Conventional sector rotation presupposes the sequential performance of sectors across business-cycle stages. For instance, Standard & Poor’s sequencing in Figure 4.1 shows that performance in the technology sector follows performance in the financial sector, which in turn follows performance in the utilities sector. Figure 4.1 further illustrates other representative sequential patterns of sector performance. While Figure 4.1 depicts largely congruent beliefs on sequential sector performance, other variations are possible. Moreover, although the analysis considers alternative stages, the actual progression of sector performance across business cycles may not fully align with those partitions. To overcome such obstacles, the ultimately analysis relaxes any assumed pattern of sequential performance and completely ignores business-cycle stages. The analysis tests whether the excess market returns of one sector predict future excess market returns of other sectors at different lags. The analysis examines lags from one to 24 months, to allow for different performance sequencing and business-cycle stage durations.
Figure 4.4 illustrates the distribution of t-statistics for cross-sector predictability of excess market sector performance. First, the analysis maps the Fama and French 49 industries to 10 equally weighted sector portfolios following Table 4.1. Next, the analysis runs individual regressions of excess market sector returns on the excess market returns of the remaining sectors at lags from one to 24 months. In total, there are 2,160 (10 x 9 x 24) t-statistics, covering all possible combinations of sectors and lags. Figure 4.4 compares the resultant t-statistic distribution against an expected normal distribution. The figure illustrates that the distribution of t-statistics for excess market predictability follows a normal distribution. Under a normal distribution and a 10 percent significance level, the estimations should indicate 5 percent positive significance and 5 percent negative significance – even in the absence of actual excess market predictability. The bottom of Figure 4.4 reports the percentage of positive and negative t-statistics significant at 10 percent for each lag and for collectively for all lags. In total, t-statistics are significantly positive 6 percent of the time and significantly negative 5 percent of the time. Most significant predictability occurs at a one-month lag,
marginally higher than a normal distribution. As such, the results suggest that cross- sector predictability occurs only randomly, without indicating any real evidence of statistically significant sequential sector performance.
Figure 4.4 Predictability of excess market industry performance
Notes: Figure 4.4 illustrates the distribution of t-statistics for cross-sector predictability of excess market performance. The analysis constructs sector rotation portfolios from the Fama and French 49 industries mapped to one of 10 GICS sectors reported in Table 4.7. The analysis tests lags from one to 24 months to allow for the possibility of different performance sequencing and business-cycle stage durations. To illustrate, the Standard & Poor’s sequence in Figure 4.1 shows financial sector performance precedes technology sector performance. As such, financial sector returns should predict subsequent technology sector returns. There are 2,160 t-statistics, covering all possible combinations of cross-sector predictability at up to 24 lags. The bottom of Figure 4.4 reports the total percentage of positive and negative t-statistics by lag and in total that are significant at 10 percent.
4.6.6.2Sub-stages
Further analysis also considers different variations of business-cycle stages that might improve the base-case scenario. Outperformance potentially occurs at the beginning or end of each stage. Considering this, the analysis divides all stages into early and late halves then reruns the main tests for sub-stages. There is no significant difference between first- and second-half returns across stages. Investors might anticipate different stages and react in shorter intervals around business-cycle turning points, rather than
0% 5% 10% 15% 20% 25% < - 3.2 9 -3 .2 9 t o -2 .5 8 -2 .5 8 t o -1 .9 6 -1 .9 6 t o -1 .6 5 -1 .6 5 t o -1 -1 to -0 .5 -0 .5 to 0 0 to 0 .5 0. 5 to 1 1 to 1. 65 1. 65 to 1. 96 1. 96 to 2. 58 2. 58 to 3. 29 > 3. 29 F req ue nc y
Statistical Significance of Excess Market Cross-Sector Predictability
Actual distribution of excess market t-statistics Expected distribution of excess market t-statistics assuming a normal distribution
L(1) L(2) L(3) L(4) L(5) L(6) L(7) L(8) L(9) L(10) L(11) L(12) L(13) L(14) L(15) L(16) L(17) L(18) L(19) L(20) L(21) L(22) L(23) L(24) Positive (% ) 0.16 0.08 0.10 0.06 0.02 0.12 0.04 0.06 0.03 0.03 0.07 0.02 0.10 0.08 0.09 0.06 0.08 0.04 0.04 0.04 0.07 0.06 0.01 0.07
Negative (% ) 0.09 0.02 0.02 0.06 0.08 0.04 0.03 0.03 0.07 0.03 0.02 0.06 0.10 0.09 0.07 0.04 0.02 0.06 0.03 0.12 0.06 0.02 0.09 0.03
Total Positive (% ) 0.06
over the full length of a stage. The analysis also considers shorter periods, testing for significant outperformance two, four and six months around turning points only. Again, there is no evidence of significant outperformance.
