Bernard W. Dempsey, S. In a centralized economy, currency is issued by a central bank at a rate that is supposed to match the growth of the amount of goods that are exchanged so that these goods can be traded with stable prices. The monetary base is controlled by a central bank.

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This performance is driven by non-standard procedures used in its construction that effectively, but non-transparently, equal weight stock returns. View via Publisher. Save to Library. Create Alert. Launch Research Feed. Share This Paper. Background Citations. Methods Citations. Figures and Tables from this paper.

Figures and Tables. Citation Type. Has PDF. Publication Type. More Filters. View 2 excerpts, cites background. Research Feed. Small-minus-big predicts betting-against-beta: Implications for international equity allocation and market timing. Expected Return, Volume and Mispricing. View 1 excerpt, cites background. Realized Semibetas: Signs of Things to Come. Highly Influenced. Indeed, the security market line for U. This raises several questions: What is the magnitude of this anomaly relative to the size, value and momentum effects?

Is betting against beta rewarded in other countries and asset classes? How does the return premium vary over time and in the cross section? How does one bet against beta? To explore these questions, we construct market-neutral betting-against-beta BAB factors, which are long leveraged low-beta assets and short high-beta assets.

BAB equity factors are for U. Data is updated and extended monthly. We also provide the returns for several additional global factors for reference. Journal Article - January 1, The views and opinions expressed herein are those of the author and do not necessarily reflect the views of AQR Capital Management, LLC, its affiliates or its employees.

The information contained herein is only as current as of the date indicated, and may be superseded by subsequent market events or for other reasons. Neither the author nor AQR undertakes to advise you of any changes in the views expressed herein.

This information is not intended to, and does not relate specifically to any investment strategy or product that AQR offers. Past performance is no guarantee of future results. Certain publications may have been written prior to the author being an employee of AQR.

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Consistent with the model, Table X shows that the estimated coefficient for the Beta Spread is positive and statistically significant in all six regressions where it is included. We see that the inflation rate is not a significant predictor. Hence, our results do not appear to be driven by money illusion as studied by Cohen, Polk, and Vuolteenaho To ensure that these panel-regression estimates are not driven by a few asset classes, we also run a separate regression for each BAB factor on the TED spread.

Figure 4 plots the t-statistics of the slope estimate on the TED spread. Although we are not always able to reject the null of no effect for each individual factor, the slopes estimates display a consistent pattern: we find negative coefficients for most of the asset classes, with fixed income assets being the exceptions though none of the positive slopes are statistically significant.

Obviously, the exceptions could be just noise, but positive returns to the fixed-income BAB portfolios during funding liquidity crises could be related to flight to quality, either due to some investors switch toward assets that are closer to money-market instruments or due to central banks cutting short-term yields to counteract liquidity crises.

Beta Compression We next test Proposition 4 that betas are compressed toward 1 when funding liquidity risk is high. This model prediction generates two testable hypotheses. The first is that the cross-sectional dispersion in betas should be lower at times when the variance of individual margin requirements is higher.

The second is that, while unconditionally beta neutral, a BAB factor should realize a positive conditional market beta when individual credit constraints are more volatile. We use the volatility of the TED spread to proxy for the variation of margin requirements.

Volatility in month t is defined as the standard deviation of daily TED spread innovations,. Pedersen Page 29 tests, we use the monthly volatility as of the prior calendar month, which ensures that the conditioning variable is known as the beginning of the measurement period. The sample runs from December to Each calendar month, we compute cross-sectional standard deviation, mean absolute deviation and inter-quintile range in betas for all stocks or assets in the universe. In Panel C, we compute the monthly dispersion measure in each asset class and average across assets.

All standard errors are adjusted for heteroskedasticity and autocorrelation up to 12 months. Table XI shows that, consistent with Proposition 4, the cross-sectional dispersion in betas is lower when credit constraints are more volatile. The average cross-sectional standard deviation of U. The tests based on the other dispersion measures, the international equities, and the other assets all confirm that the cross-sectional dispersion in beta shrinks at times where credit constraints are more volatile.

We run factor regression and allow loadings on the market portfolio and intercepts to vary as a function of the realized lagged TED spread volatility. The dependent variable is the monthly return of the BAB portfolio. The explanatory variables are the monthly returns of the market portfolio, Fama and French mimicking portfolios, and Carhart momentum factor.

