Although hospital administrators are most likely to see ...
Assignment 1: Multi-factor Residual-Based Trading Strategy
Finance 453: Global Asset Allocation & Stock Selection
Beagle Capital
Adrian Helfert
Trevor Hicks
Terry Moore
Kevin Stoll
Ben Thomason
February 26, 2004
Part 1: Introduction
The basic Capital Asset Pricing Model (CAPM) uses one risk “sensitivity” (beta) to one risk factor (the market risk premium) that may not be appropriately descriptive for all securities. Fama and French(1995) discovered that by adding two factors (HML and SMB), the model does a better job of explaining security returns. We start with the basic CAPM model and add five factors that we believe affect large U.S. companies.
In order to effectively implement a potential trading strategy, we chose to sample the highly liquid stocks in the Dow Jones Composite Index (Dow 30). We use the residuals from our model to construct a variety of screens and sort the stocks in three portfolios. Our model was estimated on a daily basis and generated daily residuals. The portfolios are rebalanced weekly. After running screens on included factors, we score each screen’s portfolios and re-sort based on the score.
Part 2: Hypothesis
We hypothesize that the expected return of an asset can be more appropriately described by the following revised asset pricing model:
Ra – rf = α + β1(Rm – rf ) + β2((Rm – rf )2) + β3(USD Returns) + β4(GS Commodity Returns) + β5(LT Bond Return) + β6(Interest Rate Slope Δ) + ε
This model is an extension of the CAPM and allows the regression to place risk sensitivities (betas) on our suggested risk factors. The risk factors were chosen based on their relevance to large capitalization stocks in the Dow 30. The results of the regressions are in Appendix A.
• β1(Rm – rf ): This is the basic risk weighting from CAPM in response to movements in the market risk premium.
• β2((Rm – rf )2): The square of the return of the market return over the risk free rate is a major factor in the model that serves as a proxy for the skew of the returns against the market. This factor heavily weights large market returns, both positive and negative. The sign of the coefficient will determine the expected effect on the security’s returns. A positive coefficient indicates the stock will outperform during big up and down moves in the market (a highly desirable feature).
• β3(USD Returns): Changes in exchange rates may affect the variability of returns for large multinational companies (such as the Dow 30 constituents) that repatriate income to the U.S.
• β4(GS Commodity Returns): We include the Goldman Sachs Commodity Index (GSCI) returns in order to capture the risk to these equities from the variability in commodity prices. Many of these large companies will be dependent on commodities as inputs for their own goods and, in the case of oil companies, their revenues are driven directly from the commodity prices.
• β5 (LT Bond Returns): The Lehman U.S. Long Term Treasury Index return is used as a proxy because of both the potential sensitivity of the companies’ debt and the equity market sensitivity to interest rates. Bond returns also represent a large portion of investor portfolios and should be considered when determining “market” risk.
• β6(Interest Rate Slope Δ): For constructing the sensitivity to the interest rate slope change, we first subtracted the 3-month U.S. Treasury Bill yield from the 20-year U.S. Constant Maturity Treasury (CMT) yield and then took the change from the previous day. Previous studies have shown that the slope of the yield curve is a useful predictor of the business cycle. This should prove a significant risk factor for large cap companies as they likely have exposure to both the long and short end of the risk curve given their exposure to various types of debt.
Part 3: Data Selection, Sources, and Rationale
In selecting an asset class for this study, we wanted to choose a family of securities that were widely traded (i.e. highly liquid) and constrained in scope of sheer size. For these reasons we choose the Dow Jones Composite Index. From the in-sample study period of 1994-2002, there were 30 securities in the Dow at the beginning of the period. We tracked these specific stocks throughout the study to avoid survivorship bias.
The stocks were Alcoa (AA), Allied Signal (ALD), American Express (AXP), Boeing (BA), Bethlehem Steel (BS), Caterpillar (CAT), Chevron (CHV), Du Pont (DD), Disney (DIS), Eastman Kodak (EK), General Electric (GE), General Motors (GM), Goodyear (GT), IBM, International Paper (IP), JP Morgan (JPM), Coca Cola (KO), McDonalds (MCD), 3M (MMM), Altria (MO), Merck (MRK), Proctor & Gamble (PG), Sears (S), AT&T (T), Texaco (TX), Union Carbide (UK), United Technologies (UTX), Westinghouse Electric (WX), Exxon (XON), and Woolworth (Z).
We used the Center for Research in Securities Prices (CRSP) as the data source for Dow returns and total market returns, for which we used the combined NYSE, NASDAQ, and AMEX components. We choose to use the combined returns from these three exchanges as we believe it is a better measure of the total returns to the stock market than just using one index, such as the S&P 500, which would be biased to large cap company returns.
