Niels Gormsen

REVISION: Does the Market Understand Time Variation in the Equity Premium?
Date Posted:Sun, 28 Aug 2022 11:49:38 -0500
We test whether the "representative agent" has intertemporally consistent expectations about time variation in the equity premium. We use option prices to estimate the expected future equity premium (the forward rate) and compare this estimate to the equity premium estimated in the future (the future spot rate). Forward rates are strong predictors of future spot rates for most stochastic discount factors (SDF), explaining around 20% of the variation at the 6-month horizon. We can, however, reject fully rational expectations for many specifications of the SDF. The expectation errors can be explained by a model in which an increase in the equity premium causes investors to overestimate the future equity premium. Alternatively, the apparent errors can be rationalized by an SDF that features a highly volatile and counter-cyclical price of discount-rate risk.

REVISION: Corporate Discount Rates
Date Posted:Sun, 28 Aug 2022 11:28:12 -0500
Standard theory implies that the discount rates used by firms in investment decisions play a key role in determining investment and transmit shocks to asset prices and interest rates to the real economy. However, there exists little evidence on how corporate discount rates change over time and affect investment. We construct a new global database of firms' discount rates based on manual entry from earnings conference calls. We show that corporate discount rates move with the cost of capital, but the relation is less than one-to-one, leading to time-varying wedges between discount rates and the cost of capital. The average discount rate wedge has increased substantially over the last decades as the cost of capital has dropped. Discount rate wedges are negatively related to future investment, with a magnitude close to that predicted by theory. Moreover, the large and growing discount rate wedges can account for low investment (relative to high asset prices) in recent decades. We find ...

REVISION: Does the Market Understand Time Variation in the Equity Premium?
Date Posted:Thu, 04 Aug 2022 10:18:24 -0500
We test whether the "representative agent" has intertemporally consistent expectations about time variation in the equity premium. First, we use option prices to estimate the expected future log equity premium (the forward rate) and compare this estimate to the log equity premium estimated in the future (the future spot rate). Forward rates are strong predictors of future spot rates, explaining 20% of the variation at the 6-month horizon. Second, using less stringent conditions than required to estimate forward and spot rates separately, we estimate and examine equity premium forecast errors. We can reject rational expectations for many specifications of the stochastic discount factor. The forecast errors can be explained by a model in which an increase in expected stock returns (spot rates) causes investors to overestimate expected stock returns in the future (forward rates). Alternatively, the forecast errors can be rationalized by a stochastic discount factor that features a ...

REVISION: Corporate Discount Rates
Date Posted:Mon, 01 Aug 2022 21:02:15 -0500
Standard theory implies that the discount rates used by firms in investment decisions play a key role in determining investment and in transmitting shocks to asset prices and interest rates to the real economy. However, there exists little evidence on how corporate discount rates change over time and affect investment. We construct a new global database of firms' discount rates based on manual entry from earnings conference calls. We show that corporate discount rates move with the cost of capital, but the relationship is less than one-to-one, leading to time-varying wedges between discount rates and the cost of capital. The average discount rate wedge has increased substantially over the last decades as the cost of capital has dropped. Discount rate wedges are negatively related to future investment, with a magnitude close to that predicted by theory. Moreover, the large and growing discount rate wedges can account for low investment (relative to high asset prices) in recent ...

REVISION: Higher-Moment Risk
Date Posted:Mon, 25 Jul 2022 04:53:45 -0500
We study time-variation in the shape of the distribution of stock returns. In a global sample covering 17 countries, returns are more left-skewed and fat tailed during good times than during bad times, with good and bad times defined as periods with a low and high volatility of the stock market. This variation in the shape of the distribution is inconsistent with leading disaster-based explanations of the equity premium, it induces pro-cyclical variation in the riskiness of volatility-managed portfolios, and it causes the normal distribution to underestimate tail risk more during periods with low volatility.

REVISION: Conditional Risk
Date Posted:Thu, 21 Jul 2022 04:58:55 -0500
Using a new and powerful conditional-risk factor, we document a global effect of time-varying market betas on stock returns. Across 23 developed countries, the major equity risk factors all load on the conditional-risk factor, which means their alpha can partly be explained by time-varying market betas. The conditional-risk factor explains 50% more alpha than traditional methods that use rolling betas to capture conditional risk. Studying the economic driver of the conditional risk, we find evidence that it arises from variation in discount rate betas (not cash flow betas) due to the endogenous effects of arbitrage trading.

REVISION: Higher-Moment Risk
Date Posted:Mon, 20 Jun 2022 09:07:03 -0500
We study time-variation in the shape of the distribution of stock returns. In a global sample covering 17 countries, returns are more left-skewed and fat tailed during good times than during bad times, with good and bad times defined as periods with a low and high volatility of the stock market. This variation in the shape of the distribution is inconsistent with leading disaster-based explanations of the equity premium, it induces pro-cyclical variation in the riskiness of volatility-managed portfolios, and it causes the normal distribution to underestimate tail risk more during periods with low volatility.

REVISION: Duration-Driven Returns
Date Posted:Mon, 20 Jun 2022 03:47:40 -0500
We propose a duration-based explanation for the premia on major equity factors, including value, profitability, investment, low-risk, and payout factors. These factors invest in firms that earn most of their cash flows in the near future and could therefore be driven by a premium on near-future cash flows. We test this hypothesis using a novel dataset of single-stock dividend futures, which are claims on dividends of individual firms. Consistent with our hypothesis, the expected CAPM alpha on individual cash flows decrease in maturity within a firm, and the alpha is not related to the above characteristics when controlling for maturity.

