### Quantifying the cost of insufficient diversification

**Our hypothetical scenario leads to a surprising conclusion**

When a client comes to us with legacy assets, such as concentrated, low cost-basis stocks, we work hard to develop an investment strategy that fits his or her unique situation. All other things being equal, individual stocks lack the diversification needed to implement modern portfolio theory. Taxes, however, are an important consideration; therefore, before any sales, we carefully review the tax consequences. If selling a stock would generate large capital gains, we may recommend keeping it, or spreading the sales across multiple years. In the meantime, the 3 Factor engine takes these legacy assets into account when optimizing the portfolio.

But this raises a question: just how important is diversification, and why? Motivated by a series of conversations, we decided to answer it by analyzing a hypothetical scenario. A Silicon Valley engineer, through a combination of hard work and luck, has her net worth go overnight from $0 to $4 million when her company, Acmenet, goes public. Now at a new firm, and with the holding period expired, should she sell? Being young, she is investing for the long term, say 25 years. To simplify things, we’ll assume she wants to be 100% invested in US large cap equities, although we would never recommend this to clients. She could sell the stock, take a huge tax hit, and use what remains to buy a high quality, low cost equity index fund, such as Vanguard’s S&P fund or ETF (such as VIFSX). Or she could sit on her stock, which has joined the S&P 500 in record time.

At this point some readers are instinctively shouting: Sell!! Despite roughly a $1 million tax hit (approximately 25%, composed of 15% long term capital gains plus 10% state taxes), we would probably recommend the same thing. But why? Moreover, she probably likes the company; after all, she played a part in its past success. Usually, when one gut feel (“Sell!!”) goes up against another gut feel (“I like the company!!”), the status quo prevails. Given the cost is $1 million, what would the benefit of selling be?

To answer this question, two numbers matter: mean (or expected) return, and standard deviation. Over the past 25 years, the S&P 500 has averaged a 10.5% return; let’s assume 8% after tax. Eugene Fama’s efficient market hypothesis says that’s also a good estimate for the expected return of Acmenet’s stock (we will leave the Small/Value effect for another day). Acmenet might be a great company, with skyrocketing profits. But great companies often don’t make good stocks. Investors, particularly institutional ones with full-time analysts and billions of dollars, bid up the stock’s price, in so doing lowering its expected return.

Standard deviation is a measure of volatility. If the average return is 8%, to what degree do actual returns vary from the average? Returns from a single stock should be more volatile than an index like the S&P 500, because in the latter’s case the high returns from one stock balance out the low returns of another. Over the past 25 years, the standard deviation for the S&P 500 has been 14.6%.

Standard deviations vary by stock, but in an empirical study professors Elton and Gruber^{1} pegged the typical stock at 49.24%. (Recently IPO’d stocks almost certainly would have even higher levels of volatility.) To be clear, 49% is huge; it reflects wild swings in returns, plus the few companies which skyrocket and the few companies which go bankrupt.

We fact-checked the 49% figure with a couple of highfliers: Apple (AAPL) and Adobe (ADBE). Sure enough, they weighed in at standard deviations of 46% and 52%.

We then modeled these two alternative 25-year investments – $4 million in one stock versus $3 million in the S&P 500 – by plugging the above returns and standard deviations into a Monte Carlo simulator^{2}. How often does each investment end up bigger? Intuition says the latter will win less than 50% of the time. While the expected return is the same, it’s starting out the race a full million dollars behind. Given a 25-year “random walk,” it’s possible for someone starting with $3 million to end up with more than another who starts with $4 million, but that doesn’t seem like the way to bet.

But intuition is wrong, emphatically so. The S&P 500 investment has a roughly 80% chance of prevailing, even when giving the single stock investment a million dollar head start.

Huh? We’ll give you our opinion in a moment, but before we do let’s add a twist to the scenario. Let’s say that, notwithstanding Fama’s efficient market hypothesis, notwithstanding the tens of thousands of full time analysts on Wall Street, our investor knows that Acmenet’s stock’s expected return exceeds the S&P 500’s by one quarter – that is to say, 10% after tax compared to 8%. People, including Fama, have won Nobel prizes proving such a difference – called Alpha in investment circles – are hard to profit from. An Alpha of 200 basis points would be beyond a grand slam home run; hedge fund managers hyperventilate when fantasizing over Alphas one tenth that size. But even with a million dollar head start and a preposterous performance advantage, the S&P 500 investment still wins roughly 78% of the time.

Ending portfolio value after 25 years at various percentiles. Mean returns after tax are 10% and 8% for single stock and S&P 500 respectively. Standard deviations are 49% and 14.6% respectively. Single stock investment is $4 million; S&P 500 investment is $3 million. Even with a $1 million head start and an unrealistic performance advantage, the single stock outperforms less than 20% of the time. How to read this chart: “75%” means that out of 2,000 Monte Carlo simulations, 75% of the runs had an ending portfolio value below the amounts listed.

**What’s going on?**

First, this simplified scenario illustrates the value of diversification. Even long term, multi-decade investors, investors who have the intestinal fortitude to slough off bad years, need to include diversification in their investment strategy.

Second, much of the expected return on a highly volatile investment, such as an individual stock, stems from a very small chance of a very large payoff. Don’t confuse average return with median return.

Finally, in fairness, we chose a simplified, single-stock scenario to make a point, not to assert that it is a common scenario. More often, clients who own individual stocks have more than one, and as a result the standard deviation for the portfolio is lower, albeit still higher than modern portfolio theory recommends. We will be exploring the implications of multiple individual stocks in a future article; stay tuned.

Bob Sawyer

February, 2014

**Disclosure**

Past performance is not a predictor of future performance.

3 Factor Indexing LLC has conducted extensive analysis concerning portfolio performance. Please refer to our website at http:3factorindexing.com/important-disclosure/ for details and disclaimers regarding a statements concerning performance, and the various assumptions we have made in our analysis.

The views and information contained within this article are provided for informational purposes only and are not meant as investment advice. They represent the author’s current good-faith views at publication time and are subject to change without notice. As with any strategy, it is important for an investor to fully understand the strategy prior to investing; seeking advice from a professional advisor can be a good place to start.

The information that is provided herein has been compiled to the best of our ability. However, the authors makes no warranty of any kind, expressed or implied, and will not be held responsible, or liable for errors, or omissions resulting in any loss or damage caused or alleged to be caused, directly, or indirectly, by information contained in 3 Factor Indexing’s publications.

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^{1} E. J. Elton and M. J. Gruber, “Risk Reduction and Portfolio Size: An Analytic Solution,” Journal of Business 50 (October 1977), pp. 415-37

^{2} Monte Carlo assumptions: 25-year investment; dividends are reinvested; annual returns are normally distributed and independent of each other; 2,000 runs