1. PAY $1: GET $2 N IF 1ST HEADS COMES UP ON NTH TOSS

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1 APPLIED ECONOICS FOR ANAGERS SESSION I. REVIEW: EXTERNALITIES AND PUBLIC GOODS A. PROBLE IS ABSENCE OF PROPERTY RIGHTS B. REINTRODUCTION OF ARKET/PRICE ECHANIS C. PUBLIC GOODS AND TAXATION II. INFORATION ISSUES A. UNCERTAINTY HOW DO AGENTS AKE CHOICES WHEN OUTCOE IS UNCERTAIN? B. PUBLIC GOOD ASPECT OF INFORATION HOW BEST TO GET INFORATION PRODUCED GIVEN THAT C OF SHARING INFORATION IS ZERO? C. ASYETRIC INFORATION ARKET OUTCOES WHEN ONE PERSON KNOWS SOETHING THAT THE OTHER DOESN T? III. IPERFECT INFORATION: RISK AND UNCERTAINTY A. BERNOULLI S ST. PETERSBURG PARADOX TOSS. PAY $: GET $ N IF ST HEADS COES UP ON NTH. EXPECTED PAYOFF: (/)$ + (/)$ + (/8)$ = B. THE EXPECTED UTILITY HYPOTHESIS. V = E(U) = p U(X ) + p U(X ) + p U(X ) p N U(X N ). RISK AVERSION: E(U) < U[E(X)] OR, WILLING TO TRADE SOE AOUNT TO GAIN CERTITUDE. CONCAVITY OF U(X) AND RISK AVERSION C. FORAL DEFINITION OF CONCAVITY: UTILITY OF EXPECTED VALUE > EXPECTED UTILITY OF POSSIBLE VALUES. EXAPLE: TWO POSSIBLE OUTCOES: X 0 WITH PROBABILITY p, AND X WITH PROBABILITY ( p). U[pX 0 + ( p)x ] > pu(x 0 ) + ( p)u(x )

2 D. CONCAVITY AND RISK AVERSION EXAPLE: TWO POSSIBLE OUTCOES: $00,000 WITH PROBABILITY 0.9 AND $60,000 WITH PROBABILITY O.. AVERAGE OR EXPECTED VALUE = 0.9x$00, x$60,000 = $76,000 = E(X). AVERAGE OR EXPECTED UTILITY = 0.9xU($00,000) + 0.xU($60,000) = E[U(X)] $ U(X) E[U(X)] $60,000 $60,000 $00,000 INCOE $76,000 NOTE: DIAGRA SAYS THAT EXPECTED UTILITY OF GETTING $00,000 WITH PROB = 0.9 AND $60,000 WITH PROBABILITY IS SAE AS UTILITY OF GETTING $60,000 FOR CERTAIN. IN OTHER WORDS, INDIVIDUAL IS WILLING TO GIVE UP $6,000 ON AVERAGE ($76,000 $60,000) TO AVOID UNCERTAINTY, TO AVOID RISK

3 IV. UNCERTAINTY AND THE CAPITAL ASSET PRICING ODEL A. ROUGH INTERPRETATION OF RISK AVERSION: PEOPLE DON T LIKE VARIABILITY VARIANCE. UNDER SOE CIRCUSTANCES, WE CAN TRANSLATE THIS INTO A PRECISE UTILITY RELATIONSHIP THAT SAYS PEOPLE GET POSITIVE UTILITY FRO A HIGH AVERAGE EXPECTED WEALTH, W, BUT DON T LIKE VARIANCE,. FOR INVESTORS, WE CAN EQUIVALENTLY USE EXPECTED RATE OF RETURN, E(R), AND VARIANCE OF THAT RETURN, B. CONSTANT UTILITY CURVES EAN VARIANCE ANALYSIS E(R) C. IPLICATIONS:. RISKIER ASSETS ARE THOSE WHOSE RETURNS HAVE ORE VARIANCE. RISKIER ASSETS SHOULD PAY A HIGHER RETURN TO COPENSATE FOR RISK. QUESTIONS: a. HOW DO YOU EASURE VARIANCE, OF STOCK S RETURNS IN AN ECONOICALLY EANINGFUL WAY? b. WHAT IS THE EXTRA RETURN FOR INCREASES IN? I.E, WHAT IS THE PRICE OF RISK?