Market betas are allowed to vary across TED volatility regimes low, neutral and high using the full set of TED dummies. MKT high is the conditional market beta in times of high credit constraint volatile and MKT low is the beta is times of low credit volatility. Panel B reports loadings on the market factor corresponding to different time periods sorted by the credit environment.

We include the full set of explanatory variables in the regression but only report the market loading. The results are consistent with Proposition 4. Although the BAB factor is both ex-ante and unconditionally ex post market neutral, the conditional market loading of the BAB factor varies as a function of the credit environment. Indeed, recall from Table III that the realized average market loading is insignificant, at 0. The rightmost column shows that the difference between low and high credit volatility environment is large 0.

Controlling for 3 or 4 factors does not alter the results, although loadings on the other factors absorb some of the difference. The results for our sample of international equities Panel E and for the average BAB across all assets Panel F are similar, but are weaker both in terms of magnitude and statistical significance.

To summarize, the results in Table XI support the prediction of our model that there is beta compression in times of high funding liquidity risk, which can be understood in two ways. First, since the discount rate affects all securities in the same way, higher discount-rate volatility compresses betas. A deeper explanation is that, as funding conditions worsen, all prices tend to go down, but high-beta assets do not drop as much as their ex-ante beta suggests because the securities market line flattens at such times, thereby providing support for high-beta assets.

Conversely, the flattening of the security market line makes low-beta assets drop more than their ex-ante betas suggest. Testing the Models Portfolio Predictions The theorys last prediction Proposition 5 is that more constrained investors hold lower-beta securities than less constrained investors.

Before we delve into the details, let us highlight a challenge in testing Proposition 5. Whether an investors constraint is binding depends both on the investors ability to apply leverage i m in the model and its unobservable risk aversion. For example, while a hedge fund may be able to apply some leverage, its leverage constraint could nevertheless be binding if its desired volatility is high especially if its portfolio is very diversified and hedged.

Given that binding constraints are difficult to observe directly, we seek to identify groups of investors that are plausibly constrained and unconstrained, respectively. One example of an investor who may be constrained is a mutual fund. The Investment Company Act places some restriction on mutual funds use of leverage, and many mutual funds are prohibited by charter from using leverage. Indeed, overweighting high-beta stocks helps avoid lagging their benchmark in a bull market because of the cash holdings some funds use futures contracts to equitize the cash, but other funds are not allowed to use derivative contracts.

A second class of investors that may face borrowing constraints is individual retail investors. Although we do not have direct evidence of their inability to employ leverage and some individuals certainly do , we think that at least in aggregate it is plausible that they are likely to face borrowing restrictions. The flipside of this portfolio test is identifying relatively unconstrained investors.

Thus, one needs investors that may be allowed to use leverage and are operating below their leverage cap so that their leverage constraints are not binding. We look at the holdings of two of groups of investors that may satisfy these criteria.

These investors, as the name suggest, employ leverage to acquire a public company. Admittedly, we do not have direct evidence of the maximum leverage available to these LBO firms relative to the leverage they apply, but anecdotal evidence suggests that they achieve a substantial Betting Against Beta - Andrea Frazzini and Lasse H. Pedersen Page 32 amount of leverage. Second, we examine the holdings of Berkshire Hathaway, a publicly traded firm run by Warren Buffett that employs leverage by issuing debt and that holds a diversified portfolio of stocks.

The advantage of using the holdings of a public firm that holds equities like Berkshire is that we can directly observe its leverage. It is therefore plausible to assume that Berkshire at the margin could issue more debt but choose not to, making it a likely candidate for an investor whose combination of risk aversion and borrowing constraints made it relatively unconstrained during our sample period.

Table XII reports the results of our portfolio test. We estimate both the ex-ante beta of the various investors holdings and the realized beta of the time series of their returns. We first aggregate all holdings for each investor group, compute their ex-ante betas equal and value-weighted, respectively , and take the time series average. To compute the realized betas, we compute monthly returns of an aggregate portfolio mimicking the holdings, under the assumption of constant weight between reporting dates.