We used Datastream to collect data for the GSCI returns, USD returns, and the Lehman U.S. Long Term Treasury Index returns.
We used the Federal Reserve website, , to obtain daily observations of the 3-month U.S. T-bill yield and 20-year CMT yield.
For our out-of-sample analysis (January 2003 – January 2004) we used return data from Yahoo! Finance. Due to data limitations, we used the S&P 500 as the market return during the out-of-sample period.
Part 4: Residual Diagnostics
We looked at the residuals in several different ways to determine the ability of our screening model to accurately predict returns.
The serial correlation tells how a lagged variable correlates to the value of the variable itself. In this scenario, a positive indication of the predictive value of the model would be the observance of significant negative autocorrelation of the residuals in the lagged periods. This would indicate that after a positive movement, the return is essentially mean reverting back to the model prediction, and so the return is reduced.
We calculated the residual autocorrelations for the Dow components (See Appendix B). Our results indicate that in the first five periods, there is significant negative autocorrelation between the residuals and the actual returns. It is interesting that the 2 day time lag reveals the most extreme results with 90% negative autocorrelations and 47% of those falling outside of a 95% confidence interval.
[pic]
Part 5: Analysis
-Steps
Once we decided on a specific model, the data, and data sources to be used, we followed a specific flow in our analysis:
1. Regress each asset with our pricing model variables
2. Perform diagnostics on the residuals
3. Use the residuals to perform screens
4. Score each screen
5. Screen based on total score
6. Evaluate the trading strategies
-Screens
We ran a total of six screens, three of which we ultimately used in the scoring process. Three were discarded due to relative underperformance.
The first screen ranks, in ascending order, the sum of residual errors over the previous five days. We hypothesize that a large negative error is associated with that stock’s relative underperformance based on its exposure to our selected risk factors and will result in subsequent outperformance as it “catches up” to its appropriate return. The opposite is true for the large positive errors. Negative autocorrelations in our residuals support this theory. Thus, the first portfolio consists of past underperformers that will outperform in the future and the third portfolio consists of the opposite. A long-short strategy would entail purchasing the first portfolio and shorting the third portfolio in each period, and this would have resulted in an annualized return of 22.2% in a value weighted portfolio.
The second screen ranks, in ascending order, the sum of residual errors over the previous thirty days. The results were similar to the first screen, but not quite as good, and thus discarded.
The third screen ranks, in ascending order, the difference between the five day moving average of residual errors and the thirty day moving average of residual errors. This is used as a technical reversal in that we expect a stock’s recent 5-day performance to track its longer term 30-day performance. Stocks with 5 day moving averages lower than 30 day moving averages have underperformed their recent trend, and will therefore be expected to “catch up” with higher returns in the future. For this screen we assigned a score of +3 for Portfolio 1 and -3 for Portfolio 3.
The fourth screen ranks, in ascending order, the difference between the five day moving average of residuals and the ten day moving average of residuals. The results were similar to the third screen, but not quite as good, and thus discarded.
The fifth screen ranks, in ascending order, the expected variance for each stock forecasted using the GARCH model. We used the residuals to estimate expected conditional variance. We hypothesize that a low expected variance is rewarded by investors and the security will outperform. The opposite is true for high expected variances. The screen performed well and we assigned scores of +3 for Portfolio 1 and -2 for Portfolio 3.
The sixth screen ranks, in ascending order, changes in expected variance for each stock forecasted using the GARCH model. We hypothesize that small changes in expected variance are rewarded by investors. However, the screen performs poorly and, thus, is discarded.
The following table depicts the long-short portfolio returns and alphas for each of the six screens. See Appendix C for a detailed overview of the screening statistics.
[pic]
The following table summarizes the scores that we assigned to each of the selected portfolios to be used in the scoring screen.
[pic]
In addition, we calculated the average correlation across the three portfolios for each of the diagnostic screens. The following table depicts these average correlations:
[pic]
Although the MA5-MA30 and 5 Day Sum screens are highly correlated, we decided to score both screens. We believe having the MA5-MA30 screen will be highly beneficial during the out-of-sample periods because it will help control for the instability of the intercept coefficient. Specifically, there is no particular reason why a positive or negative coefficient for a stock during our in-sample period will also exist in the out-of-sample period. Therefore, the intercept in the 5 Day Sum screen could bias our residuals to be consistently positive or negative for any given stock. Comparing two moving averages, however, will help to mitigate this problem because any biases will be cancelled out.
Part 6: Results
In performing the in sample screenings, there are two inherent problems. First, the residuals are calculated using our pricing model on data from 1994-2002 and used to predict the returns one week in the future. Using this same pricing model to determine the returns in 1994 would have been incorrect as you would be using data that is in the future. Secondly, the act of screen the data for the best returns and totaling the screenings for the best portfolios essentially creates the problem of data snooping. If one sorts through enough data and continually screens, eventually positive returns can be found. The true test of the effectiveness of our model which eliminates both of these factors will be in the out of sample analysis.
