**Pre-occupation with quantitative analysis in the financial markets has not necessarily served us well, says Mark Arnold. He explains how and why modern portfolio theory has failed long-term investors.**

“Beware of geeks bearing formulas,” Warren Buffett once famously warned. And certainly, modern portfolio theory the formula for measuring equity portfolio risk first devised in the 1950s that was already expiring, was finally put out of its misery by the global financial crisis.

Modern portfolio theory measures the risk of a portfolio as the standard deviation of portfolio returns and for decades has been accepted finance theory. Modern portfolio theory states that risk and return follow a linear relation and investors are compensated only for holding non-diversifiable or systematic risk.

This relies on a series of assumptions based on investor behaviour, including:

- investors consider each investment alternative as a probability distribution of expected returns over an investment horizon;
- the risk of a portfolio is measured as the variability of expected returns;
- the probability distribution of expected returns is normally distributed;
- investors’ utility curves are a function of risk and return only; and
- investors are rational.

Modern portfolio theory lacks depth in measuring portfolio risk because it does not seek to explain the underlying drivers of equity-based portfolio returns.

It simply examines the historical return volatilities and correlations between stocks to explain how to price assets and reduce portfolio return volatility through diversification.

And despite its theoretical roots and popular application, modern portfolio theory is based on assumptions that are not necessarily true in the ‘real world’.

An underlying concept of modern portfolio theory is the assumption that risk is symmetrical — that there is a spread of returns around the mean return both to the upside and downside.

However, in reality risk is one-sided because it is the component of the uncertainty of future events that relates to adverse outcomes.

Modern portfolio theory's approach to portfolio risk reduction has focused on historical correlation based diversification and index weight based portfolio construction.

One of the problems with this approach to diversification is that it is not fundamentally based and ignores the fact that stock correlations tend to move close to one during crises.

As such, it is not effective in reducing crisis related downside risk.

Also, index-based portfolio construction approaches assume that the index represents the 'market' portfolio.

It is further implicitly assumed that the index, as a proxy for the market, is properly diversified, is reflective of the underlying economy, is not over exposed to poor quality/speculative businesses and is not overpriced.

The fact that indices are constructed based on the relative liquidity and size of listed stocks, with no direct reference to the type and quality of the underlying businesses and their pricing relative to intrinsic value, would indicate there is a real risk these assumptions will not always be correct.

Another vital element not addressed by modern portfolio theory is agency risk.

While an investor wants only to maximise returns, the goal of a fund manager is to maximise returns while simultaneously expanding the amount of funds under management.

The two are largely incompatible.

The goals of investors not being fully aligned with the aims of fund managers is another factor not taken into account in modern portfolio theory.

Then there’s the fact that modern portfolio theory relies on the measurement of volatility on a time horizon that does not match the timeframe of many investors.

The modern portfolio theory approach is to measure risk in terms of absolute and relative volatility on monthly data over a short horizon. That is likely to give excessive weighting to temporary mispricing or market ‘noise’.

The fact that the short-term nature of the data makes it irrelevant to the vast majority of clients appears to be forgotten.

Overall, prior research (largely US) and an analysis of Australian data (over the period 1961 to 2009) indicate that volatility of returns is greater in the short term than in the long term.

Much of this short-term volatility appears to be unrelated to underlying fundamentals.

Downside risk appears greater for investment decisions based on an analysis of short-term returns. This is because growth in fundamental value only occurs gradually through time (normally in line with overall growth in the economy).

Earnings tend to increase, on average, in line with gross domestic product growth but with much higher levels of short-term pro-cyclical volatility.

Many investors have much longer horizons of five or 10 years, or more. Producing monthly returns focuses on much more volatility than five or 10-year results.

This can be demonstrated by comparing market volatility to changes in price/earning ratios and growth in earnings per share over one, five and 10-year time horizons. All of these three measures tend to fall as the time horizon extends.

Moreover, it is argued that the portfolio risk measure must be matched to the appropriate investment horizon in order to correctly assess the risk and return profile of a portfolio.

modern portfolio theory is also preoccupied with indices as the basic denominator of risk and, accordingly, with the assumption that higher weighted stocks represent less risk — that is, that the weighting of a stock in an index is a measure of its quality and potential return over the long term.

However, modern portfolio theory fails to address variations in the quality of index constituents.

In reality, an index can comprise low quality stocks that are weighted purely on their relative size and liquidity and not their quality.

Strong historical evidence shows that a low quality stock representing high risk — even with a high index weighting — will produce lower returns over the long term.

It is important therefore to consider fundamental aspects of the firm and its stock price relative to expected free cash flows in the assessment of risk and return.

Another questionable assumption of modern portfolio theory is that expected returns are normally distributed. There is, however, substantial evidence to the contrary — that market returns are not normally distributed and, at times, negatively skewed.

Lower quality/highly geared firms tend to produce low returns on equity, lower free cash flows, have wider return distributions and produce abnormally low returns.

These firms generally have a higher probability of going bankrupt than higher quality firms with low debt.

Extremely speculative firms with very low levels of predictability tend to have long-term return probability distributions that are dominated by a return outcome of going bankrupt.

Modern portfolio theory tends to overstate the return profile of low quality/speculative stocks.

An overreliance on the modern portfolio theory principle of diversification has also created complacency and become a poor substitute for due diligence.

Simply attempting to minimise risk by diversifying ignores some important aspects of stock correlation.

In time of crisis for instance, stock correlation tends to increase, limiting the reduction of volatility expected from diversification.

Diversification alone can be of little use when the market is near the top of a stock market bubble.

On the other hand, diversification carried out with heed to business quality, macro factors and a measure of price to value means fewer stocks are required to diversify adequately against wider systemic risks.

Diversification is a portfolio construction tool that can be used to reduce shortfall risk. It is used to reduce a portfolio’s exposure to an adverse return outcome from a particular stock or macro-economic factor.

Diversification is symmetrical in that it not only reduces a portfolio’s downside exposure, it also dilutes its upside exposure in equal measure.

The fact that the future outcomes are not known with certainty means that some stock diversification is sensible for reducing the risk of a portfolio return not achieving the minimal acceptable return (MAR) and reducing the quantum of any return shortfall below the MAR.

A final distortion created by relying on modern portfolio theory is comparing portfolio returns relative to a benchmark rather than using long-term absolute returns.

Clients perceive risk in terms of their absolute return and not whether their fund manager has provided returns greater than, for instance, the All Ordinaries.

In summary, the industry’s focus on short-term volatility and returns rather than on the underlying long-term fundamentals of the businesses comprising the portfolio is likely to result in incorrect risk assessments and sub-optimal long-term returns for investors.

Which brings us to the big question: with modern portfolio theory debunked, how should risk management be approached in the real world?

In the first instance, it should match the risk profile of the investment with the individual investor’s investment horizon.

It should ignore the sensitivity of indices and only use an index as a long-term point of comparison — not as a basis of portfolio construction.

Finally, it should be acknowledged that diversification is not a magic bullet and will not substitute for performing the required due diligence to manage shortfall risk.

*Mark Arnold is chief investment officer at Hyperion.*

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