Transcript RISK AND VOLATILITY: ECONOMETRIC MODELS AND …

DOWNSIDE RISK AND
LONG TERM INVESTING
ROBERT ENGLE
NYU STERN
2007
RISK
A Risk is a bad event that might occur
in the future.
Some risks are worth taking because
the possible benefit exceeds the
possible costs.
Finance investigates which risks are
worth taking.
NOBEL ANSWERS
Markowitz (1952) and Sharpe(1964)
and Tobin (1958) received Nobel
awards in 1990 and 1981 for
associating risk with the variance of
financial returns.
Capital Asset Pricing Model or CAPM
answer: Only variances that could
not be diversified would be rewarded.
BLACK-SCHOLES AND MERTON
Options can be used as insurance policies.
For a fee we can eliminate financial risk for
a period.
What is the right fee?
Black and Scholes(1972) and
Merton(1973) developed an option pricing
formula from a dynamic hedging argument.
Their answer also satisfies the CAPM.
They received the Nobel prize in 1997
DOWNSIDE RISK
The risk of a portfolio is that its value will
decline, hence DOWNSIDE RISK is a
natural measure of risk.
Many theories and models assume
symmetry: c.f. MARKOWITZ, TOBIN,
SHARPE AND BLACK, SCHOLES,
MERTON and Volatility based risk
management systems.
Do we miss anything important?
MEASURING DOWNSIDE
RISK
Many measures have been proposed.
Skewness - a measure of asymmetry of
returns
Skewness=E  r  / E  r
3

2 3/ 2
Value at Risk – number of $ that you can
be 99% sure is worse than what you will
lose in the next 10 days.
x is the  Value at risk if P  r   x   
PREDICTIVE DISTRIBUTION OF
PORTFOLIO GAINS
1%
$ GAINS ON PORTFOLIO
MULTIVARIATE DOWNSIDE RISK
WHAT IS THE LIKELIHOOD THAT A
COLLECTION OF ASSETS WILL
ALL DECLINE?
THIS DEPENDS PARTLY ON
CORRELATIONS
FOR EXTREME MOVES, OTHER
MEASURES ARE IMPORTANT TOO.
MULTIVARIATE DOWNSIDE
“Where are my correlations when I
need them?” – a portfolio manager’s
lament.
When country equity markets decline
together more than can be expected
from the normal correlation pattern, it
is called CONTAGION.
Correlations and volatilities appear to
move together.
MEASURING JOINT DOWNSIDE
RISK
What is the probability that one asset will
have a very bad return if another asset has
a very bad return?
Find x such that   P  ri  xi 
  P ri  xi rj  x j  P  rj  x j ri  xi 


Tail dependence (lower tail dependence) is
defined as the limit as this probability goes
to zero. What is the probability that one
asset has an extreme down move when
another has an extreme down move?
DEFAULT CORRELATIONS
A default is a random event. We can
define the correlation between two default
events.
iD, j  Corr Iri  xi  , Irj  x j 

