Arbitrage Pricing Theory and Multifactor Models of Risk and Return

Arbitrage Pricing Theory and Multifactor Models of Risk and Return

Recap : CAPM Is a form of single factor model (one market risk premium) Based on a set of assumptions. Many of which are unrealistic One factor to proxy for risk premium In CAPM, alpha assumed to be zero. But real-world test reject this. The search for better model continues..

Single Factor Model Returns on a security come from two sources: 1) Common macro-economic factor (market risk) 2) Firm specific events (specific risk) In reality, many possible common macro-economic factors. (more than 1) Gross Domestic Product Growth Interest Rates Inflation Etc

Single Factor Model : Equation

Multifactor Models

Multifactor Models Equation

Multifactor SML Models

Multifactor Model Interpretation

Multifactor Model Example Suppose Eazyjet has a theoretical market beta of 1.2 and T-bond beta of 0.7. The European market risk premium is 6% while T-bond portfolio (comprise of a basket of European Gov. bonds) is 3%. What is the expected return of Eazyjet? Sol. E(r) = 4%+1.2*6%+0.7*3% = 13.3%

Arbitrage Pricing Theory Arbitrage is the act of exploiting mispricing of two of more securities to achieve risk-free returns. Arbitrage occurs if there is a zero investment portfolio with a sure profit. Ross (1976) derived APT based on an assumption that well-functioning market preclude arbitrage opportunities

Arbitrage Pricing Theory Since the return from arbitrage opportunity is risk free and to earn such profit require zero net investment (Example : short high price long low price of the same security) Since no investment is required, investors can create large positions to obtain sure profits. Violation of APT pricing relationships will cause extremely high pressure to correct price.

Arbitrage Pricing Theory

Port Weight APT & Well-Diversified Portfolios In Asset Contribution to Excess Returns W p = 1 Portfolio P W p (α p +β p R M +e p ) = α p +β p R M +e p W M = -β p Benchmark W M R M = -β p R M W f = β p -1 Risk-free asset W = 0 Portfolio A (Will be Arbitrage Portfolio if it is well diversified e p =0) W f *0 = 0 (excess returns measured over r f ) α p +e p

APT & Well-Diversified Portfolios

Returns as Function of Systematic Factor

An arbitrage opportunity

APT Model

APT & CAPM

Multifactor APT

Two Factor model

Factor Portfolios

What factors in Multifactor model? Need important systematic risk factors Chen, Roll, and Ross used industrial production, expected inflation, unanticipated inflation, excess return on corporate bonds, and excess return on government bonds. (Macroeconomic Factors) Fama and French used firm characteristics that proxy for systematic risk factors. (HML, SMB)

Fama-French 3 factor model

Fama-French 3 factor model Motivated by the observation that average returns on small stocks (SMB) & value stocks (HML) SMB : Small (mkt. cap) minus big Small stocks maybe more sensitive to changes in business conditions HML : High (book-to-market) minus low Firms in financial distress tend to have market value close to its book value

APT : Homework The market price of security is $30. Its expected rate of return is 10%. R f =4% and risk premium is 8%. The stock is expected to pay a constant dividend in perpetuity. What will be the market price of the securities be if the beta double (all other variable remains unchanged) $18.75