For decades, asset allocation has been regarded as the most important element of investing. At its core is the Modern Portfolio Theory (MPT) and its mathematical basis in mean-variance optimization (MVO). MPT shifted the focus from the risks and rewards of individual securities to a portfolio-wide perspective.
In recent years, however, portfolio optimization has evolved as a result of real-world results. Advancements came to the fore following the 2008 global financial crisis and subsequent volatility.
The conversation centers on three specific observations:
- 1) Traditional MPT assumes asset returns fall within a “normal” bell-shaped distribution
- 2) Traditional MPT assumes investor perception of risk is defined by standard deviation of returns
- 3) Forecast bias can lead to overly concentrated portfolios using traditional MVO
Distribution of Returns: What is ‘Normal’?
Over time, and through some highly volatile markets, investors have come to realize that stock market returns have been much more volatile than previously thought.
“A normal return distribution implies that you can expect results beyond five standard deviations of the average return once every 10,000 days,” said Michael DeJuan, manager of the Portfolio Construction Desk at Northern Trust. “Based on that theory, since January 1928, the S&P 500’s daily returns would have exceeded that range twice.” In fact, there have been 84 such occurrences — 43 times on the upside and 41 times on the downside.
With much greater volatility and more highly skewed returns in real life than in a normal distribution model, it turns out that “outlier” results are much more common than once thought.
The traditional measurement of risk used in portfolio optimization models, standard deviation, puts equal focus on instances when returns are highly positive as well as highly negative. However, investors generally aren’t concerned about exceeding average market returns, but falling short or losing money. Accordingly, the risk of underperforming expected returns is where risk measurement should focus. DeJuan noted one way to do so is to adapt the optimization model to minimize “downside risk,” a statistic that captures deviations or returns below a minimum acceptable return target. “Because downside risk only measures the volatility of the returns that occur below a target return, it focuses investors on how much loss can be expected from a portfolio,” he said.
Another way to reduce downside risk is optimizing the portfolio to minimize a measure called Conditional Value at Risk (CVaR). Based on a predefined confidence level, CVaR, also known as “tail risk,” is the average loss in the worst of cases – whether in a “normal” or “non-normal” market environment.
Overcoming Forecast Limitations
Although most investors are well aware of the warning, “past performance is not a guarantee of future results,” it’s still quite common for investors to use past performance, or historical average returns, as the basis for forecasting future returns.
“In the face of highly volatile and unpredictable market events, it could be much more effective to use a variety of more sophisticated, complex and intuitive methods that reflect a sound understanding of capital markets,” DeJuan said. “One approach is to combine top-down long-term investment themes with bottom-up forecasting models.”
With any forecast methodology, biases and estimation error may exist. An unconstrained MVO model may amplify inaccurate return assumptions resulting in overly concentrated portfolios. A robust approach needs to account for uncertainty in forecasts and may involve using more than one model in order to produce a well-diversified portfolio.
Alternative models include:
Black-Litterman Model – An asset allocation model that combines refined asset class return estimates and MPT’s mean-variance optimization. It adds a tool that a portfolio manager can use to avoid a concentration of assets that might occur under a pure MVO process.
Resampling – An approach that uses Monte Carlo simulations to incorporate forecast uncertainty. Resampling develops a series of simulated efficient frontiers, each presenting an asset mix scenario. An average of all asset mix scenarios generates a resampled efficient frontier, resulting in more intuitive and diversified asset allocations.
The Best of All Worlds
Rather than use just one method or formula, several approaches can be combined. This is the approach taken by Northern Trust’s Investment Policy Committee to develop its annual strategic asset mix recommendations.
“Because we recognize that traditional mean-variance optimization has limitations, we can leverage a number of different approaches to portfolio optimization,” DeJuan said.
“There’s no single best approach. It’s about understanding each client’s needs and then finding the most suitable technique,” he added. “If clients are more concerned about avoiding capital loss, a post-modern portfolio theory approach is likely most suitable because it focuses on minimizing the tail risk and ends up with a conservative portfolio. But if you have more aggressive return objectives and are comfortable with volatility, then MPT could be best.”