81. Capital Asset Pricing Model (capm)

The capital asset pricing model (CAPM) Building on the earlier work of Harry Markowitz on diversification and modern portfolio theory, the capital asset pricing model (CAPM) was introduced by Jack Treynor (1961, 1962), William Sharpe (1964), John Lintner (1965) and Jan Mossin (1966) independently. Sharpe, Markowitz and Merton Miller jointly received the Nobel Memorial Prize in Economics for this contribution to the field of financial economics.

The general idea behind CAPM is that investors need to be compensated in two ways: time value of money and risk. The time value of money is represented by the risk-free (rf) rate. The market risk premium compensates the investor needs for taking on additional risk is calculated by taking a risk measure (beta) that compares the returns of the asset to the market over a period of time and to the market premium. Where is risk-free rate,Rm – expected market return, - the beta of asset.

Beta is the sensitivity of the expected excess asset returns to the expected excess market returns.

T he Security Market Line graphs the results from the capital asset pricing model (CAPM) formula. The x-axis represents the risk (beta), and the y-axis represents the expected return. The market risk premium is determined from the slope of the SML.

The relationship between β and required return is plotted on the securities market line (SML), which shows expected return as a function of β. The intercept is the nominal risk-free rate available for the market, while the slope is the market premium, E(Rm)− Rf. The securities market line can be regarded as representing a single-factor model of the asset price, where Beta is exposure to changes in value of the Market. The equation of the SML is thus:

It is a useful tool in determining if an asset being considered for a portfolio offers a reasonable expected return for risk. Individual securities are plotted on the SML graph. If the security's expected return versus risk is plotted above the SML, it is undervalued since the investor can expect a greater return for the inherent risk. And a security plotted below the SML is overvalued since the investor would be accepting less return for the amount of risk assumed.

82. Fama and French Three Factor Model of Assets Pricing

The traditional asset pricing model, CAPM (Rpt) = Rf +Bp[(Rmt) - Rf], uses only one variable, Bp, to describe the returns of a portfolio or stock with the returns of the market as a whole. In contrast, the Fama–French model uses three variables. Fama and French started with the observation that two classes of stocks have tended to do better than the market as a whole: (i) the portfolio based of firm size (small caps and big caps) and (ii) portfolio based on M/B (market/book) ratios (stocks with a high book-to-market ratio (customarily called value stocks, contrasted with growth stocks)). They then added two factors to CAPM to reflect a portfolio's exposure to these two classes:

(Rpt) = Rf +Bp[(Rmt) - Rf] + sp(SMB) + hp(HML) + εpt, Should rewrite the equation:

(Rpt) -Rf = εpt +Bp[(Rmt) - Rf] + sp(SMB) + hp(HML), There are three factors

• [(Rmt) - Rf] - market size premium;

• SMB = - excess return of small stocks over big stocks, they measure the historic excess returns of small caps over big caps

• HML = - excess return of high book-to-market stocks over low book-to-market stocks, they measure the historic excess returns of value stocks over growth stocks.

Βp- is the sensitivity of the asset returns to market returns,

sp, - is the sensitivity of the asset returns to return of SMB. It is the coefficient loading for the excess average return of portfolios with small equity class over portfolios of big equity class.

hp - is the sensitivity of the asset returns to return of HML. It is the coefficient loading for the excess average returns of portfolios with high book-to-market equity class over those with low book-to-market equity class.

εpt - is the error term for portfolio p at time t.

hp, sp, coefficients are determined by linear regressions and can take negative values as well as positive values. The Fama-French three factor model explains over 90% of the diversified portfolios returns, compared with the average 70% given by the CAPM (within sample). The signs of the coefficients suggested that small cap and value portfolios have higher expected returns—and arguably higher expected risk—than those of large cap and growth portfolios.