For the final results, we first performed total scoring screens on the in sample data which add up all scores from each of 3 scored screens: 5 Day residual, 5 day moving average-30 day moving average, and the expected variance. The results, shown in Appendix C showed several areas of promise:
1. Trading on a Long/Short strategy, we produced returns of 19.7% and 18.1% on the equal-weighted and value-weighted portfolios, respectively.
2. These returns were produced at standard deviations below that of the market portfolio
3. The majority of the risk weighting was on the market excess returns and the square of the market excess returns. We found positive alpha on the highest portfolios with negative alpha on the low portfolio. It seemed our scoring model found positive returns outside the risk descriptions on the high portfolio while slightly overestimating the low portfolio.
Lastly, we performed the same total scoring screens using the out of sample data. The out of sample analysis on the 2003 hold out period was not positive.
1. Although the previous years of our sample nearly always had some degree of positive spread between the high and low portfolios, 2003 was a different story. Out of sample we incurred a loss of -16.4% and -23.7% on the equal-weighted and value-weighted portfolios, respectively.
2. These returns were definitely outpaced by the Dow, which had returns in the range of 25% for 2003. One major issue is likely the oversensitivity to the alpha intercept developed from previous years’ data.
Part 8: Next Steps
The results of our analysis showed positive, market excess returns which require further analysis. Several steps would be necessary to validate the returns achieved. We used a starting sample of 30 stocks to conduct the analysis. This sample was chosen in part to avoid the problem of addressing slippage. In further analysis, it would certainly be necessary to include slippage estimates as part of the analysis. This is especially true since the high turnover predicted by the screens could significantly affect the portfolio returns depending on the invested amount and the degree of slippage.
Other interesting strategies to test are:
• Estimate a rolling pricing model instead of the fixed historical time model currently used. This would allow the risk factor coefficients to change through time rather than being fixed.
• Optimize the scoring system instead of using our subjective scores. This could be done through a mean-variance optimization procedure.
• Factor trading costs and slippage costs explicitly into the model. As mentioned above, the high turnover would decrease the trading strategy returns.
• Test a 2-day model instead of the 5-day model used. The autocorrelation results showed that the second day had 90% of the observations with negative results, and the third through fifth day showed less negative results. (See table above)
• Conduct a moving average crossover strategy with automated buy/sell signals. With this strategy, there is the risk of trading on bad signals and increased transaction costs from higher turnover.
• This screen was very sensitive to the alpha intercept and it may have biased the results downward in 2003. A possible next step would be to develop a screening model less sensitive to this.
References:
Fama, Eugene, and Kenneth French, Size and book-to-market factors in earnings and returns, Journal of Finance 50, 131-155.
Appendix A Multiple Regression Analysis on Equity Sample.
Multiple Regression - AA - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: AA - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000574158 0.000487723 1.17722 0.2391
MktPrem 0.872237 0.0395899 22.0318 0.0000
MktPrem^2 -1.15844 1.49503 -0.774857 0.4384
USD -0.10176 0.12096 -0.841269 0.4002
LT_Treas_Ret -0.215891 0.0788508 -2.73797 0.0062
IntSpreadCh 0.00387364 0.00155929 2.48424 0.0130
Comm_Ret 0.0544308 0.0391598 1.38997 0.1645
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.224782 6 0.0374636 85.69 0.0000
Residual 0.952262 2178 0.000437218
-----------------------------------------------------------------------------
Total (Corr.) 1.17704 2184
R-squared = 19.0971 percent
R-squared (adjusted for d.f.) = 18.8743 percent
Standard Error of Est. = 0.0209098
Mean absolute error = 0.0153148
Durbin-Watson statistic = 2.02181 (P=0.3051)
Lag 1 residual autocorrelation = -0.0116363