REVISION: Equity Factors and Firms’ Perceived Cost of Capital
Date Posted:Mon, 28 Mar 2022 04:36:40 -0500
We study how equity risk factors are reflected in firms perceived cost of capital using data on more than 2,000 firms. We start with the CAPM, finding that market betas are strongly related to the perceived cost of equity. The implied equity risk premia are between 3 and 6%. Going to multifactor models, we find stronger evidence for the Fama and French 3-factor model than for the 5-factor model. In further exploration of the full factor zoo, we find that many risk factors are reflected with the correct sign but that the magnitude and significance in general is modest. We explore heterogeneity across a number of firm characteristics, such as ownership structure of the firm and the education and cultural origins of the C-suite.

REVISION: Selfish Corporations
Date Posted:Wed, 08 Sep 2021 19:39:37 -0500
Motivated by the public debate regarding corporate responsibility, we construct a memory-based cognitive model of decision making to illustrate how corporate and political communication can impact policy preferences. We test the predictions of our model in a new large-scale experimental survey of U.S. citizens on their support for economic policies such as corporate bailouts. We first establish that the public demands corporations to behave better within society, a sentiment we label “big business discontent.” Then, using random variation in the order of survey sections and in the exposure to animated videos, we confirm two key predictions of our model. First, messages, or cues, that prime respondents to think about policy through the lens of corporate responsibility make people more averse to bailouts. Second, attempts to paint a positive public image of big business can actually backfire, as they focus attention on an aspect of the policy decision on which the public has ...

REVISION: Expected Stock Returns and Firms’ Perceived Cost of Capital
Date Posted:Fri, 27 Aug 2021 09:11:59 -0500
Using data from a decade of surveys of corporate managers, I find evidence that firms with higher expected stock returns have a higher perceived cost of equity and use higher discount rates in capital budgeting. Variation in expected stock returns, as measured by exposure to equity risk factors, is reflected in the perceived cost of equity with implied risk premia close to those observed in financial markets. The equity risk factors are also reflected in hurdle premia and explain up to 26% of the cross-sectional variation in the hurdle rates. The results support the hypothesis that discount rates in financial markets influence corporate discount rates and thereby corporate investment.

REVISION: Duration-Driven Returns
Date Posted:Fri, 30 Jul 2021 13:16:46 -0500
We propose a duration-based explanation for the premia on major equity factors, including value, profitability, investment, low-risk, and payout factors. These factors invest in firms that earn most of their cash flows in the near future and could therefore be driven by a premium on near-future cash flows. We test this hypothesis using a novel dataset of single-stock dividend futures, which are claims on dividends of individual firms. Consistent with our hypothesis, the expected CAPM alpha on individual cash flows decrease in maturity within a firm, and the alpha is not related to the above characteristics when controlling for maturity.

REVISION: Expected Stock Returns and Firms’ Perceived Cost of Capital
Date Posted:Tue, 20 Jul 2021 13:55:35 -0500
Using data from a decade of surveys of corporate managers, I find evidence that firms with higher expected stock returns have a higher perceived cost of equity and use higher discount rates in capital budgeting. Variation in expected stock returns, as measured by exposure to equity risk factors, is reflected in the perceived cost of equity with implied risk premia close to those observed in financial markets. The equity risk factors are also reflected in hurdle premia and explain up to 26% of the cross-sectional variation in the hurdle rates. The results support the hypothesis that discount rates in financial markets influence corporate discount rates and thereby corporate investment.

REVISION: Conditional Risk in Global Stock Returns
Date Posted:Mon, 28 Jun 2021 04:34:21 -0500
Using a new and powerful conditional-risk factor, we document a global effect of time-varying market betas on stock returns. Across 23 developed countries, the major equity risk factors all load on the conditional-risk factor, which means their alpha can partly be explained by time-varying market betas. The conditional-risk factor explains 50% more alpha than traditional methods that use rolling betas to capture conditional risk. Studying the economic driver of the conditional risk, we find evidence that it arises from variation in discount rate betas (not cash flow betas) due to the endogenous effects of arbitrage trading.

REVISION: Expected Stock Returns and Firms’ Perceived Cost of Capital
Date Posted:Tue, 08 Jun 2021 04:27:47 -0500
Using data from a decade of surveys of corporate managers, I find that firms with higher expected stock returns have a higher perceived cost of equity and use higher discount rates in capital budgeting. Variation in expected stock returns, as measured by exposure to equity risk factors, is reflected in the perceived cost of equity close to one-for-one. The equity risk factors are also reflected in hurdle premia and explain up to 26% of the cross-sectional variation in the hurdle rates. The results support the hypothesis that discount rates in financial markets influence corporate discount rates and thereby corporate investment.

REVISION: Expected Stock Returns and Firms’ Perceived Cost of Capital
Date Posted:Fri, 14 May 2021 03:11:59 -0500
Using data from a decade of surveys of corporate managers, I find that firms with higher expected stock returns have a higher perceived cost of equity and use higher discount rates in capital budgeting. Expected stock returns, as measured by analyst expectations or equity risk factors, explain as much as 40% of the variation in the perceived cost of equity. Exposure to equity risk factors further explain up to 18% of the variation in hurdle premia and up to 26% of the variation in the hurdle rates used in capital budgeting. The results support the hypothesis that pricing in financial markets influence corporate discount rates and thereby corporate investment.

REVISION: Equity Factors and Firms’ Perceived Cost of Capital
Date Posted:Tue, 27 Apr 2021 12:40:47 -0500
Using data from a decade of surveys of corporate managers, I document that firms with higher expected stock returns have a higher perceived cost of equity and use higher discount rates in capital budgeting. This result holds both when measuring expected returns using analyst forecasts and exposure to equity risk factors. In particular, exposure to the market, size, and value factors from Fama and French (1993) explains as much as 40% of the variation in perceived cost of equity with implied risk premia close to those observed in financial markets. The three factors also explain 26% of the variation in the hurdle rates used in capital budgeting and 18% of the variation in hurdle premia. The results lend support to the hypothesis that pricing in financial markets influence corporate discount rates and thereby corporate investment.

