# User:LadyGeek/Diversification

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## Introduction

Generally speaking, *diversification* is about not putting all of one's eggs into a single basket. The U.S. Securities and Exchange Commission writes:

Diversification can be neatly summed up as, “Don’t put all your eggs in one basket.” The idea is that if one investment loses money, the other investments will make up for those losses. Diversification can’t guarantee that your investments won’t suffer if the market drops. But it can improve the chances that you won’t lose money, or that if you do, it won’t be as much as if you weren’t diversified.

^{[1]}

Unfortunately, there is no single universally accepted *precise* definition for "diversification". Different authors use the word "diversification" to mean different things. This is much like the word "risk" which, for example, is used by some authors to mean "volatility" and by other authors to mean "possibility of loss". Yet, we can identify two main meanings for the word diversification in an investment context.

The first meaning appears in the text of authors who often combine the word "broad" (or a similar one) with the word "diversification" to mean "spreading one's money broadly across a market" (using capitalisation-weighting for obvious arithmetic reasons^{[2]}). For example, when discussing the creation of the Vanguard S&P 500 index fund and of the Vanguard Total Stock Market index fund, Jack Bogle wrote:

In 1975, I created the first index mutual fund, now known as Vanguard 500 Index Fund. Then, as now, I considered it the very paradigm of long-term investing,

a fully diversifiedportfolio of U.S. stocks operated at high tax efficiency and rock-bottom costs, and designed to be held, well, “forever.” It is now the world’s largest equity mutual fund.^{[3]}

The second meaning stems from economic theory, where economists, like Markowitz, define "diversification" as a technique to combine securities to reduce "risk" (defined as "volatility") without sacrificing "expected return".

The above two distinct definitions of "diversification" can be conflictual in the context of portfolio construction (much like the two definitions of "risk" mentioned above).

## "Diversified" versus "non-diversified" funds

By regulation, every mutual fund is classified as "diversified" or "not diversified." Most are officially diversified, and those that are not must say so. A summary of the requirements, known as the 75-5-10 rule, is:

- 75% of the fund's assets must be invested in securities of other issuers. Cash and cash equivalents are included.
- 5% - The investment company may not invest more than 5% of its assets in any one company.
- 10% - The investment company may not own more than 10% of any company’s outstanding voting stock.
^{[4]}

## Markowitz diversification

Within the framework of modern portfolio theory (MPT), the term *Markowitz diversification* can mean

combining securities with less-than-perfect positive correlation in order to reduce risk in the portfolio without sacrificing any of the portfolio’s expected return.

^{[5]}

This approach to diversification was introduced by Harry M. Markowitz in his ground-breaking 1952 paper, *Portfolio Selection*.^{[6]}

The basic idea of the math behind Markowitz diversification looks like this:

The vertical axis represents return; we want it to be as high as possible. The horizontal axis represents risk; we want to be as far to the left as possible. The green and red dots represent bonds and stocks, respectively. The values shown are very close to the actual historical value for intermediate-term government bonds and large-company stocks from 1926 to the present, but I've rounded them for ease in doing mental arithmetic.

Each lines joining the red and green dots show all combinations of returns and standard deviations, for every possible portfolio mixes ranging from all bonds to all stocks. A purple dot marks the return and standard deviation of a 50/50 portfolio.

The straight line shows what the results would be if stocks and bonds had moved perfectly together, a correlation of ρ = 1.0.

In reality, the correlation of stocks and bonds was almost exactly zero. Their movements have been perfectly independent. (Not perfectly **opposed**, just perfectly **independent**) The curved line shows all of the portfolio returns and standard deviations assuming a correlation of zero.

You might expect that in a 50/50 portfolio of stocks and bonds, the (arithmetic average) annual return of the portfolio would be exactly halfway in between stocks and bonds, and you would be right. It always is. It has to be. In this example, stocks averaged 12%, bonds averaged 5%, and the portfolio will averaged exactly in between, 8.5%. It was exactly the same regardless of whether the correlation, ρ, was 0.0 or 1.0.

