On June 22, 2023, American economist Harry Markowitz passed away at the venerable age of 95. Markowitz’s 1952 paper “Portfolio Selection” laid the foundation of the field of financial economics. At the time, what he presented was so novel that his doctoral advisor at the University of Chicago, Milton Friedman, once declared that his paper “was not economics.” Nevertheless, this seminal theory and other works later earned Markowitz a Nobel Prize in Economics.
Before Markowitz, finance was concerned with maximizing returns, but little was being said about risk. His theory proposed to measure risk with the standard deviation (or volatility) of returns. His base assumption was that investors are risk-averse: if offered two portfolios with the same expected return but different volatilities, they would choose the least volatile one.
This theory became interesting for practitioners when Markowitz established that returns are additive while volatility is not. Let’s take, for example, a portfolio made of two stocks. The return of this portfolio is the weighted average return of these stocks. By contrast, if these two stocks are not perfectly correlated, the volatility of the portfolio is less than the weighted average volatility of the underlying stocks. In other words, Markowitz proved that one can get the same return with less risk (volatility) with the help of portfolio diversification.
To this day, Markowitz’s original work remains the bedrock of modern portfolio theory, taught in university finance classes worldwide. However, it is sometimes misused to sell investment products. When the characteristics of an investment do not conform to the assumptions used by Markowitz, the result can be a mechanically inflated perception of the investment’s attractiveness in a portfolio.
One important thing to know about standard deviation is that it appropriately describes risk only when returns are normally distributed. An essential property of a normal distribution is its symmetry: the negative and positive sides of the probability distribution are identical. A probability distribution that isn’t symmetric can’t be normal.
An example of a non-normal distribution strategy is covered call writing. By writing calls on a stock portfolio, the manager enables the fund to pocket the premium on the options sold. Still, it also heavily cuts its potential upside while providing minimal downside protection. To make matters worse, many covered call ETFs are sector funds, and their lack of diversification amplifies their downside risk. Non-normality is a return distribution characteristic that affects covered calls and most option-based strategies, such as principal-protected notes, which are equivalent to a combination of a zero-coupon bond and a call option on a group of stocks. Standard deviation isn’t an appropriate measure of risk for those products.
Private equity and hedge funds also suffer from non-normality because of their compensation structure. The usual 20% performance fee that these funds charge entitles investors to only 80% of the fund’s positive excess return while they must absorb 100% of the negative excess returns. Even worse, empirical research has uncovered that when holding multiple hedge funds in a portfolio, their aggregate performance fees can climb to nearly 50% of excess profit.
Private equity fund managers are a segment of the investment industry famous for asserting that their funds offer diversification benefits to a public equities portfolio. Borrowing the Markowitz approach to portfolio construction, private equity funds are frequently claimed to increase portfolios’ Sharpe Ratio (the fund’s excess return over T-Bills divided by its standard deviation).
But this claim is based on an apples-to-oranges comparison. Stock and bond returns are calculated from actual daily transactions’ time-weighted rate of return (TWRR). In contrast, private equity fund returns are usually calculated from the fund cash flows’ internal rate of return (IRR). Public and private equity funds don’t use the same data or mathematical formula to estimate returns.
In other instances, private equity returns are calculated with the TWRR based on expert appraisals. These appraisals are notoriously stale, as appraisers persistently delay the devaluation of portfolio companies, especially when the stock market tanks. Private companies operate in the same global economy as publicly traded companies; their drivers of return are not inherently different because they are private. The infrequent valuations of private company shares dramatically understate the marked-to-market volatility of private equity portfolios – this feature has been referred to as “volatility laundering.” In one example, when regulation forced private equity funds to switch from cost-based to fair-value accounting, their apparent diversification benefits decreased, which in turn reduced their access to capital.
It can be argued that investing in private equity funds adds more individual companies to a portfolio, with associated diversification benefits. But these benefits are not compelling. For example, one of the world’s largest private equity managers, Blackstone, currently holds 123 portfolio companies in total,[i] valued at $137 billion. Compare that to the total world market portfolio, which includes over 10,000 stocks and is valued at $65 trillion,[ii] and you’ll realize that the added diversification from private equity is immaterial.
The true diversification benefits of private equity funds are immaterial, and their low correlation with stocks and bonds is an illusion. The same observation could apply to other private assets, such as private loans, private real estate and venture capital: their true correlations with public markets are likely much higher than appraisal- and cash-flow-based estimates suggest. Using Markowitz’s theory to find the optimal allocation to private assets will result in large weights due to their artificially low volatilities.
Markowitz’s theory describes portfolio construction as a mean-variance problem: investors aim to maximize the mean (expected return) for a desired variance (volatility) level by assembling uncorrelated assets. Sometimes, low correlations are invoked to justify investing in some instruments that help reduce portfolio volatility but do not offer any clear expected returns. Pursuing an expected return is, by definition, deferring consumption now to obtain more money in the future. In the case of a bond purchased at par, the expected return is the contractual rate of interest: if you buy $1,000 of a one-year bond paying 5%, you expect to receive a $50/$1,000, or 5% return in one year. The expected return for stocks and other equity investments, such as private equity and venture capital, are less obvious because, unlike the contractual terms of a bond, equity investment’s expected returns cannot be easily quantified in advance. However, equity investments represent participation in private businesses that produce goods and services in the hope of generating a profit. Some equity investments (such as dividend-paying stocks) have expected returns that are easier to identify; others, such as venture capital, are less obvious because many portfolio companies are not even making profits yet. But all private companies produce goods and services aiming for profits in the future.
However, many instruments presented as investments do not offer a contractual interest rate nor produce goods and services that could eventually be sold for profit—gold and other commodities, and cryptocurrencies are good examples. To me, proposing an investment with no expected return based on its diversification properties is misleadingly instrumentalizing Markowitz’s portfolio theory.
Harry Markowitz has provided an elegant demonstration that statistical analysis can inform investment portfolio construction. While modern portfolio theory has evolved in strides since the 1950s, Markowitz’s portfolio theory still provides essential insight to investors. Nevertheless, any theory has its limitations. Using standard deviation and correlation-based measures in support of financial products with a non-normal probability distribution of returns, that are not marked-to-market or do not have a clear expected return is, in my opinion, nonsense.
[i] Source: Blackstone.com
[ii]In USD. Source: MSCI
