Capital Asset Pricing Model

Capital Asset Pricing Model Capital Asset Pricing Model which is based on the Capital Market Theory deals with how a risky asset is priced in competitive or Efficient Capital Market. Capital Market theory is extension of portfolio theory of Markowitz. It was the existence of risk free asset which leads the development of modern capital market theory. Capital Asset Pricing Model helps investors to determine the required rate of return of a risky asset. An efficient capital market provides investors increasing return for increasing risk.

Assumptions  Investors make investment decisions solely on risk and return assessment.  The purchase or sale of a security can be under taken in infinitely divisible units.  Investors can borrow or lend any amount of money at risk free rate of return.  The purchase and sale by one investor can not affect the price of the security.  All investors have homogeneous expectations, i.e., they estimate identical probability distributions for future rates of return.  There is no tax or transaction cost in buying or selling assets.  Investors can short selling any amount of shares without any limit.

 Expected Return of a Risky Security-

E ( Rit ) = α i + β i X t

If alpha is 2, beta is 1.5 and Sensex is expected to give 2 percent return, then the expected return of the stock will beE(R)=2+1.5*2 =5%

 Expected Return of Portfolio-

R p = wi E ( Rit )

 Required Rate of Return of a Risky SecurityThe required rate of return of a risky asset is that return which investors expect or he should get by holding this risky asset.

Ri = R f + βi [ E ( Ri ) − R f ] If risk free return is 5%, return on risky security is 6%, beta value of the same security is 1.20, the required return will be.

=5+1.2 [6-5] or 6.2 %

 Portfolio Return when portfolio includes both risky and risk free assets Portfolio Return is the aggregate of weighted average return of risky securities and risk free securities in the portfolio.

E ( R p ) = wR m + (1 − w) R f If w =1, total fund is invested in risky portfolio. If w <1, Partial amount of total fund is invested in risky portfolio and partial amount of fund is invested in risk free portfolio. If w > 1, Investors is borrowing at the risk free rate and investing in his portfolio.

TB’s (70 m) Income Portfolio (100 m) Govt. Bonds (30 m) Balance Fund (200 m)

Reliance En. (20 m)

Growth Portfolio (100 m)

ABB (20 m)

ONGC (10 m) TISCO (50 m)

 Risk of Individual Risky SecuritiesTotal Risk = systematic Risk (Market Risk) + Unsystematic Risk (Non Market Risk)

σ =β σ 2 i

2 i

2 Xt

+e

2 it

 Portfolio Risk Portfolio risk is the aggregate weighted average risk of individual security in the portfolio. N N      2 2 2 2 2 σ p =  ∑ ( wi βi ) σ X  + ∑ wi ei    i =1   i =1

 Portfolio Market Risk Portfolio Market Risk is the aggregate of weighted average market risk of individual security in the portfolio. N

βp =∑ wi βi i= 1

A high beta value portfolio is considered high risky portfolio since the return of this portfolio is highly integrated with the return of market. Beta which is measurement of market risk of portfolio can be calculated by regressing the return of a security with the return of some index. Symbolically it can be written as

βi =

n∑ XR − ∑ X ∑ R n∑ X − ( ∑ X ) 2

2

 Capital Market Line A capital market line indicates the trade off between investors’ portfolio risk and portfolio return. Investors would be ready to take extra risk only when they will expect extra return.

 Security Market Line A Security Market Line exhibits the various combination of portfolio market risk and portfolio return. In an efficient capital market, investors want increasing return for increasing risk. They will be ready to bear extra market risk only when they will extra risk premium. SML facilitates the investors to determine the required rate of return for given level of market risk.

Arbitrage Pricing Theory Arbitrage Pricing Theory was developed by Stephen Ross in 1976. APT outlines that several systematic factors affect a security return. It recognizes the impact of several systematic factors separately. These factors are inflation, industrial production, movement in the interest rate.

E ( R) = α + β 1 X 1 + β 2 X 2 + β 3 X 3 + .....β i X i + e E ( R) = α + β ik fik + e • Expected Return on Risky Security • α Required return • βik Security Sensitivity to change in the systematic factors. • fik Return on systematic factors. • e Unsystematic factor associated to the security.