From Harvard University.. Study of past Crashes..

[bimetalaupt]

I heard Dr. Robert Barro spech on this subject.. It is about phase delay and the imput of huge cash has taken about 6.5 years to clear the banks bad debts in the past... As stated in the Introduction we see a "Fat Tail of risk" vs Bayesian curve... Sorry but I disagree with Dr. Barro on this part of the subject...Bruce VR it is also about efficiency and the USA is the world leader .. The not world class will be the not in business , real soon. UAW is looking at this as Alabama is starting to overtake the USA auto production in America of none American firms.

We estimate an empirical model of consumption disasters using a new panel data set on
consumption for 24 countries and more than 100 years. The model allows for permanent and
transitory effects of disasters that unfold over multiple years. It also allows the timing of disasters
to be correlated across countries. We estimate the model using Bayesian methods. Our estimates
imply that the probability of entering a disaster is 1.7% per year and that disasters last on
average for 6.5 years. In the average disaster episode identified by our model, consumption falls
by 30% in the short run. In the long run, roughly half of this fall in consumption is reversed.
Disasters also greatly increase uncertainty about consumption growth. Our estimates imply a
standard deviation of consumption growth during disasters of 12%. We investigate the asset
pricing implications of these rare disasters. In a model with power utility and standard values
for risk aversion, stocks surge at the onset of a disaster due to agents’ strong desire to save. This
counterfactual prediction causes a low equity premium, especially in normal times. In contrast,
a model with Epstein-Zin-Weil preferences and an intertemporal elasticity of substitution equal
to 2 yields a sizeable equity premium in normal times for modest values of risk aversion.
Keywords: Rare disasters, Equity premium puzzle, Bayesian estimation.
JEL Classification: E21, G12
∗
We would like to thank Timothy Cogley, Xavier Gabaix, Martin Lettau, Frank Schorfheide, Alwyn Young, Tau
Zha and seminar participants at various institutions for helpful comments and conversations. Barro would like to
thank the National Science Foundation for financial support.
1
Introduction
The average return on stocks is roughly 7% higher per year than the average return on bills across
a large cross-section of countries in the twentieth century (Barro and Ursua, 2008). Mehra and
Prescott (1985) argue that this large equity premium is difficult to explain in simple consumption-
based asset-pricing models. A large subsequent literature in finance and macroeconomics has sought
to explain this “equity-premium puzzle”. One strand of this literature has investigated whether the( Barro states 7% vs 4.5% used in my model from NUY and MMXI) MOST HERE KNOW I AM RISK ADVERSE.. MOST ARE NOT AND USE THE 7%..correct ROVO)
equity premium may be compensation for the risk of rare but disastrous events. This hypothesis
was first put forward by Rietz (1988).1 A drawback of Rietz’s paper is that it does not provide
empirical evidence regarding the plausibility of the parameter values needed to generate a large
equity premium based on rare disasters.
Barro (2006) uses data on GDP for 35 countries over the 20th century from Maddison (2003)
to evaluate Rietz’s hypothesis empirically. His main conclusion is that a simple model calibrated
to the empirical frequency and size distribution of large economic contractions in the Maddison
data can match the observed equity premium. In subsequent work, Barro and Ursua (2008) have
gathered a long-term data set for personal consumer expenditure in over 20 countries and shown
that the same conclusions hold using these data. Barro (2006) and Barro and Ursua (2008) analyze
the effects of rare disasters on asset prices in a model in which consumption follows a random
walk, disasters are modeled as instantaneous, permanent drops in consumption, and the timing of
disasters is uncorrelated across countries. They show that it is straightforward to calculate asset
prices in this case.
The tractability of the models used in Barro (2006) and Barro and Ursua (2008) comes at the
cost of empirical realism in certain respects. First, their model does not allow for recoveries after
disasters. Gourio (2008) argues that disasters are often followed by periods of rapid growth. A
world in which all disasters are permanent is far riskier than one in which recoveries often follow
disasters. Assuming that all disasters are permanent therefore potentially overstates the asset-
pricing implications of disasters. Second, their model assumes that the entire drop in consumption
due to the disaster occurs over a single time period, as opposed to unfolding over several years as in
the data.2 Third, their model assumes that output and consumption follow a random walk in normal
1
Other prominent explanations for the equity premium include models with habits (Campbell and Cochrane,
1999), heterogeneous agents (Constantinides and Duffie, 1996) and long run risk (Bansal and Yaron, 2004).
2
This assumption is criticized in Constantinides (2008).
1
times as well as times of disaster. A large literature in macroeconomics has debat