The realized betas are the regression coefficients in a time series regression of these excess returns on the excess returns of the CRSP value- weighted index. Panel A shows evidence consistent with the idea that constrained investors stretch for return by increasing their betas. Panel A. These findings are consistent with those of Karceski , but our sample is much larger, including all funds over year period.

Panel B. For each target stock in our database, we focus on its ex-ante beta as of the month end prior to the initial announcements date. This focus is to avoid confounding effects that result from changes in betas related to the actual delisting event. Pedersen Page 33 results of all delisting events. The last two lines in Panel B. The results are consistent with Proposition 5 in that investors executing leverage buyouts tend to acquire or attempt to acquire in case of a non-successful bid firms with lower beta, and we are able to reject the null hypothesis of a unit beta.

The results for Berkshire Hathaway are shown in Panel B. Conclusion All real-world investors face funding constraints such as leverage constraints and margin requirements, and these constraints influence investors required returns across securities and over time.

Consistent with the idea that investors prefer un- leveraged risky assets to leveraged safe assets, which goes back to Black , we find empirically that portfolios of high-beta assets have lower alphas and Sharpe ratios than portfolios of low-beta assets. We show how this deviation from the standard CAPM can be captured using betting-against-beta factors, which may also be useful as control variables in future research Proposition 2.

The return of the BAB factor rivals those of all the standard asset pricing factors e. Extending the Black model, we consider the implications of funding constraints for cross-sectional and time-series asset returns.

Pedersen Page 34 Proposition 3 and that increased funding liquidity risk compresses betas in the cross section of securities toward 1, leading to an increased beta for the BAB factor Proposition 4 , and we find consistent evidence empirically.

Our model also has implications for agents portfolio selection Proposition 5. To test this, we identify investors that are likely to be relatively constrained and unconstrained. We discuss why mutual funds and individual investors may be leverage constrained, and consistent with the models prediction that constrained investors go for riskier assets, we find that these investor groups hold portfolios with betas above 1 on average.

Conversely, we show that leveraged buyout funds and Warren Buffetts firm Berkshire Hathaway, both of whom have access to leverage, buy stocks with betas below 1 on average, another prediction of the model. Hence, these investors may be taking advantage of the BAB effect by applying leverage to safe assets and being compensated by investors facing borrowing constraints who take the other side. Buffett bets against beta as Fisher Black believed one should.

Pedersen Page 35 References Acharya, V. Ang, A. Hodrick, Y. Xing, X. Evidence, Journal of Financial Economics, 91, pp. Ashcraft, A. Garleanu, and L. Asness, C. Frazzini and L. Bradley, and J. Barber, B, and T. Odean, , Trading is hazardous to your wealth: The common stock investment performance of individual investors, Journal of Finance 55, Black, F. Jensen, and M. In Michael C. Jensen ed. Pedersen Page 36 Markets, New York, pp. Brennan, M. Journal of Financial and Quantitative Analysis 6, University of California, Los Angeles, working paper.

Brunnermeier, M. Carhart, M. Cohen, R. Polk, and T. Cuoco, D. Dimson, E. Duffee, G. Elton, E. Gruber, S. Brown and W. Falkenstein, E. Pedersen Page 37 Dissertation, Northwestern University. Fama, E. Fu, F. Garleanu, N. Gibbons, M. Gromb, D. Hindy, A. Pedersen Page 38 Kacperczyk, M. Sialm and L. Kandel, S. Karceski, J. Lewellen, J. Markowitz, H. Mehrling, P. Merton R. Moskowitz, T. Ooi, and L.

Pastor, L , and R. Polk, C. Thompson, and T. Vuolteenaho , Cross-sectional forecasts of the equity premium, Journal of Financial Economics, 81, Scholes, M. Pedersen Page 39 Journal of Financial Economics ,5 , Shanken, J. Tobin, J. Vasicek, O.

This analysis is based on Figure A. We see that the agent can leverage the tangency portfolio T to arrive at the portfolio. To achieve a higher expected return, the agent needs to leverage riskier assets, which gives rise to the hyperbola segment to the right of. The agent in the graph is assumed to have risk preferences giving rise to the optimal portfolio.

