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FM > Risk and decision making > Flashcards

Risk and decision making Flashcards

1
Q

Problems affecting investment appraisal

A

All decisions are based on forecasts

All forecasts are subject to uncertainty

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2
Q

Distinction between risk and uncertainty

A

Risk: quantifiable, where probabilities are known (e.g. a roulette wheel)

Uncertainty: unquantifiable – outcomes cannot be mathematically
predicted (most business decisions)

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3
Q

Risk profile to assume investors have in FM

A

Rational and risk averse

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4
Q

Risk averse definition

A

Investors demand an increase in return for an increase in risk or

If two projects offer the same expected return, the one with the lower risk is
preferred.

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5
Q

Practical methods of incorporating uncertainty into investment valuations

A

Sensitivity analysis

Minimum payback period

Prudent estimates of cash flows

Assessment of best and worst outcomes

Higher discount rates.

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6
Q

Expected value formula

A

∑px

P = probability
X = Value

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7
Q

A way of presenting uncertain vents following from eachother

A

Tree diagram

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8
Q

Limitations of calculating expected values

A

Discrete outcomes

Subjective probabilities

Ignores risk

Not a possible outcome, so less applicable to one-off projects.

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9
Q

What does sensitivity analysis do?

A

Works out the % change of a certain estimate that would change the decision on a project

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10
Q

Sensitivity analysis: What is sensitivity?

A

The % age change in an estimate that gives an NPV of nil

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11
Q

Sensitivity analysis: How to calculate for: Factors affecting cash flows

E.g. price, volume, tax rate

A

NPV of whole project / NPV of cash flows affected by change

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12
Q

Sensitivity analysis: How to calculate for: Sensitivity to discount rate

A

Difference between the cost of capital and the IRR

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13
Q

Sensitivity analysis: How to calculate for: Sensitivity to project life

A

Discounted payback

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14
Q

Sensitivity analysis: How affected by tax

A

Ensure NPV of factor selected is taken net of tax:

NPV of whole project / NPV of cash flows affected net of tax

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15
Q

Limitations of sensitivity analysis

A
  1. Assumes variables change independently of each other
  2. Does not assess the likelihood of a variable changing
  3. Does not identify a correct decision
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16
Q

What are predictive analytics?

A

Predictive analytics use historical and current data to create predictions about the future.

Examples include:
Linear regression models
Decision trees
Simulations

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17
Q

What are linear regression models?

A

Linear regression is a statistical technique that attempts to identify the factors that are associated with the change in the value of a key variable (e.g. a project NPV).

The variable that the business is trying to predict is called the dependent variable (e.g. sales growth), and the factors that have an impact are called the independent
variables (e.g. time/seasonality).

Regression analysis can be useful in investment appraisal to identify a set of factors that have a strong link to the returns from a project and can be expressed mathematically. The link can be determined using one independent factor or multiple independent factors (multiple regression analysis). This would also be useful for sensitivity analysis, as it can demonstrate where changes will impact the NPV.

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18
Q

Linear regression models: Advantages

A

Simple to use

Easily explained

Can be used to predict the impact from changes in estimates (e.g. sales volumes being higher than predicted)

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19
Q

Linear regression models: Limitations

A

There will not always be a linear relationship between variables and
outcomes

Linear models may identify spurious relationships as they do not consider the
difference between correlation and causation

Will be less meaningful if the data collected is inaccurate.

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20
Q

How to calculate the correlation coefficient?

A

Excel formula

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21
Q

Decision trees: What are they? Advantages? Limitations?

A

Decision trees are a predictive analytics technique that can be used to identify the
impact of different decisions on the outcome of an investment.

Advantages
Simple to explain and logical
Can be used to consider multiple decisions.

Limitations
Large decision trees, or many possible outcomes can become difficult to
interpret.

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22
Q

Simulation: What is it?

A

Assessing the impact of multiple variables changing at the same time.

Produces a distribution of the possible outcomes.

(Simulation can also assist with environmental risk analysis by giving more information about the impact of environmental costs on new ventures.)

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23
Q

Simulation: Three stages

A
  1. Specify major variables, and their probabilities
  2. Specify the relationships between the variables
  3. Simulate the environment
24
Q

Simulation analysis: Pros and cons?

A

Advantages
Provides more information about the possible outcomes and their
sensitivities
Useful for problems that cannot be solved analytically.

Limitations
Does not identify a correct decision
Time-consuming and complex without specific software
Can be expensive
Requires assumptions to be made, which may be unreliable.

25
Q

Prescriptive analytics: What is it? Pros? Cons?

A

Combining predictive analytics with Artificial Intelligence and algorithms,

Examples include:
Capital rationing decisions
Replacement analysis
Identifying the optimal balance of finance.

Advantages
Can consider multiple decisions and variables to identify optimum investment
decisions.

Limitations
Creating reliable models is complex and requires specialist data science skills
The reliability depends on the reliability of the data that they use and the ability
to predict the future based on past events.

26
Q

6 data biases:

A
  1. Selection bias – sample selection does not represent the population
  2. Observer bias – the researcher allows their assumptions to influence the
    observation
  3. Omitted variable bias – key data is not included in the analysis
  4. Cognitive bias – the presentation of data may be misleading
  5. Confirmation bias – people see data that confirms their beliefs and ignore other
    items
  6. Survivorship bias – the sample contains only items that survived a previous
    event.
27
Q

3 statistical tools used to analyse the data from a project

A
  1. Mean
  2. Standard deviation
  3. Coefficient of variation
28
Q

Mean: How to calculate

A

Formula

29
Q

Standard deviation: How to calculate

A

Formula

30
Q

Standard deviation: What does it show?

