APPLIED ECONOMICS FOR MANAGERS SESSION 13 I REVIEW EXTERNALITIES AND PUBLIC GOODS A PROBLEM IS ABSENCE OF PROPERTY RIGHTS B REINTRODUCTION OF MARKET PRICE MECHANISM C PUBLIC GOODS AND TAXATION II INFORMATION ISSUES A UNCERTAINTY HOW DO AGENTS MAKE CHOICES WHEN OUTCOME IS UNCERTAIN B PUBLIC GOOD ASPECT OF INFORMATION HOW BEST TO GET INFORMATION PRODUCED GIVEN THAT MC OF SHARING INFORMATION IS ZERO C ASYMMETRIC INFORMATION MARKET OUTCOMES WHEN ONE PERSON KNOWS SOMETHING THAT THE OTHER DOESN T III IMPERFECT INFORMATION RISK AND UNCERTAINTY A BERNOULLI S ST PETERSBURG PARADOX 1 PAY 1 GET 2N IF 1ST HEADS COMES UP ON NTH TOSS 2 EXPECTED PAYOFF 1 2 2 1 4 4 1 8 8 B THE EXPECTED UTILITY HYPOTHESIS 1 V E U p1U X1 p2U X2 p3U X3 pNU XN 2 RISK AVERSION E U U E X OR WILLING TO TRADE SOME AMOUNT TO GAIN CERTITUDE 3 CONCAVITY OF U X AND RISK AVERSION C FORMAL DEFINITION OF CONCAVITY UTILITY OF EXPECTED VALUE EXPECTED UTILITY OF POSSIBLE VALUES 1 EXAMPLE TWO POSSIBLE OUTCOMES X0 WITH PROBABILITY p AND X1 WITH PROBABILITY 1 p 2 U pX0 1 p X1 pU X U X0 1 p U X1 D CONCAVITY AND RISK AVERSION EXAMPLE TWO POSSIBLE OUTCOMES 300 000 WITH PROBABILITY 0 9 AND 60 000 WITH PROBABILITY O 1 1 AVERAGE OR EXPECTED VALUE 0 9x 300 000 0 1x 60 000 276 000 E X 2 AVERAGE OR EXPECTED UTILITY 0 9xU 300 000 0 1xU 60 000 E U X U X E U X 60 000 260 000 300 000 INCOME 276 000 NOTE DIAGRAM SAYS THAT EXPECTED UTILITY OF GETTING 300 000 WITH PROB 0 9 AND 60 000 WITH PROBABILITY IS SAME AS UTILITY OF GETTING 260 000 FOR CERTAIN IN OTHER WORDS INDIVIDUAL IS WILLING TO GIVE UP 16 000 ON AVERAGE 276 000 260 000 TO AVOID UNCERTAINTY TO AVOID RISK IV UNCERTAINTY AND THE CAPITAL ASSET PRICING MODEL A ROUGH INTERPRETATION OF RISK AVERSION PEOPLE DON T LIKE VARIABILITY VARIANCE 1 UNDER SOME CIRCUMSTANCES WE CAN TRANSLATE THIS INTO A PRECISE UTILITY RELATIONSHIP THAT SAYS PEOPLE GET POSITIVE UTILITY FROM A HIGH AVERAGE EXPECTED WEALTH W BUT DON T LIKE VARIANCE 2 2 FOR INVESTORS WE CAN EQUIVALENTLY USE EXPECTED RATE OF RETURN E R AND VARIANCE OF THAT RETURN 2 B CONSTANT UTILITY CURVES MEAN VARIANCE ANALYSIS E R C IMPLICATIONS 2 1 RISKIER ASSETS ARE THOSE WHOSE RETURNS HAVE MORE VARIANCE 2 RISKIER ASSETS SHOULD PAY A HIGHER RETURN TO COMPENSATE FOR RISK 3 QUESTIONS a HOW DO YOU MEASURE VARIANCE 2 