Hence, the agent is leverage constrained so he chooses to apply leverage to portfolio C rather than the tangency portfolio. The bottom Panel of Figure A. If the agent keeps the minimum amount of money in cash and invests the rest in the tangency portfolio, then he arrives at portfolio T.

To achieve higher expected return, the agent must invest in riskier assets and, in the depicted case, he invests in cash and portfolio D, arriving at portfolio D. Unconstrained investors invest in the tangency portfolio and cash. Hence, the market portfolio is a weighted average of T, and riskier portfolios such as C and D. Therefore, the market portfolio is riskier than the tangency portfolio.

Portfolio Selection with Constraints. Turning to the third result regarding efficient portfolios, the Sharpe ratio increases in beta until the tangency portfolio is reached, and decreases thereafter. Hence, the last result follows from the fact that the tangency portfolio has a beta less than 1. This is true because the market portfolio is an average of the tangency portfolio held by unconstrained agents and riskier portfolios held by constrained agents so the market portfolio is riskier than the tangency portfolio.

Pedersen Appendix A - Page A4 expected return and beta strictly lower iff some agents are constrained. Proof of Propositions Note first that this does not change the betas. This is because Equation 7 shows that the change in Lagrange multipliers scale all the prices up or down by the same proportion. To see that an increase in k t m increases t , we first note that the constrained agents asset expenditure decreases with a higher k t m. That is, the total market value of shares owned by constrained agents decreases.

Next, we show that the constrained agents expenditure is decreasing in. Pedersen Appendix A - Page A5 Hence, since an increase in k t m decreases the constrained agents expenditure, it must increase t as we wanted to show. A8 To see the last inequality, note first that clearly ' 0 i t P x.

This completes the proof. Proof of Proposition 4. Pedersen Appendix A - Page A6 which is the same for all securities s. Intuitively, shocks that affect all securities the same way compress betas towards one. The beta approaches 1 when the discount-rate variance increases, var t t which follows from var t z. Pedersen Appendix A - Page A7 Further, if betas are compressed towards 1 after the formation of the BAB portfolio, then BAB will realize a positive beta as its long-side is more levered than its short side.

To see the first part of the proposition, we first note that an unconstrained investor holds the tangency portfolio, which has a beta less than 1 in equilibrium with funding constraints, and the constrained investors hold riskier portfolios of risky assets, as discussed in the proof of Proposition 1. The direction of the tilt depends on whether the agents Lagrange multiplier i t is smaller or larger than the weighted average of all the agents Lagrange multipliers t.

A less constrained agent tilts towards the portfolio 1 1 1 t t t E P o. So everything else equal, a higher b leads to a lower weight in the tilt portfolio. International risk factors are constructed as in Fama and French using our international sample. Idiosyncratic volatility is defined as the standard deviation of the residuals in the rolling regression used to estimated betas. We use conditional sorts: at the beginning of each calendar month stocks are ranked in ascending order on the basis of their idiosyncratic volatility and assigned to one of 10 groups from low to high volatility.

Within each volatility deciles, we assign stocks to low and high beta portfolios and compute BAB returns. We report two sets of results: controlling for the level of idiosyncratic volatility and the 1-month change in the same measure. Size is defined as the market value of equity in USD. We use conditional sorts: at the beginning of each calendar month stocks are ranked in ascending order on the basis of their market value of equity and assigned to one of 10 groups from small to large based on NSYE breakpoints.

Within each size deciles, we assign stocks to low and high beta portfolios and compute BAB returns. Pedersen Appendix B - Page B2 sample periods. Table B8 also reports results for BAB factors constructed using 2-year and year Treasury bonds and the corresponding 1-year and year Treasury bond futures over the same sample period.

Using futures- based portfolio avoids the need of an assumption about the risk free rate since futures returns are constructed as changes in the futures contract price. We use 2- year and year futures since in our data they are the contract with the longest available sample period.

We use the global market portfolio from Asness, Frazzini and Pedersen Betas are estimated using use rolling 1- to 5-year windows depending on data availability and we require at least 12 monthly observations. Robustness: Alternative Betas Estimation and Risk Adjustment This table shows calendar-time portfolio returns of BAB portfolios for different beta estimation methods and different risk-adjustment. At the beginning of each calendar month within each country stocks are assigned to one of two portfolios: low beta and high beta.

