Teach yourself to THINK in PROBABILITIES and in MULTIPLE SCENARIOS.

Without question, Buffett's success is tied closely to number.

"One of the advantages of a fellow like Buffett is that he automatically thinks in terms of decision trees and the elementary maths of permutations and combinations."  (Charlie Munger)

Most people do not.

It doesn't appear that the majority of investors are psychologically predisposed to thinking in multiple scenarios.  

They have a tendency to make decisions categorically while ignoring the probabilities.

Thinking in probabilities

Thinking in probabilities is not impossible:  it simply requires attacking the problem in a different manner.

If your investing assumptions do not express statistical probabilities, it is likely your conclusions are emotionally biased.

Emotions have a way of leading us in the wrong direction, especially emotions about money.

But if you are able to teach yourself to think in probabilities, you are well on your way to being able to profit from your own lessons.

Not often will the market price an outstanding business or any other outstanding businesses substantially below their intrinsic value.

But when it does occur, you should be financially (have the CASH)  and psychologically prepared (have the COURAGE) to bet big. 

In the meantime, you should continue to study stocks as businesses with the idea that one day the market will give you compelling odds on a good investment.


"To the Inevitables in our portfolio, therefore, we add a few Highly Probables." (Buffett)

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

Decision making: Risk, Probability, Impact, Subjectivity, Decision trees and Expected Value

You are invited to play dice games version A and version B.  In this game, you bet $1 on the throw of a dice.  Throwing a six wins a prize; throwing any other number means you lose your $1.

In version A of this game, a bet costs $1, but you can win $10.  Faced with this game, you have two alternatives - to play or not to play.  Once playing, there is nothing you can do to affect the outcome - so your decision on whether to play has to be made on the basis of the probabilities and impacts involved.  They are depicted on the decision tree here to help your decision.

http://spreadsheets.google.com/pub?key=te9MzyHoIN6EyuoHmfDxMaw&output=html

Because the situation is simple, the probabilities of the various possible outcomes can be objectively known.  There is no subjectivity over the probabilities.  The impacts, too, are fixed and clearly set out by the rules of the games (the prizes and the cost of playing).  If a choice is made to play, the probability of winning is 1 in 6 (0.166 or 16.6%) and the probability of losing 5 in 6 (0.834 or 83.4%).  If a choice is made not to play, risk is avoided (there is a single outcome that is certain) but there is also no potential benefit. 

In version B of the dice game, the stake and odds remain the same, but you can only win $5.  The alternative not to play remains.  In each case, we have to decide whether to play or not.  There is the alternative to walk away, but this offers no benefit.  Is it better to play or not to play?  Version A seems better than version B, but how much better?  Is B worth playing as well, despite the lower prize?  How can we make a decision about where to make an investment?  Most people can offer answers to these questions based on an intuitive, subjective grasp of probability and impact.  We make decisions all the time on this basis.  But for business decisions, we need to move beyond subjectivity whenever we can.  We need to quantify things wherever possible.


The concept of expected value (EV)

To compare different alternatives against each other in a quantitative way in order to determine whether a risk is worth taking, we can use the concept of expected value (EV).  The expected value of a risk is obtained by multiplying probability by impact for each possible outcome, and adding all the results together.  If a particular impact is negative, the value for that outcome is also negative. 

The table below shows the expected value calculation for playing version A of the dice game.  The expected value is 0.66.  Because this is a positive value, it indicates that the game is worth playing.

http://spreadsheets.google.com/pub?key=te9MzyHoIN6EyuoHmfDxMaw&output=html

In version B, because of the reduced prize (a variation in impact), the picture is different.  This is shown in the table also.  Because of the reduced prize, the expected value of version B is negative.  If you play it repeatedly, you will steadily lose money over time.

In this case, the alternative not to play, although it brings no benefit, has a higher expected value (zero) than playing (-0.17).  You are better off keeping your $1.

Expected value helps us ascertain whether a particular alternative is worth taking, based on our knowledge of probabilities and impacts.  But, unless the outcome of a decision is certain, expected value can only ever be used as a guide.

In version A, for example, the expected value of not playing is zero, and this is certain.  But if you decide to play, the only possible outcomes are winning $10 or losing your $1 - in other words, values of either +9 or -1.  An impact of +0.66 (the expected value) is impossible. 
And, while a positive expected value of 0.66 makes the game nominally 'worth playing', the outcome of playing is not certain.  You might still lose.

Conversely, the negative expected value of version B, while it indicates you should not play, doesn't necessarily mean you won't win if you do.  The possible outcomes are value of +$4 or - $1.  You might play once and win.  You might even play three times in a row and win all three times, although the probabhility of this is 0.0046 (or less than 1%).  Despite the negative expected value, a positive outcome remains possible.

The actual probability of realising the expected value as a result of a single decision is zero.  However, if you played version A 100 times, you would find the average value across those many decisions tending towards 0.66 - you would have around $166 in your pocket.  This would prove the accuracy of your initial calculation of expected value.

