Concentration or Diversification? And Why Chasing the latest Meme Investments May Not Make You Rich

Should I concentrate my investments, putting them into a few selected stocks in the hope that when one or more of them appreciate in value, it increases my net worth by leaps and bounds? Or shall I instead diversify my investments, nibbling a bit of many different stocks, ensuring that in a downturn I would not suffer too much? Concentration or diversification? This may seem a moot point, since we are always told “Do not put all your eggs in one basket!” But at the same time, we live in an age where people have become very rich just holding on a one or two investments. And this is not new, as one tycoon from a by gone era has said:

Don’t put all your eggs in one basket” is all wrong. I tell you “put all your eggs in one basket, and then watch that basket!

Andrew Carnegie, 1885

Andrew Carnegie has been said to be the richest man who ever lived, amassing a net worth of more than US$310 billion in today’s dollars, so he must know a thing or two about concentration versus diversification. The quote he made back in 1885 has been wrongly attributed sometimes to Warren Buffet of Berkshire Hathaway, who is also well known for big investments.

Don’t put all your eggs in one basket? Or put them there and watch the basket closely?

So let’s take a tour through theory and practice and see whether there can be a case made for concentration or diversification when it comes to your investments.

Mathematics of Portfolio Risk and Concentration versus Diversification

Let’s start with some theory. Suppose we have a portfolio of stocks, all of them having the same volatility (i.e. the square root of variance) of 50%, and are correlated with each other with a correlated coefficient of 50%. What would be the volatility of the portfolio be when we add more and more stocks to the portfolio?

A quick check on the internet gives us the answer here. The formula for portfolio variance in a two-asset portfolio is as follows:

Portfolio variance = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov_1,2

Where:

• w₁ = the portfolio weight of the first asset
• w₂ = the portfolio weight of the second asset
• σ₁= the standard deviation of the first asset
• σ₂ = the standard deviation of the second asset
• Cov_1,2 = the covariance of the two assets, which can thus be expressed as p_(1,2)σ₁σ₂, where p_(1,2) is the correlation coefficient between the two assets

The formula for portfolio volatility is just the square root of the portfolio variance.

The first two terms on the right hand side of the equation are simply the weighted variance of the two assets or stocks in the portfolio. The third term is the cross correlation term between them. we can easily extend this to a portfolio of three assets or stocks. Only that in the three asset case, there will be 3 weighted variance terms (one for each of the three stocks), and also 3 cross correlation terms (there are three unique pairs of two stocks each which can be formed from three stocks).

So if we now extend the portfolio volatility calculation to a portfolio of three or more equally weighted stocks, we can plot the results in the chart below:

Portfolio Volatility Decreases with Increasing Number of Stocks in the Portfolio

When we only have one stock in the portfolio, the portfolio volatility will naturally be the same as the volatility for the stock by itself. But when we add more stocks, we can see that the portfolio volatility falls rapidly with each addition, resulting in a portfolio with lower risk. Hence the case for diversification. But how much diversification do we need? From the chart, we see that by the time we get to 10 equally weighted stocks in the portfolio, we already have about 90% to 95% of all the possible diversification we can get by adding more stocks. Of course we can go on adding stocks and reducing risk, but given our limited bandwidth for analysing and tracking individual stocks, it seems safe to say that if we can invest and track just 10 stocks, we can achieve a well diversified portfolio already.

But we seldom invest in 10 equally weighted stocks. Most of the time, unless we are actively rebalancing the portfolio by selling the winners and buying more of the losers, we will tend to end up with a higher concentration in one winning stock, say 20% to 30%, and nine other stocks with weights of less than 10%. So what will the portfolio volatility look like in this case?

As before, we can apply the portfolio variance formula, and we show the results of this in the chart below:

Portfolio Volatility Depending on the Weight of the Largest Holding in the Portfolio

The results here for the realistic portfolio (red line) look quite different from the equally weighted case before (blue line). In particular, as we decrease the size of the main stock holding, the portfolio volatility falls a bit slower than before. In fact, if we compare the portfolio volatility for a portfolio where the largest holding is 50%, we see that the portfolio risk is roughly the same as that of an equally weighted portfolio of 2 to 4 stocks! So a quick and dirty rule for concentration and diversification is as follows:

• The risk of the portfolio depends mainly on the size of the largest holding
• Hence a portfolio with a 50% concentration in one asset has risk similar to one with 2 to 4 equally weighted stocks
• A portfolio with a 33% concentration in one asset has a risk similar to one with 3 to 5 equally weighted stocks

This finding also explains why the historical volatility of the Straits Times Index (STI) is so high compared to other stock indices like the S&P 500. Even though the STI is an index of 30 stocks, the largest stock in the index, which is DBS, makes up roughly 16% of the index. Which as we see above, is equivalent to having about 6 or 7 stocks in the portfolio only. And when we put all the three banks together, they account for some 35% of the STI, which makes the STI behave like a portfolio of 3 or 4 stocks only!

