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2. Capital Market Expectationsand Equity Return Behavior
Fin411. Investments (Anzhela Knyazeva)
Capital market expectations
Return and risk concepts
a s ca proper es o re urns an epar ures rom e
normality assumption
Downside risk
Challenges in forming capital market expectations
International equity returns
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Capital market expectations are the investorsexpectations concerning risk and return of various
Forming capital market
expectations: overview
Essential input to formulating a strategic asset
allocation
Specify the final set of expectations needed, including the timehorizon to which they apply
Research the historical record
Forming capital market
expectations: process
pec y e me o mo e a w e use an requ reinformation inputs
Research the sources for information inputs
Interpret the current investment environment using theselected data and methods, applying experience and
judgment
Formulate the set of capital market expectations
Then monitor actual market outcomes and compare them toexpectations to inform and provide feedback to theexpectations-setting process
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Realreturns: adjusted for inflation
Nominalreturns: not adjusted for inflation
Real v. nominal returns
(1+r) = (1+rreal) * (1+ )
Why does it matter?
Even if real returns matter, cant we simply adjust by
a constant + term
Why does it matter?
Real returns may be relevant for an investor aiming toform a ortfolio that meets estimated s endin needs in
Real v. nominal returns
real terms
Individual retirement investors who seek to maintain astandard of living in retirement
Defined benefit pension plans that pay out retirementbenefits indexed to inflation
Foundations who seek to maintain su ort for charitable
causes in real terms
Well see an illustration in the Harvard Management Cocase
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Even if real returns matter, cant we simply adjust by a
constant (1+) term?
BLS annual CPI growth data: long-term mean 3.15%, but it is notnecessarily constant (stdev. 4%, serial correlation 0.7)
6
8
10
12
14
Annual inflation rate, %
-10
-8
-6
-4
-2
0
2
1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
After-tax returns: returns after accounting for taxation of
dividends, capital gains, interest
After-tax vs. before-tax returns
-
before taxes are withheld
Why does it matter? Examples?
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Does not matterfor tax-exempt institutions (nonprofits) Current tax rates would not (but future tax rates would)
-
After-tax vs. before-tax returns
Does matter for everyone else: comparing returns ondifferent types of investments,
Examples:
Money market, bonds, stocks: bank and bond interest taxed at (higher)
marginal income rates, long-term capital gains and qualified dividends
taxed at lower rates (through 2010 - marginal 15%)
Muni v. corporate bonds: muni interest is exempt from federal income
tax and usually from state taxes in issuing state
Equivalent taxable tield= rmuni/(1-t), where t is the marginal income tax
rate
Marginal individual fed. income tax rates
90%
95%
100%
40%
45%
50%
55%
60%
65%
70%
75%
80%
Source: http://www.taxfoundation.org/publications/show/151.html
20%
25%
30%35%
1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
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Mean returns: well use arithmetic mean returns (whichprovide unbiased estimate of expected returns, E(r))
Return and risk measures
,
Total risk: Standard deviation measures total risk,
In Excel, STDEV
Historical S&P500 returns
Over 1928-2009:
S&P500 returns: mean 11.3%, stdev 20.3%
Compare: 3-mo T-bill rates mean 3.8%, stdev 3.1%
10%
20%
30%
40%
50%
60%
- - . , .
Source: data from http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histret.html
-50%
-40%
-30%
-20%
-10%0%
1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
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Sharpe ratio is a basic performance measure thattrades off expected returns and risk:
Sharpe ratio
Generally prefer a higher/lower Sharpe ratio?
frrESR
)(
Correlation:measurestheextenttowhichreturnsonanytwo
assetsmovetogether, 12 (between 1and1)
* *
Correlations
12 1 2
InExcel,CORREL;covariance=CORREL*STDEV1*STDEV2
Howdoreturncorrelationsrelatetodiversification
benefits?
Cantotalportfolioriskbelessthantheriskofanindividual
asset?Explain.
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Total risk of a portfolio (wdenotes weights):
Correlations
jiijjiP ww
For two assets:
Generally, as the number of (imperfectly
correlated) assets in a portfolio goes up, total
i j
211221
2
2
2
2
2
2
2
12 wwwwP
portfolio risk decreases, all else equal.
Eventually converges to what?
Howdoreturncorrelationsrelatetodiversification
benefits?
Correlations
generatemorediversificationbenefits
Cantotalportfolioriskbelessthantheriskofanindividual
asset?Explain.
Yes,ifcorrelationsarelow.
Eventuallyconvergestowhat?
Marketrisk(allidiosyncraticriskhasbeendiversified
away)
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Correlations
Source: Coaker, 2007, "Emphasizing Low-Correlated Assets: The Volatility of Correlation," Journal
of Financial Planning
A useful starting point is the normal distribution
assumption, which simplifies portfolio problems
Stock return distribution
- positive and negative deviations from the mean are equallylikely
- can compute probabilities of future scenarios using onlytwo parameters, mean and
- returns on a portfolio of normally distributed stocks arealso normally distributed
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To find probability that returns are below x%:
With a calculator + standard normal distribution table:
1) compute z=(x mean)/
2) look up p-value that corresponds to this z in the table
For example, mean=11%, =20%, x=0%
z=-0.55, which corresponds to p=0.2912
assuming normality, annual returns are expected to
In Excel, p=NORMDIST(x,mean,,TRUE)
Skewness (positive/negative deviationsfromthemeanarenotequallylikely)
Forsymmetricdistributions(e.g.normal):equals0
Departures from normality
33)]([ rErEskew
Negativelyskewed alonglefttail.Moredownsideriskgiventhesame
meanandtotalrisk
Positivelyskewed alongrighttail.
