The benefit of diversification is often called the only free lunch in investing. The promise of generating the same ‘return’ while bearing less ‘risk’ is compelling.

For a simple illustration of this tantalising promise, assume a world where it’s either raining or sunny with equal probability, and consider an investor with the following choices:

  1. Invest 100% of her capital in a company selling umbrellas.
  2. Invest 100% of her capital in a company selling ice-cream.
  3. Invest 50% of her capital in a company selling umbrellas & 50% of her capital in a company selling ice-cream.

The expected return of the portfolio is the weighted average of the expected returns for each asset in the portfolio.

The volatility/standard deviation of the portfolio is a statistical measure of the variability around that return. This is the proxy for ‘risk’ where the greater the volatility/standard deviation, the greater the risk. The covariance between the assets is an important input to this measure.

When it’s raining the umbrella-company reaps all the profit, while the ice-cream company reaps all the profit when it’s sunny. The expected return and the volatility/standard deviation around that expected return for each of the three possible investment choices/portfolios are summarised below:

The expected return is the same for each of the three possible investment choices/portfolios, but crucially, the volatility of that return is lower for the choice of investing 50% in the umbrella-company and 50% in the ice-cream company. The choice to diversify has generated the same ‘return’ while bearing less ‘risk’. This seemingly simple insight is at the heart of modern portfolio theory, and its ubiquitous practical workhorse, the Capital Asset Pricing Model.

Developed by a varied group of US academics from the early 1950’s, some of whom subsequently received Nobel prizes for their efforts, this widely followed approach has dominated both class-room and trading-room for decades.

Often laden with obscure jargon, it might be helpful to outline the basic rationale in four simple steps:

  1. To illustrate the risk/return trade-off, modern portfolio theorists created the Capital Market Line. This is simply the graph of all the portfolios that optimally combine the risk-free rate of return and risky assets. The assumption that the higher the expected return, the higher the risk/standard deviation is clear:

2. The next key assumption is that investors are typically risk averse. In practice, this means that they prefer a certain outcome to an equivalent uncertain gamble. Graphing the relationship between utility and wealth below, the risk averse investor derives a higher utility from the certainty of $100,000 than the equivalent uncertain alternative of tossing a coin with a 50% chance of winning $50,000, and a 50% chance of winning $150,000:

3. In the risk/return framework, the assumption of risk aversion is expressed graphically in the Efficient Frontier. This is simply the frontier that maximises expected return for any given level of risk/standard deviation:

The Efficient Frontier

4. Bringing together the free lunch of diversification, the risk/return trade-off of the CML, and the assumption of risk aversion underpinning the efficient frontier, modern portfolio theory generates an optimal portfolio known as the Market Portfolio. Graphically, this is the intercept point of the CML and the efficient frontier:

The Optimal/Market Portfolio

Unfortunately, modern portfolio theory is elegant but flawed. The investor Howard Marks summarises the issue with characteristic clarity in his book ‘The Most Important Thing – Uncommon Sense for the Thoughtful Investor’:

‘Especially in good times, far too many people can be overheard saying, “Riskier investments provide higher returns. If you want to make more money, the answer is to take more risk.” But riskier investments absolutely cannot be counted on to deliver higher returns. Why not? It’s simple: if riskier investments reliably produced higher returns, they wouldn’t be riskier.

The correct formulation is that to attract capital, riskier investments have to offer the prospect of higher returns, or higher promised returns, or higher expected returns. But there’s absolutely nothing to say those higher prospective returns must materialize.

The way I conceptualize the Capital Market Line makes it easier for me to relate to the relationship underlying it all:

The Capital Market Line – Risk & Reality

Riskier investments are those for which the outcome is less certain. That is, the probability distribution of returns is wider. When priced fairly, riskier investments should entail:

  • higher expected returns,
  • the possibility of lower returns, and
  • in some cases, the possibility of losses.

The traditional risk/return trade-off (of Modern Portfolio Theory) is deceptive because it communicates the positive connection between risk and return but fails to suggest the uncertainty involved. I hope my version of the graph is more helpful. It’s meant to suggest both the positive relationship between risk and expected return and the fact that uncertainty about the return and the possibility of loss increases as risk increases.’

For investors, the more nuanced outline of risk and reality from Howard Marks is not the most significant flaw in modern portfolio theory. The Efficient Markets Hypotheses – more jargon unfortunately – and the key conclusion that trying to beat financial markets is a fool’s errand is the winner of that prize. The next piece will consider the flaws to the EMH and the case for actively managing your money.

Further reading:

A Beginners Guide to Financial Markets: Part 1- The Asset Risk Spectrum