Capital Asset Pricing Model(CAPM)

Assumptions of CAPM1. All investors aim to maximize economic utilities.

2. All investors make decision based on the return and standard deviation.

3. All investors have Homogenous expectation towards input factors that is used to make portfolio.

4. All investors can lend and borrow unlimited amount under the risk free rate of return.

5. Short selling is allowed.

6. Securities as highly divisible.

7. All securities are liquid, can be sold at current market price.

8. No transaction fee.

Assumptions of CAPM9.There is no inflation in the market.

10.There is no tax payable for investors.

11. All investors are price-takers

12. The capital market is in equilibrium.

Capital Market EquilibriumOccurs when there is no more incentive for investors to trade.

Assumptions under capital market equilibrium:

1.All investors will choose market portfolio.

2.Market portfolio contained optimized securities, efficient frontier.

Market PortfolioAB curve shows the market portfolio,

combination of risk and risk-free securities.

In equilibrium, all risk securities should be at market portfolio (M), so the market portfolio is perfectly diversified.

In practice market portfolio is only contained securities in one market (i.e. IDX), not all securities in the world.

Capital Market LineCML shows all the possible combination

of efficient portfolio, which consist of risk and risk free securities.

Premium risk shows the difference of expected portfolio with risk-free securities and market portfolio.

The slope of CML is the market price of risk for efficient portfolios.

Capital Market Line

Equation for Harga pasar dari resiko:

Securities Market LineDepict tradeoff between risk and expected return for efficient portfolio, but not for

individual securities

In portfolio, additional expected return happens because of additional risk from portfolio itself

In individual securities, additional expected return is because of additional individual securities risk which is determined by Beta

Beta determined the amount of additional expected return for individual securities with argument that for portfolio which is perfectly diversified, non systematic risk is gone

This argument is based on the assumption homogenous expectation (every investor will create perfectly diversified portfolio. leaving only Beta risk)

Securities Market LineBeta for market portfolio is 1

Securities which have beta <1 considered less risky than market portfolio risk

Securities which have beta >1 considered more risky than market portfolio risk

Securities which have beta = 1 is expected to have same expected return of market portfolio expected return

CAPM FormulaElton and Gruber (1995) introduce Capital Asset Pricing Model (CAPM)

This formula can be used to calculate the expected return from a portfolio or individual securities

RBR = Risk Free Rate (RFR)

βi = Beta

E(Rm) = Market Portfolio Expected Return

CAPM ExampleRFR = 9%;E(Rm) = 13%; βA = 1,3

E(RA) = 9% + (13% - 9%) . 1,3

= 9% + 5,2%

= 14,2%

To check whether the securities are undervalued or overvalued is by comparing the expected return with the real return

Example 2IHSGt: 2.400; IHSGt-1: 2.000; RFR: 8%

RRM = (IHSGt-IHSGt-1)/IHSGt-1 RA= (1.350-1.000)/1.000 = 35%

= 2.400-2.000/2.000 RB= (5.500-5.000)/5.000 = 10%

= 20% RC= (1.400-1.000)/1.000 = 40%

Securities A Securities B Securities C

Price at t Rp. 1.350 Rp. 5.500 Rp. 1.400

Price at t-1 Rp. 1.000 Rp. 5.000 Rp. 1.000

Beta 0,8 1,2 1,5

Example 2(Cont.)Real Return:

E(RA)= 8% + 0,8 (20%-8%)= 17,6%

E(RB)= 8% + 1,2 (20%-8%)= 22,4%

E(RC)= 8% + 1,5 (20%-8%)= 26,0%

Conclusion:

Securities A= Undervalued; Securities B= Overvalued;

Securities C= Undervalued

CAPM Model ExplainedMarket Portfolio Risk

Contribution of each securities towards market portfolio risk is depends on the return covariance with the market portfolio

BETA CALCULATIONBeta is the covariance return of individual securities

CAPM Model Explained (cont.)Market portfolio risk measured by standard deviation

Security risk contribution towards total portfolio risk contribution can be considered as a change of portfolio risk due to changes in proportion of the securities

Empirical Testing of CAPMCAPM Model can be tested if the model has been converted into ex

post model

Where:Ri.t = Return on asset i in period t

RBR.t = Risk Free Rate in period t

βi = Beta

Rm.t = Return on market portfolio in period t

ei.t = Error

The difference between Ex ante and Ex post Ex Ante

Theoretical model

Slope of Securities Market Line (SML) should be positive

Ex PostEmpirical model

Slope of Securities Market Line (SML) Should be 0 or negative

E(RM)

E(Ri)

M

RBR

0 1,0 Beta

1,0 Beta

M

RM

0

RBR

Ri

Empirical Testing of CAPM (cont.)

Predictions:Intercept δ0 is expected not differ significantly to 0

Beta is the only factor that explains return of security risk

.

Relationship between Return and Risk should be Linear

δ1 should be positive or the return on market portfolio must be higher than Risk-free Rate of Return

Results of testing the CAPM modelThe value of intercept is significantly higher than 0

The coefficient of beta has small value than return on market portfolio minus Risk-free Rate of Return

The coefficient of beta has positive value / δ1 > 0

Other factors (beside Beta) can explain the portion of securities returnP/E ratio (Basu 1977)

Firm-size (Banz 1981 and Reinganum 1981)

Dividend yield (Rosenberg and Marathe 1977, Litzenberger and Ramaswamy,1979)

Seasonality effect or January effect (Keim,1985)