Research
State-Space vs. VAR models for Stock Returns
Manuscript July 24 2008. In a “state-space” model, you write a process for expected returns and another one for expected dividend growth, and then you find prices (dividend yields) and returns by present value relations. I connect state-space models with VAR models for expected returns. What are the VAR or return-forecast-regression implications of a state-space model? What state-space model does a VAR imply? I start optimistic. An AR(1) state-space model gives a nice return-forecasting formula, in which you use both the dividend yield and a moving average of past returns to forecast future returns. The general formulas leave me pessimistic however. One can write any VAR in state-space form, and we don’t really have solid economic reasons to restrict either VAR or state-space representations. Still, the connections between the two representations are worth exploring, and if you’re doing that this paper might save you weeks of algebra.
Manuscript July 24 2008. In a “state-space” model, you write a process for expected returns and another one for expected dividend growth, and then you find prices (dividend yields) and returns by present value relations. I connect state-space models with VAR models for expected returns. What are the VAR or return-forecast-regression implications of a state-space model? What state-space model does a VAR imply? I start optimistic. An AR(1) state-space model gives a nice return-forecasting formula, in which you use both the dividend yield and a moving average of past returns to forecast future returns. The general formulas leave me pessimistic however. One can write any VAR in state-space form, and we don’t really have solid economic reasons to restrict either VAR or state-space representations. Still, the connections between the two representations are worth exploring, and if you’re doing that this paper might save you weeks of algebra.
Two Trees
(with Francis Longstaff and Pedro Santa-Clara), Review of Financial Studies 21 (1) 2008 347-385. We solve the model with two Lucas trees, iid dividends and log utility. Surprise: it has interesting dynamics. If one stock goes up it is a larger share of the market. Its expected return must rise so that people are willing to hold it despite its now larger share. Typo: Equation 39 (page 363), the numerator should read (1-s/(1-s))ln(s)/V, not 1-s/(1-s)ln(s)/V. Thanks to Egor Malkov.
(with Francis Longstaff and Pedro Santa-Clara), Review of Financial Studies 21 (1) 2008 347-385. We solve the model with two Lucas trees, iid dividends and log utility. Surprise: it has interesting dynamics. If one stock goes up it is a larger share of the market. Its expected return must rise so that people are willing to hold it despite its now larger share. Typo: Equation 39 (page 363), the numerator should read (1-s/(1-s))ln(s)/V, not 1-s/(1-s)ln(s)/V. Thanks to Egor Malkov.
Decomposing the Yield Curve
Manuscript, first big revision, March 14 2008. With Monika Piazzesi. We work out an affine term structure model that incorporates our bond risk premia from “Bond Risk Premia” in the AER. There are lots of interesting dynamics – level, slope and curvature forecast future bond risk premia, and we discover that market prices of risk are really simple. We use the model to decompose the yield curve – given a yield (forward) curve today, how much is expected future interest rates, and how much is risk premium? How does the yield or forward rate premium correspond to the term structure of expected return premia? Was the conundrum a conundrum? Slides from 2010 AFA meetings Data and Programs.
Manuscript, first big revision, March 14 2008. With Monika Piazzesi. We work out an affine term structure model that incorporates our bond risk premia from “Bond Risk Premia” in the AER. There are lots of interesting dynamics – level, slope and curvature forecast future bond risk premia, and we discover that market prices of risk are really simple. We use the model to decompose the yield curve – given a yield (forward) curve today, how much is expected future interest rates, and how much is risk premium? How does the yield or forward rate premium correspond to the term structure of expected return premia? Was the conundrum a conundrum? Slides from 2010 AFA meetings Data and Programs.
Financial markets and the Real Economy
In Rajnish Mehra, Ed. Handbook of the Equity Premium Elsevier 2007, 237-325. Everything you wanted to know, but didn’t have time to read, about equity premium, consumption-based models, investment-based models, general equilibrium in asset pricing, labor income and idiosyncratic risk.
In Rajnish Mehra, Ed. Handbook of the Equity Premium Elsevier 2007, 237-325. Everything you wanted to know, but didn’t have time to read, about equity premium, consumption-based models, investment-based models, general equilibrium in asset pricing, labor income and idiosyncratic risk.
