not risk", then you cannot use a volatility chart as absolute proof that a 25-stock portfolio is less risky than an 8-stock portfolio. You can defend diversification, of course. But you need a different argument.

That confusion is why this article exists: to explain diversification without hiding behind a volatility chart.

On the other hand, many people think that in a world where risk is perfectly known, you would simply find the opportunity with the best return/risk profile and put 100% of your capital into that one bet. In other words, they think owning several stocks is useful only as protection against ignorance. If you knew the return/risk profile perfectly, the optimal portfolio would contain just one company.

That is also false.

There is a less intuitive reason to own more than one position: even when an opportunity has an extremely high expected value, it can be optimal to allocate only a small fraction of your capital to it. Not because of ignorance, but because of survival and long-term return maximization.

Understanding the bet is not the same as seeing the future.

Three reasons not to put everything into one idea

Let us start at the beginning. An investment is good because its expected value (EV) is positive. And the higher it is, the better.

The simplified formula is:

EV = (p_win × gain) - (p_loss × loss)

Where

EV = expected value

the average outcome we would expect if we could repeat the same bet many times

p_win = probability of winning

the probability that the bet ends with a gain

gain = gain

the net return earned on the capital wagered if the bet works

p_loss = probability of losing

the probability that the bet ends with a loss

loss = loss

the net return lost on the capital wagered if the bet fails

In other words, a bet is good if the potential gain, weighted by the probability of winning, more than compensates for the potential loss, weighted by the probability of losing.

The investor's job is to find opportunities that score well in this formula and then take the right exposure to each one.

Owning several positions can serve three different purposes:

1. Margin of safety: protecting ourselves from the risk of estimating the formula's numbers badly.
2. Position sizing: being able to exploit opportunities with a low probability of success but a high payoff without going broke.
3. Optimizing compound growth: reducing the probability of large simultaneous losses so capital can keep compounding without interruption.

The first point is Warren Buffett's "protection against ignorance". It is what almost everyone has in mind when we talk about "diversification".

The second point is not diversification in the classic sense. It is position sizing, Kelly, and survival. It is about how much capital you can allocate to a specific opportunity without getting knocked out of the game before expected value has time to show up.

The third point is more subtle: looking only at the expected average return is not enough. Capital compounds period after period, and large drawdowns reduce the base on which you then compound. That is why a portfolio with the same expected value, but less extreme outcomes, can produce a better long-term return.

Because the second and third points are the least intuitive, we will start there. We will go in reverse order: first compound growth, then position sizing, and finally uncertainty and margin of safety.

Same expected value, different compound result

It helps to separate two things:

1. The portfolio's average expected value.
2. The distribution of possible outcomes.

The first is simply the result of aggregating the expected value of the positions in the portfolio. If all your bets are bad, diversification will not save them. The second is where owning several positions becomes important.

To see it, compare two cases.

Case A: concentrated portfolio.

You have a single bet:

• 50% chance of gaining 40%.
• 50% chance of losing 20%.

Its arithmetic EV is 10%:

EV_A = (50% × 40%) + (50% × -20%) = 10%

Case B: diversified portfolio.

You have two equal bets, each weighted at 50%, with the same distribution as above, but independent from each other. That creates three possible outcomes:

• Both work: 25% probability → +40%.
• One works and the other fails: 50% probability → +10%.
• Both fail: 25% probability → -20%.

Its arithmetic EV is also 10%:

EV_B = (25% × 40%) + (50% × 10%) + (25% × -20%) = 10%

Same EV, different distribution:

Portfolio	Probability	One-period outcome
Concentrated	50%	+40%
Concentrated	50%	-20%
Diversified	25%	+40%
Diversified	50%	+10%
Diversified	25%	-20%

The diversified portfolio does not have a higher EV. What changes is that the probability of the worst outcome falls from 50% to 25%, and an intermediate +10% outcome appears half the time.

Diversifying does not change the average: it changes how likely each ending is

Concentrated portfolio

one single bet

-20%50%

+40%50%

Diversified portfolio

two independent bets

-20%25%

+10%50%

+40%25%

← worst outcomebest outcome →

Both portfolios have the same average: +10%

This matters because investors do not get paid the EV of one isolated round. They live through a sequence of outcomes, and capital does not grow by adding average returns. It grows by multiplying results:

final_capital = initial_capital × (1 + r_1) × (1 + r_2) × ... × (1 + r_n)

Where

r = return in each period

the return earned in each round, year, or investment period

For example, if a portfolio strings together a +40% round and a -20% round, it starts at 100 and ends at 112:

final_capital = 100 × 1.40 × 0.80 = 112

By contrast, if it strings together two intermediate +10% results, it ends at 121:

final_capital = 100 × 1.10 × 1.10 = 121

The difference does not come from EV; it comes from dispersion. The larger the loss, the higher the subsequent return you need just to rebuild the capital base.

