The Mathematics of Diversification and Wealth Building

Over at my Investing for Beginners site at About.com, I’ve written about the fact that very few American families invest in stock directly.  For every 100 families in the United States, only 15.1 hold shares outright, rather than through a conduit like a mutual fund.  Of that 15.1% sub-group, 29.2% (or 4.41% of all households) are invested in only a single stock, 53.0% (or 8.00% of all households) held stock in only two through nine firms, and 17.8% (or 2.69% of all households) held stock in ten or more companies.  The upsetting part is, of those stockholding families, 35.5%, or 5.36% of all households, hold shares in their employer, which can be great when times are good but introduces a lot of downside if the business fails.  The last thing you want is to lose your job, dividend income, and market value all at the same time.

The numbers aren’t as bad as they look because it can be a perfectly reasonable philosophy to put the bulk of your assets in core index funds or low-cost mutual funds, then only acquire shares outright in a handful of businesses you really feel like you know, understand, and can value as a sort of augment to your family’s estate.  There is nothing at all irrational about such a policy and it can be a huge net positive if it serves a sort of real-world learning laboratory for how to evaluate operating assets.  Regardless, there does seem to be a tendency for new investors and gamblers to fall into the trap of over-concentrating their portfolio in a single stock, treating it like a lottery ticket.  A well-constructed portfolio should never give you that feeling.  It’s a telltale sign you’ve slipped into speculation.

One of the reasons I’ve found for this behavior, among several other mental models, is the math of diversification seems somewhat counter-intuitive.  These “put-it-all-on-red” types grossly underestimate its effectiveness, significantly overestimate the number of equities required to harness most of its benefits, and don’t always understand that it changes the overall compounding rate of the portfolio itself as any higher returning assets drag up the results like gravity, their geometric returns causing them to break away from the other securities.  To explain this in a sort of real-world context, it can help to look at actual numbers.

An Example of How Even Small Amounts of Diversification Can Reduce the Risk of Owning Very Bad or Mediocre Businesses

Let’s imagine on the day I was born, a successful person who had done very well in life had $500,000 to invest (that was a whole lot of money back in the early 1980s for the typical family).  He or she decided to split the funds into five piles, buying ownership in five businesses.  They stuck with ordinary companies that had been around for a long time.  They never got their hands on a once-in-a-lifetime position, like a Home Depot or Starbucks, which could have catapulted them among the richest families in the state, but they do okay.  Sadly, they have the misfortune of having selected a firm that experiences near total wipe-out; a catastrophic failure of 1/5th of the original portfolio that puts them far, far above the failure rate of the broader indices.

• The first $100,000 was invested in WD-40, a company that made a product found in nearly every home in the United States.  It was a satisfactory business.  It would now consist of $1,091,624 in stock + $396,824 in cash dividends received along the way for a grand total of $1,488,448.  That approximates a rough compounding rate of 8.66% per annum.
• The second $100,000 was invested in Clorox, the dominant bleach company in the United States and a brand nearly every person alive associated with its industry.  It would now consist of $5,073,506 in stock + $1,440,430 in cash dividends received along the way for a grand total of $6,513,936.  That approximates a rough compounding rate of 13.71% per annum.
• The third $100,000 was invested in AIG, an insurance group that had operations around the world, including Asia at a time when the west was looking to expand overseas.  It would now consist of $137,678 in stock + $217,966 in cash dividends received along the way for a grand total of $355,644.  That approximates a rough compounding rate of 3.98% per annum.  (Note: This was after a catastrophic collapse in 2008-2009, when the shares lost virtually all of their value, dropping more than 99% from a split-adjusted value of $1,600+ per share down to less than $6 a share.  That $137,678 in stock was at one point worth nearly $4,000,000 by itself.)
• The fourth $100,000 was invested in one of the biggest health care blue chips in the United States, Johnson & Johnson.  It would now consist of $3,502,946 in stock + $1,004,438 in cash dividends received along the way for a grand total of $4,507,384.  That approximates a rough compounding rate of 12.4% per annum.
• The fifth $100,000 was invested in one of the largest metals companies in the world, the Aluminum Company of America, or Alcoa.  These sorts of businesses are notoriously cyclical and it was no exception.  It would now consist of $358,732 in stock + $262,045 in cash dividends received along the way for a grand total of $620,777.  That approximates a rough compounding rate of 5.78% per annum.