This article appeared four times, getting better each time. (Why waste a good article by only publishing it once?) The link above is the last and the best. The previous versions were NBER Working paper 11193, Financial Markets and the Real Economy Volume 18 of the International Library of Critical Writings in Financial Economics, John H. Cochrane Ed., London: Edward Elgar. March 2006, and in Foundations and Trends in Finance 1, 1-101, 2005.
Portfolio theory
Feb. 20 2007 This is a draft of a portfolio theory chapter for the next revision of Asset Pricing. I (of course) take a p = E(mx) approach to portfolio theory before covering the classic Merton-style direct approach. I emphasize the importance of outside income.
Feb. 20 2007 This is a draft of a portfolio theory chapter for the next revision of Asset Pricing. I (of course) take a p = E(mx) approach to portfolio theory before covering the classic Merton-style direct approach. I emphasize the importance of outside income.
The Dog that Did Not Bark: A Defense of Return Predictability
Review of Financial Studies 21(4) 2008 1533-1575. Taken alone, returns may not look that predictable. However, price-dividend ratios vary, so either returns or dividend growth must be forecastable (or both). Implications for dividends, and long-run forecasts give strong statistical evidence against the null that returns are not forecatsable. I address the Goyal-Welch finding that forecasts do badly out of sample, and the long literature criticizing long-run forecasts. The most important practical takeaway: even if you assume that all variation in market p/d ratios comes from time-varying expected returns, and none corresponds to dividend growth forecasts, you will typically find that market-timing strategies based on fitting the regression don’t work. Corrected Table 6. Three numbers were wrong in the published version. Thanks to Camilla Pederson for catching it.
Review of Financial Studies 21(4) 2008 1533-1575. Taken alone, returns may not look that predictable. However, price-dividend ratios vary, so either returns or dividend growth must be forecastable (or both). Implications for dividends, and long-run forecasts give strong statistical evidence against the null that returns are not forecatsable. I address the Goyal-Welch finding that forecasts do badly out of sample, and the long literature criticizing long-run forecasts. The most important practical takeaway: even if you assume that all variation in market p/d ratios comes from time-varying expected returns, and none corresponds to dividend growth forecasts, you will typically find that market-timing strategies based on fitting the regression don’t work. Corrected Table 6. Three numbers were wrong in the published version. Thanks to Camilla Pederson for catching it.
International Risk Sharing is Better Than You Think, Or Exchange Rates are Too Smooth
With Michael Brandt and Pedro Santa Clara. Published Journal of Monetary Economics 53 (4) May 2006 671-698. Original July 2001 (NBER WP 8404) The equity premium means that marginal rates of substitution are very volatile, with more than 50% standard deviation. Exchange rates are the ratio of marginal rates of substitution, and they only vary by about 12%. Therefore, marginal rates of substitution must be highly correlated across countries. Risk sharing is better than you think.
With Michael Brandt and Pedro Santa Clara. Published Journal of Monetary Economics 53 (4) May 2006 671-698. Original July 2001 (NBER WP 8404) The equity premium means that marginal rates of substitution are very volatile, with more than 50% standard deviation. Exchange rates are the ratio of marginal rates of substitution, and they only vary by about 12%. Therefore, marginal rates of substitution must be highly correlated across countries. Risk sharing is better than you think.
Money as Stock
Journal of Monetary Economics 52:3, (2005) 501-528. Revision of NBER Working Paper 7498 Feb. 2000. The fiscal theory of the price level made simple. The `government budget constraint' is not a constraint. I reopen the security market at the end of the day in a cash in advance model, and show that the price level is still determinate. I also resolve the criticism that the fiscal theory mistreats the "government budget constraint."
Journal of Monetary Economics 52:3, (2005) 501-528. Revision of NBER Working Paper 7498 Feb. 2000. The fiscal theory of the price level made simple. The `government budget constraint' is not a constraint. I reopen the security market at the end of the day in a cash in advance model, and show that the price level is still determinate. I also resolve the criticism that the fiscal theory mistreats the "government budget constraint."
Bond Risk Premia
With Monika Piazzesi. American Economic Review 95:1, 138-160 (2005). We forecast one year bond excess returns with a 44% R2! More importantly, a single factor, a single linear combination of yields or forward rates, forecasts one-year returns of all maturity bonds. Read here the Appendix with lots of extra analysis. (Updated Sept 2006 to fix typos in forward rate formulas.) The NBER working paper has lots of cool stuff, including links to macro and the covariance with level result, that got trimmed from the published paper. Data and programs. Look at the pretty plot of how our forecasts work out of sample since we wrote the paper (Until the 2008 financial crisis, in which the Fama-Bliss procedure breaks down.) Read the Response to Ken Singleton regarding his criticism of our results in a paper with Dai and Yang, and then published in his book Empirical Dynamic Asset Pricing (Princeton, 2006). Overheads, useful if you want to teach the paper A summary with color graphs, and treatment of the period since the 2008 financial crisis, in lecture note form. Start on p 567.