So how much concentration in your investment portfolio should you be able to tolerate?

Now, based on our findings above, what matters for portfolio risk is very much just the maximum size of a single asset within the portfolio. And solely based on portfolio volatility, it appears that a maximum weight of 10% for any single asset in the portfolio would already give it as much diversification as the portfolio can achieve without making it a mish-mash of very tiny positions of many, many assets.

However, this would only be true if the investments were all in large-cap blue chip stocks, or in government bonds, with almost zero risk of bankruptcy or going to zero in value. In such a case, all we would be concerned about is the price volatility of the portfolio, and keeping a maximum single asset holding size of of 10% will minimize that.

But if we go about invest in mid-cap and smaller stocks, or non-investment grade bonds, there is a very real chance that the investments can go to zero. In this instance, the maximum single asset holding size will not be based only on theoretical or mathematical portfolio risk calculations, but will be based on the risk tolerance of how much you are able to bear losing if the investment collapses. Hence, maximum single asset holding sizes will be of the order of 5% or less in most cases.

Some Examples of Concentration

Having looked at how concentrated you can be with your investments, let’s take a look now at those who have actually carried it out, and how these decisions on concentration and diversification have helped or hindered them.

First up is Warren Buffet, the Oracle of Omaha, and the investment portfolio of Berkshire Hathaway. Over many years, Berkshire has achieved incredible investment success. Many have pointed to their concentrated holdings as the reason for this. But are the investment outcomes we see really the same as the investment intent at the start? For example, a look at Berkshire’s holdings at the end of 2020 shows that there is an astonishing concentration in Apple Inc (AAPL). Apple accounted for almost 44% of the total value of the Berkshire investment portfolio!

What did Berkshire Hathaway’s investment portfolio looked like at the end of 2020?

Stock	Market Value	Shares	% of holding
Apple (AAPL)	$117.7 bn	887.1 mn	43.61%
Coca Cola (KO)	$21.9 bn	400.0 mn	8.13%
American Express (AXP)	$18.3 bn	151.6 mn	6.79%
Kraft Heinz (KHC)	$11.3 bn	325.6 mn	4.18%
Wells Fargo (WFC)	$1.6 bn	52.4 mn	0.59%

But from a broader perspective, note that Berkshire’s total asset size is three times that of the investment portfolio. So while there is a 44% concentration in Apple in the investment portfolio, it is really a 15% concentration at the entire asset level. Also, while there is concentration, there is also diversification from other much smaller investments. But is this level of concentration Berkshire’s intent all along? A look at the same investment portfolio at the end of 2019 shows that the concentration back then (with the same number of shares adjusted for the split in 2020) is only around 30%.

What did Berkshire Hathaway’s investment portfolio looked like at the end of 2019?

Stock	Market Value	Shares	% of holding
Apple (AAPL)	$72.0 bn	245.2 mn	29.74%
Coca Cola (KO)	$22.1 bn	400.0 mn	9.15%
American Express (AXP)	$18.8 bn	151.6 mn	7.80%
Kraft Heinz (KHC)	$10.5 bn	325.6 mn	4.32%
Wells Fargo (WFC)	$17.4 bn	323.4 mn	7.18%

And if we go back another year earlier, at the end of 2018, which is also when Berkshire raised their stake in Apple, we find that the concentration in Apple is only about 22%. So, when we talk of Berkshire benefiting from highly concentrated investments, it is actually the result of letting their winners run, rather than any original intent of taking a 40%+ concentration in a particular investment. Which tells us we need to be careful about inferring any conclusion simply by looking at outcomes instead of the original intents.

What did Berkshire Hathaway’s investment portfolio looked like at the end of 2018?