Attachments:

[bimetalaupt]

THJE MATH.. FOR THOSE WHO CAN NOT SLEEP.. THIS EQUATION IS FOR YOU

6
Asset Pricing
We follow Mehra and Prescott (1985) in analyzing the asset pricing implications of the consumption
process we estimate above within the context of a representative consumer endowment economy.
We assume that the representative consumer in our model has preferences of the type developed by
Epstein and Zin (1989) and Weil (1990). For this preference specification, Epstein and Zin (1989)
show that the return on an arbitrary cash flow is given by the solution to the following equation:

Et β ξ
Ci,t+1
Ci,t

(−ξ/ψ)
−(1−ξ)
Rw,t,t+1 Ri,t,t+1  = 1,
(5)
where Ri,t,t+1 denotes the gross return on an arbitrary asset in country i from period t to period
t + 1, Rw,t,t+1 denotes the gross return on the agent’s wealth, which in our model equals the
endowment stream. The parameter β represents the subjective discount factor of the representative
consumer. The parameter ξ =
1−γ
1−1/ψ ,
where γ is the coefficient of relative risk aversion and ψ is
the intertemporal elasticity of substitution (IES).20
Much work on asset pricing—including Mehra and Prescott (1985), Rietz (1988) and Barro
(2006)—considers the special case of power utility. In this case, the coefficient of relative risk
aversion equals the reciprocal of the IES—γ = 1/ψ. In other words, a single parameter governs
consumers’ willingness to bear risk and substitute consumption over time. Bansal and Yaron (2004)
and Barro (2009), among others, have emphasized the importance of delinking these two features of
consumer preferences. Our results below provide additional evidence in support of a more flexible
model.
20
The representative-consumer approach that we adopt abstracts from heterogeneity across consumers. Wilson
(1968) and Constantinides (1982) show that a heterogeneous-consumer economy is isomorphic to a representative-
consumer economy if markets are complete. See also Rubinstein (1974). Constantinides and Duffie (1996) argue that
highly persistent, heteroscedastic uninsurable income shocks can resolve the equity-premium puzzle.
19
The asset-pricing implications of our model with Epstein-Zin-Weil (EZW) preference

[decoy409]

House has been in a on/off crash mode since before 200B.C.E. So the partial foundation is not relevant to the overall, 'today's version.'
However if one cares to look back as you present in modern times (to speak) they certainly will have a 'fresh look' at things instead of the original version with out all the bells and whistles.

[bimetalaupt]

MORE ON EQUITY RISK PREMIUM FOR NORMAL STOCKS ( NOT PRICED CONTROLLED UTILITIES) DR. Robert Barro (2009) find this to be about 7% over risk free Bonds.. AT one percent over inflation.. I think we were wrong on this but time will tell how well QE2 works.. It is just too small to reduce bond cost as projected due to the problems with the ECB!!! Bruce VR

