Chapter 9 CAPITAL ASSET PRICING AND ARBITRAGE PRICING THEORY The Risk Reward Relationship

1. Chapter 9 CAPITAL ASSET PRICING AND ARBITRAGE PRICING THEORY The Risk Reward Relationship

2. OUTLINE • Key Issues • Basic Assumptions • Capital Market Line • Security Market Line • Inputs Required for CAPM • Calculation of Beta • Empirical Evidence on CAPM • Arbitrage Pricing Theory

3. KEY ISSUES • Essentially, the capital asset pricing model (CAPM) is concerned with two questions: • What is the relationship between risk and return for an • efficient portfolio? • What is the relationship between risk and return for an • individual security?

4. BASIC ASSUMPTIONS • RISK - AVERSION • MAXIMISATION . . EXPECTED UTILITY • HOMOGENEOUS EXPECTATION • PERFECT MARKETS

5. CAPITAL MARKET LINE EXPECTED RETURN, E(Rp) Z • LM• • K RfSTANDARD DEVIATION, pE(Rj) = Rf + λ σj E(RM) - Rf λ = σM

6. SECURITY MARKET LINE EXPECTED • P RETURN SML 14% 8% • 0ALPHA = EXPECTED - FAIR RETURN RETURN 1.0 βi

7. RELATIONSHIP BETWEEN SML AND CML SMLE(RM ) - RfE(Ri) = Rf + σiMσM 2SINCE σiM = iM σi σME(RM ) - RfE(Ri) = Rf + iM σi σM IF i AND M ARE PERFECTLY CORRELATED iM = 1. SOE(RM ) - RfE(Ri) = Rf + σi σM THUS CML IS A SPECIAL CASE OF SML

8. INPUTS REQUIRED FOR APPLYING CAPM • RISK-FREE RETURN • RATE ON A SHORT-TERM GOVT SECURITY • RATE ON A LONG TERM GOVT BONDMARKET RISK PREMIUM • HISTORICAL • DIFFERENCE BETWEEN THE AVERAGE RETURN ON STOCKS AND THE AVERAGE RISK - FREE RETURNPERIOD : AS LONG AS POSSIBLE • AVERAGE : A.M VS. G.M.

9. DETERMINANTS OF RISK PREMIUM • VARIANCE IN THE UNDERLYING ECONOMY • POLITICAL RISK • MARKET STRUCTURE * Source : Aswath Damodaran Corporate Finance Theory and Practice, John Wiley.

10. TRIUMPH OF OPTIMISTS • ELROY DIMSON, PAUL MARCH, AND MICHAEL STANTON … TRIUMPH OF THE OPTIMISTS, (2001) • EQUITY RETURNS … 16 RICH COUNTRIES … DATA … 1900 • GLOBAL HISTORICAL RISK PREMIUM … 20TH CENTURY .. 4.6% • BEST ESTIMATE OF EQUITY PREMIUM WORLDWIDE IN FUTURE IS 4 TO 5 PERCENT

11. CALCULATION OF BETA Rit = i + iRMt+ eit iM i = M 2

12. CALCULATION OF BETA

13. ESTIMATION ISSUES • ESTIMATION PERIOD• A LONGER ESTIMATION PERIOD PROVIDES MORE DATA BUT THE RISK PROFILE .. FIRM MAY CHANGE • 5 YEARS•RETURN INTERVAL DAILY, WEEKLY, MONTHLY•MARKET INDEX STANDARD PRACTICEADJUSTING HISTORICAL BETA • HISTORICAL ALIGNMENT … CHANCE FACTOR • A COMPANY’S BETA MAY CHANGE OVER TIMEMERILL LYNCH … 0.66 … HISTORICAL BETA O.34 … MARKET BETA

14. BETAS BASED ON FUNDAMENTAL INFORMATION • KEY FACTORS EMPLOYED ARE • INDUSTRY AFFILIATION • CORPORATE GROWTH • EARNINGS VARIABILITY • FINANCIAL LEVERAGE • SIZE

