## Tuesday, August 21, 2012

### CAPM

1.    Introduction
The Capital Asset pricing model, most commonly referred to as CAPM. According to the survey conducted among the most successful US enterprises, 73-85% of the respondent claims to use CAPM as their preferred methodology (Desai, 2005). Thus, CAPM is widely used today to estimate the cost of equity capital. William Sharpe and John Lintner won Nobel Prize in 1990 for their contribution towards CAPM theory. The CAPM theory is built on Markowitz theory of mean- variance portfolio model and forms the basis of modern portfolio theory.

# 2.    CAPM

Markowitz mean- variance analysis refers to the theory of combining risky assets so as to minimize overall risk of the portfolio at desired level of return. The Markowitz theory is based on three assumption i.e. all investors are risk averse and they minimize risk for desired level of expected return or demand additional return for additional risk, all parameter of individual asset like expected returns, variance and covariance are known thereby all investors have same expectations of all asset parameter and there are no taxes or transaction cost.

Sharpe and Lintner add two key assumptions to the Markowitz model to derive CAPM i.e. all investors are price takers i.e. individual buy and sell decision does not affect asset price and  investors can borrow and lend at risk free rate and unlimited short- selling is allowed.

As all investors have same expectation and all use mean- variance analysis, they all identify the same risky tangency portfolio, the weight on each asset in the tangency portfolio must be equal to the proportion of its market value to the market value of its entire portfolio. CAPM compensates the investor only for taking priced risk.

CAPM model is used to estimate the expected return on a risky asset by adding to the risk free rate of return a market risk premium. The expected return on the asset, as per CAPM, is measured based on following formula,
E (Ri) = RF + βi[E(RM) - RF]
Where:
E(Ri) : the expected return on asset i
RF:  the risk-free rate of return
E(RM): the expected return on the market portfolio
βi: Cov(Ri, RM)/Var(RM),  is a measure of the asset’s sensitivity to movements in the market
The CAPM described above is also referred to as a domestic CAPM as all parameter consider as an input are based on domestic environment i.e. to find expected return for US security, the expected risk free rate on US treasury bonds is considered, expected return on US market portfolio and beta is measured with respect to securities traded on US exchange. This version of CAPM has its applicability only in segmented market.
The assumption that the investor consider only expected return, variance and covariance of asset in the portfolio is not practical, as the investors also consider the relation of their portfolio return with labour income and future investment opportunities that would be offered by the market. CAPM assumes that all investor have same portfolio, thereby implying that all investor have same time horizon for holding a portfolio, which is not the practical case, as the time horizon for the purpose of investment varies based on the liquidity need of the investor.  Further, the assumption that all the investor has access to same set of knowledge cannot be considered in isolation, as some information is disregarded by investor if it falls beyond their investment time horizon. In addition, the application of new / revised accounting rules may have a short term impact on profitability and may affect the stock price. The beta in CAPM measures the systematic risk in asset, the risk that cannot be diversified away. At the time of applying CAPM, the beta considered is based on past stock price volatility. However the future price cannot be solely based on historic market price. There are other fundamental factors like profitability, growth of the particular stock which also has impact on the security price. Further, the demand and supply of the security on the traded exchange affects the price of the security. Also, the stock beta varies over the time period and period for which historic stock beta is considered also has an impact on the derived expected value. Moreover, if there is a restriction on risk free borrowing or lending and on short sales of risky asset, the relation between expected return and beta will not be linear, thereby limits the applicability of CAPM formula.

# 3.    Global CAPM

The global CAPM advocates use of worldwide market index (e.g., the Morgan Stanley Capital International World Index, MSCI) to compute market risk premium and the company Beta employed would be based on global index.

# 4.    International CAPM

With globalisation, the economies are integrated and relevance of domestic CAPM is reduced. International CAPM (ICAPM) asserts that investors will hold a combination of risk free asset of home country and world market portfolio hedged against currency risk. Thus, for integrated market, ICAPM is more appropriate as ICAPM takes into consideration the exchange rate risk by considering the sensitivity of asset to all currency changes. Thereby, additional risk premium for each world currency is added to standard CAPM formula. ICAPM states that the expected return on any asset is sum of the investor’s domestic risk free rate, market risk premium and a foreign currency risk premium for each foreign currency.

# 5.    Conclusion

Many empirical studies (Chan, Karolyi and Stulz, 1992),  (Mishra and O’Brien, 2001) demonstrate that in integrated market there is influence of foreign market in determining home country’s stock price, thereby suggest use of ICAPM or global CAPM. However, there is no concrete evidence that claims superiority of latest version of CAPM to determine expected return over traditional or domestic CAPM.

# 6.    Reference

Desai (2005), ‘CAPM: The Challenge of globalization’, pp.2