Every mistake is an opportunity to learn

Error is defined as an unintentional deviation from a goal, caused by an act or omission that is in principle avoidable.

Errors happen when we make decisions. 

• By improving the way we make decisions, we can try to prevent errors, or minimise their probability. 
• By improving the way we respond when things go wrong, we can try to manage errors, or minimise their impact. 
• We can also try to create positive impacts in negative situations, by taking the opportunities for learning that mistakes provide. 

Warren Buffett's Midas touch

The decisions that have made Buffett the second wealthiest man in the world have included investments in Coca-Cola, American Express, Gillette, The Washington Post and Wells Fargo, plus some major acquisitions in the fields of insurance, house building and building materials, clothing and furniture.  During 2003 Buffett, contrary to some market expectations, engaged in currency speculation against the dollar.  By the end of the year his company held some $12 billion in foreign currency.

Buffett's success is founded on information.  When, during the 1990s, undervalued stocks were becoming more difficult to find, Buffett turned his attention to corporate acquisitions.  His next field of operation, in 2002, was junk bonds - until prices rose.  The subsequent foreign currency operation built on the US trade deficit when foreign investors were flooded with dollars.

Buffett takes a long-term view and typically shuns debt.  During the dot-com boom he preferred to steer clear of high-tech stocks, his attitude appearing old-fashioned to many.  In the event, his preference for more traditional and easily understood firms and products bore fruit.  He had correctly gauged the low probability of dotcom stocks rising.  He likes to ask 'discomforting questions' to avoid biased decision making.

Buffett also understands the need to avoid fatal downsides.  He has said that he has 'never believed in risking what my family and friends have and need in order to pursue what they don't have and don't need'.

Responding to risks: Summary

There are several possible responses to risk, ranging from tolerating to eliminating.

The right response to risk depends on the specific situation and also our calculations of probability and impact.

Transferring and insuring against risk involve others in risks, to the benefit of the business; the trade-off is increased costs.

Managing risks well depends on sharing information, clear responsibilities and consistency of approach.

Responding to risks: Insuring risks

Insuring risks is similar to transferring them, but rather than asking another company to tkae action if a risk occurs, you ask them to financially compensate you for its occurrence.

As with transferring, the company will want payment for taking on the risk in this way.  This is familair concept from everyday life, where we have to insure our household goods, cars and mortgage repayments against a number of downside risks, from theft and accident to death.

Business also invest in many types of insurance, including public liability, employer's liability and so on.

Insurance is often a good response to operational risks.  It is particualrly appropriate for low-probability downsides with hugely significant impacts, such as a fire at the workplace.

Responding to risks: Transferring risks

Transferring is the concept of placing risks with those outside the business who are best placed to manage them. 

Typically, this means using another company to take on a business process that you do not wish to carry out in-house, or are unable to do yourself.  There are benefits in terms of reducing the probability and impact of downsides and also in-house effort in managing the risk, but there will be a cost - people will want paying for taking on risks.

Risks can be transferred in different ways:

• formally:  on a contractual basis (e.g. IT service agreement), or through some other written agreement
• informally:  through discussions and meetings, on a basis of trust
• tacitly:  through assumption, perhaps based on precedent or simply beliefs.

Tacit risk transfer is generally not beneficial - it often represents a situation where one party has wrongly assumed that the other one will take an action or respond to a situation.  To prevent problems like this, you need share all information on the risk with the potential transferee:  its nature, probability and likely impact (on both parties); what you will pay them to take it on, why you want to transfer it and so on.

Payment for taking on risks will be more realistic when there is frank and realistic discussion of probabilities, impacts and costs.  Lack of communication may prompt the party taking on the risk to overcharge in order to cover themselves against the unexpected, or factors tha have not been clarified.

Responding to risks: Hedging risks

Hedging means taking additional risks that offset other risks, so that if the downside impact of one risk occurs, it is (in theory) balanced by the upside impact of the other risk. 

An example would be betting an equal sum on both sides in a sporting fixture - whatever the outcome, you cannot lose.  In investment or business, a 'perfect' hedge (one where the different outcomes are perfectly balanced) is practically impossible. A contractor can partially hedge his material cost prices of his contract with an advance order with the manufacturer for future delivery.

Hedging isn'tjust an approach to business or investment risk.  We engage in many trivial hedging behaviours all the time in our everyday lives - in any situation where we wish to avoid the risk of commitment.  When we hedge in everyday life, we set up alternatives for ourselves that will minimise the negative impact on us if things don't work out.  Consider the planning of a Friday night out.  We might make tentative plans to go out with one group of friends, but remain open to other offers.  After all, a better offer might come along - with a higher probability of positive impact (more enjoyment).  We are 'hedging our bets'.

