At its core the work or futurists is about assisting people making decisions in the face of uncertainty therefore we are always interested in analysis and techniques on how to do that. One of the central messages off this book is that risk management is about making decisions in the face of uncertainty, not just about avoiding or minimising risk. The author writes exceedingly clearly and well about a very complicated subject – quantitative analysis of financial risk.
First of all he presents evidence humans are pretty good at estimating the probabilities of outcomes that sit in the likely category but very poor when it comes to looking at the probabilities and consequences of highly unlikely events. He believes this is based on a set of "rules of thumb" that have served us well in evolutionary terms. Basically, we have evolved to be successful in making rapid decisions regarding commonly occurring events. It is fairly easy to see how this may have occurred. It is very hard to see how man could have developed a competitive evolutionary advantage in passing on his or her genes by being a really good decision maker regarding events that occur once in a hundred years.
He then moves on to talk about probabilities and divides this discussion into two basic subjects:
- Simple frequentist probabilities. If we take the example of flipping a fair coin then most people would agree that if you flip the coin enough times the distribution of results will be roughly 50:50.
- Subjective Probabilities. Once we move past the simple coin tossing experiment we move into the area where we need to make decisions about what data we will include in our assessment of probability. The author uses the example of attempting to determine the probability of the daytime high temperature above a certain level in your city tomorrow. The results will be different depending on which data sets you choose. For example, if you decide that there is a pattern of temperatures following a cloudy day and today is a cloudy day then you will select only that data which relates to cloudy days. You may also decide that recent weather is part of a warming trend or cycle. Therefore you may only choose data from the last 10 years. Every time you make one of these decisions you are both altering the dataset, and reducing the number of data points. In essence you are creating a subjective probability assessment that is based on the mental models that you have. Any statistical tools used subsequently to these decisions will carry the impacts of those decisions in their results.
The author then tells the story of a Martian that has just landed on earth and sees you flip a coin four times and come up heads. He asks "what odds would the Martian accept on the next toss". It is unlikely he would accept a 50:50 bet on tails but you would gladly accept a bet that had odds of heads at 80% because of your prior knowledge. The author’s point is that apart from true frequentist probability situations, prior knowledge and our views of the world play a large part in our assessment of risk.
He then goes on to talk about probability, risk and consequences and asks "if we had a coin that you know to be biased 60:40 for heads would you bet 20 times your annual salary on heads coming up?" No-one he has ever asked the question of has said yes. However if he changes the question to "would you bet on a thousand coin tosses?" he calculates the chances of you losing anything are 1 in 10 billion and says "a good lawyer could have you declared legally insane for turning down this gamble." This is all straight forward but then he changes the question to say that "you cannot be sure that the coin is biased 60:40, we have done several experiments which show that it is biased 60:40 with a level of uncertainty of 15% around that figure. This means it could be biased to 75% in favour of heads or 55% in favour of tails." This now moves into a question which is more like real life. You now have to make a decision in the face of uncertainty. What is your answer?
To assist you he calculates that if the coin is biased 75% towards heads the odds of you losing are so low it is not even worth writing down the number of zeros. However if the coin is biased 55% towards tails the odds of you losing are now 99.9%. The reality is that the expectation of the number of heads that will come up on average has not changed however most people turned down this bet. These are very simple stories but they contain complex understanding and form a good basis for the rest of the book. The author then goes on in the next chapter to describe more complicated situations, especially demonstrating the different behaviour depending on which side of a trade people are on (buying a lottery ticket or buying insurance). His conclusion is that "if you sell lottery tickets, even if you have badly mispriced the insurance premium you charge for rare events (i.e. the price of a ticket versus the prize payout), you can still look very clever for a long time". The opposite is true if buying insurance even if accurately priced – you can look very silly for a long time compared to someone who has not done so. Just talk to those people who pulled out of the market 2 years before the global financial crisis – they were being told they were crazy.
The author then goes on to describe in some detail various theories such as utility theory, value at risk, empirical fitting approaches, fundamental fitting approaches, Monte Carlo simulations, central limit theorems, etc. This is necessary but quite difficult reading despite his ability to simplify things. Most of it comes down to one central point on page 175: "there may well be truckloads of clever techniques to help us in our statistical analysis, but we still cannot get something for nothing"
This point is made to emphasise that many quantitative analyses are made on data that cannot reasonably support them. He states that there is significant evidence that risks that are out in the low probability range seem to act differently than those in the high probability range. At vet school we were told "if you hear hoof beats, don’t look for zebras," out in the low probability parts of statistical distributions there might be unicorns. This is particularly true of risks that might be related to each other but have a very low correlation in normal circumstances but move very strongly together in some unusual situations – a reasonable description of the Global Financial Crisis.
To illustrate his point further he describes an article in a refereed journal in 2006 where the authors calculated the 99.95% percentile (1 in 2000 year) yearly loss distribution for a corporate loan portfolio. This means they were attempting to estimate a loss that would only have occurred on average once since the birth of Christ. They used a number of statistical approaches to come to an answer using the economic data of the last five years which they deemed to be the "relevant data" for the current environment. Putting aside the issue that the global financial crisis occurred shortly after the paper was written they had ignored not just the Black Death, the fall of the Roman Empire, and the Thirty Year War but also the 1991 economic recession which one might have thought was relevant. They went on to describe not only the loss but precisely 109.7 million Euros. It sounds like the basis for a financial version of Yes Prime Minister. This sort of reasoning is rampant in financial analysis because relevant data can be so hard to determine, but risks that are extremely low probability but high impact are taken all the time and information is required by regulators on what risk is being taken.
The author finishes the book with his recommendations on "what we can do instead", quite rightly stating that it is always easy to criticise, and more difficult to propose a constructive alternative. His key points are that:
- We must understand better what we are doing and stop attributing numbers coming out of these systems as holy writ.
- That the probability of returns and the probability and consequence of risks must be assessed completely differently. The authors view is that the probability of returns are far more related to our subjective assessments and that risks are far more amenable to frequentist approaches as long as we recognise the limitations inherent in the first point.
- That we need to ask ourselves three basic questions:
- Can we survive a failure of making a decision or a trade?
- If things work out what is the plausible best case result and what is the difference between that and a riskless decision?
- How much would things have to go wrong before the result was no better or worse than a riskless decision?
A really well written and elegant presentation of a very difficult subject which moves from the simple to the difficult in a well ordered and well argued way with some excellent questions being posed.
Despite its strengths still a bit of a hard slog to read which is not the fault of the author.
Only read if you are really interested in the subject or work in an area directly affected by these issues because it is too hard a read otherwise.