The four cardinal virtues of quantitative equity investment, according to Plato

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Please note that this article may contain technical language. For this reason, it is not recommended to readers without professional investment experience.

The four cardinal virtues of quantitative equity investment

Etienne Vincent, head of quantitative management at THEAM, explains the similarities between the four main recurring sources of outperformance in equity markets and the four cardinal virtues identified by Plato in his philosophical works. While this may seem an unusual approach it is far from being anecdotal and helps to better understand the link between quantitative management and behavioural finance, as well as the value of well-constructed style diversification in an equity portfolio.

Plato said that “Human virtues are firm attitudes, stable dispositions, habitual perfections of intellect and will that govern our actions, order our passions, and guide our conduct according to reason and faith. They make possible ease, self-mastery, and joy in leading a morally good life.” The four cardinal virtues are prudence, justice, courage and temperance.

In the world of equity investment, there are also “stable dispositions”, meaning investment styles that make possible “ease, self-mastery, and joy”, as they offer recurring outperformance for a given level of risk.

The best-known of these styles is no doubt “value”, which was popularised by Eugene Fama and Kenneth French and consists in investing in the cheapest shares. Cheapness is measured, for example, in terms of valuation multiples. So this is a form of justice, in the Platonic sense of “morally providing to each person what is universally due to him”. The premium placed on the value style may be due to behavioural bias of certain investors, who allow themselves to be dazzled by a company’s talk of growth and neglect the importance of financial data in valuing companies.

The value style has in common with its corresponding virtue, justice, an absolute aspect that makes it insensitive to fashions (and bubbles).It therefore performs very well in the aftermath of a crisis, when investors return to fundamentals. However, justice also has a fault: it is blind. Some companies are indeed cheap for a reason (a structural change, for example, in the business environment). Continuing to blindly overweight such shares leads to a so-called “value trap”.

One good way of avoiding this trap is to invest in equities with momentum, i.e., with strong recent medium-term performance. An inexpensive stock that is already beginning to rally is probably not going to vanish from the scene. Taken alone, this “momentum” investment style also produces positive average returns, as long as trends are not followed too rapidly or for too long. This style appears to correspond to Plato’s virtue of Moderation (or Temperance), given that it is a form of humility that consists in acknowledging that “others” may have seen something that we overlooked and that it is therefore worth “doing like everyone else” even without a clear, explicit reason. The main justification for this style’s outperformance is derived from the observation that when humans make decisions we take time to decide but do not easily change our minds subsequently. As a result, fads, including in investments, feed on themselves up to a point.

The “momentum” style shares with its corresponding virtue a reassuring “flexible” aspect. However, moderation can also turn into indecision (manifesting itself in heavy portfolio turnover) or frivolousness, when one allows oneself to be led by fads (and bubbles) until the trend shifts.

The other pair of complementary Platonic virtues and styles is much less known.

Fortitude “is the moral virtue that ensures firmness in difficulties and constancy in the pursuit of the good. It strengthens the resolve to resist temptations and to overcome obstacles in the moral life.” In equities it’s the strategy consisting of trusting anticipations of future returns and investing on the basis of these expected returns (RoE), a style often called “quality”, which corresponds to fortitude. It is tantamount to exploiting the fact that investors tend to underestimate the importance of an activity’s profitability in its ability to develop. Even if its performance is weaker (this is the last of the virtues) it has the advantage of looking towards the future.

However, fortitude can become temerity without the first of Plato’s virtues – prudence, which sets limits. “Prudence is the virtue that disposes practical reason to discern our true good in every circumstance and to choose the right means of achieving it.” In equities, prudence consists in overweighting the least volatile shares, based on the advice of Robert Haugen, discoverer of the anomaly of low volatility. Over a long stretch, this style is not only the most profitable but also the safest, due to an entire series of decisional biases that push investors to overbuy popular and volatile stocks while neglecting overlooked stocks, which, in fact, offer greater potential for positive surprises. So when practiced in isolation, this style becomes risk-averse, meaning very low exposure to equity markets (low beta).

 Correlation to the market and among themselves of the main styles generating equity outperformance


On the whole, it is striking to see to what extent these styles are more complementary than competing or interchangeable. Each one, intrinsically, carries the seed of its dangers in its own qualities. In financial terms, the correlations of the previous chart are especially weak compared, for example, to correlations between countries, sectors or even different asset classes, and they are negative in the case of two of them. A well-organised strategic allocation of these four styles therefore makes it possible to double the expected outperformance for a given relative level of risk compared to mere juxtaposition. A true source of “ease, self-mastery, and joy”.

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