Capital Asset Pricing Model

Definition:

One of the most simple and highly revered model in finance, Capital Asset Pricing Model (CAPM) is used to estimate the required rate of return on a risky asset.

Mathematical Representation:

It is given by a simple linear equation as:

E(R_a) = RFR + β [E(R_m) – RFR]

where,

E(R_a) = expected rate of return on a risky asset.

RFR = risk free rate

β = beta

E(R_m) = Expected market return

Post-mortem of the equation:

Equation states that expected rate of return on given risky asset E(R_a) is equal to the sum of risk-free rate (RFR) and beta(β) adjusted  market risk premium ([E(R_m) – RFR]).

Before dissecting the different components of CAPM, let’s first plot this on graph.

CAPM equation is that of a straight line (y = mx + c),

Where y = E(R_a),  c= RFR, x = β and m =  [E(R_m) – RFR]

                 

 Green line represents the CAPM equation. This line is known as Security Market Line (SML).           

Also note that when β = 1, then E(R_a) = E(R_m) and the portfolio is known as market portfolio.

Assumptions of CAPM:

• CAPM is based on REM (Rational Economic Man) concept of traditional finance. It assumes that all investors are rational and risk-averse, holding a diversified portfolio with an aim to maximize economic utilities.
• All investors have a portfolio which is a combination of market portfolio and the risk-free asset, adjusted to their risk-averse appetite.
• Unlimited lending and borrowing can be done at the risk free rate.
• Transaction, administrative and other overhead costs are zero.
• Most importantly, model assumes that expected return on a risky asset can be determined as a function of its systematic risk only.

Components of CAPM explained:  

• First component of CAPM is RFR i.e. risk free rate. It is, as the name suggest, the return that you can earn risk free. Though no asset is risk free but U.S. Treasury bills and bonds are generally used as a proxy for the risk free rate. RFR to be used depends on the duration of risky asset under consideration, using long term bonds for longer risky assets and so forth.
• Second component is E(R_m) i.e. expected market return: It determines the expected return of the market as a whole and can be based on past returns or expected future returns. There are various ways to determine expected market return.
• E(R_m) – RFR is also known as market risk premium i.e. how much did market as a whole return above the risk free rate.
• β i.e. Beta : This is the most crucial of components and measures the systematic risk of holding a risky asset.Basically risk can be divided into two components: Unsystematic risk and systematic risk. Unsystematic risk also known as idiosyncratic risk refers to risk associated with individual assets.Ideally, we can reduce our unsystematic risk by holding a diversified portfolio. However, systematic risk refers to the risk that is common to all securities i.e. market risk. This cannot be reduced by holding a diversified portfolio and hence investor must be paid for exposing himself/herself to this risk. β measures this systematic risk and thus is considered while calculating the expected return on the risky asset.
  
  If β > 1, it implies that asset is riskier than the market as a whole and thus E(R_a) > E(R_m)If β < 1, it implies that asset is less risky than the market as a whole and thus E(R_a) < E(R_m)
  
  β is defined by the formula:
                                                 
  where
  
  
  Cov(i,mkt) = covariance between the asset’s return and return on the market 
  σ_mkt^2 = standard deviation of market
  

  
  

  
  

  Thus β is the standardized measure of systematic risk.

Application of CAPM:

As explained, CAPM is basically used to calculate the expected return on any risky asset.

This is really helpful when evaluating if an asset is fairly priced, overvalued or undervalued.

Fairly Valued:

If E(R_a) = R , then the asset is fairly valued

Overvalued:

If E(R_a) > R, then the asses is said to be overvalued.

Undervalued:

If E(R_a) < R, then the asset is said to be undervalued.

Implications of categorizing an asset as fairly valued, undervalued or overvalued:

If an asset is overvalued, then sell (or short sell) it as it is expected to decrease in value.

If an asset is undervalued, then buy it as it is expected to increase in value.

If an asset is fairly valued, then buy, sell or ignore. Doesn’t really matter.

Problems with CAPM:

• One of the main issues with CAPM, as is with any traditional model, is the assumptions that investors are REM (Rational and Economic Men). Rarely are the investors rational and rarely does CAPM map perfectly in the real world.
• It assumes that risk of an asset is solely dependent on beta (market risk). All other factors are ignored.
• Unsystematic risk is assumed to be compensated by holding a well-diversified portfolio. Hardly this is the case.
• Assumes there is no taxes, transaction or any other overhead cost. Nothing comes for free.
• Assumes that RFR exists. Remember we use treasury bills as proxy for RFR. Nothing is risk-free in this world.

References:

https://en.wikipedia.org/wiki/Capital_asset_pricing_model

http://www.investinganswers.com/financial-dictionary/stock-valuation/capital-asset-pricing-model-capm-1125

http://www.investopedia.com/terms/c/capm.asp

CFA curriculum: Level I, Level II, Level III (Various books)