R. Bhar, A. G. Malliaris Deviation of US Equity Return Are They Determined by Fundamental or...

R. Bhar, A. G. Malliaris www.bhar.id.au 1

Deviation of US Equity Return

Are They Determined by Fundamental or Behavioral Variables?

R. Bhar (UNSW), A. G. Malliaris (Loyola, Chicago)


Background

Focus is on the intersection of financial markets and macro-economics

Cochrane (2006) is a brilliant survey of this area

Indicates long-run averages of GDP, dividend, equity – mostly with annual data


Background

On a year by year basis deviations from long-run averages do not seem high

FRB St Louis (June 2007) shows S&P 500 return: Stable (’92-’94) Very high (’82-’83, ’97-’98)


Recent Literature

Economists at FRB St Louis assert stock market boom takes place during above average GDP growth and below average inflation

They don’t find evidence of liquidity as a factor


Recent Literature

Rapid economic growth increases corporate profitability that in turn leads to above normal increases in stock prices

Stock market boom reflects real positive macro fundamentals and monetary policy targeting price stability


Recent Literature

A strong economy growing without concern for inflation most often induce stock price boom

They also find stock market boom ends within a few months of an increase in inflation


Recent Literature

In addition to economic fundamentals, behavioral finance has offered valuable explanations for several asset pricing puzzles

Momentum return concept in the aggregate market refers broadly to continuation of short-term return


Recent Literature

Barberis and Thaler (2005) suggest momentum return in the aggregate market in the form of persistence of above average return during periods of boom can be an important behavioral variable


Aim & Hypothesis

Based on this literature review, we attempt to explain deviations of equity return from long-term average with the help of both fundamental and behavioral variables

Aim is to explain post WW II era Use important macro-economic variables: inflation, funds

rate and unemployment Also, use behavioral variable – momentum return


Data & Model

We use monthly data covering the period June 1965 to November 2005

All economic data obtained from FRB St Louis website

S&P data obtained from DataStream We use inverse unemployment rate as

suggested in Ferrara (2003)


Data & Model

Deviation from long-term average is computed as the difference between current return and the last eight months moving average

In order to understand the behavior of the variables we first tried a linear regression


Data & Model

Linear regression

We use first differences of funds rate and inverse unemployment rate – these are non-stationary

t 0 1 t 2 t 1 3 t

4 t 1 5 t 6 t 1

xsr inf inf fnd

fnd ium ium


Regression Results

In linear regression not significant

Only and are significant R-square only 6% Residual CUSUM square test shows

parameter and/or variance instability

t 1inf t 1fnd

t 1xsr


Regression Results

Linear model like this one simply captures the average effect

We need to account for structural instability in a meaningful way

Some of the insignificant parameters may be important during some ‘states’


Markov Switching Model

How do we define ‘states? A popular approach in economic

analysis is to let an unobserved Markov chain to drive transition between states

Question: How many states? What is the probability of transition?



We resort to the business cycle literature to decide on the number of states

Ferrara (2003) suggests three states for the US economy

Statistical alternative to this may not be computationally feasible



Transition probability between states inferred from the data

Computational complexity of such models is well known

We use maximum likelihood method together with Expectation Maximization (EM) algorithm



MS model without behavioral variable

Total of 30 parameters

t t t

t t

t t

t 0,S 0,S t 1,S t 1

0,S t 1,S t 1

0,S t 1,S t 1 t

xsr inf inf

fnd fnd

ium ium .



Let us first look at the model inferred plots of the probability of being in a state for each month in the data (Figure 1)

A quick look at the estimation results (Table 1)



The three states are classified in term of the level of volatility

State volatility

St=1 St=2 St=3

0.136 0.036 0.342



Transition probability

0.976 0.393 0.044

0.023 0.926 0.077

0.000 0.033 0.877



Linear regression model did not find inflation significant

In the MS model inflation is significant for St=1 and 2

State St=2 is particularly interesting It has the lowest volatility Positive average deviation in return



State St=2 and 3 show ‘ium’ ↓ ‘xsr’ Intuitively ok But the magnitude of the parameter is

much smaller for St=2 Being the lowest volatility state St=2

may be exhibiting irrational behavior



State St=2 has very high probability of occurring over the ’92 – ’96 period It is about 59 months of positive ‘xsr’ Nearly 4 times the average duration of

St=2 Now we add the behavioral variable



Define the momentum return as

The model is changed to incorporate this in addition to the previous variables

t 5 t 7

t t tt t

1mmt r r

8



New model

t t t

t t

t t

t

t 0,S 0,S t 1,S t 1

0,S t 1,S t 1

0,S t 1,S t 1

0,S t t

xsr inf inf

fnd fnd

ium ium

mmt .



New probability of states (Figure 2) There are now 33 parameters and a

quick look at the estimation results (Table 2)

Estimation results are similar to that in the previous model



Average positive ‘xsr’ in St=2 is nearly twice as much in the pervious model

St=2 has still the lowest volatility ‘mmt’ parameter only significant for

St=1 and 2 Increasing ‘mmt’ reduces available ‘xsr’



St=3 captures the most volatile periods of ’70s, ’80s and early 2000 Has the shortest expected duration (7-8

months)


Conclusions

Extensive statistical diagnostics prove the efficacy of the MS approach

Incremental explanatory power of the model with ‘mmt’ has been proved by Vuong (1989) statistic Conclusively proves the influence of the

behavioral variable for ‘xsr’


Conclusions

Markov regime based model brings out better understanding of the nature of interaction between return deviation from long-run average and macro-economic and behavioral variables

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