New Developments in Long-Term Asset Management

Supported by the Norwegian Finance Initiative
Monika Piazzesi and Luis Viceira, Organizers
Third Annual Conference
New York, New York

May 3-4, 2018

Characteristics Are Covariances:
A Unified Model of Risk and Return

Bryan T. Kelly, Seth Pruitt, and Yinan Su propose a new modeling approach for the cross section of returns: Instrumented Principal Components Analysis (IPCA). IPCA estimates market risk factors and loadings by exploiting beneficial aspects of two well-known existing approaches: “observable” factors built from characteristic-sorted portfolios exemplified by Fama and French (1993), and latent factors estimated by PCA from the panel of realized returns exemplified by Chamberlain and Rothschild (1983) and Connor and Korajczyk (1986). It estimates latent factors and time-varying loadings by introducing observable characteristics that instrument for the unobservable dynamic loadings. The IPCA mapping between characteristics and loadings provides a formal statistical bridge between characteristics and expected returns, while at the same time remaining consistent with the equilibrium asset pricing principle that risk premia are solely determined by exposure to aggregate risks.

Other Conference Papers

The Endowment Model and Modern Portfolio Theory, Stephen G. Dimmock, Nanyang Neng Wang, and Jinqiang Yang

Is Index Trading Benign? Shmuel Baruch, and Xiaodi (Eddie) Zhang

Skin or Skim? Inside Investment and Hedge Fund Performance, Arpit Gupta, and Kunal Sachdeva

Do Intermediaries Matter for Aggregate Asset Prices? Valentin Haddad, and Tyler Muir

Do Foreign Investors Improve Market Efficiency? Marcin Kacperczyk, Savitar Sundaresan, and Tianyu Wang

What Drives Anomaly Returns? Lars Lochstoer, and Paul Tetlock

Replicating Anomalies, Kewei Hou, Chen Xue, and Lu Zhang

< 2017 Conference Papers>
< 2016 Conference Papers>

Additional IPCA features make it ideally suited for state-of-the-art asset pricing analyses. It can jointly evaluate large numbers of characteristic predictors with minimal computational burden by building dimension reduction directly into the model. It operates at the stock-level, delivering intuitive tests of the asset-pricing theory restrictions that stocks’ expected returns derive from their exposures to aggregate risks. It can nest observable factors or other aggregate variables within a more general IPCA specification.

The researchers’ empirical analysis uses data on returns and characteristics for over 12,000 stocks, 1962-2014. In their benchmark four-factor specification, IPCA achieves a total R2 for individual returns of 19.4 percent. As a benchmark, the matched sample total R2 from the Fama-French five-factor model is 21.9 percent. Thus, IPCA is a competitive model for describing the proportion of stock return volatility arising from aggregate risks. Perhaps more importantly, the factor loadings estimated from IPCA provide an excellent description of conditional expected stock returns. In the four-factor IPCA model, the estimated compensation for factor exposures delivers a predictive R2 for returns of 1.8 percent. In the matched sample, the predictive R2 from the Fama-French five-factor model is 0.3 percent. If we instead use standard PCA to estimate the latent four-factor specification, it delivers a 29 percent total R2, but produces a negative predictive R2 and thus has no explanatory power for differences in average returns across stocks.

IPCA out performs the other models for jointly explaining realized variation in returns (i.e., systematic risks) and differences in average returns (i.e., risk compensation). It achieves this superior performance while estimating far fewer parameters, because of its tight restriction that estimated risk exposures vary exactly with observable asset characteristics.

The dual implication of IPCA's superior explanatory power for average stock returns is that IPCA factors are closer to being multivariate mean-variance efficient than factors in competing models. The researchers show that the tangency portfolio of factors from the four-factor IPCA specification achieves an ex ante (i.e., out-of-sample) Sharpe ratio of 2.6, versus 1.3 for the five Fama-French factors plus momentum.

They find that only a small subset of characteristics is necessary to explain variation in realized and expected stock, once they are evaluated in an appropriate multivariate context.

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