Download A BEHAVIORAL MODEL OF THE PERFORMANCES FOR E

A BEHAVIORAL MODEL OF THE PERFORMANCES FOR
EMERGING FINANCIAL MARKETS IN THE CONTEXT OF ACTUAL
GLOBAL CRISIS
Authors: Gabriela PRELIPCEAN1, Professor PhD, “Stefan cel Mare” University of Suceava,
Mircea BOSCOIANU2, Professor PhD, Military Technical Academy of Bucharest
Abstract
The interest is to model the value loss suffered by assets in the global crisis by considering
both the cross section and the time variation. The volatility of assets is given by the variations
at risk premium levels. The generalized model is inspired from the common framework for
stock, bonds, exchange rates (Cocharane, 1999, Gabaix, 2008) and is equipped with two kinds
of shocks, one real for the capital market and one nominal, for the money market
Keywords: global crisis, capital market
JEL Classification: G10, G30
Un model comportamental a performanţelor pieţelor financiare emergente în contextul
crizei globale actuale
Autori: Prof.Univ. Dr. Gabriela PRELIPCEAN, Universitatea Ştefan cel Mare, Suceava,,
Prof.Univ.Dr. Mircea BOSCOIANU, Academia Tehnică Militară Bucureşti
Abstract
Interesul constă în modelarea valorii pierderilor suferite de active pe parcursul crizei globale
prin considerarea atât a evoluţiei în secţiune transversală, cât şi a variaţiei în timp.
Volatilitatea activelor este dată de variaţiile la nivelul primelor de risc. Modelul generalizat
este inspirat din cadrul comun pentru acţiuni, obligaţiuni, rate de schimb (Cocharane, 1999,
Gabaix, 2008) şi este echipat cu două tipuri de şocuri, unul real pentru piaţa de capital şi altul
nominal pentru piaţa monetară
Cuvinte cheie: criză globală, piaţa de capital
Clasificare JEL: G10, G30
1. INTRODUCTION
The model is based on a dedicated description of the risk premia, named time-varying
intensity of disasters (in the Rietz-Barro hypothesis of additional premia result from extreme
events) and is capable to explain some dynamic asset pricing mechanisms (procyclical
variation of stock prices, long term predictability of extra returns, countercyclical variation of
market volatility) and it gives a different view of the analysis of fundamental risk factors that
1
2
E-mail address: [email protected]
E-mail address: [email protected]
604
explain financial time-series behavior. The consumption growth is modelled as an
independently and identically distributed (i.i.d.) lognormal process. The interest is to
emphasize that the model generates interesting asset price behavior internally, not from
exogenous variation in the probability distribution of consumption growth. The model's
functional form and parameters are design so that the risk-free interest rate is constant.
The framework incorporates a time-varying intensity inspired from extreme/ rare events.
In this case the asset's fundamental value falls by a time-varying amount that generates timevarying risk premia with practical implications on the analysis of volatility and return of asset prices.
Using the linearity-generating processes (Gabaix, 2007), all prices could be exactly solved in closed
form. In this framework, the following empirical mechanisms can be understood qualitatively:
equity premium puzzle; risk-free rate-puzzle; excess volatility puzzle; predictability of aggregate
stock market returns with PER (price-dividend ratios); value premium; a better explanation of the
characteristics for asset returns; the behavior of nominal yield curve in a new based on timevarying risk-aversion as a result of the investor sentiment.
2. A CRITICAL ANALYSIS OF THE LITERATURE
Rietz (1988) postulate that extreme / rare events such as economic depressions represent a
major determinant of asset risk premia. Barro (2006) has shown that these global rare events
have been sufficiently frequent and large to make the Rietz’ postulate viable and applicable in
the high risk premium on equities. The Rietz-Barro hypothesis could be formulated with
constant intensity of risk events but in this case is difficult to account for some key features of
asset markets, such as volatile PDR (price dividend ratios) for stocks, volatile BRP (bond risk
premia), and in general, the return predictability. Fahri, Gabaix (2007) formulate a variableintensity version of the rare events hypothesis, and investigate the impact of time-varying
intensity on the prices of stocks, bonds, exchange rates and the predictability of their
performances.
The value loss suffered by assets in crisis varies both along the cross-section and over
time and the time varying risk premia could be considered as a generator of volatility. Stock
prices are high when stocks bear little risk, and this perceived riskiness mean-reverts leads to a
mean-reversion of the PDR. In this case stocks always exhibit excess volatility produced by
their stochastic riskiness and risk premia.
The inspiration for a single framework for stocks, bonds and exchange rates is from
Cochrane (1999) framework, who emphasized the similarities in puzzles about those three assets.
These concern chiefly the patterns of excess volatility and return predictability. The critical
similarities suggest that the same microfoundations may have the potential to explain the
empirical regularities in all these asset markets. In a mixed/ total assets market a simple returnchasing offers superior returns. In bond markets, when the yield is high compared to money