Responding to risks: Concentrating risks

Concentrating risks is the opposite of diversifying - it means deliberately 'putting all your eggs in one basket'.  The effect is opposite too:  it increases the severity of potential impacts, but reduces management overheads, variables, unknown factors and dependencies.

An example of concentrating risk would be assigning a single person to a project full time, rather than assigning a small team part time. 
The time and cost of running the project might well be reduced, and the project might well be reduced, and the project may be run in a more coherent way, but there is a risk that the key individual will move on, damaging the chances of delivery.

The equivalent in financial terms is investing heavily in one or two stocks or products that you believe are sound, rather than spreading risk around because you are less sure of your market knowledge.

Concentrating risk depends for its success on the skill and knowledge of decision makers.  With fewer chances to correct mistakes, people need to get it right first time.

Responding to risks: Diversifying risks

Diversifying is about 'spreading risk around' - reducing your potential exposure by not having all eggs in one basket.  It reduces potential negative impact, but this normally results in extra costs.

Diversification can be a good tactic where there are problems in keeping the risk 'in one place', perhaps because there is a big potential downside.  For example, printers are dependent on paper suppliers to keep their operations running.  By setting up many suppliers for this commodity, they make it more likely that they will be able to get cover from another supplier if one can't delviver, thus reducing the potential downside risk of running out of paper.  (They also reap a number of side benefits, such as the opportunity to benchmark the prices of different suppliers, gain information about suppliers, find out about different ways of handling their orders and transactions and so on.)

However, there's always a downside.  There will be more administrative work in handling a large number of suppliers, and more management decisions to be made about which one will be used in each case; is price the only factor, or is the commercial relationship important too?

Diversification is also a good strategy for managing financial risk.  Investment vehicles that give investors the chance to invest in a range of companies offer those with little stock market knowledge a way to invest with reduced risk of exposure to market volatility in comparison with direct investment in a singloe company.

The key to diversification is keeping the different risks as separate from each other as possible, or reducing interdependencies between them.  No amount of diversification will protect against a worldwide recession, but investing in different economies around the world will offset the risk of a downturn in any particular one of them.

In a project contex, diversification can improve the chances of success.  Suppose a project has a 0.8 (80%) probability of failure.  It follows that the probability of success is 0.2 920%) - not particularly good.  Perhaps it is a speculative research and development project aimed at creating a new product.

But what if we ran two such projects?  The probability of both failing is 0.8 x 0.8 = 0.64 (64%) .  And if we ran three, the probability of ALL THREE  failing would be 0.8 x 0.8 x0.8 = 0.512 (51.2%), making the probability of having at LEAST ONE success nearly 50% (0.488 or 48.8%).  As we add more and more projects, the chances of success in at least one case steadily increases.  With 20 projects, our chances of having one success are 0.99 (99%) - we would be almost certain to succeed in one of the 20 projects. 

Diversifying risk through multiple projects:

Probabiltiy of total failure -----  Probability of single success                          
Run a single project
80% (0.8) ---- 20% (0.2)
Run two projects
64% (0.8x0.8) ---- 36% (0.36)
Run three projects
51.2% (0.8x0.8x0.8) ---- 48.8% (0.488)
Run 20 projects
1% (0.8^20) ---- 99% (0.99)

This illustrates how diversification can improve the chances of success, although at a price.  Running 20 projects will be much more expensive than running one.  But it may be that 20 modest projects, each researching a different potential product, are a better way forward than a single 'all or nothing' project puttting lots of resource into a single product.

An important point to remember is that the 'winners' must pay for the 'losers' if you choose to go for diversification.  The business must be able to afford to take all these risks, with all their respective potential downsides, and be confident that there is no risk of bankruptcy as a result.

Responding to risks: Minimising risks

If you choose to minimise a risk, you accept that it can't be eliminated, but take action to reduce its probability or negative impact (or both).  Minimising probability means taking actions so that a negative outcome is less likely to occur; minimising impact means taking actions so that the consequences will be less severe if a negative outcome does occur. 

We can see this in action by considering our own lifestyle choices.  By choosing a healthy diet and exercising well, we minimise the probability of health problems in later life.  By taking out health insurance, we hope to minimise the impact if they do occur.  Clearly, we could do both these things - minimising both probability and impact as a result.  How much action we take to minimise a risk, and the kind of actions we favour, depends on our own priorities, plus (as always) our assessment of probability and impact.  If our past medical history suggested we were more at risk from health problems, we might be more motivated to take action.

