What Is Diversification Worth?

The concept of diversification is often discussed, but I am increasingly of the opinion that many investors do not understand diversification at a deep level. This is unfortunate, because diversification is the one ‘free lunch’ in investing. Indeed, this was the genius of Harry Markowitz in showing that combining asset classes in a thoughtful way allowed investors to generate higher returns without increasing risk in their portfolios. On a practical basis, what does this mean for investors? How much more return can investors generate by being well diversified?

To explore this topic, I have used a variety of sources to estimate what I will call the diversification premium. The diversification premium is the additional return that investors can achieve by effectively diversifying their portfolios across a range of asset classes. Effective diversification requires something significantly more intelligent than just buying a bunch of funds or ETFs, but it is well worth the effort.

Calculating the diversification premium requires the use of what are called forward-looking models. If you simply choose a period of history, and calculate ‘optimal portfolios’ with the benefit of perfect hindsight, you can find some combination of investments which have generated high returns with low risk. This is the problem with ‘portfolio optimization’ on historical data: you end up estimating ‘optimal portfolio’ returns that are not achievable in real life. Forward-looking models compensate for these effects by generating statistical outlooks for portfolio performance that account for the uncertainties in the future. Forward-looking models are standard tools among institutional investors, as we will discuss below.

To estimate the diversification premium, we have taken forward-looking estimates of the best returns that can be achieved from a well diversified portfolio from a range of institutional sources, as well as from our own analysis using Quantext Portfolio Planner [QPP], a forward-looking portfolio planning model. The diversification premium is a function of the portfolio risk level, and we will be examining portfolios with annualized standard deviation of about 10%. Portfolios with 10% in annualized standard deviation are often a focus of study because this is about the risk level (on a forward looking basis) of a portfolio that is invested 60% in domestic stocks and 40% in bonds.

Ibbotson / PIMCO Study

For a very useful overview of forward-looking models, I recommend the linked analysis [pdf file] performed by Ibbotson on behalf of PIMCO,

Ibbotson used forward-looking portfolio models to analyze the improvement in the return of a diversified stock and bond portfolio that could be achieved by including commodities. Ibbotson analyzed portfolios at three risk levels using three models, albeit with the third being a combination of the first two using the Black-Litterman methodology. The analysis ultimately yielded projections of the highest return than can realistically be projected for portfolios that combined foreign and domestic stocks and bonds with commodities.

Yale’s David Swensen

David Swensen is widely known for his phenomenal 20-year track record as the portfolio manager of Yale’s endowment. Mr. Swensen focuses on strategic diversification as a core of portfolio strategy. In an interview in July of 2007, Mr. Swensen stated that the Yale portfolio is expected to return about 10.1% per year, with expected standard deviation of 11.8% per year.

These numbers, specifically stated as ‘expected,’ can only have been generated using forward-looking models.

Bridgewater’s Ray Dalio

Bridgewater (www.bwater.com) is a highly-respected institutional fund manager, with $140 Billion under management. In an article titled Engineering Targeted Returns and Risks [pdf file], Ray Dalio (the firm’s founder and Chief Investment Officer) comes up with his estimates of the maximum return that can be achieved (on a forward-looking basis) for a given level of risk. The subtitle of this article states the punch-line of the analysis: “how to achieve a 10% return with 10% to 12% risk.”

Quantext All-ETF Portfolio

Using Quantext Portfolio Planner, we previously created a broadly-diversified all-ETF portfolio with risk levels consistent with the other portfolios discussed here.

We found significant benefits from using sector specific ETF’s in energy (IGE and IYE) and utilities (XLU), as well as TIPS (TIP). We also found that certain country-specific ETF’s provided valuable diversification benefits (specifically EWJ and EWM).

Quantext Portfolio Planner 1-to-1 Result

Over the last several years, I have found [pdf file] that a wide range of portfolios converge to a result that the best that investors can realistically plan for on a forward-looking basis is about a 1-to-1 ration between average annual return and standard deviation in return for portfolios with annualized standard deviation of around 10%.

This limit is not an input, but arises consistently as we analyze a wide range of portfolios. The All-ETF portfolio discussed in the previous section is one example, but there are many more, such as this analysis of the diversification benefits provided by the top holdings of Berkshire Hathaway (BRK.A).

Calculating the Diversification Premium

To benchmark these results, we have combined an S&P 500 ETF (IVV), a Russell 2000 ETF (IWM) and a bond index ETF (AGG) to find a portfolio with a standard deviation of that matches each of the risk levels in the portfolios analyzed using the different approaches listed above.

The ‘diversification premium’ is the difference between the projected average annual return of each ‘optimal’ portfolio from the various sources and the benchmark portfolio with the same risk level. The estimated diversification premiums for portfolios with annualized standard deviation on the order of 10% are shown below.

The Ibbotson analysis ignored several factors in the forward-looking analysis that are important. First, they did not break out domestic equities into even large cap and small cap. Second, Ibbotson did not break out international equities into developed markets and emerging markets. Third, the Ibbotson study did not include REITs as a separate asset class.