Calcuating or estimating expected value wrongly - or not wanting to calculate it at all - has serious consequences for decision making.  Consider the National Lottery.  Although the prize (potential upside) is enormous, the tiny probability of winning gives the game a negative expected value.  But the lure of the prize outweighs the rational considerations of probability, making people mentally distort probabilities (if they consciously think in those terms at all) and decide to take an illogical risk.  This is the essence of the appeal of gambling, and points the way towards the psychology of risk.

So, despite the name, we can never expect the expected value.  Some may ask, in that case, why use the concept at all?  The answer is to help in making decisions, rather than in predicting the future.  As we've seen, there are no facts about the future, only probabilities.  In this case, probabilities are known but a reliable prediction of the outcome remains impossible - the dice will decide!

We have already seen how, in most business decisions, the picture is clouded by subjectivity.  Not only is it impossible to predict the future, there will also be uncertainty over impacts and probabilities.

Expected value is calculated from probability and impact information or estimates.  Whatever subjectivity or imprecision is inherent in our probability and impact figures will feed through into expected values.  There are only as good as the information from which they are calculated.  Therefore, just as with probabilities, it is important to remember, and explain to others, when subjectivity is a factor.

Subjectivity and Impacts

The problem of achieving objectivity applies just as much to assessing impacts as it does to gauging probabilities.  It can be difficult to establish a basis for comparison, praticularly in the area of 'soft' impacts.  As with probabilities, the key is to express impacts numerically.  The commonest way to do this is in financial terms.

'Hard' impacts often lend themselves to quantification and comparison, making it relatively easy to express them financially.  For example, an interruption to the operation of a production line resulting from a power cut or a fire could be translated into likely impact on revenues or profits.

'Soft' impacts are much more difficult to quantify, but they can still be hugely significant for the business.  For example, falling revenues may result in disillusionment within the business - a negative cultural impact.  This may result in talented individuals leaving the business, which could lead to a self-perpetuating cycle of decline (a strategic risk).  Quantifying impacts financially helps to express the significance of 'soft' impacts in terms that everyone can understand, putting them on the same basis of credibility as 'hard' impacts.

As with probabilities, complexity also adds to subjectivity:

• range of impacts:  impacts can affect many different areas of the business, making it hard to gauge the total impact.
• interdependence:  one impact may result in another impact in a different area of the business
• lack of precedent:  the situation may be unprecedented, or the precedent may be far in the past, making it difficult to assess the likely impact today.

Subjective Probabilities are an unavoidable part of decision making

Subjective probabilities are an unavoidable part of business decision making. 

You often have to make an opinion on strategic issues facing your business.  For example, you may be setting the five-year plan for your business.  You would have to assess all the factors which could have a big impact of the industry in which you operate in.

The situation is very complex. Your partners have different views and may not reach agreement.  On top of that, other industry leaders are making their views and this may have an impact. 

All these complexity doesn't prevent you and your partner from forming a view - maybe nothing more than an instinct or a hunch - as to what is going to happen.  Perhaps, you both agree that it is "quite likely" that a certain factor will impact the industry in the next two years.  Since this is of strategic significance to the business, you will need to accomodate this in the planning.

As you and your partner put your thoughts down on paper, what exactly does "quite likely" mean?  You may think it means "almost certain", while your partner considers it means "fifty-fifty".  In other words, you think "quite likely" equals a probability of (say) around 95%, while your partner assumes it denotes a probability of around 50%.

How can these two views be brought closer together.  Perhaps, they could use a probability that is objectively knowable - such as the throw of a dice - for comparison.  Do you think that such and such a factor is more or less likely to occur than throwing a six?  If less, the probability is lower than 1 in 6 (0.166).  If more, the probability is higher.  By discussing the issue in these terms, you and your partner can move closer to a picture of probability that you both share - and one that you can communicate with some degree of confidence.  You can both use this information to help pin down this probability - combined with your own opinions, experience and intuition. 

Let's assume you and your partner agree on a probability of 75% that a certain factor will impact on the business within the next two years.  It is important to note that just because two people have agreed a figure, the probability hasn't become any less subjective.  Using numbers adds clarity and precision but does not necessary indicate accuracy.  In your written report, you and your partner will need to explain the facts and reasoning behind your probability calculations, and stress the fact that the probability remains subjective even though it has been expressed numerically.  (You might use a range, such as '70-80%')

Some decision makers may regard this as pointless - how can that help you make a decision?  If you can't know probability objectively, why waste time trying to quantify it?  The answer is that it doesn't help you make the decision, but it does focus attention on the objective basis (if any) for assessments of probability.  It forces you to bring your information, reasoning and judgements into the open, so that others can see them. 

In the above example, you and your partner are forced to reach a shared understanding of probability so that you can communicate it and also, to others in your report.  While this doesn't necessarily makes it easier for you to make strategic decisions, it does mean that whatever decsion you take will be based on the facts that are available - or draw attention to the need for more facts.  Expressing probability numerically is also likely to focus everyone's minds on the urgency of the issue, rather than letting them adopt whatever interpretation of "quite likely" suits their own values and priorities.

Another benefit is the potential for sensitivity analysis:  to assess how the impact of a particular risk changes with respect to changes in probability of a particular factor.  Bigger changes mean higher sensitivity.