REVISION: Duration-Driven Returns
Date Posted:Mon, 26 Apr 2021 12:02:01 -0500
We propose a duration-based explanation for the major equity risk factors, including value, profitability, investment, low-risk, and payout factors. Both in the US and globally, these factors invest in firms that earn most of their cash flows in the near future. The factors could therefore be driven by a premium on near-future cash flows. We test this hypothesis using a new dataset of single-stock dividend futures, which are claims on annual dividends for individual firms. Consistent with our hypothesis, expected CAPM alpha on individual dividends decrease in maturity within a firm, but do not vary across firms once controlling for maturity.

REVISION: Equity Factors and Firms’ Perceived Cost of Capital
Date Posted:Wed, 14 Apr 2021 11:52:35 -0500
I study the relation between the discount rates firm use in capital budgeting and the pricing of the firms' assets in financial markets. Using data from surveys collected over a decade, I find that firms with high expected returns in financial markets use higher discount rates. In particular, the market, size, and value factors from Fama and French (1993) explain as much as 40% of the variation in perceived cost of equity with implied risk premia close those observed in financial markets. The three factors also explain 26% of the variation in the hurdle rates and 18% of the variation in hurdle premia. The results are largely consistent with these factors representing risk that managers incorporate in their discount rates, making the risk factors influence the allocation of capital in the economy.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Wed, 07 Apr 2021 07:43:51 -0500

I study the term structure of one-period expected returns on dividend claims with different maturity. I find that the slope of the term structure is counter cyclical. The counter cyclical variation is consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. More generally, the average and cyclicality of the slope are hard to reconcile with models with a single risk factor. I introduce a model with two priced factors to solve the puzzle.

REVISION: Equity Factors and Firms’ Perceived Cost of Capital
Date Posted:Thu, 04 Mar 2021 03:00:46 -0600
I study firms’ perceived cost of capital using a decade of survey data. Firms with higher market beta, higher book-to-market, and lower market size report a higher perceived cost of equity, consistent with the Fama and French (1993) model. The three factors explain 37% of the variation in perceived cost of equity and 26% of the variation in the hurdle rates used in capital budgeting. An increase in hurdle rates coming from exposure to the risk factors is associated with a decrease in investment rates. The results are consistent with rational mangers using risk factors in their discount rates, leading the risk factors to have real effects on the economy.

REVISION: Selfish Corporations
Date Posted:Mon, 01 Feb 2021 03:25:28 -0600
We conduct large-scale surveys of U.S. citizens aimed at measuring perceptions of large corporations’ environmental, social, and governance practices and investigate how these perceptions affect the public support for economic policies. The public demands corporations to behave better within society, a sentiment we label “big business discontent.” We experimentally vary individual perceptions through animated videos highlighting corporations’ role in society and by changing the order of survey sections. We show that higher big business discontent lowers support for corporate bailouts. The effects persist after a week, are reflected in costly behavioral actions, and span the full political spectrum.

REVISION: Implied Dividend Volatility and Expected Growth
Date Posted:Thu, 31 Dec 2020 09:24:45 -0600
A large literature is concerned with measuring economic uncertainty and quantifying its impact on real decisions, such as investment, hiring, and R&D, and ultimately economic growth. The COVID-19 pandemic underscores the importance of timely measures of uncertainty and expected growth across horizons. Asset prices, such as dividend futures and index options, provide particularly useful measures as they are forward looking and available at high frequencies.

We extend this literature by using new data on the prices of options on index-level dividends, from which we can compute implied dividend volatility. These implied volatilities differ from the VIX which measures uncertainty about stock prices, not only uncertainty about dividends. We construct a term structure of implied dividend volatilities that characterizes how uncertainty varies across horizons. We study how this term structure developed over the COVID-19 crisis, documenting a substantial increase in the volatility ...

REVISION: The Pricing and Risk of Dividends by Maturity: Theory and Evidence from the COVID-19 Pandemic
Date Posted:Wed, 23 Dec 2020 13:26:09 -0600
A large literature tries to estimate the conditional expectation and riskiness of economic growth across horizons. The COVID-19 crisis underscores the importance of this literature as households, market participants, and policymakers try to assess the impact of the pandemic on the distribution of economic growth over the next few years.

A recent literature shows the benefits of using dividend futures or index option prices for forecasting economic growth . We extend this literature by using options on index-level dividends. These options allow us to measure the implied volatility of aggregate dividends in a particular year. We construct a term structure of volatilities that characterizes how riskiness varies across dividends with different maturities. We study how this term structure developed over the COVID-19 crisis, documenting a substantial increase in the volatility of near-future dividends that has lingered even as the volatility of the overall market portfolio has ...

REVISION: Equity Factors and Firms’ Perceived Cost of Capital
Date Posted:Thu, 10 Dec 2020 15:04:33 -0600
I study firms’ perceived cost of capital using a decade of survey data. Firms with higher market beta, higher book-to-market, and lower market size report a higher perceived cost of equity, consistent with the Fama and French (1993) model. The three factors explain 37% of the variation in perceived cost of equity and 26% of the variation in the hurdle rates used in capital budgeting. An increase in hurdle rates coming from exposure to the risk factors is associated with a decrease in investment rates. The results are consistent with rational mangers using risk factors in their discount rates, leading the risk factors to have real effects on the economy.

