Maths formulas written by white chalk on the blackboard background.

Modern Portfolio Theory: Part 2

My last post told the story of how I was recently contacted by a sophisticated investor, who was wondering how they should be applying Modern Portfolio Theory to their portfolio. That post gave a quick introduction to what Modern Portfolio Theory is, and how MVO can be used to apply it to portfolios.

In summary, while MVO isn’t a great portfolio construction tool, MPT isn’t a totally useless framework. Its two core tenets are:

  1. It’s only the risk you cannot diversify away which leads to increased returns. The major prescription of MPT is to avoid idiosyncratic risk by diversifying as much as possible.
  2. The risk and return characteristics of any asset class by itself are irrelevant. The only thing which should matter is considering how the addition of an asset class impacts the risk and return of the entire portfolio.

Using these central pillars of MPT, this was my response for how I see MPT relating to portfolio construction.


Applying MPT


While it’s common knowledge that markets aren’t perfectly efficient, they are still highly efficient, which is consistent with the vast majority of academic evidence – see the ‘Active vs Passive’ section of this blog. If they weren’t highly efficient, we’d see many more active funds outperforming the market. The lack of outperforming active managers is a pretty tell-tale sign that markets are efficient enough for most investors.

Using this assumption of highly efficient markets, it follows that all risky assets should have very similar risk-adjusted returns, as market efficiency means investors will quickly take advantage of any mis-pricings. And if all assets have similar risk-adjusted returns, then investors should seek broad global diversification across every risky asset they can find – i.e. investing in the ‘global market portfolio’.

Although the global market portfolio isn’t investable, due to it including all private companies, private loans, the value of all countries’ land, and all the ‘alternative’ asset classes like art, cars, stamps etc, a globally market-cap weighted portfolio is the logical starting point for most investors. For those interested in how this global market portfolio is constructed (and why it’s un-investable), I’ve covered it in this post: ‘In search of the Global Market Portfolio’.

And so while perfect diversification isn’t possible, a global market-cap weighted portfolio, which weights all securities according to their market capitalisation, is as close as you can get.

This smells an awful lot like passive investing.

Diversifying across as many risky assets as possible is consistent with the use of MPT, as the globally market-cap weighted portfolio is also the maximally-efficient tangency portfolio under MPT.

(NB: this is true when using CAPM as your pricing model. If you believe there are additional unique, non-diversifiable, persistent, implementable risk premia (such as the academic factors), then this creates a new, higher efficient frontier. But whether factors should be included in portfolios is a whole other debate. While I think factor investing is the least-bad form of active management, I’m still on the fence about how to implement it in real-world portfolios. I’ve written about some of its drawbacks here.)

MPT further supports the use of a global market-cap weighted portfolio, as the key tenet of MPT is that investors aren’t compensated for taking idiosyncratic risk.

How many stocks it takes to completely diversify away all idiosyncratic risk is debated, but it’s many, many more than the often-touted 20-30 stocks. A portfolio of 100 stocks will eliminate about 90% of the idiosyncratic risks, but even a portfolio of 400 stocks will still retain about 5% of its idiosyncratic risks, according to William Bernstein. And I trust his maths.

To achieve maximum diversification and minimize idiosyncratic risk, investors should be buying thousands of stocks, which again supports the use of a broadly diversified global index-tracker approach (as opposed to more concentrated active funds, which hold far fewer stocks, and which reduce your chances of success).

The natural application of MPT and the EMH is therefore to adopt a globally market-cap weighted approach.

But we’re not done yet.

Passive investing is not only supported by MPT and the EMH, but also under a third theory: Sharpe’s ‘Arithmetic of Active Management’. I’ve covered Sharpe’s arithmetic before on this blog, but here’s a quick recap.

Sharpe’s arithmetic states that the passive investor is guaranteed to outperform the average active investor over the long run. This is because, by definition, the aggregate portfolio created by combining the portfolios of all active managers is “the market” (as passives do not set prices). Passive investors simply invest in the market portfolio created by active managers. Due to both active investors and passive investors receiving the market return before costs, the average passive investors will outperform the average active investor due to paying lower fees. Passive investors as a group will therefore outperform after costs. This is not only sound theory. Results have shown that this is, indeed, the case – passive and active investors do receive similar returns before costs, with passives outperforming after costs into account.

These three theories, then, all support the construction of a passive, globally diversified market-cap approach: MPT, EMH, and Sharpe’s arithmetic.