When capital compounds, reducing the dispersion of outcomes can improve compound growth even if the arithmetic EV is the same.

Same EV, many possible paths

Both with +10% EV per round · 96 simulated paths

Position sizing: do not go broke before you are right

Imagine this bet:

Do you take the bet? What percentage of your money do you put into it?

Even though the expected value is mouth-watering, betting 100% of your capital would be stupid: the most likely outcome is that you lose and end up with nothing.

But if you can choose the size, why not bet 0.1% of the portfolio? That lets you play hundreds of times. When you eventually hit, you make up for all the losses and earn a lot of money.

It is hard to imagine a bet with better EV. This is where defenders of putting everything into your best idea should ask themselves what is missing from their theory.

Using the previous formula:

EV = (1% × 999,999) - (99% × 1) = 9,999

I use gain = 999,999 because if you bet 1 euro and receive 1,000,000, your net gain is 999,999 euros. For each euro wagered, the average expected result is a 9,999-euro net gain. The EV is absurdly high.

But EV does not tell you what will happen on the next round. It tells you what would happen on average if you could repeat the bet enough times. And with p_loss = 99%, the most likely outcome of any single attempt is still losing.

If you bet 100% of your capital, you have only one bullet. Even though the bet has spectacular EV, you have a 99% probability of going broke before you benefit from that edge.

By contrast, if you bet only 0.1% of the portfolio, you can survive hundreds of losses in a row. The question stops being "can I lose this bet?" and becomes "can I play enough times for the EV to have time to show up?"

If the probability of losing each attempt is 99%, the probability of never winning after n attempts is 0.99^n. Applied to 500 attempts:

p_no_win = 0.99⁵⁰⁰ ≈ 0.66%

If you can play 500 times, the probability of never winning falls below 1%. The bet is still risky on each individual attempt, but it stops being suicidal when you break it into small positions.

This calculation assumes independent and repeatable attempts. In the stock market you rarely have 500 identical bets available one after another, but the intuition remains useful: the more asymmetric and less likely an opportunity is, the more important it is for position size to let you survive a long sequence of losses.

In an ideal world, you can calculate the optimal size using the Kelly criterion.¹ In real life, Kelly is more of a compass than an exact map.

For this explanation we use a simplified version of Kelly for a binary bet: if you lose, you lose the entire fraction wagered; if you win, you receive a net profit of b for every euro bet. In real investments, multiple scenarios are already embedded in the EV, but Kelly does not use only the EV: it needs the full distribution of outcomes, because it does not maximize the average return of a single round. It maximizes the compound growth of capital.

f* = ((b × p) - q) / b

Where

f* = optimal fraction

the percentage of capital we should wager if we know the probabilities and payoffs exactly

b = net payoff

the net gain for each 1 euro wagered if the bet works

p = probability of winning

the probability that the bet ends with a gain

q = probability of losing

the probability that the bet ends with a loss

Applied to this bet:

f* = ((999,999 × 0.01) - 0.99) / 999,999 ≈ 1%

Kelly would say that, if you knew the probabilities perfectly, you could bet roughly 1% of capital on each attempt. So the earlier 0.1% was too conservative.

This may feel strange: how can a bet with such outrageous EV recommend betting only 1%? Because Kelly does not maximize the EV, in euros, of one isolated round. It maximizes the long-term compound growth of capital.

For that, it matters how much you win when you are right, but also how much damage the losses do while you wait for that hit. In this bet b is enormous, but p is only 1% and q is 99%. Even though the prize is huge, you almost always lose the individual attempt. A position that is too large shrinks the capital base so much after a bad run that compound growth deteriorates, even if the arithmetic EV remains spectacular.

In fact, if the prize tended toward infinity, the optimal Kelly fraction would tend roughly toward p: around that same 1%. Infinite upside does not turn a bet that almost always loses into a bet suitable for concentrating the entire portfolio.

Why Kelly bets only 1%

The bet is excellent, but it is not suitable for a huge position. You need to bet in small slices to benefit from it over the long run.

Even if you know the return/risk profile of the bet perfectly, the optimal decision is not always to hold a single position in the portfolio.

This is not an argument for "diversifying for the sake of diversifying". It is a demonstration that some opportunities require small positions in order to be exploited. As a practical consequence, a good opportunity does not always justify concentrating the whole portfolio. And the capital that this idea does not deserve should go to other positive-EV opportunities, to cash, or to defensive assets.

