5. Conclusion

4.3. Strategy performance during economic recessions

96 Wavelet Theory and Its Applications

Figure 4. Out-of-sample returns—long-short strategy LA(8).

Figure 5. Out-of-sample returns—long-short strategy LA(8).

Table 13. Average 20-day cumulative returns for long-short strategy—LA(8).

While the scale level model does not seem to improve the long/short strategy overall, an examination of the returns during recessions tells a different story. As shown in Table 14 and Figures 4–6 for four of six recessions the returns at scale level exceed those using the standard model.

Standard Scale 1 Scale 2 Scale 3 Scale 4 Scale 5 Scale 6

Mean 2.47 �0.60 0.40 �0.54 1.71 �0.70 0.85 Std. dev 29.75 28.28 28.50 27.24 26.92 25.81 23.45 Skewness �0.34 0.18 �0.09 �0.07 �0.09 �0.29 �0.20 Kurtosis 2.48 1.60 1.73 1.68 2.50 1.62 0.90 Minimum �166.32 �112.08 �110.44 �117.63 �109.45 �127.75 �97.01 Maximum 106.20 115.68 105.22 100.11 125.54 87.21 74.49 Median 3.82 �0.35 1.21 �0.03 �0.07 0.35 1.08 Sharpe Ratio 0.08 �0.02 0.01 �0.02 0.06 �0.03 0.04

> The focus of this chapter is on whether adding wavelet methodology to the FF3 model is really "worth it." We attempt to show why it makes sense to add this methodology to the empirical asset pricing toolkit, and ultimately why practitioners should also consider including wavelet methodology in the mix of empirical asset pricing techniques used to provide advice and select portfolios for clients. The most fundamental reason for answering in the affirmative regarding whether wavelet methodology should have a seat at the table of empirical asset pricing models is that when an identified risk "signal" shows different behavior at different time periods, wavelet analysis, capable of decomposing data into several time scales, allows the researcher an opportunity to investigate the behavior of the risk factor/signal over various time scales. The exploration is richer because it allows windows to vary. Of course, allowing for risk measures that vary over time and across frequencies is not the same as finding that it will always matter for the results when compared to a standard approach devoid of such possibilities. Consistent with other research employing scale versions of the FF3 model, we find

industry-specific effects on size and HML factors that are absent using the standard model. The large-scale versus fine-scale information distinction that the scale version of the FF3 model is capable of capturing is found significant for portfolio performance during the majority of recessions included in our data. Finding that the wavelet-based version of the FF3 model produces better portfolio outcomes is of importance to practioners, as well as, researchers. Our main conclusion based on the inter-temporal behavior of financial characteristics estimated with the FF3 model is that risk measures that vary over time and across frequencies are needed to capture the risk dynamics associated with most downturns. The importance of scale effects during periods defined as recessions leads us to conclude that the distinct risk dynamics during recessions are better captured with a methodology that allows for scale effects, providing yet another reason why wavelet methodology is a worthwhile tool that belongs in the methodological toolbox of practitioners in finance.

Sector Industry Standard Scale 1 Scale 2 Scale 3 Scale 4 Scale 5 Scale 6 Health Drugs 0.841 0.850 0.874 0.837 0.815 0.867 0.793 Health Hlth 1.086 1.090 1.112 1.093 1.108 1.073 1.030 Health MedEq 0.938 0.949 0.972 0.949 0.911 0.903 0.776 Manufacturing Aero 1.128 1.120 1.137 1.159 1.150 1.146 1.129 Manufacturing Autos 1.216 1.208 1.199 1.220 1.269 1.193 1.151 Manufacturing Boxes 0.962 0.963 0.960 1.005 0.960 1.000 0.986 Manufacturing ElcEq 1.052 1.046 1.024 1.078 1.063 1.091 1.030 Manufacturing FabPr 1.043 1.045 1.014 1.073 1.145 1.059 1.080 Manufacturing Guns 0.868 0.883 0.816 0.848 0.863 0.900 0.858 Manufacturing LabEq 1.113 1.096 1.107 1.105 1.126 1.125 1.108 Manufacturing Mach 1.146 1.116 1.145 1.170 1.189 1.217 1.094 Manufacturing Paper 0.983 0.971 0.982 0.992 1.021 1.059 1.100 Manufacturing Rubbr 0.938 0.927 0.920 0.967 0.958 0.970 0.979 Manufacturing Ships 0.973 0.949 0.932 1.014 1.018 1.167 1.045 Manufacturing Steel 1.309 1.284 1.316 1.362 1.348 1.392 1.275 Money Banks 1.149 1.102 1.157 1.177 1.194 1.163 1.269 Money Fin 1.179 1.135 1.174 1.227 1.242 1.187 1.337 Money Insur 1.015 0.990 1.024 1.036 1.061 1.057 1.128 Money RlEst 1.021 1.021 0.988 1.050 1.035 1.028 1.122 Other BldMt 1.056 1.024 1.066 1.100 1.088 1.057 1.085 Other BusSv 1.028 1.021 1.033 1.051 1.064 1.075 1.030 Other Cnstr 1.277 1.239 1.313 1.335 1.343 1.324 1.249 Other Fun 1.155 1.162 1.182 1.141 1.131 1.161 1.206 Other Gold 0.418 0.337 0.381 0.560 0.551 0.508 0.303 Other Meals 1.006 1.011 1.002 0.990 1.010 0.967 0.926 Other Other 1.030 1.022 1.045 1.080 0.979 1.019 1.038 Other Trans 1.149 1.151 1.151 1.156 1.177 1.155 1.016 Shops PerSv 1.045 1.057 1.039 1.029 1.073 1.109 1.080 Shops Rtail 1.015 1.016 1.038 1.008 1.022 0.969 0.944 Shops Whlsl 0.982 0.988 0.968 1.000 0.998 1.037 0.936 Telecommunications Telcm 0.888 0.941 0.881 0.867 0.830 0.849 0.805 Utilities Util 0.709 0.707 0.713 0.729 0.739 0.708 0.728

An Application of Wavelets to Finance: The Three-Factor Fama/French Model

http://dx.doi.org/10.5772/intechopen.74165

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Table 15. Average betas by industry.
