Perceived and actual risk

November 12, 2022

Perceived risk is risk predicted by models, and actual risk is the fundamental underlying risk. We measure perceived risk and care about the actual risk. Those two are negatively correlated with interesting consequences.

The classification of risk as perceived or actual comes from Endogenous extreme events and the dual role of prices.

The following picture, taken from my book The Illusion of Control and where the x-axis shows time and the y-axes prices, shows a hypothetical asset price bubble in blue:

Now, run one of your friendly risk forecast models, perhaps one of these, and show the resulting risk forecast, labelled perceived risk in red. As we ride the bubble, perceived risk falls. As if we get ever higher returns at ever lower risk

It is Money for Nothing.

Then, the bubble bursts and suddenly, perceived risk shoots up. Why? Well, it depends on the model, but suppose one is using one of the volatility models from here. Then, inevitably perceived risk will increase.

The reason is that a volatility model will react to events in recent history, and if prices change a lot, so inevitably will the risk forecast. This is why one can have very low risk forecasts until the day after a crisis event.

A good example of this is the Swiss FX shock discussion, where the models failed to pick up the probability of the event and then went crazy after.

However, the actual underlying risk in the system, what we call actual risk, shown in green, increases along with the bubble and falls when the bubble deflates.

Actual and perceived risks are usually negatively correlated. Since almost every risk forecast model is of the perceived type, the result is that:

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Risk forecast models underestimate risk before a crisis and overestimate it after a crisis. As a result, the models are systematically wrong in all states of the world.

Does that matter? It all depends on one's risk horizon. It does for long term and extreme risk like macro prudential regulations.

In an earlier post, I connect perceived risk to long risk horizons.

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