How the Distribution of Outcomes Affect Portfolio Construction

Positive returns in stocks are never a guarantee. Stay far, far away from anyone who tells you otherwise.

Company-specific risks, such as competition or regulatory risk, plus market-wide systemic risks, such as interest rates hikes and global recessions, pose risks to a stock’s long-term return. These risks result in what I call a wide distribution of outcome probabilities. 

And yet, in today’s stock market, it seems that more and more investors are starting to ignore these risks and go big or even all-in on just a single stock. Some argue that the large spread in returns between winners and laggards makes a concentrated portfolio more appealing.

But before diving headfirst into building a super-concentrated portfolio, consider the following risk.

What is the distribution of outcomes?

Let’s start with the basics.

When I talk about the distribution of outcomes, I am referring to the probability-distribution of the long-term returns of a stock. For example, a company can have a 20% chance to go to zero, a 60% chance to double up and another 20% chance to triple in value over five years (note that the probability percentages add up to 100%).

As such, there is a distribution of outcome possibilities, each with its own probability of occurring.

In the example above, over a five year period, investors in the company have a 20% chance to lose all their money, a 60% chance to double their money, and a 20% chance to triple their money.

Every stock has a different distribution of outcomes. The probabilities of returns and the range of returns will also differ drastically from stock to stock.

You found a great investment… now what?

Most stocks have a curve of different outcomes but for simplicity’s sake, let’s give the example of a stock that has just two possible outcomes.

This particular stock, let’s call it Company A, has a 30% chance to go bankrupt and a 70% chance to triple in value in five years. Simple mathematics will tell you that this is an amazing bargain. A gambler will take these odds any day.

We can calculate the average expected return we get from this stock by multiplying the probabilities with the outcomes. In this scenario, the expected return is 110%* (calculation below) in five years. Annualised, that translates to an excellent 15.9% return per year, which easily outpaces the returns of the S&P 500 over its entire history.

As such, any investor should happily take this bet. But don’t get too carried away. Even though this stock is a great investment, there is still a 30% possibility that we lose our entire investment in this stock. Would you be willing to take that risk?

Diversification reduces the risk

This is where diversification comes into play.

Instead of making a single bet on Company A, we can add another company into the portfolio.

Let’s say we find another company, Company B, that has slightly lower expected returns than Company A. Company B has a 35% chance of going broke and a 65% chance to triple in value, giving it an expected return of 95%**(calculation below).

The table below shows the probabilities of investing solely in Company A or Company B or investing half into each company.

	Company A Only	Company B Only	Half Each
Expected Annual Return	15.9%	14.3%	15.2%
Chance to Lose it All	30%	35%	10.5%

From the table above, we can see that the odds of losing your entire portfolio drops to 10.5% after splitting it between the two companies.

This seems counter-intuitive. Even though you are adding Company B into the portfolio, a stock that has a higher chance of going bust than Company A, the combined portfolio still ends up with a lower chance of going to zero.

The reason is that in order for the combined portfolio to go to zero, both companies need to go broke for you to lose your entire portfolio. The probability of both companies going bankrupt is much smaller than either of Company A or Company B going broke on its own. This is true if the two companies have businesses and risks that are not co-related.

What this shows is that we can lower our risk of suffering portfolio losses by adding more stocks into the portfolio.

Even though investors sacrifice some profits by adding stocks with lower expected returns, the lower risks make the portfolio more robust.

The sweet spot

This leads us to the next question, what is the sweet spot of portfolio diversification? Ultimately, this depends on the individual’s risk appetite and one’s own computation of an investment’s probability of outcomes. 

For instance, venture capital firms bet on startups that have a high chance of failing. It is, hence, not uncommon for venture capital funds to lose their entire investment in a company. But at the same time, the fund can still post excellent overall results.

For instance, venture investments in any single company may have a 95% chance of going to zero but have a small chance of becoming 100-plus-baggers in the future. A single winning bet can easily cover the losses of many failed bets. Given this, venture capital funds tend to diversify widely, sometimes betting on hundreds of companies at a time. This is to reduce the odds of losing all their money while increasing the odds of having at least some money on a spectacularly winning horse.

Similarly, in public markets, the same principle applies. Some early-stage companies that go public early have significant upside potential but have relatively high risks. If you are investing in these stocks, then wide diversification is key. 

Key takeaway

Many young investors today see the stock market as a place to get rich quick. This view is exacerbated by the raging bull of 2020 in some corners of the stock market across the world. 

They are, hence, tempted by the allure of making huge wins by concentrating their portfolio into just one or two companies. (You likely have heard stories of many Tesla shareholders becoming millionaires by placing their whole portfolio on just Tesla shares)

Although expected returns may be high, a concentrated portfolio poses substantial risks to one’s portfolio. 

I can’t speak for every investor, but I much rather sleep comfortably at night, knowing that I’ve built a sufficiently diversified portfolio to lower my risk of losing everything I’ve worked for

Nevertheless, if you insist on building a concentrated portfolio, it is important to learn the risks of such a strategy and make sure that you are financially and emotionally prepared with the very real possibility of losses.

*(0x0.3+300%x0.7-100%)=110%

**(0x0.35+300%x0.65-100%)=95%

Disclaimer: The Good Investors is the personal investing blog of two simple guys who are passionate about educating Singaporeans about stock market investing. By using this Site, you specifically agree that none of the information provided constitutes financial, investment, or other professional advice. It is only intended to provide education. Speak with a professional before making important decisions about your money, your professional life, or even your personal life. I currently do not have any vested interest in the shares of any companies mentioned in this article. Holdings are subject to change at any time.