Here we will look at how the value-weighted and equally weighted portfolios in each decile performed. To compute portfolio returns, we use daily data from CRSP to calculate the equity value for each company, where the weights correspond to a value weight in each decile. We rebalance the portfolios each time the Federal Open Market Committee published a new report, call it time t. If we say that time t+ 1 is the time when the next report is published, then we use timetdata to calculate weights and timet+ 1 data to find the realized logarithmic returns for each company. We then sum across all firms in each portfolio to get the realized portfolio returns. Table 10-11 and Figure 8 summarizes the value-weighted and equal-weighted returns.
What the results indicate is that if you were to fit a line to these points, the slope of this line would be positive. This implies that stock returns might be proportional to the similarity loading through their filings on the common FOMC report.
Further, we see that the average market capitalization rate of the companies in each portfolio is approximately the same, as well as the number of companies that appear in each portfolio.
This indicates that none of the deciles are biased towards a particular type of company. One could perhaps think about a scenario where a specific type of company prone to substantial stock returns reappear in the last decile, whereas the opposite happens in the first decile. However, what we see is that the different companies move around in the different deciles, indicating that our sorting picks up on the time-varying structure of each company filing.
6 Adding News to FOMC Corporas
Our results from running the similarity measure on firm filings and FOMC reports seem to in-dicate that there is a positive relationship between the similarity score and return on stocks.
However, the results are noisy, and our results do not indicate a monotonically increasing be-havior. Since the FOMC reports are very general, we might fail to capture relevant firm-specific features. Therefore, we choose to update the FOMC corpora with 2.1 million news headlines, which might help to reduce the shortcomings of the generality of the FOMC reports. We then re-run the entire estimation procedures to get an updated similarity measure ˆSti. With this new measure, we hope to decrease the noisiness in the results and to get increased monotonicity.
We sort portfolios based on both ˆSti and construct both value-weighted and equally-weighted portfolios. The results are summarized for both portfolios in Table 3 and 4.
From Table 3 we see that the difference between the upper and lower decile increased sub-stantially, from being 0.29% per month (3.54% p.a.) to 0.74% per month (9.94% p.a.). Figure 10 (a) shows an increased monotonic behaviour compared to Figure 8. The equal-weighted results do no change much, and it seems that its value-weighted counterpart is the better one. It is not clear why we only see improvements in the value-weighted case. One explanation could be that the occurrences in news headlines are much more frequent if the company is larger, thus the news we incorporated has much more information on the larger companies than the smaller. If this is the case, then we would perhaps expect to see this reflected in our results the way we see, since a value-weighted approach gives a much higher weight on larger companies than on smaller.
Further, we see again that the average market capitalization rate of the companies in each portfolio is approximately the same, as well as the number of companies that appear in each portfolio. As in the previous case of non-news portfolios, this implies that none of the deciles are biased towards a particular type of company.
10PortfolioReturns,Value-Weighted Portfolio12345678910(10-1) Mean0.000.100.400.290.250.69**0.260.540.720.730.74 t-stat-0.0170.2851.2410.8720.7352.1840.7761.4842.198**2.108**2.678** t-stat*-0.0160.2661.2970.8740.7202.5000.6911.4302.209**2.384**2.384** SE*0.0040.0040.0030.0030.0040.0160.0040.0040.0030.0030.003 Skewness-3.25-1.663-1.45-1.53-0.37-1.51-2.44-1.57-1.24-1.461.86 Kurtosis23.939.71410.258.968.739.9317.0210.2111.4810.8415.94 Companies315358368391389384385379364369 Averagemarketcap$28.32$27.13$24.98$26.04$26.82$26.76$27.72$27.21$25.18$24.99 N247 *Thestandarderrorsareheteroskedasticityandautocorrelastionrobust(HAC)upto6lags. Wecalculatestandarderrorsusingaconstantregression.Meanandstandarddeviationinpercentage.Averagemarketcapinmillions. Table3:Value-WeightedwithNews-Monthly.