4.6.6.3Sub-samples
Significant events over the full 60-year sample, like the 1970s bear market and 1990s dot.com bubble could potentially drive the results. Unreported analysis also compares average industry performance for each business-cycle stage over the 1948–1977 and 1978–2007 sub-periods. Industry outperformance appears relatively constant across all sub-periods and business-cycle stages, regardless of the performance metric. Consistent with the previous analysis, early-expansion and middle-expansion industries provide inferior outperformance across sub-periods. Overall, the results are not specific to a particular sub-period.
4.6.6.4Alternative performance measures
This section evaluates two alternative performance measures to compare base-case sector rotation, market-timing, and buy-and-hold strategies. The Goetzmann, Ingersoll, Spiegel, and Welch (2007) manipulation-proof performance measure (MPPM) eliminates any bias in strategy performance attributable to non-normal iid return distributions. Goetzmann, Ingersoll, Spiegel, and Welch (2007) show the MPPM is superior to standard performance metrics, such as Sharpe ratios and Jensen’s alphas, when return distributions are potentially non-normal. The MPPM estimates portfolio performance after adjusting for benchmark risk and is comparable with the proprietary
Morning Star Risk Adjusted Rating (MRAR).105 Equation 4.10 defines the MPPM
performance measure () as follows:
1 1 1 ln( [(1 ) / (1 )] ) (1 ) T t t t r rf t
(Eq. 4.10)where t is the strategy holding period measured as a percentage of a full year, rt
strategy returns, rft the risk-free rate, and benchmark risk. The interpretation of the
MPPM performance measure is the annualized strategy return premium after adjusting for benchmark risk. Goetzmann, Ingersoll, Spiegel, and Welch (2007) estimate that benchmark risk ranges from 2 to 4 for the CRSP value-weighted market index. Unreported MPPM test results show that the market-timing strategy outperforms both the buy-and-hold and sector rotation strategies for a normal range of performance risk measures. For instance, when benchmark risk equals 3, market-timing has an annualized risk-adjusted performance of 5.2 percent, in comparison to 3.1 percent and 4.1 percent for the buy-and-hold and sector rotation strategies. Moreover, MPPM performance results show that sector rotation is inferior to market-timing at all levels of benchmark risk.
As another alternative measure, the Barrett and Donald (2003) stochastic dominance test evaluates strategy performance independent of benchmarks. Barrett and Donald (2003) argue that a stochastic dominance approach is suitable for investors who seek to maximize expected utility. Barrett and Donald (2003) show that, due to omitted risk factors, a stochastic dominance performance ranking is superior to mean-variance measures, such as Jensen’s alphas and Sharpe ratios. Based on unreported test results, the market-timing strategy second-order stochastically dominates both base-case sector rotation and buy-and-hold strategies. Interestingly, results show, from a stochastic dominance perspective, that an investor would be indifferent between sector rotation and a buy-and-hold strategy. In conclusion, both the MPPM and second-order stochastic dominance performance metrics show that base-case sector rotation is an inferior strategy – even for investors who are able to accurately time all business-cycle stages.