What is risk?

The following is taken from my book Illusion of Control.

There is no single observable phenomenon called risk. The reason is that what is measured cannot be compared to any actual reality. In statistical language, risk is latent, meaning that it cannot be directly observed. At best, one gets an imperfect measurement by observing how risk influences the world. If a stock price fluctuates a lot, it might be highly risky, but then again, it might not.

We need three different layers of analysis for risk, whereas only one is needed for temperature.

1. The recognition of what sort of risk is most important;

2. A theory of how to quantify that risk;

3. Statistical technologies for producing the actual risk measurements.

To start with, what do I want? Suppose Paul, Ann, and Mary each invest in Google stock. Their reasons for investing are different. Paul trades on his own account, his reasons are speculative, and he aims to get out in one week with a hefty profit. Ann is a fund manager, investing on behalf of her bank, and her primary concern is beating her benchmark and avoiding significant losses relative to her benchmark that would get her fired. Mary is investing for the long term and worries about getting her pension 70 years into the future when she is 95 years old and relying on the financial industry for her financial well-being.

Even though each of the three made precisely the same investment and had access to the very same risk measurement technologies, their views on risk are very different. Paul cares about day-to-day fluctuations over the next week, Ann is worried about a substantial one day loss sometime in the next six months, and Mary needs the Google stock price to continue to grow over the next 70 years and does not care about what happens to the stock in the meantime (and certainly not over the next week).

Their investment horizons are different, their objectives are different, and therefore what risk means to them is different. Each needs a different riskometer. Unlike temperature, where Celsius is the appropriate unit of measurement regardless of what it is used for, for risk, we need different concepts depending on the end-use.

So the next step for Paul, Ann, and Mary is to forecast risk. Start with the concept. With temperature, we have three units of measure, Celsius, Fahrenheit, and Kelvin. However, they all measure the same thing, temperature, and we know exactly how to go from one to the other. 100° Celsius is 212° Fahrenheit and 373.15° Kelvin. It is not the same with risk, where we have multiple concepts.

When it comes to an individual stock's risk, I may be interested in volatility, Value-at-Risk, or Expected Shortfall, just to mention the three most popular. These are not just three measurements of the same thing like Celsius, Fahrenheit, or Kelvin. It is like having three different opinions of temperature with no apparent way to compare numbers produced under one standard with another. The user has to pick the concept of risk most appropriate to her, and if she uses a generic one — a one-size-fits-all forecasting technology — the end result will not be as good as if she picked what is the best riskometer for her purpose.

Most people, even professionals who should know better, see financial risk measurements as a single concept with no difference between day-to-day risk, the risk of extreme losses, and long term risk. This is nonsense. One cannot go from one concept of financial risk to another without making what often are entirely unrealistic assumptions.

After deciding on a concept of risk, the next step is statistical measurement. When it comes to temperature, measurement is easy. Take some mercury, put it in a tube, and since mercury expands with heat, the mercury's height in the tube tells us the temperature. It is the same with prices. I can go to my Bloomberg terminal to check what the price of a stock is. That is it. I know the price. Both prices and temperature are realtime measurements.

Because risk is latent, the only way to measure it is to see what has happened in the past. If I am interested in the risk of a stock, I have to observe how the stock fluctuated in the past and infer a risk measurement. Not all that straightforward. To begin with, how far to look back? For some assets, we have a long history. The longest I know of is the exchange rate between the Dutch Guilder and the British pound, starting in the early 1600s and extending to today if I allow for the Guilder joining the euro in 1998. Some individual stocks have been traded for over 100 years.

I have observations on the most important stock market index in the world, the U.S. Standard & Poor's 500 (S&P-500), going back to the 1770s. Yes, the S&P-500 index only dates back to 1957, but economic historians have reconstructed its older values, you can find them on Bloomberg. However, the U.S. stock market was very different in the 1770s than today, so I may want to start measuring risk more recently. But when? Different starting points will give different risk measurements, and I have no clear way of identifying which is more correct. There is no single correct answer to the question of how much data to use. We could ask the experts, but they will probably say "it depends," and the more expert they are, the more likely they are to say so.

If that was not enough, I also have to pick a statistical model. Here I have a large number of choices, each with its strengths and weaknesses. Some are relatively accurate but data-intensive, while others can provide less accurate measurements with little data. Some need powerful computers and highly trained experts. Others can be implemented in Excel with minimum training. Some focus on extreme outcomes, while others are more concerned with day-to-day movements. So how do we pick a model? If you ask the experts, they will just suggest their favorite methodology. Not very helpful.

When it comes to risk, the objectives, concept of risk, and the statistical methodology should be considered simultaneously. This means that different end-users, all with the same investment and technical skills, ought to measure risk differently. In the example above, what risk is to Paul is irrelevant to Mary, and vice versa.

The riskometer

Model risk