It’s been a hot debate in finance for decades. Can you make higher returns from the stock market with lower risk? Academic Harry Markowitz was one of the first with a theory to say “no”. Markowitz’s portfolio theory essentially concludes that beating the market requires taking more risk, and this risk eventually becomes quantified by the term we know today called beta.

The academic concept called Modern Portfolio Theory (MPT) was first introduced by Harry Markowitz in 1952 and has helped shape the way that many academics and investors think about risk and reward in the stock market.

The Markowitz theory was spelled out in a study in the Journal of Finance called “Portfolio Selection”, and it’s a bit involved, so I’ll do my best to summarize the most pertinent points here.

This post will cover, in this order:

- The two rules considered in the theory
- The central thesis
- Very important clarifications on the theory
- Markowitz’s conclusions
- Investor takeaway

**Rules considered in the Theory**

**Rule #1: “the investor does (or should) maximize discounted expected, or anticipate, returns”**

Markowitz –> rejects.

The glaring problem with this rule is that there is no mention of diversification at all. Diversification, of course, is a principle that has been passed down through the ages of time as a prudent strategy for all investors regardless of the differences in goals, desires, and risk appetite.

I don’t believe that I need to untangle much of the merits of diversification, as neither did Markowitz in his piece. I think we can all agree that maximizing return at the expense of diversification is closer to gambling than prudent investing, and isn’t a desirable strategy for investors looking to put their hard earned (and saved) capital at work.

**Rule #2: “the investor does (or should) consider expected return a desirable thing and variance of return an undesirable thing.”**

Markowitz –> accepts.

The first rule was established as a setup to this rule. This second rule is characterized throughout Markowitz’s theory as the variance of returns, or **E-V rule**.

Within this explanation lies a central assumption, and then the central piece of Markowitz’s portfolio theory.

Assumption – An investor actually shouldn’t (or doesn’t) diversify between all of the securities that he expects will give the maximum return—because the law of large numbers (insuring actual yield should be very close to expected yield) can’t be accepted.

His argument – “The portfolio with maximum expected return is not necessarily the one with minimum variance. There is a rate at which the investor can gain expected return by taking on variance, or reduce variance by giving up expected return.”

Here, a simple concept is born: **you can earn more return by buying a stock with more variance, or achieve less variance by buying one with less return**.

Notice that he doesn’t explicitly say that variance = risk with his statement, though that leap has been made extensively throughout the world of academia and finance.

Markowitz accompanies this profound conclusion with extensive mathematical and geometrical calculations, which I’m choosing not to include in this summary, perhaps to its detriment. However, that math becomes irrelevant if assumptions are incorrectly made, and I’ll leave it to the astute investor to determine the validity of the assumptions, and additionally to investigate the math behind the portfolio theory if the conclusion is made that the assumptions seem reasonably valid.

**Very Important Clarifications on the Theory**

Perhaps one of the curses of establishing a theory whose ideas are so widely spread is the vast misunderstandings that come with it.

Personally, I’ve seen so many diluted opinions on Markowitz’s portfolio theory, and it becomes like that childhood game of telephone—wherein a message is passed from one person to the next until the 20^{th} person in the chain hears a widely distorted version of the original message.

Not to mention that Markowitz gets lumped in and confused with various other academic theories and ideas, like the CAPM model (and its assumptions), the definition of beta, modern applications of the ideas, the list goes on and on.

Here, I attempt to present an honest and straightforward summation of important clarifications that I believe are missed when it comes to Markowitz’s portfolio theory as presented in his *Portfolio Selection* article.

- “In a general presentation we must recognize that the probability distribution of yields of the various securities is a function of time”

I don’t mean to start with my own criticism but this is an important, albeit overlooked, assumption baked into this statement.

This is something expanded on much more thoroughly the book *The Black Swan* by Nassim Taleb, but basically the entire idea that stock market probabilities can be quantified in the normal mathematical way is a flawed premise. The fact of the matter is that there have been (and are likely to be) large historical events that have led to “4 or 5 sigma” events that lend the average bell curve distribution of probabilities to be inadequate in presenting the real probabilities/ variance in returns or results.

- “The expected return-variance of return rule, on the other hand, implies diversification for a wide range… this does not mean that the E-V rule never implies the superiority of an undiversified portfolio.”

Many critics of Modern Portfolio Theory (and Markowitz) use this exact argument to debunk the theory—I’ll admit to having doing this myself in the past too. Markowitz never states that there can’t be exceptions to the rule. Whether you can extrapolate that to make a broader statement I’ll leave open to interpretation.

- “The rule serves better, we will see, as an explanation of, and guide to, ‘investment’ as distinguished from ‘speculative” behavior.”

This is a similar concept that you’ll see in many great books about investing and stocks, and while not a profound statement it’s still worth mentioning.

- “Not only does the E-V hypothesis imply diversification, it implies the ‘right kind’ of diversification for the ‘right reason’.”

Markowitz explains here that the “right kind of diversification” includes doing so across different industries, especially when those vary in their “economic characteristics”.

I’ll add that industries within the same country or geographical region can have very different microeconomics or capital structures and/or cyclicality or exposure to various macroeconomics. And that’s not even mentioning the wide variance of returns between countries and currencies depending on the different geopolitical and macroeconomic scenarios that play out on a daily basis ever since the history of markets.

- “Variance is a well-known measure of dispersion about the expected. If instead of variance the investor was concerned with standard error, …, or with the coefficient of dispersion, …, his choice would still lie in the set of efficient portfolios.”

Adding this to note that risk as a definition in this context can also refer to error in projecting (or anticipating) returns, represented here by the definition “standard error”.

His definition efficient portfolios comes to explain Markowitz’s conclusion on the probable best application of the E-V rule that’s applicable to investors who choose to follow the theory.

**Markowitz’s Conclusions**

Quoting the piece once more:

“Perhaps-for a great variety of investing institutions which consider yield to be a good thing; risk, a bad thing; gambling, to be avoided-E, V efficiency is reasonable as a working hypothesis and a working maxim.”

He expands to say, basically, that his portfolio theory could be used for further study/ analysis or could also be used for constructing portfolios.

I find it quite interesting that Markowitz never suggests or implies that his findings are some sort of godly rule from heaven, although it has been applied in many areas of finance exactly like that.

**Investor Takeaway**

It’s hard to argue with many of the points presented in Markowitz’s portfolio theory, eventually known as Modern Portfolio Theory (MPT).

However, these ideas have been extrapolated out to such an extent—that all forms of active management are useless, or that an index fund is the most optimal form of investment for all—that the response surrounding this theory have been accompanied by vehement reactions.

One such great rebuttal of some of these ideas was shared by a famous investor (Warren Buffett) who violated the law of efficient markets himself with his own track record and the track record of other students from the same class (Graham and Dodd’s).

Buffett poked at many traditional academic concepts in his speech entitled “The Superinvestors of Graham-and-Doddsville”, and it’s most certainly worth a read. After all, if you’re not hearing both sides of an argument, you really don’t know what you don’t know.

And that’s just foolish.