2. Overview : What are the relevant factors? What are the
Long lasting question: what are the drivers of stock returns?
Paper offers a new perspective by introducing frequency domain analysis
Authors state “that different factors may be relevant at different frequencies and investigate this empirically to determine which factors are relevant in the long run, the short run, or both” 2 2

3. Methodology Asset Pricing Predictability
Factor Models
Predictability
Dynamic Factor Models
Impressive work covering diverse asset pricing methodologies and robustness analysis 3 3

4. Data US equity portfolios 25 and 100 size-value sorted portfolios,
30 industry portfolios
two sets of 40 mixed portfolios, consisting often equal-weighted size, book-to-market and gross profitability/industry
ten value-weighted momentum portfolios ( Lam, Wang, and Wei (2016) )
International Data- Portfolios? 4 4

5. Data –Frequency Analysis
Monthly data and lower frequencies, mainly by using spectral analysis to extract the low frequency component and gain new insights into the long term risk factors.
Aggregated annual and three-year returns and one-year ahead forecasts using monthly data and filtered data.

6. What factors? Firm features Macroeconomic variables PCA
No theoretical guidance
Why not the liquidity factor and the quality factor?
Well- know predictive variables as factors
Spread between long and short interest rates
Spread between high and low grade bonds
Market Dividend yield

7. Results on US Portfolios
Fundamental factors are more suitable than macroeconomic factors to explain the cross-section of equity returns in terms of R2 at multiple frequencies.
The risk premia vary in magnitude over time and horizon, especially for macroeconomic factors.
In terms of predictability, macroeconomic factors perform similarly to or better than statistical (PCA) factors based on 68 macroeconomic and financial variables

8. Results on international data
Value factor as an important factor, however there is no universal set of factors for all the countries
Exposures vary across horizons both in terms of magnitude and significance.

9. Main insights from filtering
Spectral analysis reveals different dynamics compared to aggregated data,
the importance of industrial production and the term spread at lower frequencies.
However it contrasts with the analysis on “ weak factors”
industrial production, the investment factor and momentum factor are weak factors and shrinked to zero on monthly frequency.

10. In the frequency domain analysis, we still find the normal problems in asset pricing
The way portfolios are constructed matter
Coefficients are not stable over time
No universal set of factors
Overall