REVISION: Selfish Corporations
Date Posted:Thu, 03 Dec 2020 03:27:36 -0600
We conduct representative large-scale surveys of U.S. citizens aimed at measuring perceptions of large corporations’ environmental, social, and governance performance and investigate how these perceptions affect the public support for economic policies. The public demands corporations to behave better within society, a sentiment we label “big business discontent.” We experimentally vary individual perceptions by showing animated videos that highlight the “good” and the “bad” of corporate behavior in recent years. We show that higher big business discontent lowers support for corporate bailouts. The effects are present across the whole political spectrum, but they are stronger for liberals than for conservatives, and they persist even a week after respondents viewed the videos. A second randomized experiment shows that simply making respondents think about the role of large corporations in society lowers their support for bailouts, highlighting a key mechanism whereby the public’s ...

REVISION: Selfish Corporations
Date Posted:Wed, 02 Dec 2020 10:59:09 -0600
We conduct representative large-scale surveys of U.S. citizens aimed at measuring perceptions of large corporations’ environmental, social, and governance performance and investigate how these perceptions affect the public support for economic policies. The public demands corporations to behave better within society, a sentiment we label “big business discontent.” We experimentally vary individual perceptions by showing animated videos that highlight the “good” and the “bad” of corporate behavior in recent years. We show that higher big business discontent lowers support for corporate bailouts. The effects are present across the whole political spectrum, but they are stronger for liberals than for conservatives, and they persist even a week after respondents viewed the videos. A second randomized experiment shows that simply making respondents think about the role of large corporations in society lowers their support for bailouts, highlighting a key mechanism whereby the public’s ...

REVISION: Duration-Driven Returns
Date Posted:Fri, 06 Nov 2020 03:33:17 -0600
We propose a duration-based explanation for the major equity risk factors, including value, profitability, investment, low-risk, and payout factors. Both in the US and globally, these factors invest in firms that earn most of their cash flows in the near future. The factors could therefore be driven by a premium on near-future cash flows. We test this hypothesis using a new dataset of single-stock dividend futures, which are claims on annual dividends for individual firms. Consistent with our hypothesis, expected CAPM alpha on individual dividends decrease in maturity within a firm, but do not vary across firms once controlling for maturity.

REVISION: Duration-Driven Returns
Date Posted:Mon, 02 Nov 2020 05:10:36 -0600
We propose a duration-based explanation for the major equity risk factors, including value, profitability, investment, low-risk, and payout factors. Both in the US and globally, these factors invest in firms that earn most of their cash flows in the near future. The factors could therefore be driven by a premium on near-future cash flows. We test this hypothesis using a new dataset of single-stock dividend futures, which are claims on annual dividends for individual firms. Consistent with our hypothesis, expected CAPM alpha on individual dividends decrease in maturity within a firm, but do not vary across firms once controlling for maturity.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Mon, 24 Aug 2020 10:47:57 -0500
I document that the term structure of one-period expected returns on dividend-claims is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. The counter-cyclical variation is consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. More generally, the average and cyclicality of the slope are together inconsistent with any model with a single price of risk. I introduce a new model with two priced risk factors to solve the puzzle.

REVISION: Coronavirus: Impact on Stock Prices and Growth Expectations
Date Posted:Tue, 04 Aug 2020 03:14:31 -0500
We use data from the aggregate stock and dividend futures markets to quantify how investors' expectations about economic growth evolve across horizons in response to the new coronavirus (COVID-19) outbreak and subsequent policy responses until July 2020. Dividend futures, which are claims to dividends on the aggregate stock market in a particular year, can be used to directly compute a lower bound on growth expectations across maturities or to estimate expected growth using a forecasting model. We show how the actual forecast and the bound evolve over time. As of July 20, our forecast of annual growth in dividends points to a decline of 8% in both the US and Japan and a 14% decline in the EU compared to January 1. Our forecast of GDP growth points to a decline of 2% in the US and Japan and 3% in the EU. The lower bound on the change in expected dividends is -17% in the US and Japan and -28% in the EU at the 2-year horizon. News about fiscal stimulus around March 24 boosts the stock ...

REVISION: Coronavirus: Impact on Stock Prices and Growth Expectations
Date Posted:Wed, 10 Jun 2020 04:38:47 -0500
We use data from the aggregate stock market and dividend futures to quantify how investors' expectations about economic growth evolve across horizons in response to the coronavirus outbreak and subsequent policy responses until June 2020. Dividend futures, which are claims to dividends on the aggregate stock market in a particular year, can be used to directly compute a lower bound on growth expectations across maturities or to estimate expected growth using a forecasting model. We show how the actual forecast and the bound evolve over time. As of June 8, our forecast of annual growth in dividends is down 9% in the US and 14% in the EU compared to January 1, and our forecast of GDP growth is down by 2.0% in the US and 3.1% in the EU. The lower bound on the change in expected dividends is -18% in the US and -25% in the EU at the 2-year horizon. News about fiscal stimulus around March 24 boosts the stock market and long-term growth but did little to increase short-term growth ...

REVISION: Coronavirus: Impact on Stock Prices and Growth Expectations
Date Posted:Tue, 26 May 2020 05:03:28 -0500
We use data from the aggregate stock market and dividend futures to quantify how in- vestors’ expectations about economic growth across horizons evolve in response to the coro- navirus outbreak and subsequent policy responses until May 2020. Dividend futures, which are claims to dividends on the aggregate stock market in a particular year, can be used to di- rectly compute a lower bound on growth expectations across maturities or to estimate expected growth using a forecasting model. We show how the actual forecast and the bound evolve over time. As of May 12, our forecast of annual growth in dividends is down 16% in the US and 23% in the EU compared to January 1, and our forecast of GDP growth is down by 3.6% in the US and 5.0% in the EU. The lower bound on the change in expected dividends is -29% in the US and -38% in the EU at the 2-year horizon. News about fiscal stimulus around March 24 boosts the stock market and long-term growth but did little to increase short-term growth ...

