Most important financial concerns are long-term – perhaps whether banks fail, or pensions keep their value – or are about problems that may develop at any time, today or decades in the future. Short-term risk is not particularly important.

Even the perfect, and never achievable, knowledge of risks that will materialise in the next month is of very limited value in making a decision that will involve exposures over many years.

One might therefore expect that risk management techniques used by industry and regulators reflect the importance of the long term. Instead, standard practices focus almost exclusively on the recent past, and only capture short-term risk.

This dissonance in how we think about risk is a direct result of how risk is measured and managed in practice.

## Measurement of risk

The main reason is that it is really hard to measure long-term risk. After all, extreme infrequent events are by definition very scarce. Take systemic financial crises. An OECD country suffers a crisis in one year out of 43 on average; global crises are even less frequent. Consequently, systemic risk analytics – the statistical forecasting of systemic risk – is not easy (Giglio et al. 2015).

We are taught in first-year statistics that the sample size needs to be sufficiently large for accurate statistical analysis. But modern financial markets are less than two centuries old and give us only a handful of crises for each country – much too small of a sample to draw reliable statistical interference.

To bypass the problem of lack of data, we usually resort to a statistical sleight of hand, a technique known as probability shifting (e.g. Boucher et al. 2014) – estimate the distribution of higher frequency events, perhaps the daily or monthly, and project those distributions onto longer time horizons (years or decades, even centuries).

Technically it’s quite easy to do, as it is straightforward to model short-term risk. Once we have estimated a parametric stochastic process of daily or monthly outcomes, all we have to do is to plug in extreme probabilities. As some popular systemic risk models would have it, you model the distribution of daily stock prices and plug in a probability of 0.009% and voilà, you have a 43-year crisis.

Seductive… but there is a problem. While the calculations are easy enough to do, for the numbers to have meaning we need at least two strong assumptions. Obviously, we need *ergodicity* of the underlying stochastic process, but also the *correct parametric form* of the distribution, typically fat-tailed, because we will be using it to extrapolate far beyond the region in which evidence has been obtained.

In practice, these are heroic and non-verifiable assumptions at best. Financial markets are continually evolving, violating ergodicity, and the severity of the most extreme events is bounded by a complex and evolving social process, implying that tail distributions must also evolve because risk is endogenous.

In the real world, no purely statistical technique allows us to go from the short term to the long term in a reliable manner, and there is little economic or financial theory available to help.

Take the forecasting of systemic risk. We certainly observe extreme price movements when a crisis happens. However, those are only the consequences of a crisis, reflecting the specific portfolio holdings of financial institutions at the time. Any statistical measurements are therefore specific to that particular crisis. The same fundamental vulnerability, coupled with different holders of the affected assets, would lead to different price dynamics and different associations. Those differences can be very large.

After a crisis, with the benefit of hindsight, one can of course back out the cause of the given crisis from the observed price and quantity movements, but this should not be confused with any kind of predictive or forecasting ability. The distribution of events during the crisis is not only different from that of typical events, but observations of financial variables during crises are mostly idiosyncratic with limited information value for analysing the likelihood of crises.

The consequence is that a projection of probabilities from day-to-day, or month-to-month events onto the likelihood of crises, often done with market price data or accounting data, is not informative about the likelihood of the crisis.

## The problem of risk measurement is entwined with that of risk management

Consider a sovereign wealth fund that cares about very long-term risk, decades into the future, where such a time perspective is written into its laws and mandates. However, the fund is monitored quarterly, and if it performs poorly over a few quarters, questions are raised. The effective time horizon moves to become quarters, not decades.

Similarly, many pension funds use value-at-risk or expected shortfall to monitor performance, motivated by these being state-of-the-art risk measures in banking. However, value-at-risk or expected shortfall make no sense for most pension funds that have predictable inflows and outflows over many years. The main risk is not daily fluctuations as captured by value-at-risk, but investment performance over many years.

Daily price fluctuations should be irrelevant for funds with a long-term outlook, like pension funds and sovereign wealth funds; but because they *can* be measured, they *are* measured. The funds become shorter in outlook than they should be, focused on avoiding short-term losses rather than long-term performance.

## Practical implications of the dissonance of the short and long term

The dissonance of the short and long term has several negative consequences. To begin with, the performance of long-term investments, like pension funds will likely suffer if short-term fluctuations in asset prices are a key driver of decisions.

Perhaps the asset managers will be biased towards short-term stable assets, avoiding those that can be expected to perform well in the long run even when fluctuating in the short term.

Alternatively, they may look for false diversification. Perhaps buying private equity funds, which do not exhibit much short-term volatility even though they are long-term cointegrated with equity markets. They may accept the frictional costs of dynamic trading strategies, or invest in assets with fat tails and little short-term volatility.

Excessive focus on the short-term risk can easily blind us to the risk in the long term. If the short-term risk dashboards are reassuring, as in 2006, we may easily take on undesirable levels of risk, oblivious to the dangers.

Buy low-volatility, very fat-tail assets, because volatility is what is specified in the mandate.

Such an eventuality becomes even more likely because risk is endogenous (Danielsson et al. 2009), created by the interaction of market participants. If we focus on the short term, we can become quite good at smoothing out fluctuations, and when such strategies are successful we can expect more and more assets to be managed using them.

This can change the distribution of outcomes, lowering volatility, that is the probability of intermediate losses, but increasing the intensity of tail events, as most clearly demonstrated by the portfolio insurance crisis of 1987 and the quant crisis of 2007.

## Conclusion

As the management of risk is increasingly formalised, and hence depends on statistical measurements of risk, decision making becomes increasingly biased towards the short term, even if the ultimate objectives are long-term – the dissonance of the short and long term.

The consequence is the wasting of resources, procyclicality, poor performance, and insufficient attention towards important long-term risk. The short-term bias can even be a driver of systemic risk.

There are steps we can take to mitigate the dissonance of the short and long term: focus on resilience; avoid inferring long-run risk from the short run; and use scenario planning.

## References

Boucher C, M, J Danielsson, P Kouontchou and B Maillet (2014), “Risk models–at–risk”, *Journal of Banking and Finance* 44: 72-92.

Danielsson, J, H S Shin and J-P Zigrand (2009), “Modelling financial turmoil through endogenous risk”, VoxEU.org, 11 March.

Giglio, S, B Kelly and S Pruitt (2015), "Systemic risk and the macroeconomy: An empirical evaluation", VoxEU.org, 3 April.