Returns and Betas

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This page has summaries of papers that look at stock and mutual fund returns and underlying factors, but not specifically related to trading strategies


**Variables that Explain stock return

Author: Clifford S Asness

Published: PhD Thesis University of Chicago 1994 (I have no electronic copy)

Keywords: Momentum, reversal, Value, multi-factor return model, simulation, cross-autocovariance

References: Cross-autocovariance and Own-autocovariance causing momentum and contrarian profits (1990 or 1988).

                         Size, Debt/Equity, and Book/Mkt and returns: Page 22-23 have many cites.

                        Beta not being priced (page 47)

This thesis looks at what variables have power to explain stock returns.  Asness first considers DER (the debt to equity ratio), log(book/mkt), log(mkt) [size], and various past return measures.  He finds all except beta have explanatory power ina univariate sense to explain returns, and returns are positively related to all variables. log(book/Mkt) has the most explanatory power of the fundamental variables, but the previous return data is most predictive. Finds the best specification of past returns for predicting future returns is: PAST(1,1), PAST(12,2), and PAST(60,13): the cumulative return last month, over the past 12 months excluding last month, and over the past 5 years excluding last year.  Cross-sectionally, high PAST(1,1) and high PAST(60,13) predict lower next-month returns (reversal) while high PAST(12,2) predict higher next-month returns (momentum), and these results are robust across periods and to inclusion of log(Book/Mkt), etc.

The thesis next looks at explanations.  The author brings up over-reaction, changing risk aversion (affecting high-beta stocks more), and un-adjusted corporate structures (causing past winners to have higher market equity) as reasons for return reversal/continuation.  Debt/Equity (DER) is related to expected return, since equity has higher E(ret). log(size) and log(Book/Mkt) may proxy for distress.  He also has an interesting interpretation of log(Book/Mkt):

log(Book/Mkt) = log(Debt/Mkt) - log(Debt/Book), so it's related to the capital structure "forced" on the company by the market.  He also discusses how it may proxy for distress risk. He finds that log(Book/Mkt) and log(mkt) subsume DER in explanatory power.  A January seasonal magnifies the effect of all variables except log(Book/Mkt), which has no Jan. seasonal, and PAST(12,2), which has an opposite (reversal) effect in January from the usual (continuation) effect.

The next part examines lead-lag relations among finds.  The thesis argues that last month's large-firm returns reliably lead next-month's small firm returns (leading to contrarian profits) and last month's large-firm PAST(12,2) returns are negatively related to next-months small-firm returns, leading to momentum profits for the PAST(12,2) horizon, and a somewhat similar result is found for value versus growth firms.

The next part looks at beta, giving many cites on the fact that beta isn't priced, and arguing that this is a rejection of the joint hypothesis that the Sharpe-Linter-Black model is true AND the market is efficient. He notes that the market return must be significantly greater than zero for beta to be prices, and this is barely true in the sample period.

The second half of the thesis is on simulations performed in a simulated world where the CAPM is true but stocks have different expected returns, betas, and target debt-equity ratios.  Each firm is assigned a beta and residual variance (calibrated to real-world data) and a target debt-to-equity ratio, and if a firm's debt-equity moves more than a certain tolerance from its target, it adjusts its capital structure.  Book value isn't simulated, but log(Debt / Mkt Equity) - log(target debt to equity) proxies for log(book/mkt). The results of the simulation are that PAST(36,1), log(mkt. cap), , and the proxy for log(book/mkt) can be priced, mostly due to dynamic rebalancing of capital structure, but this only happens when beta is priced, which it isn't in the real world.


**The Myth of the Absolute Return Investor

Financial Analysts Journal Mar/Apr 2006 and "CFA Hedge Fund" Conference Presentation, Philidelphia 2005

Author: M. Barton Waring (Managing Director at Barclay Global Investors) and Laurence B Siegel

Folder: Fund/Stock returns/betas

Keywords: Betas, Alphas, Absolute Returns

Very interesting, clarifies concept of alpha and absolute return. Argues that absolute return investing (non-negative and above market returns) doesn't exist, and that even alpha is a benchmark-relative concept. The slideshow argues that hedge fund returns are NOT absolute...they tend to be down when the market is down and flat when the market is up, and tend to have small betas (like 0.3 to 0.6).  The published article describes a 'good' hedge fund as one with near-zero beta in a multi-factor framework with proper risk control measures and expected positive alpha.  It also describes why zero-beta hedge funds should be considered a 'risky-cash' asset.

Score: 9/10


**Stocks vs Bonds: Explaining the Equity Risk Premium

Author: Clifford Asness

Published: Financial Analysts Journal 2000

Keywords: Equity risk premium, dividend yield, earnings yield

Asness examines the relationship between stock and bond yields using 1927 to 1998 data, the S&P as a stock market proxy, and a bond return series with a roughly constant duration.  Stock yields are earnings over price (E/P) or dividends over price (D/P), which are proxies for expected return (hence equity risk premium is like E/P - bond yield).  He looks at the anomaly that, in the first part of the century, stock yields wer emuch higher, but in the latter part bond yields were higher.  The equity risk premium is E(stocks) - E(bonds), and using the linear equation   E(stocks) = a*D/P + b, [  or a*E/P + b ] he assumes the equity risk premium is related to stock and bonds relative long-term (20-year) past realized volatilities, so that

D/P [ or E/P ] = a + b*Y + c*vol(stocks) + d*vol(bonds)  (EQ 1)

where Y=E(bonds) is the bond yield (and expected return) and D/P proxies for E(stocks).  We expect b and c to be positive, since both cause investors to require higher returns from stocks, and d to be negative since high bond return volatility makes bonds relatively less attractive and investors require less return premium to hold stocks.