10PortfolioReturns,Equal-Weighted Portfolio12345678910(10-1) Mean0.49*0.66**0.69**0.61**0.76**0.92***0.70**0.82***0.78***0.62**0.13 t-stat1.7362.3312.2702.1082.6423.2712.5362.7012.6682.1510.924 t-stat*1.7542.2872.1602.0462.5103.5452.5302.7402.6352.1310.984 SE*0.0030.0030.0030.0030.0030.0030.0030.0030.0030.0030.001 Skewness-2.18-1.829-1.73-1.55-1.50-1.06-1.24-1.771-1.51-1.37-0.68 Kurtosis14.5412.5312.6810.6310.377.958.5712.0810.868.436.43 Companies315358368391389384385379364369 Averagemarketcap$28.32$27.13$24.98$26.04$26.82$26.76$27.72$27.21$25.18$24.99 N247 *Thestandarderrorsareheteroskedasticityandautocorrelastionrobust(HAC)upto6lags. Wecalculatestandarderrorsusingaconstantregression.Meanandstandarddeviationinpercentage.Averagemarketcapinmillions. Table4:Equal-WeightedwithNews-Monthly.
7 The Long-Short Strategy
In this section, we provide insight into how a long-short strategy can yield greater risk-adjusted returns than the benchmark index. First, the statistical properties at the monthly frequency reported in Table 19 is inspected, and then we follow up with a performance evaluation at the semi-annual frequency in Table 22.
Only the value-weighted portfolio with news exhibits a statistical significant mean the the 5%
significance level. This gives us two indications. First, the value-weighted portfolio composition seems to be the better one. Second, by adding news we go from statistically insignificant results to statistical significance. From these two observations we are especially interested in investigating the value-weighted portfolios with news further, as they provide the most intriguing results.
Since we use S&P 500 listed companies exclusively, we use the S&P 500 Total Return index as the benchmark. Table 22 reports all the first four moments, as well as the correlation between the S&P500 TR index and the Sharpe-ratio for at risk-adjusted measure with a zero risk-free rate for simplification. Table 22 tells us that only the value-weighted portfolio based on the updated corpora has a higher realized return over the period, yielding more than 100% in additional returns on average each half year. Moreover, the risk-adjusted return is also significantly higher, indicating that this portfolio is better than a passive investment in the S&P index alone. We also find a negative correlation between the S&P 500 returns and three of the four portfolios, indicating to us that there could are significant diversification benefits from combining the index with these portfolios.
Due to the possible diversification benefit, we choose to look at two other portfolios, P1∗, and P2∗. P1∗ is the optimal portfolio where we allocate between the value-weighted long-short portfolio with news and the SP500 Total Return index. P2∗ is the optimal portfolio when we allocate between then ten value-weighted portfolios with the news. We set this problem up as a simple Karush-Kuhn-Tucker problem,
whereωis a vector of weights,Ris a vector of returns, and Σ is the covariance matrix associated
with these returns. We restrict |ωi| ≤3 ∀i= 1, ..., N, and we want our weights to sum to 1.
We solve this problem numerically, and the results are summarized in Table 19. We see that by just usingP1∗ we can significantly improve our results, raising the risk-adjusted ratio from 0.36 to 0.65. We also see that using all the ten value-weighted portfolios inP2∗we can further increase the Sharpe ratio, from 0.36 to 1.67. However,P2∗requires you to trade all stocks on the S&P 500 index, which will be costly both in terms of transaction costs but also through shorting fees. P1∗, on the other hand, requires you only to trade 40% of the stocks on the S&P 500 index and an ETF on the index itself. Moreover, these two portfolios are based on ex-post realizations completely, so it is not an entirely fair comparison. However, it highlights the potential diversification benefit that our sorted portfolios can yield.
8 Diagnostics
In this section, we want to robustness check our results. First, we will show that our results are robust to sub-samples by splitting the sample into two parts. Then we will investigate the sensitivity to several topics by estimating a set of new models with 25, 75, and 100 topics. Lastly, we will see how the results change if we change the number of sorted portfolios.
8.1 Splitting the Sample
First, we will evaluate our results to different sub-samples of our time-series. This is to avoid that our results are strongly affected by some events, like significant outliers. We split it in half by using up to the first half of 2008 for the first part and then use the remaining data from the second half of 2008 for the last part. This way of splitting allows us to check the performance through two financial crises, namely the technology bubble at the beginning of the current millennium and the financial crises in the later part of 2008. What we will be looking for is the same relationship as in Figure 9, that is, a positive relationship between portfolio returns and similarity score. Figure 11-12 as well as Table 25 summarizes the results.
What we see is that for the value-weighted portfolios we have a similar result as for the entire sample for both sub-periods. For the equal-weighted portfolios, we see that the strategy fails in the first sub-period, but gives similar results in the subsequent period. These results strengthen our hypothesis that portfolios can be sorted based on the company filings exposure towards a common text source and that the value-weighted portfolios are robust to different sub-samples, although the equal-weighted portfolios fail on the first sub-sample.