PI


 
ri  xi  Irj  x j
 1   
2
      / 1   
For extremes, the default correlation is the
same as the tail dependence.
IMPLEMENTING THESE MODELS
PRACTITIONERS REQUIRED
ESTIMATES OF VARIANCES AND
COVARIANCES or VOLATILITIES
AND CORRELATIONS
PRACTITIONERS REQUIRED
METHODS TO COMPUTE VALUE
AT RISK and DEFAULT
CORRELATIONS
ESTIMATES DIFFER FOR
DIFFERENT TIME PERIODS
Volatility is apparently varying over
time
What is the volatility now?
What is it likely to be in the future?
How can we forecast something we
never observe?
VOLATILITY HISTORY
U.S. BROAD MARKET INDEX
S&P500
RETURNS FROM
Jan 1963 TO Nov. 2003
.1
.0
1600
-.1
1200
-.2
800
-.3
400
0
55 60 65 70 75 80 85 90 95 00 05
SPCLOSE
SP
.06
.04
.02
.00
-.02
300
-.04
250
-.06
200
150
100
50
66 68 70 72 74 76 78 80 82 84 86
SPCLOSE
SP
.08
.04
.00
-.04
1600
-.08
1200
800
400
0
90 91 92 93 94 95 96 97 98 99 00
SPCLOSE
SP
.08
.04
.00
1600
-.04
1400
-.08
1200
1000
800
1998
1999
2000
SP500
2001
2002
SPRETURNS
2003
THE ARCH ANSWER
Use a weighted average of the volatility
over a long period with higher weights on
the recent past and small but non-zero
weights on the distant past.
Choose these weights by looking at the
past data; what forecasting model would
have been best historically? This is a
statistical estimation problem.
ARCH/GARCH VOLATILITIES
VOL_SP
.5
.4
.3
.2
.1
.0
1990
1992
1994
1996
1998
2000
2002
CONFIDENCE INTERVALS
.10
.05
.00
-.05
-.10
1990
1992
1994
3*GARCHSTD
1996
1998
SPRETURNS
2000
2002
-3*GARCHSTD
THE ECONOMICS OF
VOLATILITY
SURPRISING SUCCESS
Although the original application was
macroeconomic, the big success was
for financial data.
ARCH was ideally suited to modeling
some key features of financial data
The simple GARCH(1,1) model has
proven a good starting point for
almost every type of financial return
series. WHY?
WHY DO PRICES CHANGE?
BETTER ANSWER
Economic news on future values and
risks moves prices
Volatility is the natural response of a
financial market to new information.
This news arrives in clusters.
LONG RUN RISKS
Long episodes of high and low
volatility are evident in the data
What determines these long run or
low frequency risks?
One important measure is the flow of
new information on the macro
economy
WHAT DETERMINES LONG RUN
RISK?
A RECENT STUDY BY GONZALO
RANGEL AND MYSELF FOR 50
COUNTRIES FROM 1990-2005
FOUND SOME INTERESTING
ANSWERS.
Forthcoming RFS 2008
WHAT MAKES FINANCIAL
MARKET VOLATILITY HIGH?
High Inflation
Slow output growth and recession
High volatility of short term interest rates
High volatility of output growth
High volatility of inflation
Small or undeveloped financial markets
Large countries
WHAT MAKES CORRELATIONS
HIGH?
Correlations generally rise when
market volatility rises
Correlations within an industry or
sector will generally rise when the
volatility of that sector rises.
Thus falling markets and macro
volatility predict higher correlations
See Engle and Rangel(2007) and Engle(2007) for evidence.
CDO PRICING
The value of tranches of collateralized
debt obligations depend upon default
correlations.
Senior tranches become riskier when
default correlations rise.
Default correlations and tail
dependence rise when market
volatility rises just as do ordinary
correlations
Berd, Engle, Voronov(2007) Journal of Credit Risk
IS RISK PRICED OVER
TIME?
WHEN RISK IS PREDICTED TO
CHANGE, DO PRICES CHANGE?
When one asset is riskier than
another, we will only buy it if it is less
expensive (per dollar of expected
payout).
When an asset is predicted to be
riskier today than it was yesterday, its
price should fall.
Volatility news predicting higher
future risks should be accompanied
by falling prices.
ASYMMETRIC VOLATILITY
Asset Price declines today predict
higher volatility in the future than do
equal price increases.
Nelson and Zakoian
Volatility responds asymmetrically to
price moves
TARCH and EGARCH are popular
specifications