4 D. VARIANCE VERSUS COVARIANCE. CONSIDER ONE RISKY ASSET WITH VARIANCE. IF ONLY THIS ASSET IS HELD,THEN ONE GETS AN EXPECTED RETURN OF E(R ) AND A VARIANCE OF. NOW CONSIDER SPLITTING YOUR INVESTENTS BETWEEN TWO RISKY ASSETS, PUTTING f IN ASSET AND f [= f ] IN ASSET. THEN EXPECTED RETURN IS: f E(R ) + f f COV R, f E(R ) AND THE VARIANCE IS: ( ) R. NOW CONSIDER SPLITTING YOUR INVESTENTS THREE WAYS: f IN ASSET ; f IN ASSET ; AND f [ = f f ] IN ASSET a. EXPECTED RETURN IS: f E(R ) E(R ) E(R ) b. VARIANCE IS (,R ) f COV( R,R ) f f COV( R, ) f + f COV R R f. IN THE CASE OF FOUR ASSETS THE RESULTS ARE: f a. E(R) = f E(R ) E(R ) E(R ) E(R ) b. VAR = f f COV R, R f COV R, R + + COV ( ) ( ) ff COV ( R, R ) ( R, R ) f COV ( R, R ) f COV ( R, R ) 5. ORAL: AS ONE DIVERSIFIES ORE, WHAT ATTERS ABOUT ANY ONE ASSET IS NOT THE VARIANCE OF ITS RETURNS BY ITSELF, BUT THE COVARIANCE OF ITS RETURNS WITH THE RETURNS OF ALL THE OTHER ASSETS E. DEFINE A VERY WELL-DIVERSIFIED BUNDLE OF ASSETS AS THE ARKET BUNDLE. THIS BUNDLE HAS AN EXPECTED RETURN R AND. STANDARD DEVIATION OF THAT RETURN =

5 . DEFINE THE RISK IN ANY ASSET OR COLLECTION OF ASSETS AS A EASURE OF ITS COVARIANCE WITH THE RETURNS ON THE ARKET BUNDLE. CALL THIS TER THE ASSET BETA, I.E., β FOR ASSET.. NOTE FOR THE ARKET BUNDLE, THE BETA VALUE IS. 5. NOW IDENTIFY THE RISK-FREE RATE, R F. 6. IF THE ARKET BUNDLE HAS AN EXPECTED RETURN OF R AND SINCE IT HAS ONE UNIT OF RISK (A BETA) OF, THE PRICE PER UNIT OF RISK IS R R F 7. FOR ANY OTHER ASSET, WE EASURE ITS BETA AS A EASURE OF ITS RISK, AND THEN SAY THAT IT UST PAY A RISK PREIU OF ITS BETA TIES THE PRICE OF RISK, E.G. FOR ASSET A, THE PRICE UST BE SUCH THAT ITS EXPECTED RETURN SATISFIES: E(R A ) = R F + β A [ R R F ] F. THE FOREGOING EQUATION IS KNOWN AS THE SECURITY ARKET LINE. IT IS ONE OF THE OST FUNDAENTAL EQUATIONS IN FINANCIAL THEORY. WHILE ITS LITERAL ACCURACY IS DEBATABLE IT AKES THREE, BROAD POINTS.. PEOPLE ARE RISK AVERSE AND NEED TO BE COPENSATED FOR BEARING RISK. THE APPROPRIATE EASURE OF RISK IS COVARIANCE. YOU WON T GET COPENSATED FOR TAKING RISK THAT YOU COULD COSTLESSLY AVOID.. BEATING THE ARKET RETURN R IS EASY. JUST INVEST IN ASSETS WITH BETAS GREATER THAN ONE. THE REAL QUESTION IS DID YOU GET A HIGHER RETURN AFTER ADJUSTING FOR RISK?