Chapter 3 Risk and decision making Flashcards
1.1 Introduction to risk and uncertainty
Investment appraisal faces the following problems:
- All decisions are based on forecasts
- All forecasts are subject to uncertainty
- This uncertainty needs to be reflected in the financial evaluation
Risk averse (assume in FM all investors are this) means investors demand an increase in return for an increase in risk or if two projects offer the same expected return, the lower risk option is preferred.
Uncertainty can be addressed by minimum payback period, prudent estimates of cash flows, assessment of best and worst outcomes and higher discount rates.
2.1 Expected values
Where a number of outcomes for a decision and probabilities can be assigned to each of them, then an expected value may be calculated. The formula is EV = SUM of px,
Where p is the probability of an outcome and x is the value of an outcome
2.2 Limitations of expected values
The limitations of expected values include discrete outcomes, subjective probabilities, ignores risk and not a possible outcome – so less applicable to one-off projects.
3.1 Sensitivity analysis
Sensitivity analysis asks what percentage change in an estimate leads to us changing our decision about the project. Sensitivity is the % age change in an estimate that gives an NPV of nil. Calculating sensitivity depends on which estimate you are looking at:
- Affecting cash flows (price, volume, tax rate). Calculated as NPV of the whole project / NPV of the cash flows affected by the change
- Affecting all other factors: the sensitivity to discount rate is the difference between the cost of capital and the IRR and the sensitivity to project life is the discounted payback.
3.2 Sensitivity and tax
Sensitivity = NPV of the whole project / NPV of the cash flows affected net of tax
Limitations of sensitivity analysis:
- Assumes variables change independently of each other
- Does not assess the likelihood of a variable changing
- Does not identify a correct decision
4.1 Predictive and prescriptive analytics
This uses historical and current data to create predictions about the future. Examples are linear regression models, decision trees and simulations.
4.2 Linear regression models
Linear regression models identifies factors associated with the change in the value of a key variable. The variable the business is trying to predict is the dependent variable and the factors which have an impact are called the independent variables. Can be useful 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. The advantages include
- Models being simple and easy to use
- Models can be used to predict the impact from changes in estimates
The limitations include:
- 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
A correlation occurs when there is a connection between two or more variables, correlation measures the strength of the relationship. Correlation does not mean that a cause-and-effect relationship exists. Using a spreadsheet function to calculate the correlation coefficient = CORREL(cell range for array 1, cell range for array 2)
Data outliers are abnormal results they can be removed from the data set, to not distort the overall results. The reason for the data outlier must be investigated otherwise it is possible to introduce data bias.
4.3 Data trees
Identify the impact of different decisions on the outcome of an investment. The advantage is it is simple to explain and logical and can be used to consider multiple decisions. The limitations are large decision trees, or many possible outcomes can become difficult to interpret.
The advantages are it is simple to explain, and it can be used to consider multiple decisions. The limitations are large decision trees, or many possible outcomes can become difficult to interpret.
4.4 Simulation
Simulation improves on sensitivity analysis by looking at the impact of many variables changing at the same time. Using mathematical modelling it produces a distribution of the possible outcomes from the project. There are three stages:
- Specify major variables, and their probabilities
- Specify the relationships between variables
- Simulate the environment
Simulation can assist with environmental risk analysis by giving more information about the impact of environmental costs on new ventures. The results of a simulation exercise will usually be a probability distribution.
The advantages are it provides more information about possible outcomes and their sensitivities, and it is useful for problems that cannot be solved analytically. The limitations are it does not identify a correct decision, it is time-consuming and complex without specific software, can be expensive and it requires assumptions to be made, which may be unreliable.
4.5 Prescriptive analytics
By combining predictive analytics with AI and algorithms, prescriptive analytics can be used to calculate the optimum outcome from a variety of business decisions. Examples include capital rationing decisions, replacement analysis and identifying the optimal balance of finance.
Advantages are it can consider multiple decisions and variables to identify optimum investment decisions. The limitations are 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.
4.6 Data bias
There are several reasons that a data set could include bias:
- Selection bias: sample selection does not represent the population
- Observer bias: researcher allows their assumptions to influence the observation
- Omitted variable bias: key data is not included in the analysis
- Cognitive bias: presentation of data may be misleading
- Confirmation bias: people see data that confirms their beliefs and ignore other items
- Survivorship bias: sample contains only items that survived a previous event
5.1 Statistical tools
Tools can be used to analyse the data for a project and provide more information to make a decision. In the exam the following could be used: mean, standard deviation and coefficient of variation.
- Mean: average of data set: =AVERAGE(cell range)
- Standard deviation: shows how far on average each result lies from the mean, lower the deviation the lower the variability which suggests the project has lower risk: =STDEV(cell range)
- Coefficient of variation measures the standard deviation as a percentage of the mean. The higher the percentage, the wider the dispersion of data around the mean. Equals standard deviation / mean x 100
- Normal distribution: frequency distribution that is symmetrical around the mean. 68% of data is one standard deviation from the mean, 95% is two standard deviations and 99.7% is three standard deviations.
5.2 Skewness
With a normal distribution curve, the mean = the median = the mode at the highest point of distribution. Some will be skewed and have the majority of values on the left- or right-hand side. In these sets of data, the mean is not representative of the data as a whole, making it difficult to analyse using statistics. Skewness is often indicative of bias in the data.
6.1 Diversification and the portfolio effect
Idea that risk can be reduced by diversification. Investors holding a single share will see the return fluctuate. If an investor holds second share to their portfolio it will fluctuate but differently to the first. The average return achieved will be more stable than the return on each share independently.
If investments return profiles differ to at least some degree, then risk is reduced. Initial diversification will bring about substantial risk reduction as additional investments are added. However, risk reduction becomes insignificant once 15-20 investments have been combined. Not all risk can be eliminated by diversification
6.2 Systematic and non-systematic risk
The risk a shareholder faces is in large part due to the volatility of the company’s earnings. This volatility can occur because of specific (non-systematic) risk due to company/industry specific factors or systematic risk with market wide factors such as the state of the economy.
Systematic risk will affect all companies in the same way. The specific non-systematic factors will impact each firm differently depending on their circumstances. By diversifying an investor can almost eliminate specific unsystematic risk but cannot alter the systematic risk of the portfolio.