InExcel,SKEWcommand
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Kurtosis (characterizestheincidenceofextremeobservations)
Normal distribution: 0
Departures from normality
3)]([_44 rErEkurtosisexcess
Excess kurtosis >0 (leptokurtic): fat tails (extreme good/bad obs.
are more likely than under normality)
Excess kurtosis
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Historical stock return distribution
On aggregate, some degree of negative skewness and positive excess kurtosis
However, excess kurtosis driven by 1931-1955 period
Black swan investing article
Source: Looking for the next black swan, WSJ, 26-AUG-2010
[Reading] Black swan investing
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[Reading] Black swan investing
Total risk measure, , does not specifically account
for downside risk
Downside risk
Why should we care?
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Downside risk
Why should we care?
Individual utility may be affected by risk of loss
Downside risk
An individual or institutional investors objective to meet
liabilities or minimum liquidity needs may be
compromised in the event of a shortfall
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Downsidedeviation (semistandarddeviation):standarddeviationofreturnobservationsthatarebelowtargetreturn,rT
Downside risk measures
(e.g.mean,rf,oranothermin.acceptablereturn)
ValueatRisk% (VaR):aworstcasescenarioproxy;atleasthow
muchdowestandtolosein %ofthecases;typically, =1%,5%
Expressedin%terms,itisthe th percentileofadistribution
Alternatively,canbeexpressedin$(multiplybyportfoliovalue)
ConditionalTailExpectation(akaExpectedShortfall)istheaverageofrealizationsinthelefttail(whatwestandtoloseon
averagein5%ofthecases) Probabilityofashortfall(likelihoodthatreturnsarelessthan
thetargetreturn)
Under normality, VaR5% = mean 1.65*
(in Excel or using a calculator)
VaR
us ng re urns or - :
11.3% - 1.65*20.3%= -22.2%
For actual returns
in Excel, PERCENTILE(,0.05)
-VaR5%= -25%
alternatively, simulate an empirical distribution from past
data
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VaR in Practice
Any issues with applying VaR in practice?
Caveat: historical record need not be representative ofthe future return distribution
VaR in Practice
,Investment Practices Survey 2008 (229institutional investors and asset managers), quotedin FT Feb. 25
More than half of the asset managers use VaR in riskmeasurement. In 42% of the cases, normality is assumed
,but if you assume normality, you might as well just usevolatility.
Less than a third of asset managers surveyed use VaR-based measures to evaluate risk-adjusted performance
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Whenvolatilityislowinthemarkets asithasbeenduring
mostofthisdecade,whenVARmodelshaveflourished these
tools t icall offer a ver flatterin icture of risktakin . That
VaR in Practice
promptsbankstotakemorerisk,whichreducesmarket
volatilityfurtherasmorecashchasesassets.However,if
marketseverturnedvolatile,thisdynamiccouldquickly
unravel,theBankwarnedbackinApril.
TheformergeneralcounselofLTCM,JamesRickards,reflected
onhowanincom leteVaR modelunderminedhisfirm:"Since
wehavescaledthesystemtounprecedentedsize,weshould
expectcatastrophesofunprecedentedsizeaswell."
Need to ensure consistency in return and riskdefinitions(see above)
Capital market expectations: challenges
Be aware of potential data concerns
esp. with aggregate economic data:
definition differences (such as indexing to different
bases) and changes in methodology
accuracy and subsequent revisions, errors in
measuremen an n recor ng a a timeliness and leads/lags
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When using historical data, consider that: Means can be influenced by extreme observations check for ma or events, outliers, influential obs.
Capital market expectations: challenges
Regime changes could affect distributional properties Technological, political, legal and regulatory environments,
disruptions (war, natural disaster)
Result in nonstationarity differing underlying propertiesduring different parts of a time series
Tradeoff between using a longer time series for statisticalanalysis and increased likelihood of regime changes
can test for structural breaks in the regression; verify ifresults are sensitive to the time period used
Time period bias research findings often sensitive to startand end dates for measurement period
check sensitivity of results to time period
Capital market expectations: challenges
Conditioning information - historical averages incorporatemany economic environment parameters
condition on current environment (e.g. through multivariateregression)
Expected vs. ex post returns: history of prices could reflectpotential risk factors that did not materialize ex post (whenrisks fail to materialize risk is underestimated but return is
overestimated) does the sample period span both booms and busts?
do other methods of forecasting returns produce similarresults?
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Survivorship bias including only those entities that havesurvived for the entire measurement period (tends tooverestimate returns) a concern with returns for the
Capital market expectations: challenges
hedge fund universe
Use of appraisal (smoothed) data infrequent measurementtends to understate volatility and correlation with otherassets a concern with alternative investments (e.g. PE)
Data mining with enough data there will be randomcorrelations that are not economically meaningful
Correlation may not mean causation caution about usingcorrelation relationships in a prediction model; multivariateregression addresses some but not all issues
Caution in interpreting anomalies is the model correctlyspecified (model risk), are variables measured correctly?
Main approaches in this course: Sample estimators estimate future mean and variance on samples
past mean and variance (historical data on means/covariance matrix)
Capital market expectations: approaches
Multi-factor models explains returns to an asset in terms ofexposure to a set of risk factors (predict returns based on exposureto common sources of systematic risk, such as market risk, underequilibrium/no-arbitrage assumptions)
Other approaches: Time series estimators forecasting variable based on lagged variable
itself or lagged values of other variables (statistical methods)
. .
Survey/panel - qualitative
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The concept of returns and different types ofreturns
Define and compute average returns, total risk,
and return correlations
Discuss departures from normality in the
distribution of returns and their implications
Define key downside risk measures and compute
Discuss challenges in setting capital market
expectations