A

How far on average each result lies from the mean

The lower the deviation, the lower the variability, which suggests the project is lower risk.

31
Q

Coefficient of variation: How to calculate?

A

(Standard dev / mean) X 100

32
Q

Coefficient of variation: What does it measure?

A

The standard deviation as a percentage of the mean.

33
Q

Coefficient of variation: Benefit compared to standard deviation

A

Better comparability

34
Q

What is a normal distribution?

A

A frequency distribution that is symmetrical around the mean.

35
Q

Normal distribution: The rule

A

In a normal distribution 68% of the data is within one standard deviation above / below the mean.

In general, 95% of the data lies within two standard deviations from the mean.

99.7% lies within three.

36
Q

Are many distributions close enough to a normal distribution to be treated as one without significant loss of accuracy?

A

Yes

37
Q

What is skewness?

A

With a normal distribution curve the mean = the median = the mode at the highest point of distribution.

Some distributions however will be skewed and have the majority of values on the right or left-hand side. In these sets of data, the mean is not representative of the data as a whole, making it more difficult to analyse using statistics.

Skewness is often indicative of bias in the data.

38
Q

Portfolio effect: When does diversification make risk reduction become more insignificant?

A

15 - 20 investments

39
Q

What sort of risk isn’t eliminated by diversification?

A

Systematic risk (market risk)

40
Q

Where does the risk a shareholder faces largely come from?

A

The volatility of the company’s
earnings

41
Q

2 factors affecting volatility?

A
  1. Specific (or non-systematic) risk
    company/industry specific factors

2. Systematic risk
market wide factors such as the state of the economy

42
Q

Implications for management of the fact that most shareholders already have diversified portfolios

A
  1. In estimating risk, only need to compensate shareholders for systematic risk
  2. Don’t try and reduce risk by diversification
    (Already done)
43
Q

What is the Capital Asset Pricing Model (CAPM)?

A

A way of estimating the rate of return that a fully diversified equity shareholder would require from a particular
investment.

44
Q

How does CAPM basically work?

A

By considering the level of systematic risk of the investment compared to average

45
Q

The CAPM equation

A

Rj = Rf + ß (Rm – Rf)

Rj = required return from an investment

Rf = risk free rate
assumed to be the rate on Treasury Bills

Rm = average return on the market

(Rm – Rf) = equity risk premium

ß = systematic risk of the investment compared to market and therefore amount of the premium needed.

46
Q

When is CAPM often used?

A

The CAPM equation is commonly used to find the required return from a project in situations where the project has a different risk profile from the company’s current business operations.

47
Q

When are shares desirable in relation to CAPM?

A

When returns from the shares are higher than the CAPM return

48
Q

Other name for when returns from the shares are higher than the CAPM return

A

Positive alpha value

49
Q

What is alpha value?

A

The difference between the current return and the CAPM return

50
Q

Issue with buying shares with positive alpha value?

A

Likely to be a short-term issue, as the additional attraction of these returns will cause the share price to increase and hence the returns will be more reflective of the CAPM return

51
Q

Benefit of CAPM

A

Simplicity

52
Q

Problems with CAPM

A

1. Estimating Rm:
In practise this is usually done using historic rather than expected future returns.

2. Estimating Rf:
Gilts are not risk free, and returns on gilts will vary with the term of the bond.

3. Calculation of beta:
Betas are calculated using statistical analysis of the difference between the market return and the return of a particular share or industry. There is plenty of research to show that this is too simplistic a way to estimate risk, and that
risk premiums are made up of multiple different factors rather than just one single ‘market’ factor.

  1. Takes account of systematic risk
    only, and therefore assumes that shareholders are fully diversified
53
Q

Alternatives to CAPM

A
  1. Arbitrage Pricing Theory (APT)
  2. Bond yield plus premium approach
  3. Dividend valuation model
54
Q

Arbitrage Pricing Theory (APT)

A

This is similar in concept to the CAPM in that it adds a premium to the risk free rate, but rather than just a single premium, it divides the premium down into lots of bits.
i.e. Return = risk free rate + (beta 1 × premium for factor 1) + (beta 2 × premium for factor 2) …etc.

The problem is then to decide what the bits are! (i.e. which factors affect the risk premiums). Different authors have suggested different things such as inflation, level of industrial output, interest rates, size of the company etc.

55
Q

Bond yield plus premium approach

A

Rather than using the risk free rate as a starting point, this method uses the rate of interest the company is able to borrow at as the starting point. The logic is that the risk of the company will be reflected in its borrowing rate. Then a fixed premium is added to reflect the fact that equity is more risk than debt.

i.e. Return = Companies borrowing rate + fixed premium

56
Q

Dividend valuation model

A

Rather than trying to estimate from scratch what return SHOULD be achieved on a share due to its risk, this method takes a completely different approach.

By looking at the predicted future dividends on a share compared to its share price, we can measure what return is ACTUALLY being achieved. If we assume that the market is perfectly efficient, then this will also be the return that SHOULD be achieved to compensate for risk.

57
Q
A

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