REVISION: Duration-Driven Returns
Date Posted:Tue, 19 May 2020 02:39:02 -0500
We propose a duration-based explanation for the major equity risk factors, including value, profitability, investment, low-risk, and payout factors. Both in the US and globally, these factors invest in firms that earn most of their cash flows in the near future. The factors could therefore be driven by a premium on near-future cash flows. We test this hypothesis using a new dataset of single-stock dividend futures, which are claims on annual dividends for individual firms. Consistent with our hypothesis, risk-adjusted returns are higher on near- than on distant-future cash flows. In addition, the returns on individual cash flows do not vary across firms once controlling for maturity.

REVISION: Coronavirus: Impact on Stock Prices and Growth Expectations
Date Posted:Fri, 15 May 2020 05:23:44 -0500
We use data from the aggregate equity market and dividend futures to quantify how investors' expectations about economic growth across horizons evolve in response to the coronavirus outbreak and subsequent policy responses. Dividend futures, which are claims to dividends on the aggregate stock market in a particular year, can be used to directly compute a lower bound on growth expectations across maturities or to estimate expected growth using a simple forecasting model. We show how the actual forecast and the bound evolve over time. As of May 12, our forecast of annual growth in dividends is down 16% in the US and 23% in the EU, and our forecast of GDP growth is down by 3.6% in the US and 5.0% in the EU. The lower bound on the change in expected dividends is -29% in the US and -38% in the EU at the 2-year horizon. There are signs of catch-up growth from year 3 to year 7. News about economic relief programs on March 13 appear to have increased stock prices by lowering risk aversion ...

REVISION: Coronavirus: Impact on Stock Prices and Growth Expectations
Date Posted:Thu, 23 Apr 2020 10:56:32 -0500
We use data from the aggregate equity market and dividend futures to quantify how investors’ expectations about economic growth across horizons evolve in response to the coronavirus outbreak and subsequent policy responses. Dividend futures, which are claims to dividends on the aggregate stock market in a particular year, can be used to directly compute a lower bound on growth expectations across maturities or to estimate expected growth using a simple forecasting model. We show how the actual forecast and the bound evolve over time. As of April 20, our forecast of annual growth in dividends is down 17% in the US and 28% in the EU, and our forecast of GDP growth is down by 3.8% in the US and 6.3% in the EU. The lower bound on the change in expected dividends is -30% in the US and -46% in the EU at the 2-year horizon. There are signs of catch-up growth from year 3 to year 7. News about economic relief programs on March 13 appear to have increased stock prices by lowering risk aversion ...

REVISION: Coronavirus: Impact on Stock Prices and Growth Expectations
Date Posted:Thu, 09 Apr 2020 06:09:53 -0500
We use data from the aggregate equity market and dividend futures to quantify how investors' expectations about economic growth across horizons evolve in response to the coronavirus outbreak and subsequent policy responses. Dividend futures, which are claims to dividends on the aggregate stock market in a particular year, can be used to directly compute a lower bound on growth expectations across maturities or to estimate expected growth using a simple forecasting model. We show how the actual forecast and the bound evolve over time. As of April 3, our forecast of annual growth in dividends is down 27% in the US and 37% in the EU, and our forecast of GDP growth is down by 6.1% in the US and 8.2% in the EU. The lower bound on the change in expected dividends is -45% in the US and -58% in the EU at the 2-year horizon. There are signs of catch-up growth from year 3 to year 10. News about economic relief programs on March 13 appear to have increased stock prices by lowering risk aversion ...

REVISION: Coronavirus: Impact on Stock Prices and Growth Expectations
Date Posted:Fri, 27 Mar 2020 10:54:46 -0500
We use data from the aggregate equity market and dividend futures to quantify how investors’ expectations about economic growth across horizons evolve in response to the coronavirus outbreak and subsequent policy responses. Dividend futures, which are claims to dividends on the aggregate stock market in a particular year, can be used to directly compute a lower bound on growth expectations across maturities or to estimate expected growth using a simple forecasting model. We show how the actual forecast and the bound evolve over time. As of March 25, our forecast of annual growth in dividends is down 28% in the US and 22% in the EU, and our forecast of GDP growth is down by 2.2% in the US and 2.8% in the EU. The lower bound on the change in expected dividends is -38% in the US and -49% in the EU on the 2-year horizon. The lower bound is model free and forward looking. There are signs of catch-up growth from year 3 to year 10. News about economic relief programs on March 13 appear to ...

REVISION: Coronavirus: Impact on Stock Prices and Growth Expectations
Date Posted:Tue, 24 Mar 2020 05:43:08 -0500
We use data from the aggregate equity market and dividend futures to quantify how investors’ expectations about economic growth across horizons evolve in response to the coronavirus outbreak and subsequent policy responses. Dividend futures, which are claims to dividends on the aggregate stock market in a particular year, can be used to directly compute a lower bound on growth expectations across maturities or to estimate expected growth using a simple forecasting model. We show how the actual forecast and the bound evolve over time. As of March 18, our forecast of annual growth in dividends is down 28% in the US and 25% in the EU, and our forecast of GDP growth is down by 2.6% both in the US and in the EU. The lower bound on the change in expected dividends is -43% in the US and -50% in the EU on the 3-year horizon. The lower bound is model free and completely forward looking. There are signs of catchup growth from year 4 to year 10. News about economic relief programs on March 13 ...