 Ignoring some econometric issues, the coefficients in EQ 1 turn out to have the correct sign and have a reasonably high R^2, with either D/P or E/P as the dependant variable.  The author performs many robustness checks, including looking out of sample at an earlier time period and ruling out a linear or log-linear trend in D/P or E/P.  He notes that the regression of D/P (or E/P) on bond yield isn't significant until the bond and stock market volatilities are included, at which point it becomes very significant and positive, as expected.  He also looks at return predictability, where S&P monthly return is weakly positively related to D/P (R^2 = 0.007) but ten-year return is much more strongly related (R^2 = 0.587).  He finds that the D/P forecast by his model is even more useful for predicting long-term (ex: 5-year) S&P return, and the forecast D/P error in his model is useful for predicting S&P monthly return.  The paper also argues that the extremely low D/P in 2000 is justified by low yields and low stock-market volatility relative to bond-market volatility.


 **On Persistence in Mutual Fund Performance


Author: Mark M. Carhart

The Journal of Finance 1997

Keywords: Mutual Fund Performance, Momentum

Carhart uses a four-factor model (Fama French's market, SMB, and HML factors, plus a momentum factor) to study the persistence of mutual fund returns.   Carhart' aggregates the data from many sources, giving a complete and survivorship-bias free set.  He finds the four-factor model explains much more return variance than even Fama-French's three-factor model (Mean ABS monthly return error is .35, .31, and .14 for CAPM, Fama-French, and Carhart's four-factor model). 

  His major finding is that sorting mutual funds into equal-weighted deciles based on last years total return, decile 1 (last years winners) outperforms decile 10 by ~8% annually, with the bottom decile significantly underperforming.  The four factor model explains this return spread succesfully (almost perfectly explaining deciles 1-9), largely through loadings on the Size and Momentum factors.  Next he finds that the four-factor alphas are largely explained by expense ratio (coefficient of -1.54, so 1% expenses drops return by ~1.5%) and turnover, with a detailed discussion of implied transaction costs using a liquidity loading factor.  He finds that a given funds decile position is not remotely stable year-to-year, and the difference in return between last-year-return-sorted deciles disappears largely after two years and completely after about four years.  Surprisingly he finds that deciles sorted on loadings on the momentum factor (from the four factor model) aren't significantly different, and the deciles that had higher loadings on the momentum factor actually do slightly worse the next year. This indicates (he says) that momentum isn't an investable strategy.

  In the spirit of Fama-French finding that SMB and HML time-series factor loadings from time series correspond well with stock size and boot-to-market, he finds that his measures of time-series factor loading on momentum and liquidity correlate well with other direct measures of momentum and liquidty (volume).

Finally, he examines the explanatory power of the four-factor model.  He finds it explains almost all of the return spread between return-sorted deciles one and ten the next year, but essentially none after five years.  However the expense ratio consistently explains about one-fifteenth of the spread, one year or five years later.  Lastly, he finds that three-year four-factor alpha-sorted deciles have a smaller spread between deciles one and ten (5% per year), but that spread lasts to some extent even five years later.

This is a fantastic paper on mutual fund performance and momentum, examining many aspects of mutual fund performance in a thourough manner.  A similar paper on ETF would be a fanastic contribution to the literature.


**The Cross-Section of Expected Stock Returns

Authors: Eugene F. Fama and Kenneth R. French

Published: The Journal of Finance 1992

Keywords: Value, size,beta, non-synchronous lagged beta, book-to-market, market induced leverage, Fama-MacBeth regressions

Summary: Conditioning on firm size, beta is NOT related to future return: the unconditional relation between beta and return occurs because firm size and beta are negatively corrolated, and firm size is negatively corrolated with return.  Log(book to market) captures the differing effects of market and book leverage, and E/P doesn't have incremental ability to explain returns when combined with log(book/mkt) and log(firm size).

The authors use a sample of NON-FINANCIAL firms from 1962 to 1989, including all firms with 24-60 months of prior accounting data. They first create 100 equal-weight portfolios, first sorting on market cap (size) using NYSE breakpoints into 10 portfolios, then sorting each of these by pre-rank beta.  The pre-rank beta is calculated by regressing past returns on the market, with an adjustment for lead-lag relations. There is a large spread in pre-rank beta across portfolios (0.53 to 1.79), pre-rank beta is consistent with port-rank beta, and beta is higher for smaller firms, but conditioned on size beta is NOT related to future return.  Size (or log size) is related to return, with smaller firms having higher return.

Next they look at other variables, like book to market (BME), leverage, and earnings to price (E/P), and find that, unlike size, these aren't corrolated with beta.  The explain how log(BME) = log(bk/mkt) = log(assets/mkt)-log(assets/bk), where assets to market and assets to book are log-market and log-book leverage. They find future return is related positively to mkt. leverage but negatively to book leverage, and log(BME) captures both these relations well.  Returns for decile portfolios sorted on BME range from [0.3 0.67] per month for the two halves of the lowest BME portfolio to [1.92 1.83] for the two halves of the high BME portfolio (strangely, all these portfolios have beta > 1.2), but there is little beta variation across BME portfolio. E/P has a weaker U-shaped relation to future return, with the negative E/P portfolio averaging 1.46% per month, the lowest positive E/P portfolio at 1.04%, roughly increasing to 1.72% for the highest E/P portfolio. E/P is a clear risk proxy (if E>0) since if earnings are roughly constant high E/P implies a low price and high discount rate.  However, the relation between E/P and return is explained away in Fama-Macbeth regressions that include log(size) and log(BME).

The corralation between log(size) and log(BME) for portfolios is only 0.26, but that between log(size) and beta is -0.98, which shows why its hard to distinguish beta from the size affect.   The paper's appendix details some subtleties in the relation between firm size and beta.