Multiple Regression - ALD - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: ALD - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000573487 0.000423025 1.35568 0.1752
MktPrem 0.864358 0.0382744 22.5832 0.0000
MktPrem^2 -0.997007 1.4917 -0.66837 0.5039
USD 0.0523997 0.108002 0.485172 0.6276
LT_Treas_Ret 0.122644 0.067963 1.80457 0.0711
IntSpreadCh 0.000605045 0.00124578 0.485674 0.6272
Comm_Ret -0.0338941 0.0359732 -0.942204 0.3461
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.147887 6 0.0246479 89.34 0.0000
Residual 0.496054 1798 0.000275892
-----------------------------------------------------------------------------
Total (Corr.) 0.643942 1804
R-squared = 22.966 percent
R-squared (adjusted for d.f.) = 22.7089 percent
Standard Error of Est. = 0.01661
Mean absolute error = 0.012045
Durbin-Watson statistic = 2.12448 (P=0.0041)
Lag 1 residual autocorrelation = -0.062298
Multiple Regression - AXP - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: AXP - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000270377 0.000409657 0.660009 0.5092
MktPrem 1.33748 0.0332531 40.2213 0.0000
MktPrem^2 1.55287 1.25574 1.23662 0.2162
USD 0.186145 0.101599 1.83214 0.0669
LT_Treas_Ret 0.0122282 0.0662299 0.184632 0.8535
IntSpreadCh -0.000408465 0.00130971 -0.311875 0.7551
Comm_Ret -0.0409154 0.0328918 -1.24394 0.2135
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.509507 6 0.0849178 275.30 0.0000
Residual 0.671818 2178 0.000308456
-----------------------------------------------------------------------------
Total (Corr.) 1.18132 2184
R-squared = 43.1301 percent
R-squared (adjusted for d.f.) = 42.9734 percent
Standard Error of Est. = 0.0175629
Mean absolute error = 0.0130179
Durbin-Watson statistic = 2.11836 (P=0.0028)
Lag 1 residual autocorrelation = -0.0593178
Multiple Regression - BA - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: BA - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000884621 0.000460544 1.92082 0.0548
MktPrem 0.836573 0.0373838 22.3779 0.0000
MktPrem^2 -5.99044 1.41172 -4.24336 0.0000
USD 0.0801513 0.11422 0.701727 0.4828
LT_Treas_Ret 0.00549299 0.0744569 0.0737741 0.9412
IntSpreadCh 0.00184552 0.0014724 1.25342 0.2101
Comm_Ret -0.0689519 0.0369776 -1.86469 0.0622
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.209575 6 0.0349292 89.60 0.0000
Residual 0.84909 2178 0.000389848
-----------------------------------------------------------------------------
Total (Corr.) 1.05867 2184
R-squared = 19.7962 percent
R-squared (adjusted for d.f.) = 19.5752 percent
Standard Error of Est. = 0.0197446
Mean absolute error = 0.0141822
Durbin-Watson statistic = 1.93713 (P=0.0709)
Lag 1 residual autocorrelation = 0.0313682
Multiple Regression - BS - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: BS - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT -0.00170888 0.00119766 -1.42685 0.1536
MktPrem 0.87733 0.103952 8.43979 0.0000
MktPrem^2 4.95211 3.96933 1.2476 0.2122
USD 0.325149 0.301705 1.0777 0.2812
LT_Treas_Ret -0.39143 0.197612 -1.9808 0.0476
IntSpreadCh 0.00309992 0.00435418 0.711942 0.4765
Comm_Ret -0.0247581 0.0968084 -0.255743 0.7981
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.191877 6 0.0319795 12.82 0.0000
Residual 5.08158 2037 0.00249464
-----------------------------------------------------------------------------
Total (Corr.) 5.27346 2043
R-squared = 3.63854 percent
R-squared (adjusted for d.f.) = 3.35471 percent
Standard Error of Est. = 0.0499464
Mean absolute error = 0.0276219
Durbin-Watson statistic = 2.15514 (P=0.0002)
Lag 1 residual autocorrelation = -0.079067
Multiple Regression - CAT - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: CAT - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000136822 0.00045892 0.298139 0.7656
MktPrem 0.881293 0.0372519 23.6577 0.0000
MktPrem^2 0.504746 1.40674 0.358805 0.7197
USD 0.0360133 0.113817 0.316414 0.7517
LT_Treas_Ret -0.0839324 0.0741943 -1.13125 0.2579
IntSpreadCh 0.00321282 0.0014672 2.18976 0.0285
Comm_Ret -0.0641959 0.0368472 -1.74222 0.0815
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.223811 6 0.0373019 96.36 0.0000
Residual 0.843111 2178 0.000387103
-----------------------------------------------------------------------------
Total (Corr.) 1.06692 2184
R-squared = 20.9773 percent
R-squared (adjusted for d.f.) = 20.7596 percent
Standard Error of Est. = 0.0196749
