程序代写 Lecture 4 Autocorrelation-based Trading Strategies Momentum and Long-Term R

Lecture 4 Autocorrelation-based Trading Strategies Momentum and Long-Term Reversal
. Lochstoer
UCLA Anderson School of Management
Winter 2022

. Lochstoer UCLA Anderson School of Management ()
Winter 2022

Overview of Lecture 4
Autocorrelation in Önancial asset returns
1 Momentum
2 Long-term reversal
. Lochstoer UCLA Anderson School of Management () Winter 2022 2 / 23

Momentum Anomaly in Stocks
Can we exploit violations of weak market e¢ ciency?
there is a small amount of positive autocorrelation in individual monthly stock returns
I At shorter horizons of less than 12 months, stock returns tend to be weakly positively autocorrelated.
(in theory) this can be exploited to construct proÖtable trading strategies
. Lochstoer UCLA Anderson School of Management () Winter 2022

Momentum Anomaly in Stocks
Ken French posts momentum portfolios on his web site
I The portfolios at t are constructed monthly using NYSE prior (t 2 to
t 12) return decile breakpoints.
this is called (cross-sectional) momentum trading
I Örst discovered by Werner de Bondt, a Belgian economist now at De in Chicago, and , of the University of Chicago Booth School of Business. See and Thaler (1985).
. Lochstoer UCLA Anderson School of Management () Winter 2022 4 / 23

Momentum in US Stock Returns
Average returns on momentum portfolios. Source: data from ́s website. The portfolios are constructed monthly using NYSE prior (2-12) return decile breakpoints. Sample: 1927-2013.
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Momentum Sorting
Cross-sectional momentum, by sorting stocks into portfolios based on past performance, basically exploits (small) positive autocorrelation at short horizons between 1 and 12 months.
I To learn more about the time-series origins of cross-sectional momentum, see Moskowitz, Ooi, and Pederson (2012).
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Momentum Factor Structure
momentum stocks have a factor structure: I high momentum stocks co-move
I low momentum stocks co-move
this risk cannot be diversiÖed away
some of this may be tail risk: Daniel, Jagannathan, and Kim (2012). not a free lunch
maybe momentum returns compensate for tail risk
. Lochstoer UCLA Anderson School of Management () Winter 2022

Momentum Risk
0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1.2 -1.4 -1.6
1971 1984 1998
Monthly Log Momentum Returns data
Log Returns on Portfolio 10 minus 1. data from ́s website. The portfolios are constructed monthly using NYSE prior (2-12) return decile breakpoints. Sample: 1927-2013.
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Tail Risk in Momentum
0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1.2 -1.4 -1.6
1971 1984 1998
Monthly Log Momentum Returns data
Log Returns on 10 minus 1
μ +4*σ μ -4* σ
Log Returns on Portfolio 10 minus 1. data from ́s website. The portfolios are constructed monthly using NYSE prior (2-12) return decile breakpoints. Sample: 1927-2013. σ is 0.0971. μ is 0.0079. The skewness is ñ6.39. The kurtosis is 86.66.
. Lochstoer UCLA Anderson School of Management () Winter 2022 9 / 23

Momentum Factor Structure
This momentum strategy works well across several asset classes.
Asness, Moskowitz, and Pedersen (2013) document the pervasiveness of momentum e§ects in
I currencies,
I commodities, I bonds.
. Lochstoer UCLA Anderson School of Management () Winter 2022

Mean-Reversion Betas of Monthly Log Returns
DeÖne: rt+1 (k) rt+1 + rt+2 + … + rt+k
compute βk in
rt(k)=αk +βkrtk(k)+εt negative βk means mean reversion
positive βk means mean aversion
. Lochstoer UCLA Anderson School of Management ()
Winter 2022

Mean-Reversion Betas of Monthly Log Returns
high returns followed by low returns up to 5 years
1 2 3 4 5 6 7 8 9 10 Horizon in Years
Mean Reversion in betas
This Ögure plots βk for Monthly log excess returns on VW-CRSP Index in rt (k) = αk + βk rtk (k) + εt (k). 1926-2012. Monthly data.
. Lochstoer UCLA Anderson School of Management () Winter 2022

Mean-Reversion Betas of Monthly Log Returns
high returns followed by low returns up to 5 years
1 2 3 4 5 6 7 8 9 10 Horizon in Years
Mean Reversion in betas
This Ögure plots βk for Monthly log excess returns on EW-CRSP Index in rt (k) = αk + βk rtk (k) + εt (k). 1926-2012. Monthly data.
. Lochstoer UCLA Anderson School of Management () Winter 2022

Less Risky for the Long-Run
Some evidence of mean reversion in stock returns at investment horizons that exceed one year.
I Fama and French (1988) documented evidence of mean-reversion in stock returns using variance ratios (also see Poterba and Summers (1988)).
I Cochrane (1999) summarizes the evidence on long-run mean-reversion in returns on stocks (pp. 63-64).
I Pastor and Stambaugh (2012) point out that there is a lot of statistical uncertainty about the mean reversion in stock returns.
Mean reversion implies that stocks are less risky for long-run investors.
. Lochstoer UCLA Anderson School of Management () Winter 2022