Alongside those theories, there are other characteristics of the market which make passive investing likely to perform better than selecting active funds in the long-run. These include:

    1. Stock market returns are positively skewed. Only very few stocks account for the vast majority of the market’s gains – one famous study suggests 1% of stocks account for 99% of the market’s wealth generation. The cost of not owning these stocks which generate all the wealth is therefore very high, which argues for as much diversification as possible. Particularly when it comes for basically free, as passive funds cost so little to own. This post on active share shows how positively skewed returns are one of the major drawbacks of investing in concentrated active funds.
    2. Capacity constraints of active funds sow the seeds of their own demise. The more successful an active fund is, the larger it grows. The larger it grows, the narrower its opportunity set becomes, due to its larger flows moving the market in smaller stocks. This not only results in style drift (a departure from the style which created the initial alpha), but as the largest capacity exists in the largest stocks, the temptation is to invest more like the index, and trend towards index-tracking. Any alpha therefore trends towards beta over time.
    3. The market is not only efficient, it continues to become even more efficient. Thanks to improving technology, access to information, high-frequency trading, and passives weeding out low-skilled managers, market efficiency is increasing. This raises the bar for the remaining active managers, and makes it increasingly difficult for them to outperform as they now compete against the other higher-skilled active managers.

Those are the theoretical arguments.

When surveying the academic evidence, it’s pretty clear the evidence supports these theories. The following is a selection of evidence demonstrating the continued long-term outperformance of passive management over active:

    1. S&P Dow Jones’ SPIVA Scorecards
    2. Morningstar’s Active/Passive Barometer
    3. DFA’s Mutual Funds Landscape Report
    4. Literally any other of the dozens of academic papers included in the ‘Active vs Passive‘ section of this blog.

So passive investing has multiple theoretical bases for its outperformance, which are overwhelmingly supported by the academic evidence.

But if that’s not enough for you, there are still further practical reasons for why passive investing might be the preferred route for investors. These are really just the cherry on top, but I’ve included a smattering of my favourite reasons for good measure:

    1. As the aggregate skill levels of active managers increase due to increasing market efficiency, luck becomes a larger determinant of outperformance. This is known as the “Paradox of skill” (and applies to many other areas of competition – golf, tennis, chess, etc). This makes determining luck from skill in active manager fund selection an even tougher job than it was before – and it was already an insanely difficult job.
    2. All the problems that come with active fund marketing. Beware graphs bearing outperformance.
    3. We all know this by now, but active fund outperformance is not persistent, which also leads to active investors being pulled into performance-chasing behaviour,
    4. Passives have no minimums investing requirements, nor constraints on capacity (as opposed to actives, whose capacity constraints not only limit their opportunities for alpha, but mean their performance trends towards index performance as their size grows), and
    5. Passives are more transparent, simpler, and easier to understand, making them easier to stick with.

To wrap things up, there are several theories – the EMH, MPT, and Sharpe’s arithmetic – all of which support the use of a global market-cap weighted approach to portfolio construction.

And this theoretical outperformance of passive investing does indeed manifest in the form of real-world passive outperformance.

Alongside both the theoretical and empirical evidence supporting this approach to portfolio construction, there are several further practical reasons why investors might want adopt a passive investing approach over active alternatives.

Whether you start from the investing theory and work forwards to the evidence, or start with the evidence and back out the theory, it seems like all roads lead to passive.

So that’s my answer for how Modern Portfolio Theory can be applied to portfolio construction. Throw out your old mean-variance optimiser, and embrace a passive investing philosophy.

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Past performance does not guarantee future performance and the value of investments can fall as well as rise. The information on this site is provided for information only and does not constitute, and should not be construed as, investment advice or a recommendation to buy, sell, or otherwise transact in any investment including any products or services or an invitation, offer or solicitation to engage in any investment activity. Please refer to the full disclaimer on the disclaimer page.

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June 30, 2022 1:52 pm

Thanks Occam, your blog helped me to build a (mainly) passive portfolio that I know is backed up by sound research and evidence.

Since it is already optimised, I don’t need to tinker further despite what happens to the market & inflation etc. It’s the peace of mind that is invaluable.

Thanks for sharing your knowledge, truly appreciated.

John Williams
June 30, 2022 12:16 pm

Very interesting posts – I have never really delved into MPT before. From what you have said, it seems that a global market weighted passive investment strategy is optimal according to MPT (guess that outcome is not really a surprise even if the method of arrival at it is). However could one argue that this is only valid if the investments are going to be used ultimately for ‘global spending’? Wouldn’t MPT lead to the conclusion that, for a UK investor who plans to ultimately use their investments for spending in pounds sterling, they should be overweight on sterling based assets (either owning more UK assets relative to global total market cap, or using a degree of currency hedging)? Thus the optimal strategy for investors who plan to spend the majority of the proceeds of their investments in the UK would be global total market cap related investments plus additional UK total market cap related investments (or additional global total market cap related investments with GBP hedging).