Mean absolute error = 0.0143908
Durbin-Watson statistic = 2.04972 (P=0.1226)
Lag 1 residual autocorrelation = -0.0248649
Multiple Regression - CHV - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: CHV - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000411537 0.000367822 1.11885 0.2632
MktPrem 0.372087 0.0321674 11.5672 0.0000
MktPrem^2 -0.835545 1.191 -0.701546 0.4830
USD -0.010494 0.0923991 -0.113572 0.9096
LT_Treas_Ret 0.151166 0.0622516 2.42831 0.0152
IntSpreadCh 0.000324052 0.00140062 0.231364 0.8170
Comm_Ret 0.337925 0.0309647 10.9132 0.0000
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.0576794 6 0.00961323 44.18 0.0000
Residual 0.406659 1869 0.000217581
-----------------------------------------------------------------------------
Total (Corr.) 0.464338 1875
R-squared = 12.4218 percent
R-squared (adjusted for d.f.) = 12.1407 percent
Standard Error of Est. = 0.0147506
Mean absolute error = 0.0112362
Durbin-Watson statistic = 2.06708 (P=0.0731)
Lag 1 residual autocorrelation = -0.0343608
Multiple Regression - DD - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: DD - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000234147 0.000421617 0.555356 0.5786
MktPrem 0.756763 0.0342239 22.1121 0.0000
MktPrem^2 -0.693503 1.2924 -0.536603 0.5915
USD 0.051388 0.104566 0.491442 0.6231
LT_Treas_Ret -0.0660497 0.0681635 -0.96899 0.3325
IntSpreadCh 0.00194166 0.00134794 1.44046 0.1497
Comm_Ret -0.0360553 0.0338521 -1.06508 0.2868
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.164427 6 0.0274045 83.87 0.0000
Residual 0.711618 2178 0.00032673
-----------------------------------------------------------------------------
Total (Corr.) 0.876045 2184
R-squared = 18.7692 percent
R-squared (adjusted for d.f.) = 18.5454 percent
Standard Error of Est. = 0.0180757
Mean absolute error = 0.0130529
Durbin-Watson statistic = 1.99077 (P=0.4146)
Lag 1 residual autocorrelation = 0.00433763
Multiple Regression - KO - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: KO - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000583304 0.000389667 1.49693 0.1344
MktPrem 0.53358 0.0316305 16.8692 0.0000
MktPrem^2 -2.55016 1.19446 -2.13499 0.0328
USD -0.0919067 0.0966417 -0.951005 0.3416
LT_Treas_Ret 0.231104 0.0629981 3.66842 0.0002
IntSpreadCh -0.000576146 0.0012458 -0.462472 0.6437
Comm_Ret -0.101574 0.0312868 -3.24656 0.0012
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.0876494 6 0.0146082 52.34 0.0000
Residual 0.607853 2178 0.000279088
-----------------------------------------------------------------------------
Total (Corr.) 0.695502 2184
R-squared = 12.6023 percent
R-squared (adjusted for d.f.) = 12.3615 percent
Standard Error of Est. = 0.0167059
Mean absolute error = 0.0122047
Durbin-Watson statistic = 1.87359 (P=0.0016)
Lag 1 residual autocorrelation = 0.0631722
Multiple Regression - T- risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: T- risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.0000225941 0.000493142 0.0458167 0.9635
MktPrem 0.969617 0.0400298 24.2223 0.0000
MktPrem^2 -1.61819 1.51164 -1.07049 0.2844
USD -0.0069715 0.122305 -0.0570011 0.9545
LT_Treas_Ret -0.0599441 0.079727 -0.751867 0.4521
IntSpreadCh 0.000651581 0.00157661 0.413279 0.6794
Comm_Ret -0.0255828 0.0395949 -0.646115 0.5182
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.266995 6 0.0444992 99.55 0.0000
Residual 0.973542 2178 0.000446989
-----------------------------------------------------------------------------
Total (Corr.) 1.24054 2184
R-squared = 21.5226 percent
R-squared (adjusted for d.f.) = 21.3064 percent
Standard Error of Est. = 0.0211421
Mean absolute error = 0.0147764
Durbin-Watson statistic = 1.96095 (P=0.1807)
Lag 1 residual autocorrelation = 0.0192875
Multiple Regression - EK - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: EK - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000122764 0.000442384 0.277505 0.7814
MktPrem 0.671314 0.0359096 18.6946 0.0000
MktPrem^2 -1.51656 1.35605 -1.11837 0.2634
USD 0.153265 0.109716 1.39693 0.1624
LT_Treas_Ret -0.0685984 0.0715208 -0.959138 0.3375
IntSpreadCh -0.000428661 0.00141434 -0.303083 0.7618
Comm_Ret -0.0291828 0.0355194 -0.821601 0.4113
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.130972 6 0.0218286 60.68 0.0000
Residual 0.783445 2178 0.000359709
-----------------------------------------------------------------------------