**Are Investors Rational: Choices among Index Funds

Authors: Edwin J. Elton, Martin J. Gruber, and Jeffrey A. Busse

Published: The Journal of Finance 2004

Keywords: Index Funds, differencial return, expense ratio

Summary: The authors find that differences in performance in S&P 500 index funds are large (up to 2% a year) and predictable from past performance and expense ratio

The authors use S&P 500 index fund data for 52 funds from 1997 through 2002: this includes all such funds, so presumably has negligible survivorship bias. Defining differential return (DR) as fund return minus the index return, they find the following summary statistics [average, min, max]

Differencial Return (DR): -0.485% [ -1.85% to 0.232%]

Expense Ratio (ER): 0.44% [0.06% to 1.35%]

Betas (vs S&P) are 0.979 to 1.0 and R^2 range from 0.9999 to 1, so CAPM alphas are nearly the same as differential returns.  Next they look at how predictable DR and ER are using DR and ER three years or one year earlier.  For a three-year span, their regressions indicate DR(t+3) = .015 - 0.9999*ER(t), meaning that expense reduces performance one-for-one! Regressing DR on itself, they find DR(t+3) = -0.019 + 0.77*DR(t), so differential returns are persistant.  They get similar results for one-year-ahead predictions. Also, putting index funds in deciles by past DR, the future DR of these deciles are perfectly monotone: the higher past DR deciles have higher future DR. The difference in future DR between highest and lowest deciles is 0.97% per year.  Deciles of expese ratio are similarly persistent. They find much lower persistence in manager skill (ER + DR is what the managers earn). All funds have very similar beta and R^2 with S&P, but have largely varying levels of cap. gains distributions. Next they find that cash flows into a fund are higher for funds with past high DR, lower past ER, and with higher loads (used for marketing).  They argue that investors are for some reason failing to buy lower ER higher DR funds, despite obvious performance persistence, and find no compelling reason why rational investors would do this (they eliminate such things as preference for larger fund families).  The lack of arbitrage opoprtunity and appearent existence of irrational investors allows these inferior funds to continue.



**A Portfolio Diversification Index

Authors: Alexander M. Rudin and Jonathan S. Morgan

Published: Journal of Portfolio Management 2006

The authors develop a single number, the PDI,  that represents the amount of diversification available from a set of portfolios.  This number is based on the factor strengths of different factors after doing Principle Components Analysis on the portfolios' correlation matrix.  For a completely diversified set of portfolios, the PDI is N (the number of portfolios), while for a non-diversified set of portfolios, the PDI is 1.  They find that, with individual stocks, the PDI increases with N, but is very sub-linear, and the marginal increase in PDI is small when N is above 50 or so.  For hedge funds, treating each hedge fund strategy as a portfolio (ex: equity hedge, macro, event driven, ...), the PDI is surprisingly low, indicating that these groups of hedge funds don't offer as much opportunity for diversification as some may think.

Their definition of the PDI is: 2 * sum_k(k*W_k) - 1, where W_k is the fraction of variance explained by the k'th principle component.  I think it's more intuitive to define the PDI as one over the squared two-norm of the W_k vector, but this is a minor point.


**Why the Low Returns to Beta and Other Forms of Risk?

Author: Edward M Miller

Published: Journal of Portfolio Management 2001

The author argues that, in constructing portfolios, different investors create different estimates of E(ret) for each stock.  Because of this, the marginal investor - who buys the "last" share of stock available - has a higher expected return for that stock than the average investor (who may not even hold the stock).  Thus even if investors as a whole are unbiased in their forecasts of E(ret), holders (investors who actually hold a stock) may have overly optimistic estimates of that stocks E(ret). Also, less variance in forecast of E(ret) leads to less demand for a stock, a lower price, and higher return, since less marginal investors make large positive errors forecasting E(ret). Since marginal investors are price setters and they tend to have positive errors in forecasting E(ret), this least to bias, and higher variance in investor forecast about a stock leads to larger overestimates of E(ret), and thus higher price and lower future return.  The author argues that the same variance in investor forecast leads to higher risk measures (like beta and sigma). Thus higher risk stocks may have lower return because the marginal (price-setting) investors make larger errors in forecasts. The author finds that studies IPO performacne find that IPOs which would have high variance of investor optinion (new industry, short company history,low quality underwriters) are exactly those which underperform: this is consistent with his model.

 He argues that this "uncertainty induced bias" lowers the slope of the security market like (SML) and may make it negatively sloped: in the paper he explicitly calculates the slope of this biased SML and finds it is lower by a factor related to divergence of investor opinion and market variance.  He brings up Samuelsons fallacy of composition - one infers something is true for the whole because it is true for a part.  Here every investors is risk neutral and believes they face a positive tradeoff between risk and return, but because of forecast errors the SML may be flat or downward sloping.

For implications, he suggets that a portfolio of low-beta stocks may have superior performance, and that a Baysian adjustment to deal with forecast errors may be useful.



**The conditional relation between beta and returns

File: The conditional relation between beta and returns.pdf

Authors: Glenn N Pettengill, Sridhar Sundaram, and Ike Mathur

Journal of FInancial and Quantitative Analysis

Keywords: conditional betas, returns

This paper, unlike others, finds a strong positive and highly significant relationship between conditional betas and cross-sectional portfolio returns. Previous tests relatating beta to return have first estimated (R - R_f) = Beta*(R_M - R_M) + epsilon, and then cross-sectionally estimated R_i = gamma + gamma1*Beta_i + epsilon. These previous tests generally found at best an unstable relationship (varying across months, for example). This work shows that, CONDITIONAL on an up or down market, beta is positively related to returns in a stable manner. e.g. Letting d=1 indicate an up market and d=0 a down market, the cross-sectional regression is: R_i = gamma_0 + gamma_1*d*beta_i + gamma_2*(1-d)*beta_i + epsilon, with gamma_1 > 0 and gamma_2 < 0 with P-value 0.0001. This is largely stable scross months and high-beta quantilse are found to have much higher long-term annualized return. This paper is straightforward, an easy read for people familiar with the CAPM, and quite interesting and bold in that it makes a simple modification to standard assumptions and refutes many modern papers saying that beta isn't strongly related to return.