OF STOCK S RETURNS IN AN ECONOMICALLY MEANINGFUL WAY b WHAT IS THE EXTRA RETURN FOR INCREASES IN 2 I E WHAT IS THE PRICE OF RISK D VARIANCE VERSUS COVARIANCE 1 CONSIDER ONE RISKY ASSET WITH VARIANCE 2 IF ONLY THIS ASSET IS HELD THEN ONE GETS AN EXPECTED RETURN OF E R1 AND A VARIANCE OF 12 2 NOW CONSIDER SPLITTING YOUR INVESTMENTS BETWEEN TWO RISKY ASSETS PUTTING f1 IN ASSET 1 AND f2 1 f1 IN ASSET 2 THEN EXPECTED RETURN IS f1E R1 f2E R2 AND THE VARIANCE IS f12 12 f 22 22 2f1f 2 COV R 1 R 2 3 NOW CONSIDER SPLITTING YOUR INVESTMENTS THREE WAYS f1 IN ASSET 1 f2 IN ASSET 2 AND f3 1 f1 f2 IN ASSET 3 a EXPECTED RETURN IS f1E R1 f2E R2 f3E R3 b VARIANCE IS f12 12 f 22 22 f 32 32 2f1f 2 COV R 1 R 2 2f1f 3COV R 1 R 3 2f 2 f 3COV R 2 R 3 4 IN THE CASE OF FOUR ASSETS THE RESULTS ARE a E R f1E R1 f2E R2 f3E R3 f4E R4 b VAR f 12 12 f 22 22 f 32 32 f 42 24 2 f1f 2 COV R 1 R 2 2 f1f 3 COV R 1 R 3 2 f1f 4 COV R 1 R 4 2 f 2 f 3 COV R 2 R 3 2 f 2 f 4 COV R 2 R 4 2 f 3 f 4 COV R 3 R 4 5 MORAL AS ONE DIVERSIFIES MORE WHAT MATTERS 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 MARKET BUNDLE 1 THIS BUNDLE HAS AN EXPECTED RETURN R M AND 2 STANDARD DEVIATION OF THAT RETURN M 3 DEFINE THE RISK IN ANY ASSET OR COLLECTION OF ASSETS AS A MEASURE OF ITS COVARIANCE WITH THE RETURNS ON THE MARKET BUNDLE CALL THIS TERM THE ASSET BETA I E 1 FOR ASSET 1 4 NOTE FOR THE MARKET BUNDLE THE BETA VALUE IS 1 5 NOW IDENTIFY THE RISK FREE RATE RF 6 IF THE MARKET BUNDLE HAS AN EXPECTED RETURN OF R M AND SINCE IT HAS ONE UNIT OF RISK A BETA OF 1 THE PRICE PER UNIT OF RISK IS R M RF 7 FOR ANY OTHER ASSET WE MEASURE ITS BETA AS A MEASURE OF ITS RISK AND THEN SAY THAT IT MUST PAY A RISK PREMIUM OF ITS BETA TIMES THE PRICE OF RISK E G FOR ASSET A THE PRICE MUST BE SUCH THAT ITS EXPECTED RETURN SATISFIES E RA RF A R M RF F THE FOREGOING EQUATION IS KNOWN AS THE SECURITY MARKET LINE IT IS ONE OF THE MOST FUNDAMENTAL EQUATIONS IN FINANCIAL THEORY WHILE ITS LITERAL ACCURACY IS DEBATABLE IT MAKES THREE BROAD POINTS 1 PEOPLE ARE RISK AVERSE AND NEED TO BE COMPENSATED FOR BEARING RISK 2 THE APPROPRIATE MEASURE OF RISK IS COVARIANCE YOU WON T GET COMPENSATED FOR TAKING RISK THAT YOU COULD COSTLESSLY AVOID 3 BEATING THE MARKET RETURN R M 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