The incremental portfolio benefit of being able to differentiate between large and smallcap and emerging and developed international stocks will be positive, as will the inclusion of REITs. I believe that including these factors in developing ‘optimal’ portfolios using Ibbotson’s forward-looking models would result in higher estimates of the diversification premium.

The QPP 1-to-1 Rule result is for a portfolio with 10% in annualized standard deviation, for which the portfolio built from the three benchmark asset classes project an average annual return of 7.5%.

The agreement between these results is remarkable, given the diverse sources of the forward-looking estimates and the range of asset classes considered.

Discussion

The results of this analysis suggest that investors with portfolios in the risk range of a 60/40 portfolio of stocks and bonds can generate 2%-2.5% per year in return beyond what is achievable with a broad mix of domestic stocks and bonds. This is an estimate of the size of the ‘free lunch’ that investors will miss by being under-diversified.

These benefits are calculated in Quantext Portfolio Planner, assuming that investors own sector-focused ETFs. The Ibbotson research also treats portfolios built out of broad asset classes. These results do not mean, however, that effective diversification necessarily requires owning hundreds of stocks. My analysis of Berkshire Hathaway suggests that their equity holdings are very well-diversified, even though the Berkshire portfolio is highly concentrated.

Sadly, many investors are not even as well diversified as the benchmark portfolio that I used in this study (a mix of S&P 500, Russell 2000, and a bond ETF). For these investors, the potential diversification premium is even greater than the numbers shown here.

Going Further

My research has suggested that even greater benefits can accrue to investors who are willing to take on investments in individual stocks, as opposed to only investing in broad indices.

One reason that investors can improve on simply buying index ETFs is that market cap weights of major indices are not optimal. This has been demonstrated by a range of authors and I am partial to the research by Rob Arnott. Market cap weights in an index tend to be overweight in the assets that have recently outperformed.

My current estimates suggest that investing in individual stocks (as opposed to market cap weighted index funds) can be worth about another 1% per year in returns for a portfolio with a standard deviation of around 10%.

Investing in individual stocks does expose investors to more specific risk of a company having serious financial difficulties or collapsing altogether, but good forward-looking tools help to manage and mitigate this risk.

Let us not forget that owning individual stocks means that there are no annual expenses (except for brokerage fees from buying or selling). ETFs that focus on commodities, emerging markets, or other narrow sectors often have higher expense ratios than the 0.09% a year of an S&P 500 index ETF. Building and managing diversified portfolios out of individual stocks used to be prohibitively expensive due to brokerage fees, but firms like FOLIOfn have made this approach viable (Disclosure: Quantext is a strategic advisor to FOLIOfn).

Comments

[Robohogs]

you can use the wisdom tree etfs to get the same impact as individual stocks with less company specific risk.

Jon

[David Johnson]

Geoff excellent article.I had written an article last year on how diversification in its truest and deepest form requires uncorrelated asset classes and multiple system timeframes. How this affects long term performance is difficult for me to actually quantify. Short URL link to the article below.
tinyurl.com/4ktwrg

[Roger Beep]

Geoff,

This is a very insighful article. Your summary of other quant efforts along side yours cumulatively lays the foundation for more effective individual investor investment strategies.

Question have you comapred QPP's Diversification Metric (DM) to the diversification premium? What is an optimal DM value in relation to diversifiction premium return?

[Geoff Considine]

To robohogs/jon:

The fundamental weighting issue is not the only reason that portfolios of individual stocks can be better--there are other important features of individual stocks, as I have shown in a range of my analysis. This remains a controversial topic among financial theorists.

QPP suggests that Buffett's highly concentrated portfolio of individual stocks is more diversified than many portfolios which employe massive diversification via index funds. This goes to one of my axioms: if your investing theory suggests Buffett is wrong, your theory is probably wrong.

Diversification can be statistically measured and its not just about buyign lots of individual holdings. This is considered common sense among the high end of institutional investors (as shown here) but this idea is radical for most individual investors and even for many advisors.

[NO DooDahs]

Diversification is about allocating to different STRATEGIES, so long as said strategies have relatively low correlation to each other, and have positive expectancies.

"Buy and hold this asset class" is a STRATEGY.

One can get a diversification benefit by allocating money to different strategies in the same asset or asset class, i.e. short and long-term market timing techniques, Piotroski value and CANSLIM, etc.

[galewhitaker]

Diversification is an incredibly stupid idea. I agree that it goes some way toward reducing losses but it goes a very long way to insure that the retail investor spends a maximum amount of money on commissions and never really makes a bundle in the market. Diversification is the same kind of sillyness as "buy and hold". We are living through a market downturn that proves my point. 90% of the equities in the S&P 500 have sold off. No amount of diversification would have protected an investor from these losses. Investors would be a lot better off to use the time and effort required to diversify to search out companies that have superior fundamental and technical attributes. Making sure to be long in uptrends and short in downtrends would also beat the daylights out of any kind of hokey diversification scheme. The term "diversification" works really great on widows who are trying to keep the family fortune togather during those final years. It also works great to insure that stock brokers can make those payments on the BMW.