Score: 8/10


**Multifactor Asset Pricing Analysis of International Value Investment Strategies

Author: Bala Arshanapalli, T> Daniel Coggin, and John Doukas

Published: Journal of Portfolio Management (Summer 1998)

Keywords: International Value Investing, Fama-French model

Summary: The authors find a value spread between high and low book-to-market portfolios across European and Pacific Rim countries, and these spreads are not strongly correlated across countries

The data are returns from Jan 1975 to Dec. 1995 IIA (Independence International Assoc. of Boston) for eighteen equity markets covering four regions of the developed world.  The data is mainly large stocks, but covers over 75% of the market value in each country. IIA splits the MARKET CAP of each country into value and growth portfolios every year in January based on data available at that time: this paper finds a ~13% annualized spread between the value and growth portfolios in the US over the whole period, a slightly higher avg. spread in the Pacific Rim countries (Hong Kong, Japan, Malaysia, Singapore, and Australia), and a lower but still usually positive spread in Europe. The value portfolio beat the growth portfolio in 13 out of 21 years in North America, and more frequently in EU (16/21) and the Pacific Rim (18/21). As far as regional spread, the authors claim annualized value - growth value weight spreads of ~13%, ~10%, 17%, and 14% for (N. America, Europe, Pacific, and International [world] over the 1975-1995 period. Importantly, value minus growth spreads are very weakly correlated across countries.

Value portfolios have higher Sharpe ratios and lower coefficients of variation than growth portfolios.  Using CAPM regressions, the value minus growth spread in all countries / regions has a tiny, often slighty negative (-0.1 to 0.1) beta and tiny (~0.01 to 0.1) R^2.  Regressions of value minus growth spreads (for each country / region) on the market (for that country/region) and Fama-French's SMB factor (for that country / region) gives insignificant betas but often significantly positive loadings on the SMB factor (like 0.4): this is significant for the U.S. and most Pacific Rim countries but not for many European countries: The R^2 values are also higher, often 0.1 to 0.3.  Lastly the authors change tack and find that regressions of country industry returns on the three Fama-French factors (MKT, SMB, and HML) give good results (R^2 around 0.7 to 0.9), claiming that this means that accounting for size and book/market improves our ability to explain international industry returns as well as American ones [The authors did the country - industry Fama-French regressions because this allowed the loadings on FF factors to vary over time].


**Portfolio Advice for a Multifactor World

Author: John H. Cochrane

Published: Federal Reserve Bank of Chicago (I think)


Keywords: Multi-factor efficient frontiers, Horizon affects (where variance is less than linear in time),N-fund theorem

Summary: This is a great introduction to mutti-factor equilibrium models.  The author discusses efficient frontiers in the face of multiple priced risk factors, and discusses whether of not some of the known anomalies can be priced risk factors.

References: Forecasting returns / variance under undertainty: Barberis (1999), Kandel et. al. (1996), Market-timing with dividend yield info (Brandt 1999,Campbell et. al. 1999

The author first reviews basic portfolio theory, where everyone holds the market and a risk-free asset according to their risk tolerance. Then he moves to a world with two priced factors (one being market risk, the other example one he uses is poor performance during recession risk), where the non-market factor is normalized to be zero-beta and zero cost.  He discusses how this second factor can be priced in equilibrium in a world many people derive their income from working and will accept a lower mean-variance level to have better performance in a recession. In this multi-factor world the market portfolio isn't mean-variance efficient, since a better tradeoff could be gotten by accepting recession risk, but the market portfolio can be multi-factor efficient in the sense that getting higher return requires more market/variance risk or more recession-type risk (the second factor in his example). Now every multi-factor efficeint portfolio is a combination of the market portfolio, the risk-free asset, and a zero-beta zero-cost recession-factor portfolio.

Next he goes into horizon effects, saying how return and variance both theoretically grow linearly with time, but empirically stock variance grows less than linearly with time (mean reversion) so long-term investors can allocate more to stocks. But he says ex ante uncertainly in the level of stock mean reversion reduces the extent to which long-term investors can benefit by allocating mroe to stocks. Next he looks at market timing, using dividend to price ratios to determine expected future stock returns and loading more or less heavily in stocks based on this forecast.  He has several cites on this, and claims that long-horizon investors can almost double their Sharpe ratio over buy-and-hold, but notes that these strategies require positions from -50% to 220% in stocks. (He also notes that any manager who misses a bull-market will probably be out of a job).

He moves on to hedging demand and reinvestment risk, noting that a ten-year bond is risky in the short-run and money-market accounts have reinvestment risk in the long run, and that a long-term bond hedges reinvestment risk of short-term bonds. He says that stocks in a sense hedge their own reinvestment risk, since expected returns tend to be lower after a period of high rerurns, and expected returns are higher after a period of low returns (this is related to the fact that the long-term annualized variance is lower than the short-term annualized variance).

Lastly he looks at anomalies like high performance of momentum (which he seems to dismiss as hard to capture)and value strategies.  He cautions that the market acts as a big insurance market and the average investor holds the market. But he considers several possibilities regarding anomalies. (1) high return to value stocks represents compensation for some risk, and only investors who are more able to bear that risk than average should pursue it to achieve higher return [the average investor CAN'T pursue a value strategy since the average investor holds the market] (2) value anomalies are caused by behavioral reasons, in which case they probably will persist but any investor deciding whether or not to pursue a value-strategy in favor of higher returns should still consider if it represents a risk they can bear (3) Value anomalies are an inefficiency, in which case they will probably disappear.

His conclusion advises investors to consider their horizon, and what are and aren't their risks, and to avoid taxes and snake oil!  The appendix has a linear-algebra derivation of multi-factor efficient frontiers and discusses how Sharpe ratios relate to regression R^2 values.

