Chapter 5 risk & return

 A measure of relative dispersion, useful in comparing the risk of assets with differing expected returns. The higher the coefficient of variation, the greater the risk.. Correlation,

Learning Goals:

 Understand the meaning of risk, return and risk

preferences.

 Measure the risk and return of a single asset.

 Measure the risk and return of a portfolio of assets.

 Explain beta and the CAPM model.

 Analyse shifts in the securities market line.

Fundamentals Of Risk

 Risk is defined as “the chance of financial loss”.

 Refers to the variability of returns associated with

a given asset.

Shareholder Specific Risks

Firm & Shareholder Risks

Fundamentals Of Return

 Return is defined as “the total gain or loss

experienced on an investment over a given period

 Calculated using the formula:

r t = C t + (P t – P t-1 ) [Equation 5.1]

P t-1 Where:

r t = Actual, expected or required rate of return

during the period t

C t = Cash flow received from the investment in the time period [t – 1 to t]

P t = Price of the asset at time t

P t-1 = Price of the asset at time t - 1

Fundamentals Of Return

Calculating Return

Risk Preferences

 Three Preferences:

compensate for taking higher risk.

greater risk.

change in response to a change in risk.

Risk Preferences

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Risk Assessment Of A Single Asset – Scenario Analysis

 Uses a number of possible return estimates to

obtain a sense of the variability among outcomes.

 Often uses the best, most likely [expected] and

worst returns associated with a given asset

 The best and worst outcomes are then used to

determine the range of the asset’s risk.

 Provides a more quantitative, yet behavioural,

insight into an asset’s risk.

 Measures the dispersion around the expected

value.

 The expected value of a return k [the most likely

return on an asset] can be calculated by:

Where:

r i = Return for the i th outcome

Pr i = Probability of occurrence of the i th outcome

n = Number of outcomes considered

Risk Measurement – Standard Deviation

 The higher the standard deviation the higher the

risk.

 Standard Deviation Of Returns σ r is calculated by:

[Equation 5.3]

 Also used to calculate risk on a portfolio of assets.

Risk Measurement – Standard Deviation

i n

Risk Measurement – Standard Deviation beta.xlsx

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Risk Measurement – Standard Deviation

 A normal probability distribution will always resemble a bell shaped curve.

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 A measure of relative dispersion, useful in comparing the risk of assets with differing expected returns.

 The higher the coefficient of variation, the greater the risk.

 Allows comparison of assets that have different

expected returns.

Risk Measurement – Coefficient

Of Variation

 Is calculated by:

[Equation 5.4]

Where:

CV = Coefficient of variation

σ r = Standard deviation of returns

r = Expected value of a return (most likely)

Which Asset Is Riskier?

 A portfolio is a collection of assets.

 An efficient portfolio is:

 One that maximises the return for a given level

of risk.

OR

 One that minimises risk for a given level of

return.

 A statistical measure of the relationship, if any,

between a series of numbers representing data of any kind.

 The degree of correlation is measured by the correlation coefficient.

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 Combining two assets with less than perfectly

positive correlations can reduce the total risk to a level below that of either asset.

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Correlation, Diversification,

Risk & Return

 The lower the correlation between asset returns, the greater the potential diversification of risk.

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Correlation, Diversification,

Risk & Return

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Returns From International

Diversification

 Significantly influenced by fluctuating exchange rates (both Australian and foreign)

 Work on the theory that fluctuations in currency

values and relative performance will average out over long periods and that an internationally diversified

portfolio will tend to yield a comparable return at a

lower level of risk than similar purely domestic

portfolios.

Capital Asset Pricing Model

 Total Risk contains Two Types Of Risk:

asset’s risk associated with random causes that can be eliminated through diversification.

Capital Asset Pricing Model (CAPM)

an asset’s risk associated with market forces that affect all firms, and cannot be eliminated through diversification.

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 Is a measure of non diversifiable risk.

 Is an index of the degree of movement of an asset’s return in response to a change in the market return.

 The majority of beta coefficients fall between 0.5 and 2.0

 The beta coefficient of the market β = 1.0

Capital Asset Pricing Model

(CAPM) – Beta Coefficient

Capital Asset Pricing Model (CAPM) – Beta Coefficient

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Market model

Y = a + bx

where y = return on a given share

x = return on the market portfolio Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX 2 -

(ΣX) 2 )

Capital Asset Pricing Model (CAPM) – Beta Coefficient

Capital Asset Pricing Model (CAPM) – Beta

Computing Beta Coefficient

 Are interpreted exactly the same way as individual asset betas

 Can calculated by:

[Equation 5.7]

Where:

w j = The proportion of the portfolio’s dollar value represented by asset j

β j = The beta of asset j

Capital Asset Pricing Model (CAPM) – Portfolio Betas

 Calculated by:

[Equation 5.8]

Where:

r j = Required return on asset j

R F = Risk free rate of return

β j = Beta coefficient for asset j

F

j R r R

 Referred to as the SML.

 Is the result of the CAPM being depicted graphically.

 Is always upward sloping.

 Reflects the risk return tradeoff.

 Reflects for each level of non diversifiable risk (beta) the required return in the marketplace.

Capital Asset Pricing Model

(CAPM) – Security Market Line

Capital Asset Pricing Model

(CAPM) – Security Market Line

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 Shifts in SML can result in a change in required return, even though risk might not necessarily change.

 SML Position & Slope are affected by:

 Affect the risk free rate of return.

 Result in parallel shifts in the SML.

 Result in changes to the incline of the SML

slope.

Capital Asset Pricing Model

(CAPM) – Security Market Line

 Based on historical data Does past data reflect

future patterns?

 Based on the assumption of an efficient market.

 Can we place much confidence on a model based on