volatility and returns

Eric Falkenstein

Tests are of any theory the framework allowsThere are an infinite number of theories

allowedFramework is untestable

f m m f size small big value value growthi r r r r r r rr

Return VolatilitySmall Stocks 17.30% 33.4%

Stocks 13% 20.2%

Corporate Bonds 6.0% 8.7%

Government Bonds 5.70% 9.4%

T-bills 3.90% 3.2%

Brealey and Myers Investments Book

My Dissertation (1994) page 53

Theory that some liked volatility not an equilibrium theory

Pre ‘behavioral finance’ popularityNo fancy empirical test (didn’t use GMM)Makes no sense—arbitrage[I took equity risk premium as given]Theory more important than data

Burned by calendar effects

Ang,, Hodrick, Xing and Zhang (JoF 2009)1980-2003Use Fama French Model

f m m f size small big value value growthi r r r r r r rr

Beta-Low Beta0.5 Beta1.0 Beta1.5 Beta-High

AnnRet 10.8% 11.4% 11.4% 8.2% 4.5%

AnnStdev 13.1% 11.6% 17.4% 26.2% 33.9%

Beta 0.57 0.57 1.04 1.44 1.78

Sophie Ni (2007)Return from Bid-Ask midpoint to expiration-36%??

Moskowitz, and Vissing-Jorgensen (2002)

Penman, Richardson, and Tuna. 2007

Debt/Equity

Expected Returns

rD

rE

Theory

Beta and Returns UnremarkableRuss Wermers JoF 2000 piece (persistence,

turnover)Burton Malkiel JoF 1995 piece (persistence,

alpha)Carhart JoF 1997 (persistence, momentum)

Beta irrelevantThe biggest criticism is not adverse

statements, but neglect

% change in yen+riskprem?yenAUDr r

5.5% 0.3% 5.2%

5.5% 0.3% 1.4%

Return in AUD=Return in Yen+Appreciation in Yen/AUD

% change in currency unpredictable

1990-2008 Dollar Annualized Returns, Standard DeviationsMorgan Stanley Capital International (MSCI)MSCI Emerging Markets Index: 7.3%, 35%MSCI World (Developed) Index: 4.4%, 19%

Dimson, Marsh, Staunton (2005)17 Countries, 1900-2005, Annual Data

No Return Premium to High Yield Bonds over Investment Grade

Merrill High Yield Master II (HOAO) Merrill BBB-AA Index (COCO)

20 HY Funds, 12 IG funds

1% premium from 0.25 to 3 yearsNo premium from 5 to 30 yearsVolatility, Covariance, increasing linearly

Futures return from rollHarvey and Erb (2007) copper, heating oil,

and live cattle were on average in backwardization,

corn, wheat, silver, gold, and coffee were in contango

What covariance, volatility has to do with this ???

Campbell, Hilscher, and Szilagyi (2006) Find high distress firms have lower returns

Source: Author. Data from Moody’s, S&P, Compustat

Longshot biasHorse Track: 1-10 odd horses 3% average return on

investment100-1 odd horses have -86% average returnBias not there in smaller odds, as in baseball

Devany and Walls (1999), 2015 movies from 1984-96

Steve Sharpe and Gene Amromin (2005). People have higher expected returns when they have lower expected volatilities

Most studies find no positive aggregate volatility/return correlation over time

2

, 0m mf mfE r r a b

a b

IPO has a lot of UncertaintyJay Ritter (see his website). 1980-2008.IPO Returns -3.7% annually below size-

matched firms for first 5 years

Deither, Malloy, and Scherbina (2002). Table 2. Data from 1983-2000.

Data ‘strongly reject the interpretation of dispersion in analysts’ forecasts as a measure of risk’

Turnover of stock a proxy for disagreementHighly correlated with beta

Equity Beta Volatility

Equity options Distressed stock returns Analyst Disagreement Trading Volume IPOs Leverage and stock returns

LotteriesHorse racing

Equity Over time

Across Countries

BBB to B bond returns

FuturesCurrenciesPrivate InvestmentsMoviesMutual FundsLow Odds Sport Bets

Initial story was about total volatilityTotal volatility flat or negatively correlated

with returnBeta flat or negatively correlated with returnunrelated to risk.Volatility, Beta Uncorrelated, negatively

correlated, with ‘true’ betas ???