market performances, bond generates a higher total return (interest plus capital appreciation).
In currency markets, the higher-yielding currency generates a higher total return (interest plus
currency appreciation) than low-yielding currencies. In equity markets, times when stocks have
high DPR are also the periods when stocks have a high future returns (dividend plus capital
appreciation).
In the stock market the processes and mechanisms of interest are the following: equity
premium puzzle; risk-free rate puzzle; excess volatility puzzle (stocks are more volatile than
warranted by a model with a constant discount rate); aggregate return predictability (partly
predicted by PER, DPR and consumption aggregate wealth ratio (CAWR).
The main aspects about the cross-section of stocks are: the value-growth puzzle; the
characteristics vs. covariance puzzles (stock characteristics like PDR often predict future returns
as well or better than covariance with risk factors); the nominal bond puzzles (the yield curve
slopes up on average and the premium of long-term yields over short-term yields is too high to
be explained by a traditional RBC model). The interest is also on Fama-Bliss, Campbell605
Shiller, Cochrane-Piazzesi empirical mechanisms (a high slope of the yield curve predicts excess
high positive returns on long term bonds and along term interest rates will fall).
The crisis leads to a jump in inflation that has a greater detrimental impact on long-term
bonds, and so they imply a high risk premium relative to short-term bonds. This partially
explains the upward slope of the nominal yield curve. If the expected jump in inflation itself
varies, the slope of the yield curve will vary, and will predict excess bond returns. A high
slope will mean-revert, hence predicts a fall in long rate, and high returns on long term bonds.
The same mechanism is also available for stocks. If the crisis reduces the fundamental value by a
time-varying amount, this yields a time-varying risk premium which generates a time-varying
PDR and excess volatility. When investors perceive the intensity of the crisis as low, the PDR is
high and future returns low. Using this mechanism, stocks with low PDR (value stock) have
high subsequent returns. The model is capable to analyze also other assets, such as corporate
bonds, and options. If high quality bonds default mostly during crises, they should command a
high premium. For options prices, is possible to generate a volatility smirk (a high put price
and hence implied volatility) for deep out-of-the-money puts.
The changing beliefs about the intensity of possible crises are very close to what the
behavioral literature calls animal spirits, and the recent rational literature calls perception of
distant risks, or time-varying risk aversion. This structure offers a consistent way to think about
the impact of changing sentiment on prices and performances in the time-series and the crosssection.
The framework uses the traditional isoelastic expected utility framework and the present
model (which is in an endowment economy) can be directly mapped into a production
economy, with the traditional real-business cycle features. Based on the linearity-generating
processes developed in Gabaix (2007) the model is particularly tractable. Using, stock and
bond prices have linear closed forms. As a result, asset prices and premia can be derived and
understood fully, without recourse to simulations. This model is based on a different
hypothesis about the origins of risk premia, namely the fear of rare disasters, which has some
plausibility, and allows agents to have moderate risk aversion. This framework accounts easily
for some facts that are harder to generate in other models.
The model exhibits time-varying risk premia. In that, it is similar to models with timevarying risk-aversion (Abel, 1990; Campbell, Cochrane, 1999). The model is complementary
to the literature on long term risk which views the risk of assets as the risk of covariance with
long-run consumption (Bansal, Yaron, 2004; Bansal, Shaliastovich, 2007).
Bekaert, Hodrick, Marshall (1997) is the first model for bonds, stocks and agent rates.
They construct a two-country, monetary model, where agents have first-order risk aversion.
They find it impossible to match quantitatively the return predictability observed in the data.
Also, they have mostly international finance stylized facts in mind but they do not study the
own-currency predictability of bond returns or the own-currency predictability of the stocks
market via price-dividend ratios.
In the literature that studies jumps (Liu, Pan, Wang, 2004; Santa Clara, Yan, 2006) the
jumps in happens every few days or few months, and affect consumption by moderate amounts,
whereas the jumps in the rare-disasters literature happens perhaps once every 50 years, and are
larger. Moreover those authors do not analyze the impact of jumps on bonds and return
predictability.
3. THE FRAMEWORK FOR CRISIS EVENTS
The framework is based on Rietz-Barro contributions and adds a stochastic probability and
intensity of crisis events. Let an economy with a representative agent with the utility
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  t Ct1  1
E0  e
  0  0
1   
 t 0
The pricing kernel is the marginal utility of consumption M t  e t Ct and the price of


