Date post: | 23-Dec-2015 |
Category: |
Documents |
Upload: | morris-moore |
View: | 216 times |
Download: | 1 times |
DOWNSIDE RISK AND LONG TERM INVESTING
ROBERT ENGLENYU 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
Value at Risk – number of $ that you can be 99% sure is worse than what you will lose in the next 10 days.
3/ 23 2Skewness= /E r E r
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?
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?
Find x such that i iP r x
i i j j j j i iP r x r x P r x r x
DEFAULT CORRELATIONS
A default is a random event. We can define the correlation between two default events.
For extremes, the default correlation is the same as the tail dependence.
,
2
,
1
/ 1
i i j j
i i j j
Di j r x r x
r x r x
Corr I I
P I I
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
0
400
800
1200
1600
-.3
-.2
-.1
.0
.1
55 60 65 70 75 80 85 90 95 00 05
SPCLOSE SP
50
100
150
200
250
300
-.06
-.04
-.02
.00
.02
.04
.06
66 68 70 72 74 76 78 80 82 84 86
SPCLOSE SP
0
400
800
1200
1600
-.08
-.04
.00
.04
.08
90 91 92 93 94 95 96 97 98 99 00
SPCLOSE SP
800
1000
1200
1400
1600
-.08
-.04
.00
.04
.08
1998 1999 2000 2001 2002 2003
SP500 SPRETURNS
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
.0
.1
.2
.3
.4
.5
1990 1992 1994 1996 1998 2000 2002
VOL_SP
CONFIDENCE INTERVALS
-.10
-.05
.00
.05
.10
1990 1992 1994 1996 1998 2000 2002
3*GARCHSTD SPRETURNS -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 dataThe 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 correlationsBerd, 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 ZakoianVolatility 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
600
800
1,000
1,200
1,400
1,600
-.08
-.04
.00
.04
.08
00 01 02 03 04 05 06 07
ADJ_CLOSE SP
MSCI ITALY EWI: Nov 21, 2007
10
15
20
25
30
35
40
-.10
-.05
.00
.05
.10
.15
00 01 02 03 04 05 06 07
ADJ_CLOSE_EWI EWI
AUSTRIA MSCI : EWO: Nov 21, 2007
0
10
20
30
40
50
-.08
-.04
.00
.04
.08
00 01 02 03 04 05 06 07
ACLOSE_EW O EWO
MSCI EAFA: EFA: Nov 21, 2007
20
40
60
80
100
-.06
-.04
-.02
.00
.02
.04
.06
.08
2002 2003 2004 2005 2006 2007
ADJ_CLOSE_EFA EFA
ALL GARCH VOLATILITIES
.0
.1
.2
.3
.4
.5
2002 2003 2004 2005 2006 2007
VOLAUSTRIA VOLITALYVOLUS VOLEFA
ALL GARCH VOLATILITIES 2007
.05
.10
.15
.20
.25
.30
.35
.40
VOLAUSTRIA VOLITALYVOLUS VOLEFA
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 dataSome inappropriate or fraudulent lendingSecuritization 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 deficitsBalance of payments deficitExpensive War going badlyChinese ownership of vast US debtHigh energy pricesToo 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 retirementFund 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 StudiesEngle and Rangel(2007), “The Factor Spline GARCH model for high and low frequency correlations” NYU Discussion PaperEngle(2007) “High Dimension Dynamic Correlations” forthcoming in Volume in honor of David HendryBerd, Engle and Voronov(2007) "Underlying Dynamics of Credit Correlations," Journal of Credit Risk