6.1
The Equity Premium with Epstein-Zin-Weil Preferences
The asset-pricing results for our model are presented in Table 6. Specification 1 in the table is
for our baseline model and preferred preference parameters. The table also presents results for a
number of alternative specifications. For each specification, we present results on the one hand for
a long sample with a representative set of disasters and on the other hand for a long sample for
which agents expect disasters to occur with their normal frequency but no disasters actually occur.
This latter case is meant to capture asset returns in “normal” times, such as the post-WWII period
in most OECD countries. The statistics we report are the logarithm of the arithmetic average gross
return on each asset (log E[Ri,t,t+1 ]).
For the baseline model with IES = 2 and γ = 6.5, the model generates an unleveraged equity
premium of 4.8% per year. Our disaster model thus matches the equity premium and the risk-free
rate observed in the data for these preference parameters. The equity premium generated by the
model is quite sensitive to the value of γ. With γ = 4.5, the model generates an equity premium of
1.8%, while it generates an equity premium of 8.8% when γ = 8.5. For comparison, specification
9 in Table 6 presents results for a version of the model without disasters. In this case, the model
generates an equity premium that is too small by a factor of 10. This last finding is in line with
Mehra and Prescott (1985).
Figure 6 depicts equity and bond returns over the course of a “typical” disaster when IES = 2
and γ = 6.5. When the news arrives that a disaster has struck, the stock market crashes. In
contrast, bills are risk-free in the short run. Their returns are thus not affected in this initial
period. The crash in the stock market at the onset of the disaster coincides with a sizable drop in
consumption. Stocks must thus yield a considerable return-premium over bills in normal times to
compensate for the risk of a disaster.
When the news arrives that the disaster has ended, stocks surge relative to bills. The crash
at the beginning of the disaster and the boom at the end of the disaster are roughly equally large
and the average equity premium during the disaster (excluding the initial crash and the boom at
the end) is similar to the average equity premium in normal times. The average equity premium
in a long sample with a representative number of disasters is thus similar to the average equity
premium in a long sample for which agents expect disasters to occur with their normal frequency
but no disasters actually occur (the case considered in the three rightmost columns of Table 6).
22
Two major differences between our disaster model and earlier models of disasters are that our
model allows for partial recovery after disasters and that in our model disasters unfold over several
years. To assess the importance of these features for our asset pricing results, specifications 4 and
5 in Table 6 report results for two alternative versions of the model. In specification 4, we consider
a case in which disasters are completely permanent.26 This specification of the model matches the
equity premium in the data when γ = 4.5. The fact that our model allows for partial recovery
after disasters thus accounts for a large part of the difference in our results and the results of Barro
(2006) and Barro and Ursua (2008). With permanent disasters and γ = 6.5, the equity premium
rises to almost 14%. This reflects the fact that the equity premium is highly non-linear in γ in the
disaster model. A world in which disasters are completely permanent is clearly much riskier than
a world in which there is substantial recovery after disasters.
In specification 5, we consider a case in which disasters are both completely permanent and
occur in a single period.27 For this specification, we can match the equity premium in the data
with γ = 2.7.28 The main reason why the single-period case yields a lower γ is that in this case
the drop in consumption and the drop in the price of stocks are fully coincident. In contrast, in
a multi-period disaster, stocks crash at the onset of the disaster — when the news arrives that
the disaster has struck (see Figure 6)— while a large fraction of the drop in consumption occurs
in subsequent periods. A second reason why the γ needed to match the equity premium is lower
when disasters occur in a single period is that agents have a greater desire to save at the onset of
a multi-period disaster since they expect consumption to keep falling for several periods and wish
to smooth their consumption over the disaster. This desire to save limits the fall in stock prices at
the onset of disasters in our baseline model. The same savings effect does not arise when the entire
disaster occurs in a single period.
26
We consider a version of our model in which φi,t = θi,t and set the mean and variance of these shocks for each
year of the disaster equal to the mean and variance of peak-to-trough drops in consumption due to disasters in our
baseline model divided by the expected length of disasters.
27
We set the probability of exiting a disaster equal to one, assume that φi,t = θi,t and that the distribution of
these shocks is equal to the distribution of the peak-to-trough drop in consumption over the course of disasters in
our baseline model.
28
The model analyzed in specification 3 is very similar to the model analyzed by Barro and Ursua (2008). Their
model matches the equity premium when γ = 3.5, while the model in specification 3 matches the equity premium
for a slightly lower value of γ = 2.7. This difference arises because the size distribution of disasters in our model is
relative to trend, while the peak-to-trough distribution used by Barro and Ursua (2008) does not adjust for trend
growth over the course of the disaster and because of differences between our approach to estimating the distribution
of disasters and the non-parametric approach of used by Barro and Ursua (2008).
23
Specifications 10-12 in Table 6 consider the case in which the short run disaster shocks follow a
