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

2. 2 Overview 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

3. 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. 4 St Petersberg Paradox Wealth from Bet Expected Wealth

5. 5 Subjective Expected Utility 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

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

7. 7 Arrow-Pratt Risk Aversion Coefficient 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-bX 1-β if β >0 U(x)= ln X if β =1 – Quadratic U(x)= a+bX-cX 2

8. 8 Constant Absolute Risk Aversion

9. 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. 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. 11 Allais Paradox a1 1.00 chance of $1m a2 0.10 of $5m 0.89 of $1m 0.01 of 0 a3 0.10 of $5m 0.90 of 0 a4 0.11 of $1m 0.89 of 0

12. 12 Preference Reversal Most players prefer a 1 in the first game. They prefer a 3 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. 13 Kahneman and Tverskey: Common Ratio Effect c1 1.00 chance of $3000 c2 0.80 of $4000 0.20 of 0 c3 0.25 of $3000 0.75 of 0 c4 0.20 of $4000 0.80 of 0

14. 14 Capital Asset Pricing Model 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.

15. 15 Security Market Line 0 r RmRm Beta 1

16. 16 Market for Loans 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

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

18. 18 Collateral as a sorting device R C RHRH RLRL

19. 19 Conclusions With asymmetric information, all firms will claim to be low risk. The Bank can offer two contracts. – No collateral but repayment of R H – 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.