Score: 9/10


**New Facts in Finance

Author: John H. Cochrane

Published: Federal Reserve Bank of Chicago (I think)

Online: Here

Keywords: Multifactor models, anomalies, currency intererest rates and expected appreciation/depreciation, expectations hypothesis

Summary: The author mentions some old bedrocks of finance: the CAPM, forward rates as expected future spot rates (in bonds and foreign exchange), and random walks of asset prices. Then he summarizes newer ideas: return models must be multifactor, accounting data predicts long-term stock returns, higher interest rate currencies don't depreciate enough to eliminate the interest differential, higher long-term bond yields mean don't always forecast higher short-term rates in the future, and autocorrelated stock volatility.

The author begins with an example of a possible theoretically well-founded two-factor world: market risk and recession risk (i.e. stocks whose performance is poor in a recession have higher expected return). He notes that priced factors must be related to events that make the average investor worse off: events that make roughly the same number of investors worse off and better off shouldn't be priced. He then explains why one expects multiple priced factors to exist.

Next he covers predictability, looking at the performance of 25 Fama-French portfolios jointly sorted into size and book-to-market quintiles.  He finds that the Fama-French's three-factor model explains the returns to these portfolios well via their loadings on the market, value, and size factors (R^2 ~= 0.9), with low regression intercepts.  (Had a regerssion intercept in one of the 25 portoflios been significantly positive and the R^2 high, there would have been an arbitrage according to the APT where we go long the portfolio and short the mimicing factors, and we would earn something like the intercept with risk like one minus the regression R^2). He also looks at predicting returns to the market index using the aggregate price to divident ratio (high price/divident implies lower future returns) and finds increasing predictability at longer intervals (one-year predictions have an R^2 of .17, five-year predictions have an R^2 of .59).

He also looks at the relation between implied forward rates rates and realized future spot rates (repeating a Fama-French study).  He finds high forward rates don't lead to high future spot rates in the short term, but due in the long term.  He finds a similar result for currencies: in the short-run (e.g. a few months, a year), high interest rate currencies actually appreciate a little, but in the long interest rate differentials do predict changes in FX rates. He also looks at mutual funds, noting that most funds have a negative Fama-French alpha, small loadings on value and size factors, and fund persistence only comes from persistence in factor loadings, not stock picking.

He concludes with an interesting discussion of offsetting events.  He discusses how implied forward rates should predict future spot rates (the expectations hypothesis): the fact they don't means we can predict returns to different fixed-income strategies. For example, if forward rates don't predict future spot rates, a high year-one to year-two forward rate means lending for two years and borrowing for one year, then rolling over the borrowing for another year, has positive expected return. Finally, he notes that the exact magnitude of the "extra" return on value stocks, small stocks, and momentum strategies is unknown and may be declining.


**Market Efficiency, Long-term Returns, and Behavioral Finance

Author: Eugene F Fama

Published: SSRN Working Paper 1997 (

Keywords: Market Efficiency, behavioral finance, buy-and-hold versus average returns, return methodology

Fama looks at a wide range of event-type studies (IPOs, missed dividends, new dividends, mergers, splits) and find that over-reaction is about as common as under-reaction, and thus concludes that studies like these are not a challenge to market efficiency.  He notes that market efficiency can only be tested jointly with a model of returns. 

One part of the paper is about cognitive models.  He uses two cognitive models of investors (Barberis, Shleifer, and Vishny (BSV) and Daniel, Hirshleifer, and Subramanyam (DHS) and finds that, while they do a good job explaining the "anomolies" they were created to explain, they make the wrong prediction on other anomalies.   Then he suggests that a good behavioral model should be tested against a broad range of empirical phenomena.

Another is about methodology.  He notes that buy-and-hold returns, which are compounded, are statistically hard to deal with and skewed, and aren't a good metric: average returns are more stable (he has cites on dealing with these issues).  he also notes that many studies use equal-weighted data, which massively overweights tiny stocks and greatly skews results


**What Determines Chinese Stock Returns

Authors: Fenghua Wang and Yexiao Xu

Publishedd: Financial Analysts Journal 2004

The authors look at returns on Chinese A-class shares (held by domestic investors) from 1993  to 2002 on the Shanghai or Shenzhen exchanges and see how ln(market cap), beta, book-to-market, and free float influence returns.  They note that the Chinese market is unique in that (1) it's very new so not much data is available (2) accounting data are all suspect (3) many shares are state owned, and often less than half are truly "floating", so free float is an important factor (4) the sample period consists largely of a highly speculative bull market.  They find that, like other markets, smaller firms perform significantly better: from 1996-2002, the smallest quintile earned 2.42% per month while the largest earned 0.77% per month, even though firms have small cross-sectional dispersion in mkt. cap. compared to other countries.  Unlike other markets, the book-to-market ratio is less useful for explaining returns compared with other market, though high book-to-mkt firms do somewhat better.  Free float (the % of tradable shares for an issue) is positively related to future return, with about as much explanatory power as book-to-market.  They find betas are unstable, and like other markets beta doesn't explain returns well. They use a three-factor model with beta, free float (FF), and mkt. cap., and find 25 dual-sorted portfolios on FF and size have huge variation in returns: 5.3% a month for the small-cap high FF porfolio, 1.9% a month for the large-cap low FF portfolio.  Like the Fama French model, they construct factors using mkt. returns, returns of small-cap minus large-cap, and returns of high free-float minus low free float. The returns to portfolios constructed on size or free float are explained well through loadings on these factors(though the adjusted R^2 values in table 8 are far too low, don't match the text, and are too different from table 9??).  Since free float is corrolated with ln(mkt. cap), their regressions find reisdual free float (after accounting for mkt. cap.) has more explanatory power.


**Idiosyncratic Risk and the Cross-section of expected stock returns

Author: Fangjian Fu

Published: June 2005 EFA 2005 Moscow Meetings Paper


Keywords: Idiosyncratic risk

References: Goetzman 2004 - investors hold underdiversified portfolios. Merton (1987) - positive relation between idiosyncratic risk and returns

The author cites a theoretical equilibrium model of Merton's where, if investors are under-diversified, idiosyncratic risk is positively related to return.  The author claims previous studies failed to find this relation because they assumed that idiosyncratic risk is stationary.  So he uses daily data and does a time-series regression of each stock's daily return on the three fama-french factor daily returns for each stock i and month t, and defines the idiosyncratic volatility as the standard deviation of the regression residuals for that stock in that month.  He uses these results to show that idiosyncratic volatility is not stationary.

