©2012 McGraw-Hill Ryerson Limited 1 of 31 Learning Objectives 5.Describe and apply the techniques of certainty equivalents, simulation models, sensitivity.

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©2012 McGraw-Hill Ryerson Limited 1 of 31 Learning Objectives 5.Describe and apply the techniques of certainty equivalents, simulation models, sensitivity analysis and decision trees to help assess risk. (LO5) 6.Assess how a project’s risk may be considered in a portfolio context. (LO6)

©2012 McGraw-Hill Ryerson Limited 2 of 31 Portfolio Effect Risk inherent in an individual investment ( σ) is not enough. Impact of a given investment on the overall risk of the firm – the portfolio effect should also be taken into account. Overall risk depends on its relationship to other investments – the covariance or coefficient of correlation. LO6

©2012 McGraw-Hill Ryerson Limited 3 of 31 LO6

©2012 McGraw-Hill Ryerson Limited 4 of 31 Portfolio Equations Expected value: Covariance: Coefficient of correlation: Portfolio standard deviation: (13- 4) (13- 6) (13- 7) (13- 8) (13- 5) Portfolio standard deviation: LO6

©2012 McGraw-Hill Ryerson Limited 5 of 31 Portfolios  Covariance becomes more significant in a portfolio than variance –An individual investment might be quite risky itself but it may reduce a portfolio’s risk (standard deviation) if it has a negative coefficient of correlation with the other investments  In a portfolio with less than perfectly correlated investments risk is reduced –Unsystematic or unique risk is eliminated (to a large extent) –Systematic risk thus properly describes the risk-return relationship (leading to the CAPM) –Investors will price assets on systematic risk if diversification can be achieved LO6

©2012 McGraw-Hill Ryerson Limited 6 of 31 Measures of Correlation Coefficient of correlation shows the extent of correlation among projects Has a numerical value of between -1 and +1 Its value shows the risk reduction between projects: –Negative correlation (-1)  Large risk reduction –No correlation (0)  Some risk reduction –Positive correlation (+1)  No risk reduction Coefficient of Correlation  Coefficient of Variation LO6

©2012 McGraw-Hill Ryerson Limited 7 of 31 Table13-6 Measures of correlation LO6 Coefficient of CorrelationConditionExampleImpact on Risk Negative correlationElectronic components, food products Large risk reduction 0No correlationBeer, textilesSome risk reduction +1Positive correlationTwo airlinesNo risk reduction

©2012 McGraw-Hill Ryerson Limited 8 of 31 Table 13-7 Rates of return for Conglomerate, Inc., and two merger candidates LO6

©2012 McGraw-Hill Ryerson Limited 9 of 31 The Efficient Frontier Firm chooses combinations of projects with the best trade-off between risk and return 2 primary objectives of management: 1.Achieve the highest possible return at a given risk level 2.Provide the lowest possible risk at a given return level The Efficient Frontier is the best risk-return line or combination of possibilities Firm must decide where to be on the line (there is no “right” answer) LO6

©2012 McGraw-Hill Ryerson Limited 10 of 31 The Share Price Effect Firm must be sensitive to the wishes and demands of shareholders Aversion of investors to unpredictability (and risk) is confirmed by the fluctuations in share price of cyclical stocks compared to more predictable growth stocks Each company must analyze its own situation to determine the appropriate tradeoff between risk and return. LO6

©2012 McGraw-Hill Ryerson Limited 11 of 31 Figure Risk-return tradeoffs LO6