Gamma distribution. With γ = 6.5 and an IES of 2, the equity premium is 3.4% and the risk-free
rate is 2.0%. The gamma model matches the equity premium and risk-free rate when γ = 7.5.
This difference arises because the gamma model allocates slightly more of the overall volatility in
consumption to the short-run shock than to the long-run shock than does the baseline model.
The asset-pricing exercises discussed above are based on the posterior means of the parameters
of our model. These calculations thus ignore sampling error in our parameter estimates. Given the
limited amount of data we have to estimate the frequency, size, and shape of rare disasters, the
posterior standard deviation of the parameters governing disasters are in some cases substantial.
Using the posterior distribution of the parameters of our model, we can calculate a posterior
distribution for the equity premium. This allows us to investigate the precision of our model’s
implications for the equity premium. The posterior distribution for the equity premium implied
by the posterior distribution of the parameters of our model is plotted in Figure 7. In calculating
this distribution, we assume that agents have β = exp(−0.034), γ = 6.5 and ψ = 2. Figure 7
shows that our estimates place more than 90% weight on parameter combinations that generate an
equity premium of more than 3%. The centered 90% probability interval for the equity premium
is [0.032, 0.073].
An important question is whether our results regarding the equity premium are somehow “built
in” to our prior or estimation algorithm. To assess the degree to which our results on the equity
premium are driven by the data as opposed to our priors and estimation algorithm, we simulate
an artificial dataset of the same size as our data (24 countries and a total of 2685 observations)
from our model with the disaster probabilities set to zero. We then estimate our model on these
data and calculate the posterior distribution of the equity premium. This distribution is plotted in
Figure 8. For this alternative data set, our model places a large probability (roughly 77%) on the
equity premium being below 1%. Clearly, our results would be very different if there in fact were
no disasters in the data. The distribution has a long right tail reflecting the fact that even a data
set the size of ours with no disasters would not entirely rule out the possibility that such events
could occur.
We can also calculate the posterior distribution of the value of the coefficient of relative risk
aversion that matches the equity premium. This distribution is plotted in Figure 9. The centered
24
90% probability interval for γ is [5.2, 8.2]. Our disaster model thus implies a fairly tight distribution
for the coefficient of relative risk aversion.
During the disaster, consumers expect consumption to keep falling and thus have an incentive
to save. This force drives up the price-dividend ratio for assets and drives down their expected
returns. As a consequence, stock and bill returns are lower on average during disasters then during
normal times even after the initial crash (see Figure 6). Furthermore, the return on stocks and bills
is temporarily high during the recovery period after a disaster. These features of asset prices in
our model line up well with the data. Barro (2006) reports low returns on bills and stocks during
many disasters. He also presents evidence that real returns on U.S. Treasury bills were unusually
low during wars. This regularity is inconsistent with many macroeconomic models (Barro, 1997,
Ch. 12). There is furthermore some evidence that real returns on bills are temporarily high after
wars; for example, in the United States after the Civil War and WWI.
In our model, consumption growth is predictable following major disasters, as the country re-
covers to the level of potential consumption. Outside of disasters and their immediate aftermath,
however, consumption growth is hard to forecast. The explanatory power of the price dividend
ratio in predicting future consumption growth at medium and short horizons is close to zero.29 In
this regard, our model differs from the long-run risks model of Bansal and Yaron (2004) which gen-
erates substantial forecastability of consumption growth using the price-dividend ratio. Beeler and
Campbell (2009) argue that this feature of the model is hard to reconcile with the U.S. consumption
data, particularly in the post-WWII period.
One way to think about the importance of the features we have added relative to earlier work
on disasters is to ask how we could recalibrate the simpler model used in Barro and Ursua (2008)
to generate an equity premium of the same size as the one our model yields. Recall that, in Barro
and Ursua (2008), disasters are modeled as instantaneous and permanent drops in consumption.
The appropriate calibration for this model may, therefore, differ from the observed probability and
size of (partially transient) disasters in the data. The equity premium in Barro and Ursua (2008)
is given by
log ERe − log Rf = γσ 2 + pE{b[(1 − b)−γ − 1]},
where p denotes the probability of disasters, b denotes the permanent instantaneous fraction by
29
Specifically, we have analyzed regressions of consumption growth at one, 3 and 5 year horizons on the current
price dividend ratios. The R2 of such regressions is consistently 3% or less.
25
which consumption drops at the time of disasters, σ 2 denotes the variance of consumption growth
in normal times, and γ denotes the coefficient of relative risk aversion. For simplicity, consider a
version of this model in which b is a constant. Barro and Ursua’s (2008) results can be roughly
replicated with p = 0.0363 and a constant size of disasters of b = 0.36. In contrast, the simple model
with constant-sized, permanent disasters of size b = 0.36 matches our results for a probability of
disasters p = 0.008. The substantially lower probability of disasters in our calibration—and the
correspondingly lower equity premium for any given value of risk aversion—is due to the partial
recoveries we estimate after many disasters as well as the gradual fall in consumption after disasters
begin.