You might expect that the risk of the portfolio, measured by 𝛔, sigma, the standard deviation, would also be exactly halfway in between stocks and bonds, but it turns out that this is not true. If stocks and bonds were perfectly correlated--correlation coefficient ρ = 1.0--then it would be true, as indicated by the straight line and the midpoint. When the correlation is 1.0, the risk of the 50/50 portfolio exactly splits the difference between that of stocks, 𝛔 = 20, and bonds, 𝛔 = 6. For the 50/50 portfolio, 𝛔 = 13.

However, with a correlation coefficient of zero, the return of the portfolio is not changed, but the risk of the portfolio is somewhat reduced. This is shown by the fact that the ρ = 0 line is curved, and that it is always on the left of the ρ = 1.0 curve.

When the correlation is imperfect, the returns from one asset may *sometimes* *partially* fill in gaps in the returns from another. The result is that the fluctuations in the portfolio as a whole are somewhat smoothed out. In this case, the smoothing is manifested as a reduction in 𝛔 from 13 to 10.44.

How important is this? Well, John C. Bogle wrote "An extra percentage point of long-term return is priceless, and [a] extra percentage point [reduction in] short-term standard deviation is meaningless." But in this case, we have a 2.56% reduction in standard deviation.

This, then, is the diversification effect in portfolios, from the point of view of modern portfolio theory. Portfolios of uncorrelated assets have an efficient frontier that bows toward the left. The *return* is just the weighted average of the returns of the holdings, but if they are uncorrelated, the *standard deviation is less* than the weighted average of the standard deviations of the holdings.

Two points should be noted. First, this doesn't imply that diversified portfolios are crashproof. The effect is there, but for realistic asset characteristics it is fine tuning. It is an edge, not armor plate. Whenever I have read official fund documents, if "diversification" is mentioned as a benefit, I have always seen a boilerplate disclaimer, "Diversification does not ensure a profit or protect against a loss in a declining market,"

Second, the effect as I've illustrated is just math. It applies in the real world if the assumptions behind the model apply. It doesn't if they don't. If we knew for sure that over the next ten years stocks and bonds would duplicate their historic values--returns of 12% and 5% respectively, standard deviations of 20% and 6% respectively, and correlation of 0.0--then of course we would know that a 50/50 portfolio would have a return of 8.5% and a standard deviation of 10.44%. But past returns are not a sure predictor of future returns, and the same is true of standard deviations or correlations. In fact, correlations seem to be even less stable than return itself.

## Jack Bogle on Diversification

John C. Bogle has written "Diversify, diversify, diversify!"^{[7]}. His views that investors should prefer to invest using broadly diversified stock and bond mutual funds is a core element of the Bogleheads® investment philosophy.

Bogle also cautioned against succumbing to salesmanship under the guise of diversification: "And let me say this about a better diversifier: Better diversification is the last refuge of the scoundrel."^{[8]}

## References

- ↑ The Securities and Exchange Commission[1]
- ↑ Equal-weighting can't be applied to the total market: Bogleheads® forum post: What's wrong with this critique of indexing?.
- ↑ The Clash of the Cultures, John C. Bogle, 2012.
- ↑ 15 U.S. Code § 80a–5 - Subclassification of management companies. Based on forum discussions, it is does not seem to be clear exactly what is or is not allowed outside the 75%
- ↑ Francis, Jack Clark; Kim, Dongcheol (213).
*"Modern Portfolio Theory"*. "John Wiley & Sons, Inc.". p. 120. ISBN 9781118417201. - ↑ Markowitz, H.M. (March 1952). "Portfolio Selection". pp. 77–91. Unknown parameter
`|publication=`

ignored (help) - ↑ "The Twelve Pillars of Wisdom", point #5
- ↑
*The Man in the Arena: Vanguard Founder John C. Bogle and His Lifelong Battle to Serve Investors First,*Knut A. Rostad, John Wiley & Sons, 2013

## Further reading

- Bogleheads® forum topic: What Experts Say About "Asset-Allocation & Diversification"
- Bogleheads® forum topic: "When It Comes to Diversification, Don't Be Naive"