This is not exactly a beautiful portfolio.  You had one near total-wipeout, one sub-par, low-return, barely-beat-inflation metals company, an okay-but-not-spectacular lubricant and cleaning business, an excellent medical and pharmaceutical enterprise, and a glorious bleach company that showered you with money.

Despite all of the setbacks, your $500,000 has now grown into $13,486,189, consisting of:

• A pile of $3,321,703 in cash dividends received
• A pile of $10,164,486 in stocks .  Specifically:
  • $1,091,624 in WD-40 stock
  • $5,073,506 in Clorox stock
  • $137,678 in AIG stock
  • $3,502,946 in Johnson & Johnson stock
  • $358,732 in Alcoa stock

This was achieved even though you spent all of your dividend income on stuff like new cars, furniture, a beach house, tuition for your kids and grandkids, travel, charitable donations, or whatever else provided you with utility.

Some of you may have spotted an interesting fact.  The average stock in the portfolio compounded at 8.9%.  The portfolio itself compounded at a substantially higher rate of 10.67%.   That meant a tremendous amount of additional wealth at the end of the period.  How it that possible?  It’s the math of diversification.  Portfolio construction can make up for a lot of sin and folly, redeeming otherwise painful experiences.  Up to a certain point, the more equities you add to the basket, the greater you improve your chances of experiencing better results because, as a company becomes more successful and experiences a higher rate of compounding, it naturally finds itself weighted more heavily in the portfolio composition despite that same portfolio starting out as equally weighted.  The higher returning corporations begin to exert a disproportionately large effect on the portfolio as a whole.  Provided the diversification is adequate, this can be a powerful wealth accelerator.  That wealth accelerator is one of the reasons the S&P 500 and other major indices have done so well (most don’t rebalance at the end of every year, they simply buy and hold a basket of stocks, albeit with the methodology shortcomings I mentioned earlier this month).

An Example of How Diversifying Can Create a Situation Where a Single Incredible Investment, Even if a Minority Position at the Time of Construction, Can Drag Up the Rate of Return of the Entire Portfolio

Doubt it?  Let’s reconfigure the above scenario, keeping all of the stocks.  Instead, though, let’s divide that $500,000 pile into six companies, adding a superstar like Home Depot.  Each business would have started out with $83,333+ in initial investment.

Assuming no reinvestment of dividends, by the time you arrived in the present, your holdings would have grown into $84,162,488, consisting of:

• A pile of $9,486,519 in cash dividends received
• A pile of $74,675,969 in stocks.  Specifically:
  • $909,987 in WD-40 stock
  • $4,227,921 in Clorox stock
  • $114,732 in AIG stock
  • $2,919,122 in Johnson & Johnson stock
  • $298,943 in Alcoa stock
  • $66,205,264 in Home Depot stock

The Home Depot position compounded at almost 23.2% for more than 32 years.  This new portfolio, which had less risk because of greater diversification, made the other one look cute in comparison.  With it added to the mix, the average holding in the portfolio compounded at 11.29%, yet the portfolio itself compounded at 17.1%.

The mistake most inexperienced investors make, at least in my experience, is thinking they can predict which of the businesses will turn out to be a Home Depot. It’s foolish.  It’s a trap.  While you can generally tell which types of business will do better than average (even with nose-bleed valuations and several bankruptcies and near obliterations along the way, the so-called “Nifty 50” were so superior as a basket to the broader index, they actually beat the market within a quarter-of-a-century as the underlying, incredible economic engines made up for those shortcomings) total investor return has generally tracked industry return on capital over long periods of time, you can’t know with certainty whether any one, specific firm will shoot out the lights; e.g., shipbuilders have been terrible for long-term wealth accumulation while alcohol companies have been fantastic.  Put another way, it isn’t an accident that most of the top returning companies of the past few generations have all been clustered around a handful of industries that share certain characteristics.  In times like the past 12 months, things like airlines might crush everything else but you can bet with a high degree of certainty – though no guarantee – that a quarter-century from now, a basket of pharmaceutical firms will have obliterated a basket of airline shares.  This is no secret to analysts and academics, there’s really no getting around the math or empirical evidence, it’s just that people who are attracted to this sort of thing are generally stock traders who are looking to get rich quick next week or next month.  Very few people, other than the richest of the rich as John Bogle once pointed out when examining the behavior of Vanguard clients, seek out investments that can be held satisfactorily for a lifetime.  It takes a very special sort of temperament, and a willingness to ignore the benchmarks year-to-year, to think like a business owner acquiring subsidiaries.