I have used an extreme case, but the same thing happens in real life with opportunities where you would not bet everything, but you might bet 80%, 50%, or 20% of the portfolio.

The world we actually live in is far more complex, which brings us to the part of diversification that protects us from our own ignorance.

Uncertainty: your numbers are not that good

So far we have spoken as if p_win, gain, p_loss, and loss were written down somewhere and your only job was to put them into a calculator. In real life, those numbers are estimates.

To illustrate, take another bet:

Applied to this case, the expected value is:

EV = (51% × 100%) - (49% × 100%) = 2%

That is not bad if you can repeat it many times. You are not going to bet the house, but if you play consistently you can make money. It is like playing roulette with the wheel rigged in your favor.

Using Kelly, this bet would call for wagering 2% of capital:

f* = ((1 × 0.51) - 0.49) / 1 = 2%

In this case the Kelly fraction equals the EV because b = 1. In other words, it lines up because when we win and when we lose, we gain or lose the same amount of money.

If the numbers are correct, this is a good bet and Kelly recommends betting 2% of capital.

Where is the problem?

Those numbers are almost never correct. We do not know whether p_win is 51%, 52%, or 49%. Nor do we know whether gain will be 100%, 105%, or 70%. Small differences matter a lot when the mathematical edge is narrow.

Suppose we are slightly wrong:

• p_win = 49% instead of 51%
• gain = 90% instead of 100%
• p_loss = 51% instead of 49%
• loss = 100%, same as before

Now the expected value is:

EV = (49% × 90%) - (51% × 100%) = -6.9%

Ouch. We went from making a little money to losing quite a lot, without any astronomical change. We simply filled in the formula badly.

And this assumes we knew all the relevant risks. In investing, even that is not true. Beyond misestimating known risks, there are events you do not know that you do not know: competitive deterioration, management mistakes, fraud, regulatory changes, disruption, or poorly understood incentives.

That is why full Kelly is usually too aggressive in real life. Kelly assumes that we know the probabilities and payoffs well, and that is almost never the case. A common solution is to use "fractional Kelly": betting only part of what the formula recommends.

For example, if Full Kelly recommends a 20% position, Half Kelly would bet 10%, and Quarter Kelly would bet 5%. This reduces the damage if your estimates were too optimistic, though it also reduces returns if they were correct.

What does this have to do with diversification? If Full Kelly suggests a very high concentration, uncertainty around our estimates usually justifies a smaller position. The leftover capital should not automatically go into more stocks: it should go into new ideas only if they also have positive EV and sufficiently different drivers. If not, the rational alternative may be cash, bonds, or a more diversified low-cost exposure.

This does not mean buying companies at random. It means there is also a cost to dedicating all your time and capital to one idea: your estimates will still be imperfect, and some risks will never have made it into the model.

Real diversification

When we diversify to protect ourselves from our own ignorance, the new position has to be fundamentally different. Buying 10 companies with the same business model, in the same country, and in the same industry barely dilutes the risk. You would probably be better off with 2 truly different positions.

The summary of what we have covered is:

1. Two portfolios with the same arithmetic EV can compound differently if their distribution of outcomes is different.
2. The optimal position size is not always 100%, even when the opportunity is excellent.
3. Diversification, when done correctly, is an antidote to ignorance.

Now we need to connect expected value with the right way to diversify: making sure your bets are as independent as possible.

Do not repeat the same risk under a different name

Diversification reduces risk, but it is not free. In the ranking of your best ideas, adding position number 2 means giving up the chance to put more money into number 1. That opportunity cost is the real price of diversification.

Even so, we diversify because we are human, we estimate badly, and we want to keep playing for many years. The important question is not "how many stocks do I own?", but "which risks am I repeating?"

Here we return to expected value. So far we have presented it as one probability of winning, one gain, one probability of losing, and one loss. But a real investment does not work like that. Its EV is the sum of many scenarios, each with its own probability and outcome:

EV_total = (p_1 × outcome_1) + (p_2 × outcome_2) + ... + (p_n × outcome_n)

Where

EV_total = total expected value

the investment's expected average outcome after adding all relevant scenarios

p_i = scenario probability

the probability that a specific scenario occurs

outcome_i = scenario outcome

the gain or loss that scenario would produce if it happened

i = scenario

each possible branch that can affect the investment

For example, the EV_total of a stock might look more like this:

EV_total = EV_base + EV_viral_product - EV_fraud - EV_recession - EV_bad_allocation

Where

EV_total = total expected value

the investment's expected average outcome after adding all relevant scenarios

EV_base = base business

the expected value of the main thesis if the business develops in a reasonably normal way

EV_viral_product = viral product

a positive scenario that can increase the gain or the probability of success

EV_fraud = accounting fraud

a company-specific negative scenario that adds loss without adding gain

EV_recession = recession

a shared scenario that can affect several positions in the portfolio at the same time

EV_bad_allocation = bad allocation

value destruction from poor capital decisions, expensive acquisitions, or misaligned incentives

This example is meant to make the idea visible: an investment thesis is not one single bet, but a collection of small overlapping bets. Some add to EV, others subtract from it, and many are hard to estimate.

