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FIN2101
BUSINESS FINANCE II Module 2
Module 2
Capital Asset Pricing Model
(CAPM) Student Activities
Student Activities
Reading Text, Chapter 6 (pp. 21021 only) Text Study Guide, Chapter 6 (part only) Study Book, Module 2 (inc. Appendices 2.1, 2.2 & 2.3)
Tutorial Work Tutorial Workbook, Self Assessment Activity 2.1 Text Study Guide, Chapter 6, T/F 9 & 10, MC 13 to 15, Problems 5, 7 & 8 Capital Asset Pricing Model
Capital Asset Pricing Model CAPM describes how prices of individual securities are determined.
Portfolio theory.
An asset’s return is equal to the riskfree rate plus a risk premium equal to the asset’s beta multiplied by the market risk premium.
Linear relationship between return and risk. Risk and Return
Risk and Return Return is a function of risk Higher risk warrants a higher return Return = Riskfree return + risk premium Risk
Risk
Total risk:
= unsystematic risk + systematic risk
= unique risk + market risk
= diversifiable risk + nondiversifiable risk Expected Return Single Asset
Expected Return Single Asset Risk Single Asset
Risk Single Asset
σk = ∑ (k
n i =1 i ∑ (k )  k × Pri n σk = i =1 2 i k n 1 ) 2 Expected Return & Risk of a Expected Return & Risk of a Portfolio
n kp = ∑ w j × k j
j=1 σ k p = w σ + w σ + 2w 1w 2 r1,2σ 1σ 2
2
1 2
1 2
2 2
2 Correlation Coefficient
Correlation Coefficient A measure of the relation between the returns on two securities.
Can be + or or 0.
Diversification is of greatest benefit in risk reduction when the correlation between the returns on the two securities is negative. Efficient Frontier
Efficient Frontier Holding the correlation coefficient constant, we could change the weights of the two assets in the portfolio.
We could then determine a number of expected risk and return coordinates for the portfolio and plot these in riskreturn space.
It is possible to derive a complete curve by simply varying the weights by small increments. Efficient Frontier
Efficient Frontier We could examine a number of twoasset portfolios and derive their curves by changing the weights of the assets.
From these the efficient frontier is derived.
The efficient frontier is the envelope curve of all of the individual curves. Efficient Frontier
Efficient Frontier Consists of only those portfolios of risky assets that give the highest possible return for a given level of risk.
Dominance principle.
Each investor will try to hold a portfolio on the efficient frontier.
Personal preference will determine where on the frontier. Indifference Curves
Indifference Curves Show the investor’s tradeoff between risk and return. The steeper the slope, the more risk averse the investor. The higher the indifference curve, the greater the utility. Efficient Frontier and Investor Efficient Frontier and Investor Utility All points along the efficient frontier are potentially optimal. Portfolio selection depends on risk tolerance. An investor will choose the portfolio that is tangent to the highest attainable indifference curve. Risk Tolerance
Risk Tolerance Conservative investors select portfolios at the left end of the efficient frontier. Aggressive investors select portfolios at the right end of the efficient frontier. Capital Market Line (CML)
Capital Market Line (CML) The efficient frontier is concerned with portfolios of risky assets.
A riskfree asset increases the investment options available: zero variance and a certain return zero covariance with any other asset no risk
New efficient frontier CML. CML
CML
Options are: 100% riskfree asset (10% return)
Combination of risky & riskfree assets
Through borrowing, an increased investment in risky assets Riskfree Lending
Riskfree Lending Purchase of the riskfree asset = riskfree lending. Such an investor would choose a point on the CML between RF and M. Riskfree Borrowing
Riskfree Borrowing Buy the risky portfolio with available funds and then borrow at the riskfree rate to acquire further assets.
Higher returns means higher risk.
Lie beyond point M on the CML. Market Portfolio M
Market Portfolio Contains all risky assets in proportion to their market value. It is a completely diversified portfolio, affected only by systematic risk (due to macroeconomic factors). Capital Market Line (CML)
Capital Market Line (CML) Represents all possible market investments proportionately.
The new efficient frontier (dominance principle).
Shows tradeoff between expected return and risk for all efficient portfolios.
Linear & positive relationship between risk & return. CAPM
CAPM When the market is in equilibrium, an asset is expected to provide a return commensurate with its systematic risk.
CAPM looks at an asset’s systematic risk in relation to the market as a whole.