The data in this study are CRSP data on NYSE, NASDAQ, and AMEX firms from July 1963 to Dec 2002.

The next part of the paper (section 2B in my draft) isn't clear: he uses exponential GARCH to model expected idiosyncratic volatility, where the EGARCH models the residuals of the fama-french regression, but now he's using monthly data i think.  This gives the expected idiosyncratic volatility for the next month, which he uses in cross-sectional regressions to argue that expected idiosyncratic volatility E(IVOL) is positively related to return (again, I think). His cross-sectional regressions (Fama-MacBeth regressions I think) show that realized idiosyncratic vol. is positively related to return even when other variables related to momentum and turnover are included.  He also shows that the top quintile by E(IVOL) [the 20% of stocks with the expected highest idiosyncratic volatility] have a return of 3.53% per month, versus 0.6% for the 20% of lowest E(IVOL) stocks.  However, the higher E(IVOL) stocks are riskier (beta= 1.4, avg. Mkt. cap. = ~15M, Bk/Mkt=.57) than the low E(IVOL) stocks (beta=0.9, avg. mkt. cap. = 128M, Bk/Mkt=0.87).  The return of the value-weighted high-E(IVOL) portfolio is much lower-1.62% per month.  The author does quite a few robustness checks, and also notes that in the presence of E(IVOL), the size premium is reversed.  That is, conditioning only on market cap., small stocks do better, but conditioning on E(IVOL) smaller stocks actually perform worse. I think table IX claims that dual-sorting stocks into quintiles on E(IVOL) and market cap, the smallest capitalization stocks with the highets E(IVOL) earns 7% per month.

This paper is interesting: I wish the results weren't driven to such a large extent by small stocks, and I wish it was a little more clear when monthly or daily data is being used, and what model (what order of EGARCH) is used to compute E(IVOL).



**Long-Term Returns on the Original S&P 500 Companies

File: Long-Term Returns in the Original S&P 500 Companies.pdf

Author: Jeremy Siegel and Jeremy Schwartz

Published: Financial Analysts Journal 2006

Keywords: S&P 500, Buy and Hold, Long term returns

Summary: Siegel shows that a buy-and-hold like strategy in the original 1957 S&P 500 companies (these surivors now make up 31% of the 2003 S&P 500's market value) had a higher annualized geometric mean return (by about 0.5% to 1.5%) than the actual complete S&P index.  The variation comes from how spin-offs are treated and whether the INITIAL allocation was equal or value weighted.  Siegel points out that many interesting facts about the S&P index's history and changes, and shows that the buy-and-hold outperformence over the continually updated S&P occurs in almost all industry sectors, and that it incurs fewer transactions and taxes.

Score: 8/10


**The Importance of Being Value

Authors: Francois Bouruignon and Marielle de Jong

Published: The Journal of Portfolio Management 2006

Keywords: Value, transitive and structural value

Using book to market ratio (BM) as a proxy for value, the authors decompose a stock's "value" into two factors: a structural and a transitory one.  They do this by decomposing BM(t) = BM_bar + BM_trans, where BM_bar is the historical average book-to-market over some relatively long period (years) and BM_trans is a "transitory" component. They they use a three factor model, where each stock's return is defined by three loadings (beta, BM_bar, and BM_trans) on three factors (the market, an unobserved structural value factor, and an unobserved transitive value factor).  Using monthly data from 1989-2003, they do regression to estimate the unknown structure and transitory value factor returns every month, they find a mean return fo 8.7% for the structural and 12.7% for the transitory value factors (the single unified value factor has a mean return of 11.8%), and find very similar results in other European and Asian markets.  They claim the three-factor model is better at explaining returns (this seems trivial since larger models should always explain returns better) and is better at reducing out-of-sample risk. Their intuition is that the transitive value factor captures short-term price effets and structural value captures firm characteristics.  They mention that, in order to capture the higher returns to the transitive value factor with a trading strategy, one would incur very high turnover, but the lower returns to the structural value factor could be obtained with low turnover.


**Multifactor Explanations of Asset Pricing Anomolies

Authors: Eugene F. Fama and Kenneth R. French

Published: The Journal of FInance 1996

Keywords: Fama-French factors, risk adjustment, size, value, SMB, HML

References: contrarian investment (Lakonishok, Shleifer, and Vishny's (LSV) 1994). International small and value returns (Chan, Hamao, and Lakonishok (1991), Capaul, Rowley, Sharpe (1993))

Summary: Explains the Fama-French three-factor APT-type model of risk, where the three factors are the market return, a factor related to the relative performance of small-capitalization stocks, and a factor related to the relative performance of high book-to-market "value" stocks. They show that this three-factor model explains returns to a huge number of portfolios sorted on various accounting criteria and LT reversals, but doesn't explain momentum.

The authors define the three factors; MKT is the value-weighted stock market return, SMB is the value-weighted return of small-cap stocks minus that of large-cap stocks (controlled for book-to-market), and HML is the return of high book-to-market minus low book-to-market stocks (controlled for size) (see, Then factor loadings of a portfolio on a factor are obtained through time-series regression (NOT through accounting data for the portfolio).

These three factors explain returns on portfolios dual-sorted by size and book-to-market, and on deciles created on Cash Flow to price, Earnings to price, with R^2 generally over 0.9 and tiny intercepts.  The FF factors largely explain portfolios sorted by 5-year sales rank (exempting the extreme decile which has a non-trivial intercept), and double-sorted 5x5 portfolios sorted on sales rank and CF/P, E/P, or Book/Mkt.  Tthe three-factor model explains over-explains long-term reversals, in the sense that the past loser portfolio (stocks with poor performance t-48 to t-2) have higher return, but load so heavily on SMB and HML that they have a lower FF intercept. But the R^2 for the extreme deciles (sorted on LT past return) aren't high. But, the FF model doesn't explain stock price momentum (based on returns from t-12 to t-2) at all: in fact it predicts reversals.