Nevertheless, the temptation to indulge these lottery ticket fantasies is real, though.  They see a portfolio like that and immediately re-work the numbers.  “Oh man!”, they say excitedly.  “If I had put the entire $500,000 into Home Depot, I’d be sitting on $297,231,600 in stock plus I’d have received $40,310,601 in cash dividends along the way for a grand total of $337,542,201.”

You could have just as easily put the entire $500,000 into Alcoa and ended up with $1,793,660 in stock plus $1,310,255 in cash dividends received along the way for only $3,103,885.  Or worse, ended up like these people (though, to be fair, if you were following the tenants of basic Security Analysis like Graham, who insisted on a strong balance sheet as an absolutely non-negotiable requirement for building a position in the first place, a situation like that is far less likely than something like, perhaps, the Worldcom bankruptcy, which resulted from accounting fraud and took down one of the premier blue chip telecommunication firms of the 1990s).

Even a so-called “focused” investor like Warren Buffett isn’t, quite, what he seems on this front.  Buffett is famously quoted as calling diversification an insurance policy against ignorance.  His point, in its context, was a good one.  Throwing money into companies you don’t believe in or think are reasonably priced simply for the sake of additional names on the portfolio roster is a stupid way to behave.  But it often leads to an inaccurate impression of his actual behavior.  Berkshire Hathaway holds stock in 70+ direct operating businesses (some of which, in turn are made up of dozens of other operating companies) plus the equity portfolio has another 47 or so publicly traded stocks and there is a huge roster of individual fixed income securities held at the insurance subsidiaries.  Yes, the money is concentrated in the biggest positions but even the largest public stockholding, Wells Fargo, which makes up 23.23% of the portfolio, represents less than 4.9% of assets and 10.6% of net worth.

The Moral of This Diversification Tale

If your entire portfolio consists of only 2 or 3 stocks, it’s probably not a very wise risk-adjustment trade-off.  Even though that is how most individual stock investors seem to be behaving, better portfolio construction, including reasonable diversification, is both prudent and responsible because if you are right and the businesses prosper, you’ll still get rich, anyway, as the Home Depot example illustrates, whereas, if you’re wrong and they turn out to be destined for bankruptcy court, you’ll lessen the damage.  In addition, you’re losing sight of the fact that diversification is about reducing correlated risk.  You want a collection of cash generating assets that produce streams of money in almost all environments, under almost all conditions, so you can maintain your standard of living even if a Great Depression were to hit.  Real estate has its place in the asset class mix.  Bonds have their place in the asset class mix (though at present the pricing is still deranged).  Return alone is not sufficient.  Risk-adjusted return is what counts.  I’d take an 8% return over 25 years with a near 0% of wipeout during that time period over a 15% return over 25 years with a 4% probability of wipeout in any given year.  At the end of the period, I’ll likely be richer.  I’ll never have to “Go back to Go”, to borrow a phrase.  Job number one is to not lose money, which, I should point out, is not the same thing as avoiding quoted market value decline over the short-term.  To reiterate that final point, if you have a well-constructed portfolio of equities, and you invest for long enough, history has shown that it is all but inevitable you will see your consolidated positions decline by 50% or more several times.  You must learn to accept this.

How many individual stocks are ideal if you are holding specific companies rather than indexing?  Academia has looked at that question – it differs whether you are using borrowed money or not (around these parts, the correct answer is “not”).  I’ve written about it extensively in a piece called How Much Diversification Is Enough?, also over at my Investing for Beginners site, that you might find interesting.