[Geoff Considine]

To Gale Whitaker:

Your points are addressed in my article her on SA called Black Swans, Portfolio Theory, and Market Timing. Quite to the contrary of what you have said:

1) Market timing costs investors on average 2.5% per year (see DALBAR, for example)

2) People like David Swensen and Warren Buffett have delivered the most consistent risk adjusted returns we have records for and they believe in strategic diversification.

3) A solid diversification strategy does not incur high brokerage / transaction fees--but trying to time the market sure does. There is abundant data that the more, on average, people trade, the worse their results.

4) Actually, a well diversified portfolio has helped many portfolios to reduce losses substantially in this market, without incurring taxable events or transaction fees.

There are all these books on timing strategies for retail investors and they are in opposition to the solid research that institutions use. Hmm.

diversification does not mean simply "buy and hold"---read the article I refer to above.

Regards,

Geoff

[Smart ETF]

Good try but you have an archaic application to asset allocation. Asset allocation relies on four basic attributes: Risk, Return, Dependency (Correlation), and Data Management. These four attributes are managed in a 3 step process: the first step, called a ‘Univariate Model’, measures the risk & return of an asset, the second step, or ‘Bivariate Model’ measures the dependency between two securities, and the third step ranks the bivariate model in what is called a ‘Multivariate Model’ to create the efficient frontier. Your model contains four critical flaws:
First you use the most simplistic measure of dependency to diversify a portfolio with the use of correlation. Correlation assumes a fixed relationship between two securities over the sampled time period and is purely academic. Correlation increases dramatically during extreme events, in fact during any volatile market. If you want a lesson in correlation look to the merry band of MPT disciples at Long-Term Capital Management for a classic case study, or look at Merriweather’s current performance! As the adage goes ‘the only thing that goes up in a down market is correlation’. Trash the static correlation model and move to a dynamic correlation model like Copula Dependency.
Second, you measure risk using standard deviation (σ). Standard deviation, semi-variance and Value-at-Risk are all hyper-flawed because they all rely on normal distributions. Do you really think a 5σ event will only occur every 7000 years or an 87’ magnitude crash will only happy once in every three lifetimes of the universe? Enlighten yourself to the world of Stable Distributions using logarithmic, not arithmetic distributions. You will find 5σ events really occur every 3-4 years. I recommend you convert to Expected Shortfall as you new method of risk measurement.
Third, how can you forecast using any of the methods you suggest? Running a simulation model using Black-Litterman (an Arbitrage Pricing Theory model) or the other solutions are simply band-aids on the old MVO model; the only difference is you are trying to tilt the results to more of a bullish or bearish state. This doesn’t solve the problem it just makes it less damaging. Why not take a scientific physics approach and use a data management tool like GARCH (that won the Noble Prize in 2002) instead of relying on Markowitz and his methodology from 1959? You do know you have faster processors and electronic data exchanges and advanced math models; why not upgrade after 40 years?
Since this article is ostensibly an advertisement for Quantext, I feel its fair game to point out the inherent flaws in your model as well as other suggested models using old mathematical applications and theories. I’m happy to unconditionally prove the superiority of newer models and their specific attributes and will cite the works of Benoit Mandelbrot and Extreme Value Theory as a comparative solution. Set yourself free from averaging thinking!

[Geoff Considine]

Smart ETF:

First, QPP is non-stationary--which is really important. Second, I hope that you forwarded your insightful comments to David Swensen at Yale, Ray Dalio at Bridegwater, and Ibbotson. I am sure that all of these leading firms will gain value from your insights. BTW, you never mention that Mandelbroit himself has said that his methods are not ready for operational use.

If you can prove the superiority of your approach, just do it--and post your articles to SA, but its is not useful to say that you can do it without showing anything for support.

[Meckaneck]

Geoff,
Long time reader of your articles. I would appreciate and feedback, comments or suggestions on the following portfolio. I am in my mid 30's and looking to invest for long term retirement purposes. Thanks in advance for your consideration.

30%- Total US Market (VTI)
10%- US Small Cap Value (RZV)
5%- US Microcap (IWC)
5%- US REIT (VNQ)
10%- Europe Large (VGK)
10%- Pacific RIM ex Japan (EPP)
2.5%- Bric Fund (EEB)
7.5%- Emerging (VWO)
7.5%- Int Small Cap Value (DLS)
12.5%- Inflation Protection (VIPSX)

[montag]

"Diversification is a protection against ignorance. It makes very little sense for those who know what they're doing."

Warren Buffet on Diversification. I have to say I agree with Warren, people diversify themselvse out of gains.

[Geoff Considine]

To Montag:

Ahh--but perhaps you have missed my point. I consider Warren Buffett's portfolio to be well diversified. I analyzed top Berkshire holdings using Monte Carlo and the model showed that Berkshire is well diversified. When Buffett talks about diversification he is talking about the 'buying everything' school of diversification. Smater diversification is quite different:

seekingalpha.com/article/17192-monte-car...

You can be well-diversified and concentrated--this is not a contradiction in terms. Diversification does not, by any real definition, mean buying some of everything. Diversification means having a portfolio in which the parts exhibit low enough correlation that you can extract more return for a given level of risk than you can with the individual parts. This does not require hundreds of holdings.