Stock	Market Value	Shares	% of holding
Apple (AAPL)	$39.4 bn	249.6 mn	21.51%
Coca Cola (KO)	$18.9 bn	400.0 mn	10.35%
American Express (AXP)	$14.5 bn	151.6 mn	7.89%
Kraft Heinz (KHC)	$14.0 bn	325.6 mn	7.66%
Wells Fargo (WFC)	$19.7 bn	426.8 mn	10.74%

If we rewind Berkshire’s investments a little bit further back to the end of 2017, we can get a little more insight into the upsides and downsides of concentrated investment positions. Investing in Apple is clearly a coup for Berkshire, and the current concentration and profits from it are more of indication of the investment strategy of letting winners run, rather than any original intention of building such a large position in it. If we look at the other Berkshire stalwarts such as American Express and Coca Cola, on which Berkshire built its earlier investment successes, we can see that they still form concentrated positions within the investment portfolio, but they have not really paid off for Berkshire over the past few years, merely maintaining their investment value over time.

What did Berkshire Hathaway’s investment portfolio looked like at the end of 2017?

Stock	Market Value	Shares	% of holding
Apple (AAPL)	$28.0 bn	165.3 mn	14.63%
Coca Cola (KO)	$18.6 bn	400.0 mn	9.60%
American Express (AXP)	$15.1 bn	151.6 mn	7.87%
Kraft Heinz (KHC)	$25.3 bn	325.6 mn	13.24%
Wells Fargo (WFC)	$0.0 bn	0.0 mn	0.00%

But the concentrated positions taken on by Berkshire also tell of its failures. Kraft Heinz and Wells Fargo are two of the big, concentrated investments made by Berkshire in the past few years. Unfortunately, Kraft Heinz has shrunk from a $25 bn position, accounting for 13% of the portfolio back in 2017, to only $11 bn at the end of 2020. Similarly, Wells Fargo was a concentrated $20 bn investment in 2018, accounting for 11% of the portfolio. It was unceremoniously sold off in large part in 2020, when the share price halved. So concentrations in investment bring about their own risks of massive losses as well!

Will concentration or diversification really make a difference to building wealth?

One of the hardest temptations to resist in today’s investment environment is to put a big bet on popular investments like Bitcoin, or Tesla or other meme investments. However, the truth is that such big moves will probably not make a lot of difference in your investment journey in the long run.

Let’s do a simple thought experiment. Suppose after having read this blog post, you decide that you are willing to go up to a concentration of 10% in a single meme investment, just like the investors you idolize. Now, suppose further that you can put 10% of your portfolio into an investment which can be worth 10 times it’s value in 10 years’ time. For the rest of your portfolio, you will put it into a diversified portfolio which can return 10% a year for the next 10 years (driven by the same liquidity wave which is pushing up the values of meme investments). How will this decision turn out?

Here’s your starting positions:

Investment	Amount now
Meme investment	$100,000
Diversified portfolio	$900,000

And here’s where you’ll get to in 10 years’ time under the best case:

Investment
Meme investment	$1,000,000
Diversified portfolio	$2,334,000
TOTAL	$3,334,000

In the case where you had not invested in the meme investment, you’ll have ended up with $2,594,000 in 10 years’ time. Hence, the difference chasing a meme investment makes is the difference of $740,000 in the very best case. This seems like a lot of money. However, when compared to the baseline of $2.6 million, it is not quite enough to really make a significant difference in wealth or lifestyle. And you can end up with less than the base case in the worst case outcome if the meme investment falls significantly in value. Also, you’ll need to take into account the amount of heart wrenching volatility you may have to live through for the meme investment to finally end up where it will be in 10 years’ time!

And this is for a fairly concentrated investment of 10% of the portfolio into this meme investment. Any investment which is less, say for example, 5%, will have even less of an impact on your overall wealth.

Conclusion: Concentration or Diversification?

While there is no lack of examples showing the potential gains and losses to concentrations versus diversification in investments, there is also no shortage of belief that concentration is the only way to go. This is especially when they are young and hungry for profits. After all, the richest people in the world, like the Bezos and the Musk,s are all heavily concentrated in the shares of the companies that they have built.

Again, outcomes do not necessarily tell us the whole story. Bill Gates remains one of the richest people in the world, despite selling off his Microsoft shares as fast as possible over he past coupe of decades, and reinvesting in a diversified portfolio of S&P stocks. Clearly, his diversified approach to investments has not made him lag behind the Ellisons, the Ambanis, the Jack Mas and the Walton and Koch families, despite the latter’s investment concentration in their own businesses.

Concentrated investments may help you build wealth a little bit faster than diversification, but not that much faster, and at a very high cost of having to deal with the volatility of the portfolio value

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