A parallel from business would be typical responses to operational risks.  Employees should be protected from physical harm wherever possible (minimising probability), but the employer is also obliged to have systems in place to deal with injuries should they occur (minimising impact).

Another example of minimising impact is double redundancy in computer systems.  Here an entire duplicate system is created and maintained, so that it can take over in the event of malfunction.  This hugely reduces the potential impact (though not the probability) of crucial data systems going offline; there is of course a trade-off in terms of cost.  This is often the case: in general, the more you reduce impact, the more cost is involved.  The business might choose to instate a repair contract with an IT service company instead, but this would not provide the same reduction of impact as the double-redundancy system.

Responding to risks: Tolerating risks

Your assessment of probability and/or impact may lead you to the conclusion that is is acceptable to tolerate a risk.  Such a decision is likely to be based on one (or both) of these two perceptions:

• the probability of the downside is so low that it can be ignored
• the impact of the downside would be so insignificant that it can be ignored.

If you are satisfied that one or both of these is true, a decision to tolerate the risk may well be the right one.

By making the choice to tolerate a risk, you are basically saying that you will do whatever is necessary to recover from a downside when it occurs, but nothing to prepare for it in advance.  However, this decision clearly rests on your understanding of probability and impact.  If you cannot be certain of probability, you may not be on safe ground tolerating the risk of a downside.

We have seen how impacts can often be quantified in financial terms, so that they can be compared to each other.  If you tolerate a risk, the business needs to be financially prepared to sustain the impact of its occurrence.

For example, if there is a risk that one in every hundred units made in a factory will be defective, but changing the manufacturing process is prohibitively expensive, the risk may be tolerated.  But the business needs to be sure that the waste resulting  from this decision to tolerate a risk will not damage its profits.  A decision might be taken to increase the selling price of the item, or sacrifice some profit margin, to offset the cost of the risk occurring.

Responding to risks: Eliminating risks

Clearly, if a risk has potentially negative consequences, then eliminating it is the best alternative. Given the choice, we would like to live without the potential for downsides to occur.

In business terms, this is clearly the most desirable action to take - it reduces management effort both now and in the future if you don't have to worry about a particular risk any more.  However, this is seldom possible - few risks can be eliminated completely, and some risk is going to be present in nearly every business situation.,

The key to considering elimination is the risk profile.  As we've seen, any risk that involves a fatal downside is a strong candidate for elimination, since the occurrence of the downside, however low its probability, is totally unacceptable. 

We would not choose to play a dice game that might bankrupt us.  In business terms this might equate to changing manufacturing processes that endangered people's lives in some wqay.  However unlikely the outcome, it would not be acceptable simply to tolerate the risk. 

Eliminating a risk may involve doing things in completely new ways.  If significant business change is involved in getting rid of a risk, you may need to consider what new risks will be created as a result.

Responding to risks

Responding to risks - the actions you can take once you've identified a risk and understood its probability and impact.

There are usually risks that cannot be avoided in business, no matter what alternative we choose.  Our decisions therefore focus on how we will respond to them, rather than trying to avoid them.   Responses to risk will vary from business to business and from risk to risk, but they tend to fall into one of these categories:

• eliminating
• tolerating
• minimising
• diversifying
• concentrating
• hedging
• transferring
• insuring

Deciding which of these responses is appropriate in any given situation requires careful analysis of the risk in terms of probability, impact and potential outcomes (expected values).

Getting it right

Whatever approach you choose to the risks you face, there are central themes to risk management that have to be in place for it to be successful.

Effective decision making and risk management are based on understanding, information and consistency.  It is vital that everyone involved is working from a shared idea of the significance of the risks facing the business, the probability of them occurring and the actions that they need to take in order to minimise downsides (or maximise upsides).

Here are some questions to ask in key areas to assess your risk management capabilities:

understanding operational risk:

• are the risks that can arise in key business process understood?
• are the implications of choosing or creating particular new processes understood?
• are the impacts of operational risk understood, in terms of their immediate impact and also any potential impacts at higher levels?

understanding strategic risk:

• are decision makers aware of the strategic risks facing the business?
• are the implications of 'doing nothing' or continuing along the present course understood?
• has 'business as usual' been examined in the same way as a 'risky' new direction would be?
• have the risks implied simply by entering or remaining in a particular market been examined?

understanding probability:

• have probabilities been quantified in a consistent way, that allows for comparison?
• what evidence is there to support estimates of probability?
• where there is uncertainty, has this been understood and acknowledged by decision makers?
• is there shared understanding of the subjectivity involved in probability calculations?

understanding impact:

• have impacts been quantified wherever possible, to allow for comparison?
• is it clear where risks might impact on more than one area of the business?
• is there the potential for risks to have interdependencies, making the occurrence of two or more risks together more significant?
• are the different levels of impact understood (operations, strategy, financial, cultural)?

information:

• documenting:  how will risks, responses and results be documented?  what proceducres will be used for recording the actions taken to manage risks and their results?
• sharing:  how will information on risks and the success (or otherwise) of particular response be disseminated throughout the business, to avoid duplication of effort?
• communicating:  who owns key information? who does it need to reach in order to support decisions on risk? what are the best media, formats and techniques for communicating?

clear roles and responsibilities:

• whose responsibility is each risk? who 'owns' it by default?
• who has enough authority and/or information to take a decision on how risks will be managed?
• who will take action to manage the risk?  who will become its new 'owner'?

reporting and monitoring:

• who needs to know what, and when?
• what is the best medium or channel to provide information on risks, such that those who need to take decisions have the information they need in a format they will find conducive?

consistency of approach:

• if similar risks occur in different parts of the business, is the response the same?
• could risks easily be aggregated across the business if this kind of concentration brought benefits?

consistency of analysis:

• where possible, are risks assessed using standard, objective criteria, or at least those that are agreed by all within the business?

consistency of tools and techniques:

• where decision-making tools are used, are they used in a consistent way across departments and teams?
• is there a genuine shared perspective on risks that affect different groups?

consistency of terminology:

• are risks described in terms that allow meaningful comparison and evaluation across the business?
• are common terms used with the same sense throught the business?
• are there any aspects that need to be quantified, or made less subjective, to allow for more focused discussion between those involved?

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

It's important to remember that people are the real decision makers.

Tools and techniques for decision making:  Means, not ends

However you go about making decisions, it's important to remember that people are the real decision makers.  Tools and techniques such as decision tress help to generate insight into a problem, stimulate communication and build a shared understanding of it, but they cannot take the decision for you.  In the last analysis, business decisions are about people - in every sense. 

Our favoured courses of action often flow more from our own values than from what is objectively 'right' in a situation.  Our estimates of probability are similarly subjective.  And in assessing impact, we are likely to be highly subjective too, perhaps concentrating on those areas of downside or upside that affect us most directly. 
The danger of using models such as those discussed in the previous postings is that they can give the illusion of objectivity.  Writing things down and analysing them is important, but the main benefit of doing so is to bring clarity to a decision, rather than precision.

We have to remember that tools and techniques are only as good as the information we put into them.  They are dependent on the extent and accuracy of information available at the time the decision is taken.  No matter how we present or analyse the information we have, we cannot add to it or make it any more reliable than it already is.  All we can do is aim for a shared sense of what we know and what we don't know, to build an informed consensus for particular courses of action.

Only people can build a bridge from the information that is available to a decision that can be taken forward.


Tools for risk assessement: and decisions making:
Probability
Subjective probabilities
Impact: hard and soft
Decision trees
Expected value
Fatal downsides
Life decisions
A business decision
Break-even analysis
Risk profiles
Probability/Impact matrix

The Information Trade-Off

Obtaining more information can help improve the quality of decisions by providing more detail about impacts and reducing subjectivity over probabilities.  It also helps to build up awareness of other alternatives that could be taken.  In general, it is a given that seeking more information will be beneficial to decision makers, having the general effect of reducing the level of uncertainty involved in a decision, and making it more likely that the outcomes of particular decisions will provide opportunities for learning.

However, there is a trade-off to be made.  Decisions usually have to be taken within a particular timeframe, and getting more information takes time.  It can also cost moneuy.

Both of these have implications for the level of extra effort that goes into facilitating more informed decision making.

The decision makers can reduce subjectivity by researching what is going on in various areas.  As they learn more and more, the probability that they are assessing becomes less and less subjective.  In the end (in theory at least), they can arrive at an objective probability.  However, there are some important issues facing them:

• getting information takes time:  the report must be submitted at a given deadline, even if they havent't pinned down the probability of the event occuring.
• gettting information costs money:  doing research will use up the resources of the business; you have to decide how much investment in information to support decision making is appropriate; this means assessing how sure you can be of the information you do have, and how much more certainty can be achieved for a reasonable cost
• situations change over time:  as you collect information to help you make a decision, the context or nature of the decision may be changing; there may be a limit to the accuracy you can achieve.

Inevitably, decisions have to be made with limited information.  Before you make a decision, you have to decide whether the information at your disposal is sufficient to make the decision, or whether you are going to make an investment (in terms of time or money, or both) in getting more information - and how this might affect the nature of the decision itself.  (You also need to guard against certain psychological traps.)