Total (Corr.) 0.914417 2184
R-squared = 14.323 percent
R-squared (adjusted for d.f.) = 14.0869 percent
Standard Error of Est. = 0.018966
Mean absolute error = 0.0127543
Durbin-Watson statistic = 1.9241 (P=0.0380)
Lag 1 residual autocorrelation = 0.0342236
Multiple Regression - GE - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: GE - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.0000032632 0.000316162 0.0103213 0.9918
MktPrem 1.22957 0.0256638 47.9107 0.0000
MktPrem^2 2.42673 0.969141 2.504 0.0123
USD 0.145467 0.0784115 1.85517 0.0636
LT_Treas_Ret 0.0316559 0.0511144 0.619314 0.5357
IntSpreadCh 0.0010562 0.00101079 1.04492 0.2961
Comm_Ret -0.0673053 0.025385 -2.65139 0.0080
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.43129 6 0.0718817 391.24 0.0000
Residual 0.400156 2178 0.000183727
-----------------------------------------------------------------------------
Total (Corr.) 0.831447 2184
R-squared = 51.8723 percent
R-squared (adjusted for d.f.) = 51.7397 percent
Standard Error of Est. = 0.0135546
Mean absolute error = 0.0101076
Durbin-Watson statistic = 2.00052 (P=0.4951)
Lag 1 residual autocorrelation = -0.000356134
Multiple Regression - GT - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: GT - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT -0.00093344 0.000485287 -1.92348 0.0544
MktPrem 0.860963 0.0393922 21.8562 0.0000
MktPrem^2 1.0762 1.48756 0.723462 0.4694
USD 0.341237 0.120356 2.83522 0.0046
LT_Treas_Ret -0.246454 0.078457 -3.14126 0.0017
IntSpreadCh 0.00181627 0.0015515 1.17065 0.2417
Comm_Ret -0.0347776 0.0389642 -0.892553 0.3721
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.223919 6 0.0373198 86.22 0.0000
Residual 0.942773 2178 0.000432862
-----------------------------------------------------------------------------
Total (Corr.) 1.16669 2184
R-squared = 19.1926 percent
R-squared (adjusted for d.f.) = 18.97 percent
Standard Error of Est. = 0.0208053
Mean absolute error = 0.0144954
Durbin-Watson statistic = 1.9548 (P=0.1454)
Lag 1 residual autocorrelation = 0.0225142
Multiple Regression - IBM - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: IBM - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000231967 0.000445974 0.520136 0.6030
MktPrem 1.15568 0.0362011 31.9238 0.0000
MktPrem^2 3.22126 1.36706 2.35635 0.0185
USD -0.119923 0.110606 -1.08423 0.2783
LT_Treas_Ret -0.172878 0.0721013 -2.39771 0.0165
IntSpreadCh 0.00000767005 0.00142581 0.00537941 0.9957
Comm_Ret 0.00485222 0.0358077 0.135508 0.8922
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.378199 6 0.0630332 172.42 0.0000
Residual 0.796215 2178 0.000365572
-----------------------------------------------------------------------------
Total (Corr.) 1.17441 2184
R-squared = 32.2032 percent
R-squared (adjusted for d.f.) = 32.0165 percent
Standard Error of Est. = 0.0191199
Mean absolute error = 0.013432
Durbin-Watson statistic = 1.991 (P=0.4167)
Lag 1 residual autocorrelation = 0.00438561
Multiple Regression - IP- risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: IP- risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000357344 0.000458131 0.780004 0.4354
MktPrem 0.742657 0.0371879 19.9704 0.0000
MktPrem^2 -2.58882 1.40433 -1.84346 0.0653
USD -0.0742795 0.113622 -0.653745 0.5133
LT_Treas_Ret -0.116925 0.0740668 -1.57864 0.1144
IntSpreadCh 0.000525511 0.00146468 0.358788 0.7197
Comm_Ret -0.040841 0.0367839 -1.1103 0.2669
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.158394 6 0.0263989 68.43 0.0000
Residual 0.840216 2178 0.000385774
-----------------------------------------------------------------------------
Total (Corr.) 0.99861 2184
R-squared = 15.8614 percent
R-squared (adjusted for d.f.) = 15.6296 percent
Standard Error of Est. = 0.0196411
Mean absolute error = 0.0143378
Durbin-Watson statistic = 2.14654 (P=0.0003)
Lag 1 residual autocorrelation = -0.0733207
Multiple Regression - JPM - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: JPM - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT -0.000606263 0.000414717 -1.46187 0.1438
MktPrem 1.34257 0.0336639 39.8815 0.0000
MktPrem^2 5.48299 1.27125 4.31308 0.0000
USD 0.170448 0.102854 1.65718 0.0975
LT_Treas_Ret -0.113033 0.067048 -1.68586 0.0918
IntSpreadCh 0.00151507 0.00132588 1.14269 0.2532
Comm_Ret -0.0514358 0.0332981 -1.54471 0.1224