REVISION: Coronavirus: Impact on Stock Prices and Growth Expectations
Date Posted:Fri, 20 Mar 2020 05:23:00 -0500
We use data from the aggregate equity market and dividend futures to quantify how investors’ expectations about economic growth across horizons evolve in response to the coronavirus outbreak and subsequent policy responses. Dividend futures, which are claims to dividends on the aggregate stock market in a particular year, can be used to directly compute a lower bound on growth expectations across maturities or to estimate expected growth using a simple forecasting model. We show how the actual forecast and the bound evolve over time. As of March 18, our forecast of annual growth in dividends is down 28% in the US and 25% in the EU, and our forecast of GDP growth is down by 2.6% both in the US and in the EU. The lower bound on the change in expected dividends is -43% in the US and -50% in the EU on the 3-year horizon. The lower bound is model free and completely forward looking. There are signs of catchup growth from year 4 to year 10. News about economic relief programs on March 13 ...

REVISION: Corona Virus: Impact on Stock Prices and Growth Expectations
Date Posted:Tue, 17 Mar 2020 09:57:48 -0500
We use data from the aggregate equity market and dividend futures to quantify how investors’ expectations about economic growth across horizons evolve in response to the corona virus outbreak and subsequent policy responses. Dividend futures, which are claims to dividends on the aggregate stock market in a particular year, can be used to directly compute a lower bound on growth expectations across maturities or to estimate expected growth using a simple forecasting model. We show how the actual forecast and the bound evolve over time. As of March 16, expected growth over the next quarter declined by 2.5% in the US and 3.5% in Europe (both annualized) compared to the beginning of the year. The lower bound on expected GDP growth has been revised down by as much as 10% in the US and 12% in the EU. There are signs of catch-up growth from year 4 to year 10. News about economic relief programs on March 13 appear to have increased stock prices by lowering risk aversion and lift long-term ...

REVISION: Higher-Moment Risk
Date Posted:Wed, 19 Feb 2020 02:51:16 -0600
We use a new method to estimate ex ante higher order moments of stock market returns from option prices. Even and odd number higher order moments are strongly negatively correlated, creating periods where the return distribution is riskier because it is more left-skewed and fat tailed. The higher-moment risk increases in good times when variance is lower and prices are higher. This time variation is inconsistent with disaster-based models where disaster risk, and thus higher-moment risk, peaks in bad times. The variation in higher-moment risk also has important implications for investors as it causes the probability of a three-sigma loss on the market portfolio to vary from 0.7% to 1.9% percent over the sample, peaking in calm periods such as just before the onset of the financial crisis.

REVISION: Conditional Risk in Global Stock Returns
Date Posted:Thu, 09 Jan 2020 03:38:41 -0600
We estimate the premium associated with time-varying market betas without using rolling betas or instruments. Instead, we use a new conditional-risk factor, which is a market timing strategy defined as the unexpected return on the market times the ex ante price of risk. The factor is a powerful tool for documenting a global effect of conditional risk on stock returns: across 23 developed countries, all major equity risk factors load on our conditional-risk factor with the right sign, meaning their alpha can partly be explained by the time variation in their market betas. The conditional-risk factor explains 50% more alpha than traditional methods that use rolling betas to capture conditional risk.

REVISION: Duration-Driven Returns
Date Posted:Thu, 02 Jan 2020 10:02:36 -0600
We propose a duration-based explanation for the major equity risk factors, including value, profitability, investment, low risk, and payout factors. Both in the US and globally, these factors invest in firms that earn most of their cash flows in the near future. The factors could therefore all be driven a premium on near-future cash flows. We test this hypothesis using a novel dataset of single-stock dividend futures, which are claims on annual dividends of individual firms. Consistent with our hypothesis, risk-adjusted returns are higher on near- than on distant-future cash flows. In addition, firm-level characteristics do not predict returns on the cash flows once controlling for maturity.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Thu, 03 Oct 2019 05:28:08 -0500
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. The counter-cyclical variation is consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. More generally, any one-factor model will fail to explain both the average downward slope and the counter-cyclical variation. I therefore introduce a new model with two priced risk factors to solve the puzzle.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Tue, 01 Oct 2019 03:51:22 -0500
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. The counter-cyclical variation is consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. More generally, any one-factor model will fail to explain both the average downward slope and the counter-cyclical variation. I therefore introduce a new model with two priced risk factors to solve the puzzle.

REVISION: Duration-Driven Returns
Date Posted:Thu, 06 Jun 2019 11:39:01 -0500
We propose a duration-based explanation for the return to major equity risk factors, including value, profitability, investment, low risk, and payout factors. Both in the US and globally, firms with high expected returns predicted by these factors also have a short cash-flow duration, meaning that these firms are expected to earn most of their cash flows in the near future. The returns to the factors can thus be explained by a simple model where near-future cash flows have high risk- adjusted returns, which is consistent with the evidence on the equity term structure. We find evidence for such a model using a novel dataset of single-stock dividend futures that allow us to study fixed-maturity equity claims for a cross-section of firms.

REVISION: Higher-Moment Risk
Date Posted:Tue, 26 Mar 2019 08:23:50 -0500
We estimate and analyze the ex ante higher order moments of stock market returns. We document that even and odd higher-order moments are strongly negatively correlated, creating periods where the return distribution is riskier because it is more left-skewed and fat tailed. Such higher-moment risk is negatively correlated with variance and past returns, meaning that it peaks during calm periods. The variation in higher-moment risk is large and causes the probability of a two-sigma loss on the market portfolio to vary from 3.3% to 11% percent over the sample, peaking in calm periods such as just before the onset of the financial crisis. In addition, we argue that an increase in higher- moment risk works as an "uncertainty shock" that deters firms from investing. Consistent with this argument, more higher-moment risk predicts lower future industrial production.

