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## Behavioral Finance

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**Behavioral Finance**Economics 437**Reading by Today**• Fama • Malkiel (online) • Shiller (online) • Shleifer (book, Ch 1) • This Week: • Black • Shleifer (Chapter 2)**Black on “Noise”**• Black strong believer in noise and noise traders in particular • They lose money according to him (though they may make money for a short while) • Prices are “efficient” if they are within a factor of 2 of “correct” value • Actual prices should have higher volatility than values because of noise**What is a short sale?**• Sell 100 shares of GOOG at 1101 • What happens? • You enter an order to sell 100 shares at 1101 • The order is “executed” – meaning that you have sold 100 shares to someone else somewhere • Mechanically, how do provide the 100 shares to the buyer? • You borrow the 100 shares from an institutional holder (like UVA’s Endowment) • You provide collateral equal to the value of the stock ($ 110,100) and perhaps a little more collateral in case the stock price goes up. • You mark to market • If stock goes to 1096, you send $ 500 more in cash to lender • If stock goes to 1106, lender sends you $ 500 in cash • Where do you get the $ 110,100? The buyer gives you $ 110,100 and you pass that through to the stock lender • On some future date, you buy 100 shares at say 900, paying $ 90,000 which you receive back from the stock lender when you return the 100 shares to the lender**Short Sale Mechanics**100 shares of GOOG at 1101 Stock buyer Short seller 100 shares $ 110,100 UVA Endowment Short seller 100 shares $ 110,100**The Law of One Price**• Identical things should have identical prices • But, what if two identical things have different names? • Example: baseball, hardball • Another example: two companies with exact same cash flow but they are different companies in name, but in every other way they are different (think of two bonds, if it makes any easier to imagine)**Fungibility (convertibility from one form to another)**• Imagine two “different” products • Product A • Product B • Imagine a machine that you can plug A into and out comes B and you can plus B into and out comes A • This is called “fungibility” • You can easily turn one thing into another and vice versa costlessly**The Mysterious Case of Royal Dutch and Shell (stocks)**• Royal Dutch – incorporated in Netherlands • Shell – incorporated in England • Royal Dutch • Trades primarily in Netherlands and US • Entitled to 60% of company economics • Shell • Trades predominantly in the UK • Entitled to 40% of company economics • Royal Dutch should trade at 1.5 times Shell • But it doesn’t**Decifering Shleifer Chapter 2**• The assets • The players • Their behavior • Equilibrium • Profitability of the players**Imagine an economy with two assets (financial assets)**• A Safe Asset, s • An Unsafe Asset, u • Assume a single consumption good • Suppose that s is always convertible (back and forth between the consumption good and itself) • That means the price of s is always 1 in terms of the consumption good (that is why it is called the “safe” asset – it’s price is always 1, regardless of anything)**Safe asset, s, and unsafe asset, u**• Why is u an unsafe asset? • Because it’s price is not fixed because u is not convertible back and forth into the consumption good • You buy u on the open market and sell it on the open market**Now imagine**• Both s and u pay the same dividend, d • d is constant, period after period • d is paid with complete certainty, no uncertainty at all • This implies that neither s or u have “fundamental” risk • (If someone gave you 10 units of s and you never sold it, your outcome would be the same as if someone gave you 10 units of u)**The players**• Arbitrageurs • Noise Traders**Utility Functions**• “Expected Utility”, not “Expected Value” • U = -e-(2λ)w Utility wealth**Overlapping Generations Structure**• All agents live two periods • Born in period 1 and buy a portfolio (s, u) • Live (and die) in period 2 and consume • At time t • The (t-1) generation is in period 2 of their life • The (t) generation is in period 1 of their life • So, they “overlap” t1 t2 t3 t4**How many are arbitrageurs? How many are noise traders?**0 1 The total number of traders are the same as the number of real numbers Between zero and one (an infinite number) The term “measure” means the size of any interval. For example the “measure” of the interval between 0 and ½ is ½. Interestingly, the measure of a single point (a single number) is zero. The measure of the entire interval between zero and one is 1. You can think of it as a fraction of the entire interval. The measure of noise traders is µ and the measure of arbitrage traders is 1 - µ. That is, the fraction of noise traders is µ and everybody else is an arbitrage traders**What is a noise trader?**Pt+1 is the price of the risky asset at time t+1 Ρt+1 is the “mean misperception” of pt+! Ρt+!**What is an “arbitrage trader”**• Arbitrage traders “correctly” perceive the true distribution of pt+1. There is “systematic” error in estimation of future price, pt+1 • But, arbitrageurs face risk unrelated to the “true” distribution of pt+1 • If there were no “noise traders,” then there would be no variance in the price of the risky asset…..but, there are noise traders, hence the risky asset is a risky asset**Arbitrageurs expectations are “correct;” noise traders**expectations are “biased” Difference is ρt+1 Correct mean of pt+1