Understanding Risk and Decision Making

Key ideas:

Probability is the likelihood of an outcome.  Probabilities are expressed numerically, but are often subjective.

Impact is the effect that a particular outcome will have.

Decision trees help us get a grip on our alternatives.

The concept of expected value helps us compare alternatives based on probability and impact.

Risk profies take us beyond expected value to consider unacceptable or fatal downsides.

Getting more information to reduce subjectivity in decision making takes time and costs money


Ref:
Risk:  How to make decisions in an uncertain world
Editor:  Zeger Degraeve

A picture of complex risks and their profiles is more useful than knowing expected value is positive or not

Risk profile

A risk profile is a graph showing value - usually expressed in financial terms - and probability.  Looking at the profile of a risk can give a more sophisticated view of it than expected value alone. 

http://spreadsheets.google.com/pub?key=tHk2EpsXiBSmmV6BILRm7IA&output=html


Let's consider a third version of the dice game - version C.  As before, throwing different numbers brings different outcomes.  But in this version, there is the possibility of a severe downside.  Thowing 5 or 6 wins $10; throwing 2, 3, or 4 wins $5; throwing 1 incurs a $10 penalty.

The different outcomes and probabilities are shown in the table above, along with the calculation of expected value for this game.  As before, expected value is calculated by adding together the products of impact and probability for all possible outcomes. 

At first glance, this game looks like the best so far - its expected value is far higher than that of either version A or version B.   ( http://spreadsheets.google.com/pub?key=te9MzyHoIN6EyuoHmfDxMaw&output=html)

But what about the potential downside?  With $5 in our pocket to play with, we could easily incur a debt that we can't pay, and have to declare ourselves bankrupt.  With $20 to play with, we would be a bit safer (the wealth effect). 

The key to this decision is the profile of the risk.  (see the diagram of the risk profile for dice game version C above).    Each vertical black coloured bar represents a possible outcome.  Its position denotes its impact (negative to the left, positive to the right); its height denotes its probability.  The positive side of the graph looks promising, with high probabilities for positive outcomes.  But over on the left, we see the possibility of a serious negative outcome - a potentially fatal downside.  The risk may have an unacceptable profile for us, despite its positive expected value.

More complex risk profiles bring in more and more possible outcomes and probabilities.  They build up a picture of complex risks and their profiles that is more useful than the simple question of whether the expected value is positive or not.

Histograms plot value against probability density, to give a continuous version of the risk's profile.  They are created through advanced risk anlalysis involving techniques such as Monte Carlo simulations, where a large number of probabilities is used to create the risk profile.

Making Life Decisions: appraising cost, risk and expected value, with limited information about the future

The dice games are simple parallels with the type of decision we take every day in our lives.  Investments offer the most direct comparison.  With a limited sum to invest, you have to evaluate the probability of making a profit, the expected value and the risk involved for each investment alternative.  And, as with the dice, you hve the alternative not to play, which is 100% safe, but will not make you any money.

We make other kinds of decisions too, where the investment is not always financial:

• selecting a savings account (which will make you richest in the long term?)
• buying a house ( will prices fall or rise?)
• deciding which people to socialise with (who will turn out to be better company?)
• renting a film to watch (which will you enjoy the most?)

However vaguely or subconsciously, we are appraising cost, risk and expected value, with limited information about the future, all the time - even if the only cost is our leisure time, the only expected value a fleeting enjoyment, and the only potential loss a mild feeling of irritation.