Dive into your imagination and pretend for a moment that you work as a journalist. You’ve just landed a big interview with the most successful investor in the world. You are beaming with excitement. The big day has finally arrived – the interview.
You’ve been invited inside the private office of this investing wizard.
You walk into his penthouse suite atop the tallest building in the city. His office is grand, surrounded with floor to ceiling glass. From the door, you spot him in the distance. He’s reclined in his chair, feet upon his granite desk, arms crossed, hands folded, grinning, and he says, “Have a seat.” The two of you smile and nod at one another.
You nervously take out your notepad and pen. Time for the interview to begin. You start by asking the typical journalistic lead-in question:
“Exactly how did you manage to become such a wizardly investor?”
There is a slight pause in his reaction, and instead of responding right away, he opens one of his desk drawers and begins rummaging around. After a few moments, he holds up . . . a Magic 8-Ball . . .
You’re confused, stumped for words. Seeing your perplexed expression, the wizard clarifies:
You see, all you have to do is place the Magic 8-Ball in your hands, close your eyes, ask a simple question, ‘What stock should I purchase?’ give it a little shake, and magically a company name appears amidst the purplish, blue water. And a few seconds later, it disappears.”
You clarify, “So, by using this method, you choose each stock to purchase?”
The investor wizard grins and replies, “Indeed, but there’s one caveat – the stocks chosen in this manner are not guaranteed successes. As an alternative, the stocks indicated by the Magic 8-Ball either double or lose half their value during the next year. Both possibilities are equally likely, and there’s no way of knowing which one will happen.”
The investor wizard has taken a liking to you and, in exchange for a glowing article, has loaned you his Magic 8-Ball for a day. It’s yours to use as many times as you like for 24 hours, but then it’s back to the investor.
The question now is, ‘How can you best apply this Magic 8-Ball methodology to grow your savings?’
Table of Contents
Let’s Dive into the Magic With 1 Stock Possibility
The concept and correlation of the Magic 8 Ball is to understand that having a portfolio of several ‘diversified’ assets is ideal. The ideas below will demonstrate that having more than 1 stock will continue to lower the “uncertainty” or standard deviation. By doing this you will avoid large swings in your portfolio.
Story Continued…
So now you have this Magic 8-Ball methodology, but you’re not exactly sure if you should use it to buy 1, 3, 10, or even 50 stocks. You want to use it to the best of its ability to provide you the maximum value in the long run, with the least amount of variation. Remember each stock chosen will either double or halve, and we definitely do not want to lose half of our money!
Throughout your career, you have been saving and investing your money and have managed to accumulate $1M. Not obscene wealth, but not too bad either.
Sure, you could gamble on a single stock. It would be nice if all you needed to do is pull out the Magic 8-Ball, give it a shake, and voilà, you have your stock ticker! Invest the full $1M in the stock and hold onto it for a full year.
How might investing $1M in just one stock affect your portfolio?
With a little luck, your money will double in value within a year – you’ll get a 100% return – $1M will then be $2M. However, if your luck is bad, that $1M could turn into only $500,000. Consider that a 50% loss.
This table demonstrates that, on average, a return of +25% can be expected:
The one catch is that the spread (or degree of uncertainty) is 75% for the average value of 25%.
One helpful technique to analyze the return is to separate it into an “Average Return” (AR) and “Uncertainty” (U) around the average.
Ideally, AR will be high, and U will be low. This would provide a more stable return because the uncertainty would be more constrained.
You’ve likely heard of the term “standard deviation.” This is another way of saying “how much the average can vary.” Our 1 stock strategy shows that the standard deviation is exactly 75%, as shown in U.
Let’s Look at a 3 Stock Strategy
If we were to “diversify” with our Magic 8-Ball and let it choose 3 stocks rather than 1, then we can divide our $1M into 3 stocks. How do you think this will affect the outcome?
Our “3 Stock Strategy” now has 4 different possible outcomes. (D Double) (H Halve). All 3 stocks could double, denoted by DDD.
- 0 stocks halve | 3 stocks double: DDD
- 1 stock halve | 2 stocks double: HDD
- 2 stocks halve | 1 stock doubles: HHD
- 3 stocks halve | stock doubles: HHH
Using the “3 Stock Strategy,” I have compiled the table below showing all the outcomes, probabilities, and the return for each case.
As the table shows, whether you invest in just one stock or three stocks, your “average return” is the same: +25%. But if you spread your money out among 3 stocks, your “standard deviation” (the uncertainty around your average return) goes down from 75% to 43.3%.
Your First Lesson | More Diversification – Lower Variability
Spreading your money around in a variety of identical stocks lowers the variability of your returns while maintaining the average you’d get from a single stock.