Careful: these terms are not always independent or mutually exclusive. A recession can increase the probability of poor capital allocation, force a dilutive equity raise, or expose a fraud. The formula is simply a reminder that a real thesis is made of several positive and negative drivers that can overlap.

There are idiosyncratic scenarios, which affect only one company. If the CEO commits accounting fraud, the damage is concentrated in that company. This kind of risk is easy to dilute: by adding other companies, its impact on the portfolio falls sharply.

Then there are shared scenarios. A recession, a rate hike, a fall in the oil price, or a regulatory change can affect several positions at the same time. They do not necessarily affect all of them in the same way, but the root risk is the same.

That is why two portfolios can have the same EV and still be very different. If a stock has a 50% probability of rising 40% and a 50% probability of falling 20%, its EV is 10%. If you buy two stocks with the same distribution and they are perfectly correlated, you still have a portfolio that can rise 40% or fall 20%. You own two names, but one economic bet.

If those two stocks are independent, the average EV may still be 10%, but the distribution improves: you no longer need both to work. One can work and the other can fail, and you can end up with an intermediate result. Diversification has not turned a bad investment into a good one; it has reduced the probability of ending in the worst scenario.

Good diversification means not repeating the same negative scenarios too many times. If you own five different companies but all of them depend on the same country, the same credit cycle, the same supplier, or the same commodity, you do not have five independent bets. You have five exposures to the same negative term in the formula.

And be careful: diversification does not turn a bad investment into a good one. If you make many negative-EV bets, all you achieve is losing money more smoothly. Diversification improves the portfolio when you reduce common risks without giving up too much expected value.

That is why diversification is not about completing a sector, industry, and country checklist. That checklist can help, but it is not the goal. The goal is to reduce dependence on the same fundamental drivers.

Imagine a low-cost airline and an energy-intensive chemical company. They look like different businesses: one sells flights, the other sells industrial products. But both can suffer if the price of fuel or energy rises. By contrast, an oil producer may benefit from the same scenario that hurts the other two.

That is the difference. You are not diversifying by sector labels; you are looking at which variable actually moves the outcome.

The goal is to look for uncorrelated return drivers. And by "uncorrelated" I do not mean only the share price. I mean any factor that moves the investment outcome: demand, costs, financing, suppliers, regulation, currency, interest rates, price paid, liquidity, balance sheet, margins, and time horizon. Price can serve as a proxy, but it does not capture the full structure of the bet.

Building a portfolio: diversify or offset

If there is something better than diversifying a risk, it is offsetting it. If some positions suffer when the oil price rises, it may be useful to own others that benefit from that same event. That way, the impact of oil on the portfolio becomes more neutralized.

But offsetting does not mean buying any asset that "looks like" it should benefit from the opposite scenario. You need to estimate sensitivities. An oil company can partially hedge the energy risk of an airline, but it also introduces new risks: reserves, capex, taxes, regulation, debt, and execution.

This is not mandatory, but it helps build a more stable portfolio. The goal is not just to select the best individual bets, but to build the best aggregate bet. Some positions may not be spectacular on their own, but they make a lot of sense as part of the team.

Returning to the opening chart: if volatility does represent a risk for you, perhaps because you use leverage, adding less profitable but more stable companies may make sense. The return you give up in those positions can be offset by a more robust portfolio that lets you use debt without breaking.

Playing with more pieces allows more combinations, but you pay for it with opportunity cost. Diversification makes sense when it improves the portfolio's return/risk trade-off. Not when you buy handfuls of companies with no control or strategy.

Conclusion

The question is not how many companies you own. The question is what can go wrong. And, above all, how many times you are betting against that same scenario.

Diversification is not about buying more stocks to feel prudent. It is about reducing real dependencies without destroying too much expected value.

An 8-company portfolio can be better diversified than a 40-company portfolio if its return engines are more independent. And a 40-company portfolio can be a hidden concentration if everything depends on the same cycle, the same country, the same type of customer, or the same macro variable.

Diversification is not about counting positions.

It is about counting risks.

Footnotes

1. Kelly is optimal under strong assumptions: known probabilities, known payoffs, enough repetition of comparable bets, independence, no liquidity constraints, no taxes or relevant frictions, and an objective of maximizing logarithmic capital growth. ↩