Risk is the volatility of the asset’s returns relative to the volatility of the market portfolio’s returns. Characteristic Line
Characteristic Line We can plot the historical sensitivity of an individual asset’s returns to the returns on the market portfolio. The characteristic line is a line of best fit through the points. Beta
Beta The slope of the characteristic line is the sensitivity of the asset’s returns relative to the market returns and its measurement is called the beta coefficient.
Beta is a measure of an individual asset’s systematic risk relative to the market risk.
Beta of the market is 1.0. Beta
Beta bj = Cov ( k j , k m ) σ 2
km Sample Betas
Sample Betas
Company
Amcor
NAB
Coca Cola Amatil
BHP
CSR
Boral
Mayne Nickless
Coles Myer Beta
1.11
1.09
1.05
0.99
0.90
0.84
0.80
0.65 Source: Ross et al, Fundamentals of Corporate Finance, p.346. Portfolio Beta
Portfolio Beta
n bp = ∑ w j × b j
j=1 Security Market Line (SML)
Security Market Line (SML) SML is a graphical representation of the tradeoff between expected return and systematic risk, as measured by beta, for every asset, including inefficient portfolios.
Risk is labeled as beta, therefore beta can replace variance as the measure of portfolio risk.
Only interested in systematic risk. Security Market Line (SML)
Security Market Line (SML)
Called the CAPM and written for an individual asset
as follows: Required Return Security Market Line
Security Market Line Risk
Premium km
RF Riskfree
Return
β M = 1.0
1.0 Systematic Risk (Beta) Example of SML Calculations
Example of SML Calculations
R F = 6%; k m = 12%; b = 1
k j = 6 + 1(12  6)
= 12% SML Example (Continued)
SML Example (Continued)
b =1.5
k j = 6 +1.5(12  6 )
=15%
b = 0.5
k j = 6 + 0.5(12  6 )
= 9% Security Market Line (SML)
Security Market Line (SML) In equilibrium, all assets (single assets and portfolios of assets) will lie on the SML. An asset which plots above the SML is underpriced. An asset which plots below the SML is overpriced. Security Market Line
Security Market Line
Required Return Stock X (Underpriced)
Direction of
Movement Rf Direction of
Movement Stock Y (Overpriced)
Stock
Systematic Risk (Beta) Determination of the Required Rate of Return
Lisa Miller at Basket Wonders is attempting to Lisa Miller at determine the rate of return required by their stock investors. Lisa is using a 6% RF and a longterm market expected rate of return of 10%. A stock analyst following the firm has calculated that the firm beta is 1.2. What is the required rate of return on the stock of Basket Wonders? BWs Required Rate of Return
KBW = RF+ βj(KM RF)
KBW = 6% + 1.2(10% 6%)
KBW = 10.8%
The required rate of return exceeds the market rate of return as BW’s beta exceeds the market beta (1.0). Determination of the Intrinsic Value of BW
Lisa Miller at BW is also attempting to determine the Lisa Miller at BW is also attempting to determine the intrinsic value of the stock. She is using the constant growth model. Lisa estimates that the dividend next period will be $0.50 and that BW will grow at a constant rate of 5.8%. The stock is currently selling for $15. What is the intrinsic value of the stock? Is the stock over or underpriced? Determination of the Intrinsic Value of BW
= $0.50
10.8%  5.8%
5.8% = Intrinsic
Value $10 The stock is OVERVALUED as the The stock is market price ($15) exceeds the intrinsic value ($10). Implications of CAPM
Implications of CAPM All investors hold the aggregate market portfolio.
The market portfolio will be the optimal risky portfolio.
Investors can obtain a desired riskreturn position by combining the risky portfolio with borrowing/lending at the riskfree rate. Separation Theorem
Separation Theorem Investment is always made in the same risky asset portfolio.
The only difference among investors is the financing decision they make.
Division of investment and financing decisions is the ‘separation theorem’. CAPM Assumptions
CAPM Assumptions Wealth maximisation Risk and return are key factors Homogeneous expectations Identical time horizons CAPM Assumptions
CAPM Assumptions Free and information simultaneous access Riskfree asset No taxes and transaction costs Assets are marketable and divisible to Testing of CAPM
Testing of CAPM Is there a linear relationship between risk and return? Market portfolio Testing of CAPM
Testing of CAPM Stability of beta Conclusions
Conclusions Unrealistic assumptions.
Does not describe what has occurred and is therefore likely to be wrong.
Forecasting beta, the riskfree rate and the market rate is so difficult that it renders the model virtually useless. ...
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 Summer '11
 Qilei
 Finance, Pricing

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