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Full Version: An Effective Capital Allocator
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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 the mathematical expectation of 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. The wider range of expectation in 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:

  1. What is the expected return?

  2. How does it compare to the least attractive idea in my portfolio?
Stock selection is a tough job. To select and concentrate the portfolio on a small number of stocks makes it much more challenging. How can you be so sure that these few stocks you selected are the ones that will do well, while the rest will not? 

Because of the uncertainties surrounding each stock, detractors of concentration say it is a dangerous and speculative strategy. Certainly, if one's portfolio were concentrated in (insert securities which have gone down by half or more), the damage would be devastating and probably irreversible.

Yet, if the investor chooses to diversify instead of concentrating, will the efforts in picking stocks for a diversified portfolio be worthwhile? In other words, will it beat the benchmark index?

Following where RJT left off, the 1965 partnership letter also discussed the difference between a concentrated and diversified portfolio:

We are obviously following a policy regarding diversification which differs markedly from that of practically all public investment operations. Frankly, there is nothing I would like better than to have 50 different investment opportunities, all of which have a mathematical expectation (this term reflects the range of all possible relative performances, including negative ones, adjusted for the probability of each - no yawning, please) of achieving performance surpassing the Dow by, say, fifteen percentage points per annum. If the fifty individual expectations were not intercorelated (what happens to one is associated with what happens to the other) I could put 2% of our capital into each one and sit back with a very high degree of certainty that our overall results would be very close to such a fifteen percentage point advantage.

It doesn't work that way.

We have to work extremely hard to find just a very few attractive investment situations. Such a situation by definition is one where my expectation (defined as above) of performance is at least ten percentage points per annum superior to the Dow.

Why is it not possible to buy a while bunch of dollar bills for fifty cents, so that I may earn superior returns while lowering my risk? Buffet seems to suggest that it is not possible because the market is closer to being 'more efficient,' than it is to less 'efficient'. In other words, he seems to be suggesting that there are usually very few truly undervalued securities capable of producing superior returns. 

Amongst local securities, there are numerous low-debt property holding companies selling at large discounts to RNAV. Are they undervalued? Yes. But can they produce superior returns? That depends on whether their value can be unlocked, which most of the time, they do not. Perhaps then if I own a portfolio of these companies, my chances of hitting one where management unlocks value is higher. Indeed it is. But the diversification of doing so will also diminish the returns from such unlocking of value of any one holding. Nevertheless, I imagine such a strategy could be somewhat profitable, and there is safety of capital. But will it out-perform the benchmark? I'm not sure. I've not seen such a portfolio and its results being published. 

WB goes on to add:

There is one thing of which I can assure you. If good performance of the fund is even a minor objective, any portfolio encompassing one hundred stocks (whether the manager is handling one thousand dollars or one billion dollars) is not being operated logically. The addition of the one hundredth stock simply can't reduce the potential variance in portfolio performance sufficiently to compensate for the negative effect its inclusion has on the overall portfolio expectation.

The optimum portfolio depends on the various expectations of choices available and the degree of variance in performance which is tolerable. The greater the number of selections, the less will be the average year-to-year variation in actual versus expected results. Also, the lower will be the expected results, assuming different choices have different expectations of performance.

The evidence of a very diversified portfolio's returns converging with the benchmark can be seen from Aggregate Value Fund, where they own about a hundred securities in their portfolios.

AVF uses MSCI Asia Pacific ex Japan as their benchmark. The first 3 years of their operation saw growing out-performance against the benchmark, but this has since been reduced to 1.38% CAGR since inception. 

Inclusif Value Fund runs a similar strategy, but does not compare their performance against a benchmark, and has a shorter track record. Since their investment universe is similar to AVF, the MSCI Asia Pacific ex Japan should be appropriate for use as a benchmark for comparison sake. Shares of IVF's B class shares -- which has 0% management fee and 20% HWM performance fee, similar to AVF -- returned -11.26% from March 2018 (inception) to December 2018. During the same period, the benchmark returned approximately -16.8%, which is a 5.5% out-performance for IVF. Will IVF's strategy and ability to pick stocks out-perform the benchmark? It will be clearer over time. 

Perhaps over a longer period of time -- say, 10 years -- AVF may also produce admirable out-performance against its benchmark. 


As a portfolio moves away from more diversity to more concentration, it shields itself from the unknown/unexpected. For the journeyman investor who wishes to earn above benchmark returns, perhaps the middle way is the best: just enough diversification, which is said by some to be 30 securities. As stock picking ability achieves success, the journeyman may move towards more concentration. The challenge though, is in producing a thorough investment thesis required for a concentrated portfolio, as the investor relies on his diversification strategy (it's ok, its only 3% of my portfolio anyway) as an excuse to avoid thorough research.
IMO, how conc you want to be, depends on

- source of funds, redeemable OPM or own money
- age, older better not too conc
- type of equities, small cap, illiquid, deep value,
- cashflow, if like Buffett got tons of float, conc jialat jialat also can. coz next month, another batch of premiums to invest.

30 stocks is too many, Munger also said something somewhere about conc . Thinks he said less than 8 stocks.
I know of crazy guy with 70% concentrated on 2 illiquid stocks.