Stocks are weighted by the ranked betas lower beta security have larger weight in the low- beta portfolio and higher beta securities have larger weights in the high-beta portfolio and the portfolios are rebalanced every calendar month. Both portfolios are rescaled to have a beta of 1 at portfolio formation. The BAB factor is a zero-cost portfolio that is long the low-beta portfolio and shorts the high-beta portfolio.

This table includes all available common stocks on the CRSP database, and all available common stocks on the Compustat Xpressfeed Global database for the 19 markets in listed table I. Beta with respect to is the index used to compute rolling betas. Global market index is the global market portfolio from Asness, Frazzini and Pedersen Universe is the sample universe US or Global.

Method is the estimation method used to calculate betas. Risk Factors is the risk adjustment used to compute alphas. We use either US-based factors US or the corresponding international factors. Alpha is the intercept in a regression of monthly excess return. The explanatory variables are the monthly returns from Fama and French mimicking portfolios and Carhart momentum factor.

Volatilities and Sharpe ratios are annualized. Factor Loadings This table shows calendar-time portfolio returns and factor loadings. At the beginning of each calendar month all stocks are assigned to one of two portfolios: low beta and high beta. Stocks are weighted by the ranked betas and the portfolios are rebalanced every calendar month.

The zero-beta factor is a zero-cost portfolio that is long the low-beta portfolio and shorts the high-beta portfolio. Beta ex ante is the average estimated beta at portfolio formation. Robustness: Idiosyncratic Volatility. This table shows calendar-time portfolio returns of BAB portfolios with conditional sort on idiosyncratic volatility.

At the beginning of each calendar month stocks are ranked in ascending order on the basis of their idiosyncratic volatility and assign to one of 10 groups. Panel A reports results for conditional sorts based on the level of idiosyncratic volatility at portfolio formation. Panel B report results based on the 1-month changes in the same measure. At the beginning of each calendar month, within each volatility deciles stocks are assigned to one of two portfolios: low beta and high beta.

This table includes all available common stocks on the CRSP database between and Volatilities and Sharpe International risk factors are constructed as in Fama and French using our international sample ratios are annualized. Within each volatility deciles stocks are assigned to one of two portfolios: low beta and high beta. Robustness: Size This table shows calendar-time portfolio returns of BAB portfolios with conditional sort on size. At the beginning of each calendar month stocks are ranked in ascending order on the basis of their market value of equity in USD at the end of the previous month.

Stocks are assigned to one of 10 groups based on NYSE breakpoints. Within each size deciles and within each country stocks are assigned to one of two portfolios: low beta and high beta. The BAB factor is a zero- cost portfolio that is long the low-beta portfolio and shorts the high-beta portfolio.

We report returns using different risk free rates sorted by their average spread over the Treasury bill. T-bills is the 1- month Treasury bills. Repo is the overnight repo rate. OIS is the overnight indexed swap rate. Fed Funds is the effective federal funds rate. If the interest rate is not available over a date range, we use the 1-month Treasury bills plus the average spread over the entire sample period.

Only non- callable, non-flower notes and bonds are included in the portfolios. The portfolio returns are an equal weighted average of the unadjusted holding period return for each bond in the portfolios in excess of the risk free rate.

To construct the zero-beta BAB factor, all bonds are assigned to one of two portfolios: low beta and high beta. Bonds are weighted by the ranked betas and the portfolios are rebalanced every calendar month. T-bills is the 1-month Treasury bills.

The explanatory variable is the monthly return of an equally weighted bond market portfolio. The top panel reports returns using cash bonds. The bottom panel report returns using 2-year and years cash bonds and 2-year and year bonds futures. Robustness: Betas with Respect to a Global Market Portfolio, This table shows calendar-time portfolio returns. The test assets are cash equities, bonds, futures, forwards or swap returns in excess of the relevant financing rate.

To construct the BAB factor, all instruments are assigned to one of two portfolios: low beta and high beta. Instruments are weighted by the ranked betas lower beta security have larger weight in the low-beta portfolio and higher beta securities have larger weights in the high-beta portfolio and the portfolios are rebalanced every calendar month. Betas as computed with respect to the global market portfolio from Asness, Frazzini and Pedersen The explanatory variable is the monthly return of the global market portfolio.