Using fancy terms, this reduces “tail risk,” or the chances of getting a return that is far from average, both for better and worse.
If you increase your stock holdings from one to three, for instance, the likelihood of suffering a 50% loss, drops from 50% to 18%. This same logic also applies to your chances of 100% return as well.
Lucky Number 7
So how does this apply to larger numbers of stocks? We all know that 7 is the luckiest number of all. Let’s look at the distribution of returns for the ‘lucky 7 strategy.’
We still accomplish the same rate of return of 25%, but now we’ve lowered the standard deviation to 28.35%.
Your Second Lesson | Diminishing Benefits of Diversification
The standard deviation of your portfolio would decrease by 32% (from 75% to 43%) if you added just two stocks (from 1 to 3). But the subsequent four stocks only brought the standard deviation down by about 15%.
Also, keep in mind that it all started with a Double or Half bet, which is a bit extreme. What does that mean exactly? Remember – 25% (AR) +/- 75% (U).
What if we used outcomes that were a little more moderate? Let’s change the rules a bit.
- Now (U) Uncertainty = 50% rather than 75%.
- And the terms “Gain 75% or Lose 25%” are used in place of “Double or Halve” in this case.
Let’s take peak at the table below comparing the standard deviations of portfolios with varying degrees of diversification (from one stock to one hundred) and two different values of (U) (75% and 50%).
You can see that diversification often has a smaller effect when U is smaller.
Your Third Lesson | More Conviction = Fewer Bets
In the previous table you see U = 50% (low uncertainty), it takes just 25 stocks to get to 10% standard deviation. But with U = 75% (high uncertainty), it takes ~50 stocks.
Here is a chart that shows various U and N. You can see as U decreases, so does the impact of diversifying.
Charlie Munger and Warren Buffett like to use the phrase, “invert, always invert” – it’s the idea of looking at thing from a backwards perspective or “inverted.”
Instead of asking, “What is the standard deviation when we have N stocks in our portfolio?” they’ll ask, “What is the smallest number of stocks we need to have in order to reach a target standard deviation?”
Let’s review the table:
It’s obvious that a small number of carefully selected wagers is all that’s required if you want to win.
If you want your portfolio to have a standard deviation of 5%, for instance, all you need are four stocks, each of which can account for a maximum of 10% of the total.
This is why investors like Warren Buffett can have extremely concentrated portfolios and still sleep well at night. Before investing in a company, he understands the business inside and out, and therefore can have high conviction in his bet.
Of course, you might not be so sure of your ability to analyze and understand companies. This is normal, especially if you are just starting out with investing. Continue researching, analyzing, and absorbing information. Just make sure your portfolio has the appropriate amount of diversification if you want to avoid large swings.
Ray Dalio calls diversification the “Holy Grail of Investing,” and suggests diversifying across 15 or more uncorrelated assets to reduce your risk.
Here are some examples of different assets to get the general idea:
- Cash (even foreign currency)
- Bonds
- Real Estate
- Gold/Silver/Commodities
- Energy
- Pharmaceuticals
- Medical
- Telecommunications
- Finance
- Healthcare
- Foreign Markets (Europe, China)
- Emerging Markets (up and coming)
- Technology
- Cryptocurrencies
- Artwork
- Collectibles
Conclusion
If you’ve made it this far into taking responsibility for your investments, then you’ve clearly thought through the concept of diversification. But many people miss the fact that diversification requires uncorrelated assets to truly have diversification. That doesn’t mean that you shouldn’t own two stocks in the same asset class, such as Microsoft and Apple, but understand that these stocks will typically be affected by market conditions in the same manner. So, the importance of diversification is to spread your investments out across different assets “classes” that are not correlated. This gives you the best opportunity to grow with “certainty.”
Another thing to note, is that if you look at the best investors in the world, they are always diversified, but they hold larger amounts of specific stocks that they have high conviction in. Meaning, they are very confident in their purchase, so they don’t need to have a portfolio of similar assets, because in their mind they have chosen the best of the asset class.
Additional Formula
If you’re curious about the formula to use to calculate the standard deviation, here is an example:
The standard deviation of a diversified portfolio with (N) stocks, given (U).
Keep in mind, the formula below only applies to assets that are completely uncorrelated. If the asset is correlated, then the precise standard deviation is not exact. But the primary goal in portfolio diversification is to have uncorrelated assets.
Definitions
The Average Return (AR) is the simple mathematical average of a series of returns generated over a specified period of time.
Diversification is a strategy of risk management that combines an array of investments within a portfolio. A diversified portfolio contains a blend of distinct asset types and investment instruments in an attempt to limit exposure to any single asset or risk.
Tail risk is the chance of a loss occurring due to a rare event, as predicted by a probability distribution.