Next they look at the ICAPM and find that any three factor model using three of MKT, S, B, H, or L (here S is the return of small stocks, H the return of high book-to-mkt stocks, etc) will explain the returns of other portfolios (CF/P, E/P, Book/MKT, long-term reversal) equally well.  e.g. Having picked any three of these (except MKT and B are redundant) explains the other: the regression of MKT on S, L, and H has R^2 = 0.98.  However, MKT, SMB, and HML have the lowest pair-wise correlation, so they make the best model because the coefficients will be easiest to interpret. FF also note that CF/P and E/P portfolios correlate so highly with Book/Mkt portfolios (0.99) that they could replace HML easily in a three-factor model.

FF strongly reject the CAPM, since regressing portfolio returns (e.g. CF/P portfolios) on MKT alone and doing an F-test on all coefficient being zero is strongly rejected. Thus the market portfolio does not lie on the efficient frontier. They next discuss interpretations.  (1) Asset pricing is rational and three-factor APT or ICAPM is true.  This is supported since SMB and HML represent  undiversifiable risk that is priced and not related to MKT, APT or ICAPM require a state variable of hedging concern to be associated with each factor, and FF says HML loading proxies for distruess (high book-to-mkt firms tend to have weak past earnings growth) but the issue isn't resolved (perhaps SMB proxies for liquidity risk?). (2) The three-factor model describes returns and asset pricing is irrational. FF disagree with LSV and say, for exampl, that HML returns look just like market returns, with positive expected return but non-trivial standard deviation and many down months, and that variance isn't a sufficient proxy for risk. (3) CAPM is true and the tests suffer from data snooping, survivor bias. Here they cite several papers on HML and SMB returns internationally, and point out that data-snooping appearently hasn't been that effective, since there aren't many return anomalies to explain (momentum, SMB, and HML basically). Lastly, they admit that momentum returns are utterly unexplained by the three-factor model.


**The Increasing Importance of Industry Factors

Authors: Stefano Cavaglia, Christopher Brightman, and Michael Aked

Published: Financial Analysts Journal 2000

Keywords: Industry Factors, Country Factors, Factor Models

References: The second page (42) cites many previous studies (including by Grinold and Beckers) on industry and country factors.

Summary: The authors argue that industry factors are of increasing importance, and perhaps now supercede country factors, in modelling return and providing diversification

The authors find large variance among previous studies regarding things like the R^2 for industry factor models (0.05 to 0.4), the marginal contribution of industry factors in a model that already has country factors (0.04-0.15), and the percentage of time an industry factor is significantly different from 0 (9% to 70%). But they note that most previous research found country factors to be more important.

This paper uses a factor model where each stock has unit exposure to its industry and country, and a world market factor. The model uses 35 industry and 20 country variables. They then note that the return of an industry factor is the return on a portfolio that is country-neutral (same mix as world market) for that industry, in excess of the world market, and the return on a country factor is the extent to which industries in that country outperformed their peers. Empirically they find that the mean average deviation (MAD) of the pure industry factors is increasing over time (1989 to 1999), while MAD of country factors isn't increasing.  Also finds that industry factors and country factors have roughly equal cap-weighted average correlations in 1999, while in 1989 industry factors had much higher average correlations, implying that the relative diversification benefit of country factors has decreased.  They also find that a maximal optimized Sharpe ratio portfolio of industry factors outperforms one of country factors, though of course an optimized  portfolio of industry and country factors outperforms both.


**Long-Term Memory in Equity Style Indexes ... It appears to have faded

Author: Daniel Coggin

Published: Journal of Portfolio Management 1998

Keywords: Mean reversion, long-term memory, random walks,variance ratio test, rescaled range statistic

The author cites a Fama,French,Poterba,Summer (1988) study which did find long-term memory in equity returns (I think in the market index) and disputes it, saying the FFPS results were largely pre-world-war-II and a statistical artifact. The author uses the variance ratio test (compare longer-term to shorter-term variance) and rescaled range statistic to look for evidence of mean reversion in 11 value-weighted indexes.  The data is from 1963 (1975 for some data) through 1996, and includes the market return, CRSP size and value idnexes, S&P size and value indexes, and the return spreads for value minus growth and small minus large stocks.  Both tests essentially find zero evidence of long-term memory in returns for any of the indexes.


**Is Systematic Downside Beta Risk Really Priced 

File: Is Systematic Downside Beta Risk Really Priced.pdf 

Authors: Don Galagedera and Robert Brooks

Published: Working Paper May 2005 Monash University Australia


Keywords: Beta, Downside Risk, Emerging Markets

Uses recent data (no later than 1987) in 27 emerging markets to see if there is evidence that downside beta (variosuly defined as beta when the market is down and beta when both market and stock are down) is priced, and generally finds that it isn't i.e. downside systematic risk doesn't explain much of price.  However results seem to indicate a decent fit using market downside co-skewness together with downside beta or CAPM beta as a risk measure.  The paper is easy to read and well written, using no overly fancy techniques.  The authors use three definitions of downside beta from recent literature and also define the three related downside co-skewness emasures.  They then regress cross-sectional returns on one or more of these.  Though their results are inconclusive, and strangely when including the CAPM beta in a two-variable model where the second variable is a downside-beta, there is often a negative relationship between the downside beta and return (though considering the strong correlation between downside beta and CAPM beta perhaps this isn't too surprising).