REVISION: Conditional Risk
Date Posted:Thu, 20 Dec 2018 17:05:33 -0600
We show theoretically that the required compensation for time-varying betas in the CAPM can be estimated by a precisely defined conditional-risk factor, which can be used in factor regressions. Both in the U.S. and global sample covering 23 countries, all major equity risk factors load on our conditional-risk factor, meaning that their market betas vary over time and that this variation explains part of their average returns. Studying the economic drivers of these results, we find evidence that this conditional risk arises from variation in discount rate betas (not cash flow betas) due to the endogenous effects of arbitrage trading.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Wed, 05 Dec 2018 07:55:36 -0600
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. This new stylized fact implies that long-maturity risk plays a central role in asset price fluctuations, consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. I present the theoretical source of the puzzle and suggest a new model as a resolution. My model also shows that the counter-cyclical term structure has implications for real activity, which I verify empirically: in bad times, long-duration firms decrease their investment and capital-to-labor ratio relative to short-duration firms.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Sun, 23 Sep 2018 06:48:47 -0500
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. This new stylized fact implies that long-maturity risk plays a central role in asset price fluctuations, consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. I present the theoretical source of the puzzle and suggest a new model as a resolution. My model also shows that the counter-cyclical term structure has implications for real activity, which I verify empirically: in bad times, long-duration firms decrease their investment and capital-to-labor ratio relative to short-duration firms.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Sun, 16 Sep 2018 15:24:46 -0500
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. This new stylized fact implies that long-maturity risk plays a central role in asset price fluctuations, consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. I present the theoretical source of the puzzle and suggest a new model as a resolution. My model also shows that the counter-cyclical term structure has implications for real activity, which I verify empirically: in bad times, long-duration firms decrease their investment and capital-to-labor ratio relative to short-duration firms.

REVISION: Betting Against Correlation: Testing Theories of the Low-Risk Effect
Date Posted:Thu, 21 Jun 2018 11:32:52 -0500
We test whether the low-risk effect is driven by (a) leverage constraints and thus risk should be measured using beta vs. (b) behavioral effects and thus risk should be measured by idiosyncratic risk. Beta depends on volatility and correlation, where only volatility is related to idiosyncratic risk. We introduce a new betting against correlation (BAC) factor that is particularly suited to differentiate between leverage constraints vs. lottery explanations. BAC produces strong performance in the US and internationally, supporting leverage constraint theories. Similarly, we construct the new factor SMAX to isolate lottery demand, which also produces positive returns. Consistent with both leverage and lottery theories contributing to the low-risk effect, we find that BAC is related to margin debt while idiosyncratic risk factors are related to sentiment.

REVISION: Conditional Risk
Date Posted:Thu, 25 Jan 2018 23:02:31 -0600
We present a new direct methodology to study conditional risk, that is, the extra return compensation for time-variation in risk. We show theoretically that the conditional part of the CAPM can be captured by augmenting the standard market model with a conditional-risk factor, which is a specific market timing strategy. Both in the U.S. and global sample covering 23 countries, all major equity risk factors load on our conditional-risk factor, implying that each factor has a higher conditional market beta when the market risk premium is high or the market variance is low. Accordingly, these factor returns can be partly explained by conditional risk. Studying the economic drivers of these results, we find evidence that conditional risk arises from variation in discount rate betas (not cash flow betas) due to the endogenous effects of arbitrage trading.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Wed, 24 Jan 2018 11:10:08 -0600
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. This new stylized fact implies that long-maturity risk plays a central role in asset price fluctuations, consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. I present the theoretical source of the puzzle and suggest a new model as a resolution. My model also shows that the counter-cyclical term structure has implications for real activity, which I verify empirically: in bad times, long-duration firms decrease their investment and capital-to-labor ratio relative to short-duration firms.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Mon, 01 Jan 2018 05:43:03 -0600
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. This new stylized fact implies that long-maturity risk plays a central role in asset price fluctuations, consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. I present the theoretical source of the puzzle and suggest a new model as a resolution. My model also shows that the counter-cyclical term structure has implications for real activity, which I verify empirically: in bad times, long-duration firms decrease their investment and capital-to-labor ratio relative to short-duration firms.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Mon, 25 Dec 2017 09:35:16 -0600
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. This new stylized fact implies that long-maturity risk plays a central role in asset price fluctuations, consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. I present the theoretical source of the puzzle and suggest a new model as a resolution. My model also shows that the counter-cyclical term structure has implications for real activity, which I verify empirically: in bad times, long-duration firms decrease their investment and capital-to-labor ratio relative to short-duration firms.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Fri, 15 Dec 2017 00:44:17 -0600
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. This new stylized fact implies that long-maturity risk plays a central role in asset price fluctuations, consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. I present the theoretical source of the puzzle and suggest a new model as a resolution. My model also shows that the counter-cyclical term structure has implications for real activity, which I verify empirically: in bad times, long-duration firms decrease their investment and capital-to-labor ratio relative to short-duration firms.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Thu, 07 Dec 2017 01:24:23 -0600
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. This new stylized fact implies that long-maturity risk plays a central role in asset price fluctuations, consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. I present the theoretical source of the puzzle and suggest a new model as a resolution. My model also shows that the counter-cyclical term structure has implications for real activity, which I verify empirically: in bad times, long-duration firms decrease their investment and capital-to-labor ratio relative to short-duration firms.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Wed, 06 Dec 2017 01:45:45 -0600
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. This new stylized fact implies that long-maturity risk plays a central role in asset price fluctuations, consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. I present the theoretical source of the puzzle and suggest a new model as a resolution. My model also shows that the counter-cyclical term structure has implications for real activity, which I verify empirically: in bad times, long-duration firms decrease their investment and capital-to-labor ratio relative to short-duration firms.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Sun, 03 Dec 2017 01:03:38 -0600
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. This new stylized fact implies that long-maturity risk plays a central role in asset price fluctuations, consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. I present the theoretical source of the puzzle and suggest a new model as a resolution. My model also shows that the counter-cyclical term structure has implications for real activity, which I verify empirically: in bad times, long-duration firms decrease their investment and capital-to-labor ratio relative to short-duration firms.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Thu, 23 Nov 2017 00:41:50 -0600
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. This new stylized fact implies that long-maturity risk plays a central role in asset price fluctuations, consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. I present the theoretical source of the puzzle and suggest a new model as a resolution. My model also shows that the counter-cyclical term structure has implications for real activity, which I verify empirically: in bad times, long-duration firms decrease their investment and capital-to-labor ratio relative to short-duration firms.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Sun, 19 Nov 2017 01:32:11 -0600
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. This new stylized fact implies that long-maturity risk plays a central role in asset price fluctuations, consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. I present the theoretical source of the puzzle and suggest a new model as a resolution. My model also shows that the counter-cyclical term structure has implications for real activity, which I verify empirically: in bad times, long-duration firms decrease their investment and capital-to-labor ratio relative to short-duration firms.

