PROSPECT THEORY AND ASSET PRICES Nicholas Barberis Ming Huang Tano Santos Course: Financial Economics, Ales Marsal, Presentation of the paper:

Outline Game The story Assumptions What makes the paper different Model Intuition Numerical Results

Game You were granted by 50 mil. Ales dollars (50 forints) Ales mutual fund, probability 0.5 -> 20% growth; 0.5-> -20% 50% tax on holding cash, you invest = exempt of tax YOU CAN WIN UP TO 125 mil A. dollars!!!

The Story In consumption based models C=D, not in the data, investors have non-dividend income Investors derives direct utility from consumption and financial wealth (concern about financial wealth fluctuation The point of the game was: 1) to show that investors may or may not? be more sensitive to reductions in financial wealth than to increase, 2) after prior gains less loss averse Introduction of changing risk aversion

The story After a fall in stock prices, investor becomes more wary of further losses->more risk averse Idea comes from prospect theory from psychology (i.e. evidence: subjects are offered a sequence of gambles, after gain people appear to be more risk seeking than usual, taking bets normally not accepted, ‘house money’ effect; TV show Card Sharks) one explanation is that gains cushion the subsequent loss and losses are more painful than usual following prior losses vs. break even effect

What makes the paper different? Prospect theory Consumption based models Volatile risk aversion -> price grows more than dividends = volatile returns External habits, time varying risk aversion as current consumption moves farther from habit Changes in risk aversion driven by past stock market movements Changes in risk aversion are driven by C Risk aversion about financial wealth Risk aversion about total wealth function Investor cares about fluctuation in financial W independently of g(C) Assets are risky - cov(m,R) C = D + Y, Y = income or human capital… C = D

Assumptions Continuum of identical infinitely lived agents One risky asset and one risk free asset paying R f,t+1, R t+1 Risky asset is claim to a stream of perishable output represented by dividend sequence Agents choose C and allocation to the risky asset No large selling out

Model First term in eq. 1 standard one Second term – utility the investor receives from gain or loss on his financial investment as a function of value of risky assets (S) and prior gains and losses (state variable z) Eq. 2 dividend sequence

Model Captures feelings unrelated to consumption, after big loss in the stock market, an investor may experience a sense of regret over his decision to invest in stock, or feeling of humiliation in front of friends People get utility also from other sources than just consumption and anticipate those sources

Model - gains and losses

Model – gains and losses assumption: consumer cares only about fluctuations in the value of risky assets and evaluate their investment once per year You buy risky asset (S) for 100, its value goes up to 120, risk free rate is 5% (otherwise you would be disappointed if at least not risk free => you compare 120 to 105, your gain is 15

The model – prior outcomes

Loss coming after substantial prior gains – you say: “shit happens, I am still up” relative to a year ago To model this, authors use concept of historical benchmark level Z t respectively z= Z t /S t z<1 prior gains z>1 prior loss

The model – utility function

The case of prior gains: value of risky investment is 100 after prior increase from benchmark level 90, next period it falls down to 80, the disutility will be calculated as follows: *in the actual model, 100 and 90 is multiplied by risk free rate

The model – penalty lambda Case of prior losses: current stock value S t =100, Z t =110,z t =1.1 and lambda is 2 and k=3

The model – dynamics of benchmark level If stock price moves up a lot, the benchmark level moves up but less If price falls sharply, the benchmark level does not adjust downwards by as much b is scaling term which ensures that price- dividend ratio and risky asset risk premium are stationary

The model - equilibrium

How the model works Ability of model to generate returns that are more volatile than dividends: high positive dividend innovation in the period ->generate a high stock return->less risk averse investor ->he discounts the future dividend stream at a lower rate=>more volatile prices This fact also generate predictability in long horizon: growing prices->growing price-dividend ration->lower returns, inverse relationship between future returns and price-dividend = Fama and French (1988) Volatile stocks = substantial equity premium (investor is loss averse and fears frequent drop) Low correlation of dividends and consumption

The Results

K determines how much more painful losses are when they come on the heels of other losses, k=3 makes the investor average loss aversion close to 2.25 which is based on micro data b determines the relative importance of the prospect utility, no data->range Increase in dividend volatility makes stocks more volatile, scaring the investor, although stocks are less correlated with consumption than in consumption based model, it does not matter since the investor cares about fluctuations in stock market per se