an asset yielding the dividends Ds st is given by Lucas formula: Pt  Et  st M s Ds / M t .
In the crisis happens the dynamics of the consumption and the marginal utility of
consumption are given by the following relations:
g
if there is no disaster at t  1
Ct 1 
e
 g
Ct

e Bt 1 if there is a disaster at t  1
R
if there is no disaster at t  1
M t 1 
e
   R 
Mt

e Bt 1 if there is a disaster at t  1
(1)
(2)
where R    g c is the risk free rate.
Let define the dynamics of dividends after the shock:
Di ,t 1
Dit




gi D
D

if there is no disaster at t  1
e 1   i,t 1
  gD
D
i

e 1   i ,t 1 Fi ,t 1 if there is a disaster at t  1
(3)
To model time variation of recovery rate is introduced the expected resilience of the
assets:


H it  pt Et Bt1 Fi ,t 1  1 There is a disaster at t  1
(4)
In linearity generation process (Gabaix, 2007) that make prices linear in the factors
and independent of the functional form of the noise:
1  H * H ˆ
Hˆ t 1 
e H t   tH1
1 Ht
(5)
The nominal yield curve slopes up on average and there is a stochastic bond risk
premium that increases with the difference in the long term rate minus short term rate. The
dynamics of the real value of money is expressed:
Q
if there is no disaster at t  1
Qt 1 1  it   t 1

Qt
 1  it   tQ1 Ft $1 if there is a disaster at t  1


(6)
The default could be an outright default or a burst of inflation that increase the price
level reducing the real value of the coupon. In this mechanism to isolate the bond effects is
assumed the case where
 
 
H S  pt Et Ft $1 Bt1  1 is a constant.
(7)
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Inflation is decomposed as it  i*  iˆt
variable part:


where i* is the constant component and iˆt the

1  i* i ˆ
iˆt 1 
 e it  1Disasterat t 1 j*  ˆjt   ti1
1  it
(8)
In the crisis the inflations jumps with j*  ˆjt and this makes the bonds particularly
risky. The expression for this jump is:
ˆjt 1  1  i* e  ˆjt   t j1
1  it
(9)
where  t j1 has a zero mean and is uncorrelated with disasters and  tQ1 .
The expected return of an asset conditional on no crisis is:
rte 
1
1  pt
#
 R


 e  pt Et  Bt1 Pt 1    1

Pt  


(10)
In the limit of small intervals:


P#  
rte  R  pt 1  Et  Bt t   
Pt  


(11)

 P # 
rte  rf  pt Et  Bt 1  t 
Pt 


with
rf  R  pt Et Bt  1

(12)

(13)
representing the real risk free rate.
4. CONCLUSIONS
This is a simple but intuitive way to analyze the impact of crises on stock and bond prices and
its implication for time-varying risk premia and asset predictability. Given the architecture of
the model is quite simple to state and to solve in closed form, it can serve as a simple
benchmark for various questions in macroeconomics and finance. Moreover, the model does
suffer from several limitations, and suggests several questions for future research.
For future work it would be crucial to examine empirically the predictions that the
model jointly generates, for stocks, bond, options. Another interesting future contribution will
be the estimation on how investor might know update their estimates of resiliencies. Risk
premia seem to go down after good news for the economy and for individual firms (the
growth firm’s effect) and a relevant updating will involve resiliencies going up after good
news about the fundamental values of the economy, or the individual stocks. Modelling that
would lead to a link between recent quantities, risk premia, and future predictability. Some
authors (Gabaix, 2007) suggests that various puzzles in international macroeconomics
(including the forward premium puzzle and the excess volatility puzzle on exchange rates)
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can be accounted for a global version of the present framework, giving an interesting
perspective for the analysis of contagion mechanisms of the actual global crisis (2008-2009).
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