Good and Poor Risk-Reward Ratios and their relationships to Expected Return

When the Risk-Reward Ratio is Good:
The Probability of Loss is Lower
The Expected Return is Higher

When the Risk-Reward Ratio is Poor:
The Probability of Loss is Higher
The Expected Return is Lower

http://www.centaur.co.za/investment_methodology/index.html

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

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.

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.

Using Decision trees to see how probability and impact relate to each other

We can use the simple example of a dice game.  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. 

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 game (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 16.66%) 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.


Decision tree for dice game version A:

Decision:  Play dice game with chance of winning $10?  Yes or No

NO
Decision ---->  Risky Event  ---> Possible outcomes ---->   Probability ----->  Impact

No   ----->  Nil ------>  Avoid risk, keep money in pocket ----> 1.0 (certain) ----->  Neurtral: spend ntohing, win nothing


YES
Decision ----> Risky Event ---> Possible outcomes ----> Probability -----> Impact


Yes ----->  Stake $1 on throw of dice ----> Number 6  ----> 0.166 (1 in 6) ----> Gain Spend $1 Win $10
or
Yes -----> Stake $1 on throw of dice -----> Number 1, 2, 3, 4, or 5  -----> 0.834 (5 in 6) ---->  Loss Spend $1 Win nothing


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

Understanding IMPACT of a decision

Probability is the likelihood that a particular outcome will occur.

Impact is the effect that a particular outcome will have if it does occur.

Impacts can be positive or negative.  We call positive impacts 'upsides' and negaive impacts 'downsides'.  A single decision may involve the potential for both upsides and downsides.

Considering impact helps us

• weigh up different possible outcomes against each other,
• to assess how bad they will be for the business (if they are downsides), or
• how much benefit they will realise (if they are upsides).

We can think of impacts as 'hard' and 'soft'. 

'Hard' impacts affect areas of the business such as:

• financial:  losing or making money; changing profit margins; changes in share price
• performance:  changes in turnover; changes in business volumes; problems with quality, or improvements; losing or gaining customers; growing the business or seeing it decline
• business continuity:  whether business operations can continue when problems arise; whether new demands, or peaks in demand, can be met; the availability of business-critical systems
• individuals and groups:  physical safety; financial status and reward; working conditions; workload; level of responsibility; status and authority; prospect for the future.

'Soft' impacts affect areas of the business including:

• reputation and brand equity:  how the business, its products or services and its actions in society are perceived in the wider world
• morale and motivation:  how people feel about working for the business
• faith in management:  whether people believe in mangement's abilities and vision for the future
• sense of community:  whether people identify with the business and its aims and fell part of the business's culture
• social standing:  people's sense of value or relevance to the business; their sense of authority or power.

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.

To measure risk we have to use probability

To manage risk, we have to be able to measure it, and to measure risk we have to use probability.  Probability is the quantitative language of risk and uncertainty.

The probability of an outcome is a number expressing the likelihood of it actually happening.  It can be a number between 0 and 1, where 0 indicates an impossible outcome and 1 a certain one, or it can be expressed as a percentage (a number between 0 and 100).

In some situations, probability is objective and factual.  For example, the probability of calling the toss of a coin correctly is 0.5 or 50%.  However, tossing a coin is a very simple event.  It is easy to use past experience and real-world knowledge to assess the probability of a 'heads' or 'tails' outcome. 

As situations become more complex, it becomes progressively more difficult to be objective about probabilities; they become more subjective.  Business situations are extremely complex, and therefore the probabilities involved are highly subjective. 

Because the decisions we make in business are so important, it is vital to try and pin down the probabilities involved, even though it may be impossible to achieve complete objectivity.  The more precision we can bring to the situation, the firmer the foundation on which we make a decision.  To move towards precision, we need to look at subjective probabilities.