PRICING LONG RUN RISKS
When long run risks look greater,
prices today are lower.
Solving long run risks will increase
asset prices today
Macroeconomic policy is important
FINANCIAL RISKS TODAY
S&P 500 Nov 21, 2007
.08
.04
.00
1,600
-.04
1,400
-.08
1,200
1,000
800
600
00
01
02
03
04
ADJ_CLOSE
05
SP
06
07
MSCI ITALY EWI: Nov 21, 2007
.15
.10
.05
.00
40
35
-.05
30
-.10
25
20
15
10
00
01
02
03
04
ADJ_CLOSE_EWI
05
06
EWI
07
AUSTRIA MSCI : EWO: Nov 21, 2007
.08
.04
.00
50
-.04
40
-.08
30
20
10
0
00
01
02
03
04
ACLOSE_EWO
05
06
EWO
07
MSCI EAFA: EFA: Nov 21, 2007
.08
.06
.04
.02
.00
100
-.02
-.04
80
-.06
60
40
20
2002
2003
2004
2005
ADJ_CLOSE_EFA
2006
EFA
2007
ALL GARCH VOLATILITIES
.5
.4
.3
.2
.1
.0
2002
2003
2004
VOLAUSTRI A
VOLUS
2005
2006
VOLITALY
VOLEFA
2007
ALL GARCH VOLATILITIES 2007
.40
.35
.30
.25
.20
.15
.10
VOLAUSTRIA
VOLUS
VOLITALY
VOLEFA
11
/1
10
/1
9/
3
8/
1
7/
2
6/
1
5/
1
4/
2
3/
1
2/
1
.05
WHY ARE VOLATILITIES SO
HIGH -- WILL THEY STAY HIGH?
For most assets, they are high
relative to the last several years but
not high relative to 2000-2002.
In the US, I think this is due
A) Macroeconomic uncertainty
B) Credit problems particularly
associated with subprime mortgages
MACROECONOMIC
UNCERTAINTY
Will the housing slowdown bring a
recession or will the export industries
keep the economy growing?
Is recession or inflation the greater
threat?
What will the FED do?
CREDIT INDUSTRY
Subprime mortgage holders generally
expect some defaults. They are now
predicted to be greater than historically
observed. Why is this a surprise?
Our last housing crisis was in the early 90’s
before subprime lending was important so there
is little useful data
Some inappropriate or fraudulent lending
Securitization of these contracts has made it
difficult to know the risks. Senior tranches were
rated AAA and are now downgraded.
A related argument applies to the large
credit needs of private equity.
WHY WERE US VOLATILITIES SO
LOW UNTIL SUMMER 2007?
MANY REASONS TO THINK THE RISKS
WERE HIGH:
Massive budget deficits
Balance of payments deficit
Expensive War going badly
Chinese ownership of vast US debt
High energy prices
Too many private equity and hedge funds
But volatility remained low because these
risks were in the future and there was little
information on their outcomes.
WERE WE PREPARED?
VERY LONG RUN RISKS!
ARE WE READY FOR THESE?
TWO VERY LONG RUN RISKS
CLIMATE CHANGE
PUBLIC PENSION FUND SOLVENCY
BOTH OF THESE ISSUES WILL REQUIRE
MAJOR TAXES AND EXPENDITURES AT SOME
TIME IN THE FUTURE.
PRESUMABLY BOTH RISKS ARE
RESPONSIBLE FOR SOME REDUCTION IN
ASSET PRICES AND INVESTOR CAUTION
TODAY.
A PROPOSED SOLUTION
Most Economists believe the best
solution to climate change is a
comprehensive tax on carbon
emissions and other greenhouse
gases.
Only if it is comprehensive will it
encourage alternative energy solutions
Only if it is comprehensive will efforts to
avoid the tax be socially beneficial.
SOLVE BOTH PROBLEMS AT
ONCE!!
Establish a fund as many countries have
done to support long run social costs such
as retirement
Fund it with a carbon tax.
Both risks are reduced as they offset each
other.
Tax a “bad” rather than income or other
“good”.
Delay implementation to reduce initial
impact but still get benefit.
CONCLUSION
Make sure you take only the risks you
intend to take
Keep an eye on long run risks
Policy makers remember: reducing
long run risks gives benefits today
REFERENCES
Engle and Rangel(2008) “The Spline Garch Model
of Low Frequency Volatility and its Global
Macroeconomic Causes”, forthcoming Review of
Financial Studies
Engle and Rangel(2007), “The Factor Spline
GARCH model for high and low frequency
correlations” NYU Discussion Paper
Engle(2007) “High Dimension Dynamic
Correlations” forthcoming in Volume in honor of
David Hendry
Berd, Engle and Voronov(2007) "Underlying
Dynamics of Credit Correlations," Journal of Credit
Risk