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In Warren Buffett’s 1965 partnership letter, he gave us a glimpse on how to think about capital allocation:

“The question always is, “How much do I put in number one (ranked by expectation of relative performance) and how much do I put in number eight?” This depends to a great degree on the wideness of the spread between themathematical expectationof number one versus number eight. It also depends upon the probability that number one could turn in a really poor relative performance. Two securities could have equal mathematical expectations, but one might have .05 chance of performing fifteen percentage points or more worse than the Dow, and the second might have only .01 chance of such performance. Thewiderrange of expectationin the first case reduces the desirability of heavy concentration in it.”

The essence can be drill down to two words: Mathematical expectation & Range of expectation. Mathematical expectation is also called expected return – is the sum of all outcomes derived from the probability of each outcome and its respective gains and losses. If you enrol in an online course that cost $500 and there’s a 70:30 chance you can use it to earn an extra $1,000 income or none at all, the expected return is $550, [(70% of extra income*$1,000) + (30% of earning nothing* -$500)].

In investing, you are trying to predict an uncertain future where many possibilities can happen. This underlines the danger of satisficing by finding the most satisfactory explanation as supporting evidence to own a stock. We tend to extrapolate things will continue the way it is without considering other potential outcomes. Thinking in expected return allows you to develop a more accurate judgment by seeing things through multiple lenses instead of extrapolating through that rose-tinted glasses.

When you make a prediction, you should consider at least 3 scenarios on how things might unfold:

- Positive – Things turn out better or quicker than you expected.
- Neutral – Your original thesis on how things are most likely to be.
- Negative – Unexpected scenario that can destroy your thesis.

Once you’ve done that, assign a subjective probability to each scenario together with its respective gains and losses, then sum up the expected return of all 3 scenarios. As an example, if a $1.00 stock has a 30% chance of hitting $2.00 due to better than expected result; 40% chance of reaching $1.50; and a 30% chance that an unanticipated event can cause the price to fall to $0.50, the expected return for this stock is $1.35, or a 35% expected gain from the current share price. Both expected return and expected gain are interchangeable, it’s just a matter of expressing one in numerical, and the other in percentage change relative to the current price.

Expected return concerns the value of all outcomes, whereas the range of expectation deals with the number of outcomes. If a business that sells commoditized products which require strict government regulations, tight supply, robust demand and macroeconomic tailwinds in order to earn a decent return, you can say this business has a wide range of expectation where many things can happen. Any changes to those factors will have a negative impact on the earnings. Contrast this with a business that has a sticky customer base thanks to a strong network effect in its business model and a lack of product substitution. This stock’s range of expectation is relatively smaller because its profitability is less susceptible to competitions or any adverse economic condition due to the durability of the business. Coming up with the initial expected return is only the beginning. Imagine trying to keep a balloon in the air while bringing it from one end of a room to the other, you have to make many small adjustments to keep it in the right direction. Your prediction is like the balloon, you should adjust it gradually every time you receive new, material information so it improves over time.

From here, we can derive two rule of thumb on capital allocation:

- A stock with a higher expected return deserves a bigger position than a lower one.
- If two stocks have the same expected return, the one with a smaller range of expectation deserves a bigger position.

Thinking in expected return immediately solve two vexing questions we commonly encounter – “Should I buy this stock?”, and “How much should I put into it?” The role of an investor is to allocate capital wisely in order to achieve the highest compounded return in the long run. With that in mind, the decision whether to buy a stock comes down to comparing its expected return with those in the portfolio. Imagine your portfolio as a dream team that consists of the finest 11 soccer players of all time. They’re not going to win every single match, but on the overall, you can expect them to deliver the highest win rate. Now, if you discover another talented player during a scout, it makes sense to compare him to the *weakest *player in the team before you decide if you should add him to the squad. If he isn’t close to being as good as the weakest player, bringing him in would reduce the team’s winning rate.

In the same way, the weakest investment idea in a portfolio becomes the benchmark for evaluating new ideas. Assume a portfolio is sufficiently diversified, a new idea is only a buy if it beats the portfolio’s *least attractive *idea in expected return. Otherwise, it dilutes the long-term return. This also clears up the misconception that one should buy a stock because it is undervalued. It makes little sense to own an undervalued stock if it is your 50th best idea (ranked by expected return) when there are another 49 ideas that can deliver a better return. If a stock somehow made it into the portfolio, how much should you put into it, again, goes back to its expected return in proportion to other stocks. If the expected return for the number five is half of number one, its position should be half the size as well.

The best investors always look at their opportunity cost when making decisions. A dollar invested in an opportunity is a dollar not available for investment elsewhere so they always ask “How can I best allocate every dollar in hand to maximize my long-term return?” In other words, you want to compare opportunities you understand across the universe whether they are equities, fixed-incomes, real-estate, business venture and so on. As a thought experiment, assume your uncle offered you to invest in his business at a 90% discount to its business value (you’re his beloved nephew), the expected return could be astronomical that most of your capital should be in the business instead of the stock market. Opportunity cost removes the mental *silos *we use to categorize different types of investment opportunities and examine them indifferently under the lens of expected return.

Thinking in expected return is not easy. While we know there’s a 16.6% (⅙) chance that each side of a dice can turn up in a throw, trying to predict the performance of a company for the next 5 years is far from exact. There are many possibilities. But that shouldn’t be an excuse for abandoning it. Rather, it is precisely the reason why we should think in probability because the future is never certain. Expected return is more than just a tool to compare opportunities, it is an approach to better thinking. It prevents narrow framing such as selling winners early or holding on losers. It reduces silly mistakes. It reminds us of how much we don’t know so we can stay open-minded and constantly update our perception. The advantages far outweigh the feeling of discomfort we seek to avoid. Next time, before you buy a stock, always ask:

- What is the expected return?
- How does it compare to the least attractive idea in my portfolio?

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#### If you like this article, check out:

Bullish but Bearish – Expected value is the probable payoff of all possible outcomes. Warren Buffett explained using expected value to make decisions, “Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect but that’s what it’s all about.”

When Do You Sell? – When do you sell will depends on your investment strategy and previously, I wrote about how to create strategy here when discussing position sizing. The strategy that you choose will determine how you pick and what you buy, which in turn decides how you allocate your capital and ultimately, when do you sell them.

How Much Should I Put in A Stock? – Position sizing or how much to put into a stock is as important as picking the right one. While one will miss the chance to earn a superior return if too little is placed into a stock that turns into a winner, having too much inside one that becomes a lemon is a disaster. Therefore, finding the middle ground is the key and here we will go through some simple ways you can apply to increase the odds of superior return while keeping risk in check.

Hi Ricky,

Wonderful post and work in general.

I have a query- In the scenario you have explained above, you have calculated the expected return of the all three possible scenarios as 1.35. However, given that the negative scenario results in a loss of 50%, shouldn’t the expected return be -0.15 rather than 0.15 ? This would lead the total expected value to be 1.05 rather than 1.35.

Grateful if you could let me know what I am missing

Regards,

Hi Neil, under the negative scenario, the outcome is $0.50, or -50% of the $1 share price. And since there is a 30% chance of that happening the expected value is $0.5 x 0.3 = $0.15. The expected return is the stock price itself, so it can’t be negative. I think you’re thinking of this:

Positive: 30% chance of $100 gain = $30

Neutral: 40% chance of $50 gain = $20

Negative: 30% chance of $50 loss -$15

$30+$20-$15 = $35. Which is 35% expected return or $1.35 expected value