Empirical Security Returns

8/3/2019 Empirical Security Returns

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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.


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


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


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

Empirical Security Returns

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