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.518805 6 0.0864675 273.52 0.0000
Residual 0.688518 2178 0.000316124
-----------------------------------------------------------------------------
Total (Corr.) 1.20732 2184
R-squared = 42.9715 percent
R-squared (adjusted for d.f.) = 42.8144 percent
Standard Error of Est. = 0.0177799
Mean absolute error = 0.0126375
Durbin-Watson statistic = 2.1164 (P=0.0033)
Lag 1 residual autocorrelation = -0.0582175
Multiple Regression - MCD - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: MCD - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000446643 0.000404905 1.10308 0.2700
MktPrem 0.550998 0.0328674 16.7643 0.0000
MktPrem^2 -4.00628 1.24117 -3.22783 0.0012
USD 0.0385459 0.100421 0.383845 0.7011
LT_Treas_Ret 0.0700071 0.0654616 1.06944 0.2849
IntSpreadCh 0.00167328 0.00129451 1.2926 0.1962
Comm_Ret -0.0616687 0.0325102 -1.8969 0.0578
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.091674 6 0.015279 50.70 0.0000
Residual 0.656321 2178 0.000301341
-----------------------------------------------------------------------------
Total (Corr.) 0.747995 2184
R-squared = 12.256 percent
R-squared (adjusted for d.f.) = 12.0142 percent
Standard Error of Est. = 0.0173592
Mean absolute error = 0.0125203
Durbin-Watson statistic = 2.00393 (P=0.4634)
Lag 1 residual autocorrelation = -0.00228805
Multiple Regression - MRK - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: MRK - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000986 0.000393178 2.50777 0.0121
MktPrem 0.679059 0.0319155 21.2768 0.0000
MktPrem^2 -3.40026 1.20522 -2.82128 0.0048
USD -0.104359 0.0975124 -1.07021 0.2845
LT_Treas_Ret 0.151967 0.0635657 2.39071 0.0168
IntSpreadCh -0.00107075 0.00125702 -0.851815 0.3943
Comm_Ret -0.0876495 0.0315687 -2.77647 0.0055
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.135485 6 0.0225809 79.47 0.0000
Residual 0.618856 2178 0.00028414
-----------------------------------------------------------------------------
Total (Corr.) 0.754341 2184
R-squared = 17.9607 percent
R-squared (adjusted for d.f.) = 17.7347 percent
Standard Error of Est. = 0.0168564
Mean absolute error = 0.0124745
Durbin-Watson statistic = 1.88808 (P=0.0045)
Lag 1 residual autocorrelation = 0.05425
Multiple Regression - XON - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: XON - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000299718 0.000359439 0.83385 0.4044
MktPrem 0.626799 0.0393048 15.9472 0.0000
MktPrem^2 -0.358648 1.51104 -0.237352 0.8124
USD 0.0526749 0.093684 0.562261 0.5739
LT_Treas_Ret 0.224063 0.0617122 3.63077 0.0003
IntSpreadCh 0.00047221 0.00134046 0.352274 0.7246
Comm_Ret 0.238484 0.0343692 6.93888 0.0000
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.0588744 6 0.00981239 61.69 0.0000
Residual 0.223305 1404 0.000159049
-----------------------------------------------------------------------------
Total (Corr.) 0.282179 1410
R-squared = 20.8642 percent
R-squared (adjusted for d.f.) = 20.526 percent
Standard Error of Est. = 0.0126115
Mean absolute error = 0.00945575
Durbin-Watson statistic = 2.08018 (P=0.0661)
Lag 1 residual autocorrelation = -0.0418231
Multiple Regression - DIS - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: DIS - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.0000157038 0.000448937 0.03498 0.9721
MktPrem 0.99604 0.0364416 27.3325 0.0000
MktPrem^2 -0.722352 1.37614 -0.524912 0.5996
USD 0.354165 0.111341 3.1809 0.0015
LT_Treas_Ret -0.119197 0.0725803 -1.64228 0.1005
IntSpreadCh 0.000180964 0.00143529 0.126082 0.8997
Comm_Ret 0.0114269 0.0360456 0.317013 0.7512
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.292066 6 0.0486776 131.40 0.0000
Residual 0.806829 2178 0.000370445
-----------------------------------------------------------------------------
Total (Corr.) 1.09889 2184
R-squared = 26.5781 percent
R-squared (adjusted for d.f.) = 26.3759 percent
Standard Error of Est. = 0.0192469
Mean absolute error = 0.0135814
Durbin-Watson statistic = 2.08399 (P=0.0248)
Lag 1 residual autocorrelation = -0.0421967
Multiple Regression - MMM - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: MMM - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.00029465 0.000358805 0.821199 0.4115
MktPrem 0.658684 0.0291253 22.6155 0.0000
MktPrem^2 0.462525 1.09986 0.420532 0.6741
USD 0.0753409 0.0889875 0.846646 0.3972
LT_Treas_Ret 0.0156092 0.0580085 0.269084 0.7879