Management actions feed into decisions and affect their outcomes, whether this is in the form of considering decisions for longer, obtaining more information or just bringing different personal perspectives and experience to bear on the decision.  There will always be uncertainty involved, but by putting time and effort into decision making, its negative effects can be minimised.  In many decision situations, there is a 'third way' - the choice not to follow one of the branches on the tree, but to invest more effort in refining the picture of the decision before it is taken.

This poses interesting questions:

• how much is your time worth?
• what potential downside of this decision would you be prepared to accept if you could spend the time thinking about another issue instead?
• what potential upside do you regard as being a good 'purchase' to make with your time?

Up to this stage, you have acquired the knowledge you need to assess whether simple games of chance are worth playing.  Business decisions are much more complex and subltle than this, and you will never reach a point where you 'know everything', as in the dice game.  The issue is how much time to put into making a decision, and whether to put additional resource in obtaining more information before making the decision. 

In the end, this is likely to be a judgement call.  While time can be quantified and given a nominal cost,k the benefit to be obtained from it is likely to be very difficult to quantify.  In fact, until you actually invest the time, you cannot know how beneficial the information you gain will be.  We have to deal with this contradiction every time we take a business decision.

Probability/impact matrix to compare importance and urgency of one risk relative to another.

Probability/impact matrix


Having gauged the probability and impact of a number of risks, you can use the probability/impact matrix to compare them by assessing their importance or urgency relative to one another.  This diagram shows some risks that many of us face in our working lives, by way of illustration.  http://spreadsheets.google.com/pub?key=t5huetUWENmggchcXyeL9MQ&output=html

As with the other tools in this section, the matrix functions as a starting point for decision making.  It's a good way to display or share information on a number of risks facing the business, perhaps to form the basis for a meeting.  It might be possible to compare the different risks to each other, perhaps in order to highlight situations where disproportionate effort is being put into managing a particualr risk that is unlikely to occur, while another risk that is far more likely is being neglected.  Where risks are only expressed in verbal terms, there is a tendency to concentrate on those that sound worst rather than those that really do present the most likely or severe downside to the business.  The matrix can be used to help prioritise actions or focus efforts where they will have the most beneficial effect. 

As with the other tools, it is important to remember that the probability/impact matrix is only useful in proportion to the accuracy of your own assessments of probability and impact.  You only get out of it what you put in.


Tools for risk assessement:
Probability
Subjective probabilities
Impact: hard and soft
Decision trees
Expected value
Fatal downsides
Life decisions
A business decision
Break-even analysis
Risk profiles
Probability/Impact matrix

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.

Fatal downside and Wealth effect

Although the overall expected value of dice game version A is positive, there is one situation in which you should not play it - when the potential downside would be fatal or disastrous for you.

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

If you had just $1 in your pocket, played the game once, and failed to throw a six, you would be bankrupt.  The positive expected value of the game would be no help to you, since you would be unable to play any more - a fatal downside would have occurred.  In other  words, it is not enough just o look at the expected value of a decision.  The probability of a fatal or disastrous worst-case scenario has to be considered too. 

The presence of a fatal downside might temper your enthusiasm for a decision with a positive expected value, perhaps encouraging some kind of trade-off between expected value and the potential for exposure to a fatal downside.  You might be better finding another dice game perhaps a version that cost 10 cents to play, with a prize of 50 cents.  This would have the advantage of allowing you to stop playing before you went bankrupt, should you hit a bad losing streak.

By doing this, you would be spreading the risk around rather than going for an 'all or nothing' risk- trading off a better risk profile for a lower expected value.  (This approach to managing risk is known as 'diversifying'.)

In business terms, this translates into considering whether the downside of a risk, if it occurred, would result in bankruptcy or any situation from which the business could not recover.  The possibility of this, however remote, would have to be taken into account when contemplating a risk with positive expected value.

The fact that fatal downsides in investment loom much larger for smaller companies results in the 'wealth effect' - the relative ease with which larger companies can accumulate wealth.  They can take investment risk with positive expected values but serious potential downsides, because the fear of bankruptcy is more distant for them.  And the more positive-value decisions they take, the more money they accumulate and the more risks they can tolerate in their investments.  They can also afford to take more risks when considering and trying out new directions.  Individuals can also exhibit the wealth effect:  people with more cash saved up can afford to take bigger risks with their careers, perhaps allowing them to achieve greater successes.

It is the nature of know risk probabilities that the longer the run of risk taking, the closer one gets to the delivery of expected values.  This is how gambling becomes a science - with deep enough pockets (the wealth effect) and enough time, pay-offs come to reflect odds.  It is in the short run that 'luck' brings fortune or disaster.

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.