With Monika Piazzesi. American Economic Review 95:1, 138-160 (2005). We forecast one year bond excess returns with a 44% R2! More importantly, a single factor, a single linear combination of yields or forward rates, forecasts one-year returns of all maturity bonds. Read here the Appendix with lots of extra analysis. (Updated Sept 2006 to fix typos in forward rate formulas.) The NBER working paper has lots of cool stuff, including links to macro and the covariance with level result, that got trimmed from the published paper. Data and programs. Look at the pretty plot of how our forecasts work out of sample since we wrote the paper (Until the 2008 financial crisis, in which the Fama-Bliss procedure breaks down.) Read the Response to Ken Singleton regarding his criticism of our results in a paper with Dai and Yang, and then published in his book Empirical Dynamic Asset Pricing (Princeton, 2006). Overheads, useful if you want to teach the paper A summary with color graphs, and treatment of the period since the 2008 financial crisis, in lecture note form. Start on p 567.
Liquidity, Trading and Asset Prices
NBER reporter, Jan 2005. A review of these issues in asset pricing.
NBER reporter, Jan 2005. A review of these issues in asset pricing.
Time series for macroeconomics and Finance
Jan 2005 Lecture notes for PhD time series course. This revision finally includes the figures!
Jan 2005 Lecture notes for PhD time series course. This revision finally includes the figures!
The Risk and Return of Venture Capital
(published version) Journal of Financial Economics, Volume 75, Issue 1, January 2005, 3-52. Last Manuscript Estimates the mean return, standard deviation, alpha and beta of venture capital investments, correcting for selection bias that we only see returns for successful projects. Even if you don’t like venture capital, the selection bias correction is interesting. Original December 2000. Appendix containing data and program descriptions plus extra algebra. See above data and programs link for data and programs.
(published version) Journal of Financial Economics, Volume 75, Issue 1, January 2005, 3-52. Last Manuscript Estimates the mean return, standard deviation, alpha and beta of venture capital investments, correcting for selection bias that we only see returns for successful projects. Even if you don’t like venture capital, the selection bias correction is interesting. Original December 2000. Appendix containing data and program descriptions plus extra algebra. See above data and programs link for data and programs.
The fiscal foundations of monetary regimes
(paper, and powerpoint presentation) January 2003. The choice of monetary regime – interest rate rule, exchange rate peg, currency board, dollarization, etc. depends on fiscal constraints, especially for developing countries. Talk given at the 2003 NBER/NCAER Neemrana conference, India.
(paper, and powerpoint presentation) January 2003. The choice of monetary regime – interest rate rule, exchange rate peg, currency board, dollarization, etc. depends on fiscal constraints, especially for developing countries. Talk given at the 2003 NBER/NCAER Neemrana conference, India.
Stocks as Money: Convenience Yield and the Tech-Stock Bubble
May 2002. Published in William C. Hunter, George G. Kaufman and Michael Pomerleano, Eds., Asset Price Bubbles Cambridge: MIT Press 2003. The “arbitrage opportunity” in Palm vs. 3Com stock might be like the arbitrage opportunity between money and treasury bills. I document many similar features, including high turnover in the “overpriced” security. Presented at the Chicago Fed Conference on asset price bubbles, April 2002.
May 2002. Published in William C. Hunter, George G. Kaufman and Michael Pomerleano, Eds., Asset Price Bubbles Cambridge: MIT Press 2003. The “arbitrage opportunity” in Palm vs. 3Com stock might be like the arbitrage opportunity between money and treasury bills. I document many similar features, including high turnover in the “overpriced” security. Presented at the Chicago Fed Conference on asset price bubbles, April 2002.
The Fed and Interest Rates – a High Frequency Identification
American Economic Review 92 (2002), 90-95. With Monika Piazzesi (previously NBER WP 8839) . We measure monetary policy shocks by how they surprise daily bond markets. There's a beautiful Taylor rule in interest rate forecasts.