Score: 7/10



**The Persistence of Risk-Adjusted Mutual Fund Performance.pdf

Authors: Edwin J. Elton, Martin J. Gruber, and Christopher R. Blake

Published: Journal of Business April 1996. pp133-157, Vol 69

Keywords: Mutual Fund Performance, persistence in this performance, mutual fund performance measures

Folder: Fund/Stock Returns,Betas

Good literature review. Looks at mutual fund alphas and persistence of alphas using four proxies: S&P, small-large, growth minus value, and a bond index. Shows optimal portfolio weights as (w=alpha_i / squared residuals from the regression of fund returns versus mkt returns). Finds strong persistence in returns measured by one- and three-year alphas, and find excess return from holding optimal weights given by the above equation. That being said, the excess returns are ~1% / year, and this doesn't seem like a very practical strategy for trading.

Score: 7/10


**Beta and Their Regression Tendencies

Marchall E Blume


Published: The Journal of FInance.  Vol XXX No 3, June 1975

Folder: Fund and Stock Returns and Betas

File: Betas and their Regression Tendencies.pdf

Keywords: Beta, Mean Reversion

Shows, using from the 1970's and earlier, that portfolio betas tend to regress towards 1 over time.  Notes that, to some extent, this is an artifact of regression tendency because of measurement error, but shows that even after adjusting for this error there is still strong evidence that betas regress towards 1 over time,

Score: 6/10



**Asymmetries in Stock Returns: Statistical Tests and Economic Evaluation

Anymmetries in Stock Returns - Statistical Tests and Economic Evaluation.pdf

Authors: Yongmiao Hong, Jun Tu, and Guogu Zhou

Folder: Fun/Stock Returns,Betas

Talk: 14th Annual Conference on Financial Economics and Accounting (FEA)

(I think, am not sure, the 2006 version I have is in Journal of Finance)

Keywords: Return asymmetries, Beta asymmetries

The authors test correlation asymmetry, (p+ = corr(R_1,R_2 | R_1>0R_2>0), p- = corr(R_1,R_2 | R_1<0R_2<0)) and detail a model-free test for this asymmetry. They model joint stock returns as a mixture of a Clayton copula and a normal Gaussian mixture. They find evidence of beta asymmetries in small stock portfolios (not in large stock portfolios) and show that portfolio construction considering these asymmetries can improve utility, under some disappointment aversion utility assumption. This paper, in my opinion, is more useful to the statistics community than to financial practitioners, and many financial practitioners may find it very dry. Most of the paper is devoted to the mathematical derivation of the statistical tests and symbolic manupulations of proposed investor utility functions. However, the statistical tests for (the authors' definition) of correlation asymmetries may be useful to practitioners

Score: 5/10

**Do the Fama French Factors Proxy for Innovations in Predictive Variables

File: Do the Fama French Factors Proxy for Innovations in Predictive Variables (2006).pdf

Year: 2006

Author: Ralitsa Petkova

Journal of Finance

Keywords: Long term returns, Fama-French Factors

Folder: Fund/Stock returns,Betas

Argues that Fama-French factors (price/book and size) are explained by innovations (changes?) in macro variables (dividend yield, default spread, one-month T-bill yield). This paper uses an interesting two-step process to find returns the different risk factors (one regression to get all the betas, another to get the returns to those betas). Paper is not as straight forward as it could be and some topics weren't explained that well (i.e. assumed some knowledge that a casual reader might not have) but has good references and makes an interesting contribution.

Score: 6/10

**Who Needs Hedge Funds? A Copula-Based Approach to Hedge Fund return replication

File: Who Needs Hedge Funds.pdf

Authods: Harry M Kat, Helder P Palaro

SSRN Working Paper (Last version I saw was Nov 2005 version)

Folder: Fund/Stock Returns, Betas

Keywords: Hedge Funds, return replication, Copula

The authors claim that a strategy can be created to replicate hedge fund returns by alternating between a risk-free asset and a stock portfolio (like S&P). They make the assumption that hedge fund's dont have excess return, so replicating the risk factors gives the same expected return. They not only try to replicate a hedge fund's marginal return, but the joint distribution of hedge fund and portfolio returns, which will give the replicated strategy the same market correlation as the hedge fund. The author's give a clear explanation (without unnecasary details) about how copulas work, and give a decent description of how to determine the desired payoff function, but do a very poor job of explaining how to generate the desired payoff function, or how the trading strategy is created once the 'cheapest payoff function' is known. They give only the unhelpful comment 'Once we are able to determine the desired payoff function, we can work out the controls of the dynamic trading strategy generating it by straightfoward partial differentiation of the value function'. Other than this glaring short-coming that their replication strategy isn't clear, the experiments are interesting and convincing, and the concept is quite novel.

Score: 4/10


Empirical tests of the mean-semivariance CAPM

(note: my review concerns the Aug 2005 version)

File: Empirical tests of the mean-semivariance CAPM.pdf

Authors: Thierry Post and Pim Van Vilet


Folder: Fund/Stock Returns, Betas

Keywords: Pricing Kernels, Downside or conditional Betas, asymmetry, semi variance

Contains good references to: downside beta

The authors claim that downside market beta (semi-variance CAPM) better explains the cross-section of US stock returns than normal beta and CAPM, though the explanatory power of semi-variance CAPM is lower in recent years.  Understanding this paper requires an understanding of pricing kernels (which I don't have), and is difficult because the authors make the egregious and surprisingly common mistake of introducing undefined variables (T^-1 in equation 6).  That being said, the authors empirical work looking at downside beta to explain stock returns is first-rate.  They also define downside beta in a non-obvious way (i.e. not simply beta observed when the market is down).  They justify their original definition of downside beta by saying "The downside beta is sometimes defined as the traditional market beta computed over teh domain of losses...Appendix C demonstrates that this definition is flawed".  Appendix C proceeds to show that the authors' definition of downside beta is indeed different from traditional market beta computed over down markets, but this DOESN'T justify which definition is better.  Perhaps a later version of this paper that clearly explains pricing kernels will be stronger.

Score: NA (I don't understand pricing kernels well enough to score this)