Applied Economics For Managers Recitation 5 Tuesday July 6th 2004 Outline 1 Uncertainty and asset prices 2 Informational efficiency rational expectations random walks 3 Asymmetric information lemons moral hazard UNCERTAINTY Economics of uncertainty might seem a bit abstract so useful here to review what are the important things you should take away i RISK AVERSION We derived risk aversion with the concept of expected utility but we won t be testing you on this so its most important that you simply understand the idea PEOPLE PREFER CERTAIN SITUATIONS TO RISKY SITUATIONS This means that economic value is created by taking undesirable risk off people s hands Another way of saying this is that people who choose to take on risk for example by buying stocks will be economically rewarded for doing so RISK HAS A PRICE All the economics of uncertainty is concerned in one way or another with determining how risk is priced By introspection this is how most people behave If I offered you a choice a 1m for sure b toss a coin heads you get nothing tails you get 2m which do you prefer Most people would choose a they have the same outcome on average but b is more risky if you dislike b it is only because of the risk Example with expected utility theory We formalize the intuitive idea with EXPECTED UTILITY THEORY The idea is that you don t compare situations just according to the expected monetary value of the payoffs but instead according to the UTILITY that can be obtained with that money The EXPECTED UTILITY IS THE AVERAGE UTILITY THAT YOU WILL ACHIEVE WHEN FACED WITH A RISKY SITUATION EXPECTED UTILITY IS THE METRIC USED WHEN COMPARING RISKY CHOICES Expected utility formalizes RISK AVERSION because of DIMINISHING MARGINAL UTILITY The value of a dollar in terms of what you can do with it declines with increasing wealth This implies that when faced with risk you are more concerned about a 1 loss than a 1 gain This asymmetry leads immediately to risk aversion a gamble which is neutral in terms of expected wealth e g 50 chance of winning or losing a 1 is not neutral in terms of utility since the possible loss of utility outweighs the possible gain Example Suppose agent has a utility function U w W 1 2 Consider the following situation the agent has 100 and faces a 50 chance of losing 36 What is the expected utility of the agent bearing this risk How much would the agent be willing to pay to avoid the risk Thus the expected payoff of the risky situation exceeds the value that the agent effectively attains The agent would pay 1 to avoid the risk as 81 for sure is worth the same as the gamble with average payoff 82 We can illustrate this with a diagram This illustrates the general principle that AGENT TRADES OF EXPECTED PAYOFF FOR RISK BECAUSE OF RISK AVERSION More general statement of this principle If agent gets x with probability p and y with probability 1 p then Z x with prob p Z y with prob 1 p First term is the expected utility bearing the risk and second term is the value of the average payoff with the risk removed Risk aversion just states that the average payoff with the risk removed is better than the same average payoff with risk added The mathematical reason for this inequality is because the utility function is CONCAVE L I r 9 Another way of thinking about this is that people voluntarily purchase insurance ii MEAN VARIANCE A crude way to think about risk aversion is to suppose that people like things which are better on average 2m better than lm but they dislike things which are more risky lm better than the gamble above This is particularly useful when we think about asset pricing We want to answer the question of how a stock price gets determined A stock is risky in that its price has variance An asset pricing model tells us how that risk is priced i e what compensation in the form of average retum is required for an asset with a more risky return The only question we have to answer is what is how to measure risk iii DIVERSIFIABLE RISK We measure the risk of a stock by the variance of its returns but there is a subtlety DIVERSIFIABLE RISK IS NOT PRICED In other words it is always possible to offset the risk of holding a stock by holding it in a portfolio with other stocks Often there are idiosyncratic reasons why one goes up and the other goes down In a DIVERSIFIED PORTFOLIO many of these shocks will cancel out so there is less risk left Since it is free to diversify just buy a mutual fund this risk has no economic value it can be costlessly avoided so no one gets compensated for bearing it Instead what is left is the common component the amount by which all assets go up and down together THIS IS THE ONLY RISK THAT IS PRICED iv CAPITAL ASSET PRICING MODEL This idea is expressed in the CAPM it tells us the price of risk for any security the average return investors demand depends on the extent to which it is exposed to this common component MARKET RISK We measure market risk with BETA Beta is the covariance between the asset and the market The more market risk an asset has the higher its beta and the better return investors will demand for holding it We can make this precise in the SECURITY MARKET LINE RMis the RETURN ON THE MARKET RF is the RETURN ON THE RISK FREE ASSET E G TREASURIES RM RFis the PRICE OF RISK or RISK PREMIUM PAis the AMOUNT OF MARKET RISK IN THE ASSET A i e RMand RFare properties of the market as a whole PAis a property of the particular asset in question and we would measure it with historical data on the covariance of the returns on the given asset A and the market as a whole How should we think about CAPM It is basically about the CROSS SECTION of stock returns It allows us to compare how risk across different assets at a given point in time the beta and how that risk will be reflected in the price the expected retum with the caveat that it only measures the risk of an asset WHEN IT IS HELD IN THE CONTEXT OF A DIVERSIFIED PORTFOLIO An implication of the CAPM is that you would never want to have undiversified stock holdings then beta would not be giving you a good measure of the risk you are actually facing as you would also be holding unnecessary idiosyncratic risk which you could have avoided by spreading your portfolio more widely assuming everyone else is diversifying that risk will not be priced and so your portfolio will be inefficient in the sense of holding more risk than necessary to achieve a given expected return Information and Financial markets While