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 theoryProspect theory Consumption based Consumption based

modelsmodelsVolatile 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

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Assumptions

Continuum of identical infinitely lived agents One risky asset and one risk free asset

paying Rf,t+1, Rt+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

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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

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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

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The model – prior outcomes

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 Zt respectively z= Zt /St

z<1 prior gains z>1 prior loss

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The model – utility function

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

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The model – penalty lambda

Case of prior losses: current stock value St=100, Zt=110,zt=1.1 and lambda is 2 and k=3

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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

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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

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