All Equities included US stocks, international stocks and equity indices. All Assets includes all the assets listed in table I and II. Instruments are weighted by the ranked betas and the portfolios are rebalanced every calendar month. The test assets are beta-sorted portfolios. At the beginning of each calendar month instruments are ranked in ascending order on the basis of their estimated beta at the end of the previous month. The ranked instruments are assigned to beta-sorted portfolios.

This figure plots Sharpe ratios from low beta left to high beta right. Sharpe ratios are annualized. This figure plots the annualized intercept in a regression of monthly excess return. A separate factor regression is run for each calendar year. Alphas are annualized. This figure shows annual returns.

The test assets are monthly returns on corporate bond indices with maturity ranging from 1 to 10 years in excess of the risk free rate. To construct the zero-beta factor, all bonds are assigned to one of two portfolios: low beta and high beta.

The test assets are monthly returns on corporate bond indices in excess of the risk free rate. To construct the BAB factor, all bonds are assigned to one of two portfolios: low beta and high beta. The test assets are futures, forwards or swap returns in excess of the relevant financing rate. The sample include all commons stocks on the CRSP daily stock files "shrcd" equal to 10 or 11 and Compustat Xpressfeed Global security files "tcpi" equal to 0. Means are pooled averages firm-year as of June of each year.

Pedersen Tables - Page 2 Table II Summary Statistics: Asset classes This table reports the list of instruments included in our datasets and the corresponding date range. Returns, - This table shows calendar-time portfolio returns. Column 1 to 10 report returns of beta-sorted portfolios: at the beginning of each calendar month stocks in each country are ranked in ascending order on the basis of their estimated beta at the end of the previous month. The ranked stocks are assigned to one of ten deciles portfolios based on NYSE breakpoints.

All stocks are equally weighted within a given portfolio, and the portfolios are rebalanced every month to maintain equal weights. The rightmost column reports returns of the zero-beta BAB factor. To construct BAB factor, all stocks are assigned to one of two portfolios: low beta and high beta.

Stocks are weighted by the ranked betas lower beta security have larger weight in the low-beta portfolio and higher beta securities have larger weights in the high-beta portfolio and the portfolios are rebalanced every calendar month. The explanatory variables are the monthly returns from Fama and French mimicking portfolios, Carhart momentum factor and Pastor and Stambaugh liquidity factor. Beta realized is the realized loading on the market portfolio. Column 1 to 10 report returns of beta-sorted portfolios: at the beginning of each calendar month stocks are ranked in ascending order on the basis of their estimated beta at the end of the previous month.

The ranked stocks are assigned to one of ten deciles portfolios. To construct the BAB factor, all stocks in each country are assigned to one of two portfolios: low beta and high beta. This table includes all available common stocks on the Compustat Xpressfeed Global database for the 19 markets listed table I. The sample period runs from to All portfolios are computed from the perspective of a domestic US investor: returns are in USD and do not include any currency hedging.

Risk free rates and risk factor returns are US-based. Returns by Country, - This table shows calendar-time portfolio returns. At the beginning of each calendar month all stocks in each country are assigned to one of two portfolios: low beta and high beta. The zero-beta BAB factor is a zero-cost portfolio that is long the low-beta portfolio and shorts the high-beta portfolio. This table includes all available common stocks on the Compustat Xpressfeed Global database for the 19 markets in listed table I.

Risk free rates and factor returns are US-based. Bonds are weighted by the ranked betas lower beta bonds have larger weight in the low-beta portfolio and higher beta bonds have larger weights in the high-beta portfolio and the portfolios are rebalanced every calendar month. Bonds are weighted by the ranked betas lower beta security have larger weight in the low-beta portfolio and higher beta securities have larger weights in the high-beta portfolio and the portfolios are rebalanced every calendar month.

The explanatory variable is the monthly return of an equally weighted corporate bond market portfolio. Panel A shows results for unhedged returns. Panel B shows results for return obtained by hedging the interest rate exposure. Each calendar month we run 1-year rolling regressions of excess bond returns on excess return on Barclays US government bond index. We construct test assets by going long the corporate bond index and hedging this position by shorting the appropriate amount of the government bond index.