American Economic Review 92 (2002), 90-95. With Monika Piazzesi (previously NBER WP 8839) . We measure monetary policy shocks by how they surprise daily bond markets. There's a beautiful Taylor rule in interest rate forecasts.
Macroeconomics in Russia
In Economic Transition in Eastern Europe and Russia: Realities of Reform, Edward Lazear Ed., Hoover Institution Press, 1995. Imagine for a moment that the Federal Reserve imposed the following policies in the United States: Every company must pay for all its inputs before they are shipped, and taxes must also be prepaid. But there is no trade credit, and banks do not make working capital loans to purchase inputs. Checks take 90 days to clear… Chaos would result… This is roughly what happened in Russia during the summer of 1992. The story… points to the importance of macroeconomic policies, and the unintended macroeconomic effects of policy, in understanding developments in Russia and the Former Soviet Union. It also suggests that many macroeconomic problems are not inevitable consequences of the transition to a market economy, but rather that they are avoidable unintended effects of partial liberalizations.
In Economic Transition in Eastern Europe and Russia: Realities of Reform, Edward Lazear Ed., Hoover Institution Press, 1995. Imagine for a moment that the Federal Reserve imposed the following policies in the United States: Every company must pay for all its inputs before they are shipped, and taxes must also be prepaid. But there is no trade credit, and banks do not make working capital loans to purchase inputs. Checks take 90 days to clear… Chaos would result… This is roughly what happened in Russia during the summer of 1992. The story… points to the importance of macroeconomic policies, and the unintended macroeconomic effects of policy, in understanding developments in Russia and the Former Soviet Union. It also suggests that many macroeconomic problems are not inevitable consequences of the transition to a market economy, but rather that they are avoidable unintended effects of partial liberalizations.
Review of Famous First Bubbles: The Fundamentals of Early Manias
Journal of Political Economy 109, (October 2001),1150-1154. Review of the very nice book by Peter Garber, looking at the facts behind the tulip “bubble” and related myths. It turns out they are mythical. I had a lot of fun with this one.
Journal of Political Economy 109, (October 2001),1150-1154. Review of the very nice book by Peter Garber, looking at the facts behind the tulip “bubble” and related myths. It turns out they are mythical. I had a lot of fun with this one.
Long term debt and optimal policy in the fiscal theory of the price level
Econometrica 69, 69-116 (2001). The fiscal theory with long term debt, and how to match the fiscal theory with business-cycle variation in debt and inflation. We typically write fiscal theory models with one-period debt, but the maturity structure turns out to matter a lot. For example, if the government pays off a perpetuity, then the price level is determined by the coupon coming due each year and that year’s taxes, with no present value of future taxes. I also resolve the empirical puzzle that inflation and deficits seem not to commove. That’s exactly what we expect of a government that’s trying to smooth inflation in the face of fiscal shocks.
Econometrica 69, 69-116 (2001). The fiscal theory with long term debt, and how to match the fiscal theory with business-cycle variation in debt and inflation. We typically write fiscal theory models with one-period debt, but the maturity structure turns out to matter a lot. For example, if the government pays off a perpetuity, then the price level is determined by the coupon coming due each year and that year’s taxes, with no present value of future taxes. I also resolve the empirical puzzle that inflation and deficits seem not to commove. That’s exactly what we expect of a government that’s trying to smooth inflation in the face of fiscal shocks.
Explaining the Poor Performance of Consumption-Based Asset Pricing Models
(With John Y. Campbell). Journal of Finance 55(6) (December 2000) 2863-2878. The CAPM outperforms the consumption-based model in artificial data from the habit persistence model used in "By force of Habit.."
(With John Y. Campbell). Journal of Finance 55(6) (December 2000) 2863-2878. The CAPM outperforms the consumption-based model in artificial data from the habit persistence model used in "By force of Habit.."
A rehabilitation of stochastic discount factor methodology
Manuscript, July 2000 A short note showing how Kan and Zhou (1999) went wrong. Adapted from comments I gave to Jagannathan and Wang given at the spring 2000 NBER asset pricing meeting. The Journal of Finance does not publish corrections, even to flat-out mistakes, alas.
Manuscript, July 2000 A short note showing how Kan and Zhou (1999) went wrong. Adapted from comments I gave to Jagannathan and Wang given at the spring 2000 NBER asset pricing meeting. The Journal of Finance does not publish corrections, even to flat-out mistakes, alas.