15. BETAS BASED ONACCOUNTING EARNINGS REGRESS THE CHANGES IN COMPANY EARNINGS (ON A QUARTERLY OR ANNUAL BASIS) AGAINST CHANGES IN THE AGGREGATE EARNINGS OF ALL THE COMPANIES INCLUDED IN A MARKET INDEX. LIMITATIONS• ACCOUNTING EARNINGS .. GENERALLY SMOOTHED OUT .. RELATIVE .. VALUE OF THE COMPANY• ACCOUNTING EARNINGS … INFLUENCED BY NON - OPERATING FACTORS • LESS FREQUENT MEASUREMENT

16. BETAS FROM CROSS SECTIONAL REGRESSIONS 1. ESTIMATE A CROSS - SECTIONAL REGRESSION RELATIONSHIP FOR PUBLICLY TRADED FIRMS:BETA = 0.6507 + 0.27 COEFFICIENT OF VARIATION IN OPERATING INCOME + 0.09 D/E + 0.54 EARNINGS - .00009 TOTAL ASSETS (MILLION $)2. PLUG THE CHARACTERISTICS OF THE PROJECT, DIVISION, OR UNLISTED COMPANY IN THE REGR’N REL’N TO ARRIVE AT AN ESTIMATE OF BETABETA = 0.6507 + 0.27 (1.85) + 0.09 (0.90) + 0.54 (0.12) - 0.00009 (150) = 1.2095

17. EMPIRICAL EVIDENCE • ON CAPM • SET UP THE SAMPLE DATARit , RMt , Rft • 2. ESTIMATE THE SECURITY CHARACTER- -ISTIC LINESRit -Rft = ai +bi (RMt -Rft) + eit • 3. ESTIMATE THE SECURITY MARKET LINERi = 0 + 1 bi + ei, i = 1, … 75

18. EVIDENCEIF CAPM HOLDS•THE RELATION … LINEAR .. TERMS LIKE bi2 .. NO EXPLANATORY POWER•0 ≃ Rf•1 ≃ RM -Rf•NO OTHER FACTORS, SUCH AS COMPANY SIZE OR TOTAL VARIANCE, SHOULD AFFECT Ri•THE MODEL SHOULD EXPLAIN A SIGNIFICANT PORTION OF VARIATION IN RETURNS AMONG SECURITIES

19. GENERAL FINDINGS • THE RELATION … APPEARS .. LINEAR •0 > Rf •1 < RM -Rf • IN ADDITION TO BETA, SOME OTHER FACTORS, SUCH AS STANDARD DEVIATION OF RETURNS AND COMPANY SIZE, TOO HAVE A BEARING ON RETURN • BETA DOES NOT EXPLAIN A VERY HIGH PERCENTAGE OF THE VARIANCE IN RETURN

20. CONCLUSIONS PROBLEMS • STUDIES USE HISTORICAL RETURNS AS PROXIES FOR EXPECTATIONS• STUDIES USE A MARKET INDEX AS A PROXY POPULARITY • SOME OBJECTIVE ESTIMATE OF RISK PREMIUM .. BETTER THAN A COMPLETELY SUBJECTIVE ESTIMATE• BASIC MESSAGE .. ACCEPTED BY ALL• NO CONSENSUS ON ALTERNATIVE

21. ARBITRAGE - PRICING THEORY RETURN GENERATING PROCESS Ri = ai +bi 1I1+ bi2 I2…+bij I1 + ei EQUILIBRIUM RISK - RETURN RELATIONSHIP E(Ri) = 0 + bi1 1 + bi2 2 + … bijj j = RISK PREMIUM FOR THE TYPE OF RISK ASSOCIATED WITH FACTOR j

22. SUMMING UP • The relationship between risk and expected return for efficient portfolios, as given by the • capital market line, is: • E (Ri) = Rf +  i • The relationship between risk and expected return for an inefficient portfolio or a single • security as given by the security market line is : • E (Ri) = Rf + E (RM) – Rf x • The beta of a security is the slope of the following regression relationship: • Rit = i + iRMt + eit • The commonly followed procedure for testing CAPM involves two steps. In the first step, • the security betas are estimated. In the second step, the relationship between security • beta and return is examined. • Empirical evidence is favour of CAPM is mixed. Notwithstanding this, the CAPM is the • most widely used risk-return model because it is simple and intuitively appealing and its • basic message that diversifiable risk does not matter is generally accepted. • The APT is much more general in that asset prices can be influenced by factors beyond • means and variances. The APT assumes that the return on any security is linearly related • to a set of systematic factors. iM M2