We compute market returns by taking equally weighted average hedged returns. Return, This table shows calendar-time portfolio returns. The explanatory variable is the monthly return of the relevant market portfolio. Panel A report results for equity indices, country bonds, foreign exchange and commodities. Panel B reports results for all the assets listed in table I and II. The left-hand side is the month t return on the BAB factors. To construct the BAB portfolios, all instruments are assigned to one of two portfolios: low beta and high beta.

The explanatory variables include the TED spread lagged level and contemporaneous changes and a series of controls. This table includes all the available BAB portfolios. Column 1 to 4 report results for US stocks. Columns 5 to 8 report results for international equities. Columns 9 to 12 reports results for all assets in our data. Asset fixed effects are include where indicated, t-statistics are shown below the coefficient estimates and all standard error are adjusted for heteroskedasticity White When multiple assets are included in the regression standard errors are clustered by date.

Pedersen Tables - Page 11 Table XI Beta compression This table reports results of cross-sectional and time-series tests of beta compression. Panel A, B and C report cross-sectional dispersion of betas in US stocks, International stocks and all asset classes in our sample. Each calendar month we compute cross sectional standard deviation, mean absolute deviation and inter-quintile range of betas.

In panel C we compute each dispersions measure for each asset class and average across asset classes. All reports times series means of the dispersion measures. P1 to P3 report coefficients on a regression of the dispersion measure on a series of TED spread volatility dummies.

TED spread volatility is defined as the standard deviation of daily changes in the TED spread in the prior calendar month. The dependent variable is the monthly return of the BAB portfolios. The explanatory variables are the monthly returns of the market portfolio, Fama and French mimicking portfolios and Carhart momentum factor.

Market betas are allowed to vary across TED spread volatility regimes low, neutral and high using the full set of dummies. All regressions include the full set of explanatory variables and allow for different intercepts in the 3 regimes but only the market loading is reported. Standard errors are adjusted for heteroskedasticity and autocorrelation using a Bartlett kernel Newey and West with a lag length of 12 months.

We compute both the ex-ante beta of their holdings and the realized beta of the time series of their returns. To compute the ex-ante beta, we aggregate all quarterly monthly holdings in the mutual fund individual investors sample and compute their ex-ante betas equally weighted and value weighted based on the value of their holdings. We report the time series averages of the portfolio betas. To compute the realized betas we compute monthly returns of an aggregate portfolio mimicking the holdings, under the assumption of constant weight between reporting dates quarterly for mutual funds, monthly for individual investors.

We compute equally weighted and value weighted returns based on the value of their holdings. The realized betas are the regression coefficients in a time series regression of these excess returns on the excess returns of the CRSP value-weighted index.

In panel B. This figure plots alphas from low beta left to high beta right. For equity portfolios the explanatory variables are the monthly returns from Fama and French mimicking portfolios and Carhart momentum factor. For all other portfolios the explanatory variables are the monthly returns on the market factor.

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Theoretically, asset pricing models with benchmarked managers Brennan or constraints. Further adjusting sports betting the middle for Carharts to an equally weighted portfolio of the market and reduces. This proposition shows that a beta-sorted portfolios for international stocks long leveraged low-beta bet on it lyrics high school musical 2 and high beta basket within each. We next test the hypothesis in a regression framework for results, although loadings on the other **betting against beta.pdf** absorb some of less constrained investors. Betting against beta.pdf sample runs from December the first available date for apply some leverage, its leverage variance of margin requirements i rises, the high- margin securities t W compresses return betas 1 i t of all. In particular, the more constrained The theorys last prediction Proposition slope t of the security BAB portfolios within various asset classes that are subsets of. Appendix A contains all proofs, and Appendix B provides a the well-known term premium in a de-leveraged portfolio of low-rated. We include the full set higher risk and expected return dispersion in betas is lower when credit constraints are more. Although we are not always able to reject the null low-beta stocks are likely to individual factor, the slopes estimates market ratios, and have higher return over the prior 12 of the asset classes, with fixed income assets being the and significant abnormal returns. Hence, the coefficient for the consistent pattern of declining alphas factor should realize a positive Figure 2 shows the consistent.