REVISION: Conditional Risk
Date Posted:Thu, 16 Nov 2017 03:37:04 -0600
We present a new direct methodology to study conditional risk, that is, the extra return compensation for time-variation in risk. We show theoretically that the conditional part of the CAPM can be captured by augmenting the standard market model with a conditional-risk factor, which is a specific market timing strategy. Both in the U.S. and global sample covering 23 countries, all major equity risk factors load on our conditional-risk factor, implying that each factor has a higher conditional market beta when the market risk premium is high or the market variance is low. Accordingly, these factor returns can be partly explained by conditional risk. Studying the economic drivers of these results, we find evidence that conditional risk arises from variation in discount rate betas (not cash flow betas) due to the endogenous effects of arbitrage trading.

REVISION: Higher-Moment Risk
Date Posted:Wed, 15 Nov 2017 05:37:21 -0600
We show how the market's higher order moments can be estimated ex ante using methods based on Martin (2017). These ex ante higher order moments predict future realized higher order moments, whereas trailing realized moments have little predictive power. Higher-moment risks move together in the sense that skewness becomes more negative when kurtosis becomes more positive. In addition, higher-moment risk is high when volatility is low, suggesting that risk doesn't go away - it hides in the tails. Higher-moment risk has significant implications for investors; for example, the tail loss probability of a volatility-targeting investor varies from 3.6% to 9.7%, entirely driven by changes in higher-moment risk. We empirically analyze the economic drivers of these risks, such as financial intermediary leverage, market and funding illiquidity, and potential bubbles.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Wed, 15 Nov 2017 02:15:21 -0600
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. This new stylized fact implies that long-maturity risk plays a central role in asset price fluctuations, consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. I present the theoretical source of the puzzle and suggest a new model as a resolution. My model also shows that the counter-cyclical term structure has implications for real activity, which I verify empirically: in bad times, long-duration firms decrease their investment and capital-to-labor ratio relative to short-duration firms.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Sat, 14 Oct 2017 11:18:39 -0500
I study the time variation of the equity term structure of expected returns, documenting that the slope of equity term structure is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. This new stylized fact implies that long-maturity risk plays a central role in financial fluctuations, consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. I present the theoretical source of the puzzle and suggest a new model as a resolution. My model also shows that the counter-cyclical term structure has implications for real activity, which I verify empirically: in bad times, long-duration firms decrease their investment and capital-to-labor ratio relative to short-duration firms.

REVISION: Betting Against Correlation: Testing Theories of the Low-Risk Effect
Date Posted:Thu, 29 Jun 2017 23:20:02 -0500
We test whether the low-risk effect is driven by (a) leverage constraints and thus risk should be measured using beta vs. (b) behavioral effects and thus risk should be measured by idiosyncratic risk. Beta depends on volatility and correlation, where only volatility is related to idiosyncratic risk. Hence, the new factor betting against correlation (BAC) is particularly suited to differentiating between leverage constraints vs. lottery explanations. BAC produces strong performance in the US and internationally, supporting leverage constraint theories. Similarly, we construct the new factor SMAX to isolate lottery demand, which also produces positive returns. Consistent with both leverage and lottery theories contributing to the low-risk effect, we find that BAC is related to margin debt while idiosyncratic risk factors are related to sentiment and casino profits.

REVISION: Time Variation of the Equity Term Structure
Date Posted:Wed, 21 Jun 2017 06:47:54 -0500
I study the time series variation of the term structure of expected equity returns. I find that the slope of equity term structure is counter-cyclical: the term structure is more upwards sloping (or less downwards sloping) in bad times. This result has broad implications for the source of the equity premium. Indeed, I show that the counter-cyclical term structure is consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the time variation is inconsistent with recent models constructed to match the average downward sloping shape.

REVISION: Betting Against Correlation: Testing Theories of the Low-Risk Effect
Date Posted:Wed, 08 Feb 2017 08:45:07 -0600
We test whether the low-risk effect is driven by (a) leverage constraints and thus risk should be measured using beta vs. (b) behavioral effects and thus risk should be measured by idiosyncratic risk. Beta depends on volatility and correlation, where only volatility is related to idiosyncratic risk. Hence, the new factor betting against correlation (BAC) is particularly suited to differentiating between leverage constraints vs. lottery explanations. BAC produces strong performance in the US and internationally, supporting leverage constraint theories. Similarly, we construct the new factor SMAX to isolate lottery demand, which also produces positive returns. Consistent with both leverage and lottery theories contributing to the low-risk effect, we find that BAC is related to margin debt while idiosyncratic risk factors are related to sentiment.