[bimetalaupt]

WXYZ,
As you know FTI and I have had this game on defending our system balance... He won as I am shifting to the Equity side due to the increased ERP calculations by Robert Barro vs Dr. A. Damodaran , PhD 5.2% ERP.... Yiou can see where I got my 4.36% from.. OK it is out of date...4.36% +3.843 = 8.203% total return for 10 year risk free of 3.843% as of 12/31/2009

Bi Metal Au Pt..
For the record from Dr. Damodaran site on NYU Stern School of business....

Implied Equity Risk Premium (US)

I will be posting my updates on the implied equity risk premium (ERP) on the S&P 500 on a monthly basis at the end of each month. (To see my explanation of the implied equity risk premium, please download my paper on the ERP)

Implied Premium on 1/1/11 =5.20%
Implied Premium in previous month = 5.08%


Implied ERP (US) on 12/31/09= 4.36%
Implied ERP on 12/31/08 = 6.43%
Implied premiums by month for recent months

Download spreadsheet to compute implied premium

[robinking]

Listening to politicians try to manage the economy is like listening to a surgeon trying to manage a major league baseball team. We need common sense solutions, but will get political bandaids.

[usaone]

Were would we be without Frank and Bimetal!?!? ;D ;D

Karma for both. ;D ;D

[bimetalaupt]

Jan 21, 2011 14:39:39 GMT -5 @franktheimpaler said:

OK...we should do 15%-20% (approx) for 2011

Frank,
Good Morning.. Well we are at it again.. Market down and Equity Risk Premium (ERP)up..
It look like the talking heads are telling the world all the industrial production has stopped.. Great buying season is almost at hand.

Current total return 8.60652352438%
current 10 year t-bond 2.2800000%
implied ERP 6.32652352438%
MMXII Aug 31,2012 Target 16943.0274375289 (Wild)!!

What are your wild thought this morning!!

Just a thought,
Bi Metal Au Pt
Now we are at a 55% ROE for some of the Eagle-Ford formations drilled in 2010!! Bets the market.. Your thoughts??

[Aman A.K.A. Ahamburger]

Now we are at a 55% ROE for some of the Eagle-Ford formations drilled in 2010!! Bets the market.. Your thoughts??

I can tell you my thoughts!! That's what it's all about.. Low rates and assets for free!!