178.307 Markets, Firms and Consumers

1. 178.307 Markets, Firms and Consumers Lecture 4- Capital and the Firm

2. Readings 7: 209-211 Chapter 14 We begin with the theory of making ‘risky decisions’. We conclude with examining methods of dealing with risk. Key Concepts Expected Utility Theory Risk Aversion EU Paradoxes CAPM Model Bank Loans and collateral Overview

3. Expected Utility Theory • Replaced Expected Wealth theory • St Petersberg Paradox refuted EW theory. • Based on a gamble (tossing heads) • Fall in odds matched by rise in payoff Odds of Winning

4. St Petersberg Paradox Wealth from Bet Expected Wealth

5. Payoffs are evaluated in subjective terms. Choices are represented as lotteries. vN-M Utility function is a cardinal, weighted sum of utilities of lottery payoffs. Axioms Certainty Independence of Order Compounding Independence Continuity Montonicity Subjective Expected Utility

6. Risk aversion is implied Map utility against wealth Implies that a certain-equivalent gives a higher payoff than lottery. Risk Aversion

7. Risk aversion can be inferred from the slope of u(x). Arrow-Pratt formula CARA U(x)=a-b exp(-rX) Two other forms are- CRRA U(x)= a-bX1-βif β >0 U(x)= ln X if β =1 Quadratic U(x)= a+bX-cX2 Arrow-Pratt Risk Aversion Coefficient

8. Constant Absolute Risk Aversion

9. CARA • Assume that x is normally distributed with mean μ and standard deviation of σ. • The EU CARA function can be derived (via a Taylor approximation)

10. Violations of EU Theory • Two main paradoxes emerge • Common Consequence Effect • Common Ratio Effect • Allais Paradox is earliest example of Common Consequence effect.

11. Allais Paradox

12. Preference Reversal • Most players prefer a1 in the first game. They prefer a3 in the second game. • Game 1 establishes that 0.11U(1m) > 0.10U(5m) • Game 2 establishes that 0.10U(5m) > 0.11U(1m).

13. Kahneman and Tverskey: Common Ratio Effect

14. Suppose a firm wishes to raise capital for an investment. The systematic risk should be incorporated in the cost of capital. The idiosyncratic risk should not be. The measure of systematic risk is the beta β. Firm’s whose systematic risk is greater than market mutual fund pay premium. Capital Asset Pricing Model

15. Security Market Line Rm r 0 1 Beta

16. The problem of asymmetric information. Borrower has private information about the risk of the project. Bank cannot distinguish ‘high risks’ from ‘low risks’. Bank can charge average interest rate Penalises low risk, benefits high risk. May create adverse selection rpoblem Low risk firms get alternate finance Bank left with high risk projects Market may collapse Market for Loans

17. Suppose risks are binomial Cashflow equals 0 or y Borrowers are either high risk θH or low risk θL. Their reserve repayment is either RH or RL RH > RL Assume borrowers can put down collateral C. If y=0, borrower loses C and bank gains δC. If y>0, bank gets Rk, borrower gets y-Rk. All bargaining power lies with the bank. Collateral

18. RH RL C Collateral as a sorting device R

19. With asymmetric information, all firms will claim to be low risk. The Bank can offer two contracts. No collateral but repayment of RH Require collateral and lower repayment schedule. High risk firms unwilling to bet their collateral Select the first contract. Low risk firms prepared to bet their collateral for lower repayments. They select second contract (weakly dominates) Collateral is used to sort the two types of firms Bank does not need to know each firm’s type. Conclusions