Long-Term Reversals in Stocks
cross-sectional trading strategy that exploits individual stock returns reversals
there is a small amount of negative autocorrelation in individual monthly stock returns at longer horizons
I At horizons in excess of 12 months, stock returns tend to be weakly negatively autocorrelated.
this can be exploited to construct proÖtable trading strategies French posts LT reversal portfolios on his web site
I The portfolios at t are constructed monthly using NYSE prior (t 13 to t 60) return decile breakpoints.
this is called (cross-sectional) LT reversal trading
. Lochstoer UCLA Anderson School of Management () Winter 2022 15 / 23

Long-Term Reversals in Stocks
18 16 14 12 10
1 2 3 4 5 6 7 8 9 10
Average returns on 10 reversal portfolios
Average returns on reversal portfolios. Source: data from ́s website. The portfolios are constructed monthly using NYSE prior (13-60) return decile breakpoints. Sample: 1931-2013.
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Reversal Risk
1.6 1.4 1.2
1 0.8 0.6 0.4 0.2 0 -0.2 -0.4
1930 1943 1957
1998 2012 2026
Monthly Log Reversal Returns (1 minus 10) data
Source: Log Returns on Portfolio 1 minus 10. data from ́s website. The portfolios are constructed monthly using NYSE prior (13-60) return decile breakpoints. Sample: 1927-2013.
. Lochstoer UCLA Anderson School of Management () Winter 2022 17 / 23

Little Tail Risk in LT Reversals
1.6 1.4 1.2
1 0.8 0.6 0.4 0.2 0 -0.2 -0.4
1930 1943 1957
1998 2012 2026
Monthly Log Reversal Returns data
Log Returns on 1 minus 10
μ +4*σ μ -4* σ
Source: Log Returns on Portfolio 1 minus 10. data from ́s website. The portfolios are constructed monthly using NYSE prior (13-60) return decile breakpoints. Sample: 1927-2013. σ is 0.0971. μ is 0.0079. The skewness is 7.46. The kurtosis is 86.66.
. Lochstoer UCLA Anderson School of Management () Winter 2022 18 / 23

Long-Term Reversals and Value
LT reversal is closely related to ëvalueí
I returns on portfolios sorted by B/M ratios are correlated with returns on portfolios sorted by returns over past 5 years
This LT reversal/value strategy works well across several asset classes.
Asness, Moskowitz, and Pedersen (2013) document the pervasiveness of LT reversal/value e§ects in
I currencies,
I commodities, I bonds.
LT reversal returns are negatively correlated with momentum returns! adding momentum and LT reversals increases the e¢ ciency of the portfolio
. Lochstoer UCLA Anderson School of Management () Winter 2022 19 / 23

Over- and Underreaction
behavioral interpretation (Barberis, Shleifer, and Vishny (1998))
I under-reaction of investors to news is responsible for positive autocorrelations at horizons up to 12 months: news is slowly incorporated into prices
I over-reaction of investors is responsible for negative autocorrelations at horizons after 12 months: securities that have experienced good news become overpriced.
. Lochstoer UCLA Anderson School of Management () Winter 2022 20 / 23

Conclusion
stock returns have:
1 positive autocorrelation at horizons of less than one year
F exploited by momentum trading strategies
2 negative autocorrelation at horizons of more than one year
F exploited by reversal trading strategies
In the short-run (daily to a month) there is also “Short-term Reversal” ñ
negative autocorrelations.
. Lochstoer UCLA Anderson School of Management () Winter 2022

References
Asness, C. S., T. J. Moskowitz, and L. H. Pedersen (2013). Value and momentum everywhere. The Journal of Finance 68(3), 929-985.
Barberis, N., A. Shleifer, and R. Vishny (1998). A model of investor sentiment. Journal of Financial Economics 49(3), 307-343.
Cochrane, J. H. (1999). Portfolio advice for a multifactor world. Economic Perspectives, Federal Reserve Bank of Chicago 23(3).
Daniel, K., R. Jagannathan, and S. Kim (2012, June). Tail risk in momentum strategy returns. National Bureau of Economic Research, Working Paper Series.
, W. F. M. and R. Thaler (1985). Does the stock market overreact? The Journal of Finance 40(3), 793-805.
Fama, E. F. and K. R. French (1988). Permanent and temporary components of stock prices. Journal of Political Economy 96(2), pp. 246-273.
. Lochstoer UCLA Anderson School of Management () Winter 2022 22 / 23

References
Grossman, S. J. and J. Stiglitz (1980). On the impossibility of informationally e§cient markets. American Economic Review 70(3), 393-408.
Ljung, G. M. and G. E. P. Box (1978). On a measure of a lack of t in time series models. Biometrika 65(2), 297-303.
Moskowitz, T. J., Y. H. Ooi, and L. H. Pedersen (2012). Time series momentum. Journal of Financial Economics 104(2), 228-250.
Pastor, L. and R. F. Stambaugh (2012). Are stocks really less volatile in the long run? The Journal of Finance 67(2), 431-478.
Poterba, J. M. and L. H. Summers (1988). Mean reversion in stock prices: Evidence and implications. Journal of Financial Economics 22(1), 27-59.
. Lochstoer UCLA Anderson School of Management () Winter 2022 23 / 23

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