Back in 1952, Harry Markowitz’s portfolio theory made the significant assumption that investors are risk averse. This means that when faced with two assets offering the same expected return, investors will always opt for the least volatile one. His theory also introduced the concept of diversification as a “free lunch”: a diversified portfolio can yield the same expected return as a concentrated one with less volatility. In this article, I’ll challenge that notion and argue that diversification comes with a cost that investors must understand to make informed decisions about their portfolio strategy.
In the 1960s, Bill Sharpe and other academics introduced the Capital Asset Pricing Model (CAPM), which stands out for its simplicity and elegance in estimating securities’ expected returns.
The CAPM observes that volatility is composed of two types of risk: security-specific and non-diversifiable market risk. Portfolio risk can be diminished by combining imperfectly correlated securities. Since security-specific risk can be eliminated through diversification, the only risk that should influence expected returns is market risk.
Put simply, the CAPM asserts that an asset’s expected excess return (above the “risk-free” interest rate) is solely determined by its “beta,” or sensitivity to the market return. To illustrate, a stock with a beta of 1.5 would be expected to have 1.5 times the excess return of the market.
During the 1970s, academics came up with another proposition: expected excess returns are determined by multiple factors, rather than just beta. The Intertemporal CAPM (Merton, 1973) and the Arbitrage Pricing Theory (Ross, 1976) argued that not all investors share a single obsession with beta but could also be sensitive to other variables, or “factors.” While the ICAPM and the APT did not specify what these factors were at the time, Fama and French (1992) came up with an empirical study suggesting two factors should be added to beta: value and small stocks have higher expected returns than growth and large stocks. The Fama-French three-factor model and later the five-factor model (2015; market, value, size, profitability, and investment) were born.
The Fama-French five-factor model identified certain types of stocks that are very volatile and provide extremely low expected returns, such as small growth stocks with low profitability. The very existence of these securities with very poor investment characteristics raises a legitimate question: Why does anyone invest in these securities? Are these so-called lottery stocks acquired by irrational investors?
Another theory formulated in the 1970s suggests that risk—as measured by volatility—could influence expected returns positively rather than negatively.
In a seminal article, Black and Scholes (1973) suggested that for a corporation that is financed with debt and equity, the equity portion of the balance sheet is equivalent to a call option on the company’s assets. Imagine a company whose assets are worth $100, which are financed with a one-year bond worth $35 and $65 in stocks. When the bonds mature, shareholders can exercise their option (pay $35 to reimburse the bondholders), just like holders of a call option would pay the exercise price at expiry to acquire the underlying asset.
Option pricing models, which work well in practice, state that the higher the volatility of the underlying asset, the greater the option’s value. Replacing the word “option” with “stock” means that according to the option pricing theory, higher volatility translates into higher stock prices. Since asset prices and expected returns are inversely related, higher volatility leads to lower, not higher, expected returns.
To summarize, the CAPM says volatility and expected returns are positively correlated, while the option pricing theory says the exact opposite. However, I believe multifactor models such as the Fama-French five-factor model reconcile these conflicting viewpoints.
The option pricing theory and multifactor asset pricing models tell us that buyers of “speculative assets” or “lottery stocks” are neither stupid nor irrational. They are risk-seeking investors who may not even care about expected returns. What they care about is the possibility of extremely high returns, which is very different. Broadly diversified portfolios are appropriate for long-term investors who seek to build wealth slowly but surely and manage risk rigorously. Concentrated portfolios, especially when holding volatile stocks, are for those who are looking to multiply their wealth quickly or to multiply their wealth to a much greater extent in the long run. They pursue this strategy despite the high likelihood of failing to give themselves a chance to become extremely wealthy, as one does when buying a lottery ticket.
There’s a price for everything. If you want to build significant wealth patiently and methodically, with high odds of success, a diversified portfolio is what you need. If you’re looking to build extreme wealth, a concentrated portfolio is the legitimate choice. But be warned: odds are, you’re going to end much poorer than the methodical investor next door.
So, what kind of investor are you?