IntSpreadCh 0.000302634 0.00114713 0.263819 0.7919
Comm_Ret -0.0154693 0.0288088 -0.536964 0.5913
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.123432 6 0.020572 86.94 0.0000
Residual 0.51538 2178 0.00023663
-----------------------------------------------------------------------------
Total (Corr.) 0.638812 2184
R-squared = 19.3221 percent
R-squared (adjusted for d.f.) = 19.0999 percent
Standard Error of Est. = 0.0153828
Mean absolute error = 0.0110683
Durbin-Watson statistic = 2.0554 (P=0.0977)
Lag 1 residual autocorrelation = -0.0277418
Multiple Regression - MO - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: MO - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000835403 0.000488879 1.70881 0.0875
MktPrem 0.431775 0.0396838 10.8804 0.0000
MktPrem^2 -2.48988 1.49858 -1.6615 0.0966
USD 0.0090123 0.121247 0.0743299 0.9407
LT_Treas_Ret 0.246969 0.0790378 3.12469 0.0018
IntSpreadCh -0.00382621 0.00156299 -2.44801 0.0144
Comm_Ret -0.0417979 0.0392526 -1.06484 0.2869
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.0623244 6 0.0103874 23.65 0.0000
Residual 0.956784 2178 0.000439295
-----------------------------------------------------------------------------
Total (Corr.) 1.01911 2184
R-squared = 6.11558 percent
R-squared (adjusted for d.f.) = 5.85695 percent
Standard Error of Est. = 0.0209594
Mean absolute error = 0.0144508
Durbin-Watson statistic = 2.06448 (P=0.0659)
Lag 1 residual autocorrelation = -0.0325664
Multiple Regression - PG - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: PG - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000961383 0.000417224 2.30423 0.0212
MktPrem 0.490461 0.0338674 14.4818 0.0000
MktPrem^2 -3.84392 1.27893 -3.00557 0.0027
USD 0.0503442 0.103476 0.48653 0.6266
LT_Treas_Ret 0.291234 0.0674533 4.31756 0.0000
IntSpreadCh 0.000932096 0.0013339 0.698776 0.4847
Comm_Ret -0.112691 0.0334994 -3.36397 0.0008
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.0812555 6 0.0135426 42.33 0.0000
Residual 0.696867 2178 0.000319957
-----------------------------------------------------------------------------
Total (Corr.) 0.778123 2184
R-squared = 10.4425 percent
R-squared (adjusted for d.f.) = 10.1958 percent
Standard Error of Est. = 0.0178874
Mean absolute error = 0.0121684
Durbin-Watson statistic = 2.02321 (P=0.2937)
Lag 1 residual autocorrelation = -0.0116812
Multiple Regression - S- risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: S- risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.0000298602 0.000521307 0.0572795 0.9543
MktPrem 0.93333 0.042316 22.0562 0.0000
MktPrem^2 -0.182879 1.59798 -0.114444 0.9089
USD 0.286611 0.12929 2.21682 0.0266
LT_Treas_Ret -0.0926624 0.0842804 -1.09945 0.2716
IntSpreadCh 0.000478379 0.00166666 0.287029 0.7741
Comm_Ret -0.102604 0.0418562 -2.45135 0.0142
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.255903 6 0.0426506 85.39 0.0000
Residual 1.08792 2178 0.000499504
-----------------------------------------------------------------------------
Total (Corr.) 1.34382 2184
R-squared = 19.0429 percent
R-squared (adjusted for d.f.) = 18.8199 percent
Standard Error of Est. = 0.0223496
Mean absolute error = 0.0153494
Durbin-Watson statistic = 2.02428 (P=0.2852)
Lag 1 residual autocorrelation = -0.0122026
Multiple Regression - TX- risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: TX- risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000645131 0.00038214 1.6882 0.0914
MktPrem 0.360834 0.0334196 10.7971 0.0000
MktPrem^2 -2.36446 1.23737 -1.91088 0.0560
USD 0.0764987 0.095996 0.796894 0.4255
LT_Treas_Ret -0.00475672 0.0646749 -0.0735482 0.9414
IntSpreadCh -0.00234511 0.00145514 -1.6116 0.1070
Comm_Ret 0.322622 0.0321701 10.0287 0.0000
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.0545516 6 0.00909193 38.71 0.0000
Residual 0.438936 1869 0.000234851
-----------------------------------------------------------------------------
Total (Corr.) 0.493487 1875
R-squared = 11.0543 percent
R-squared (adjusted for d.f.) = 10.7688 percent
Standard Error of Est. = 0.0153248
Mean absolute error = 0.0114435
Durbin-Watson statistic = 2.14597 (P=0.0008)
Lag 1 residual autocorrelation = -0.0739587
Multiple Regression - UTX - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: UTX - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.00123802 0.000397387 3.1154 0.0018
MktPrem 0.928856 0.0322571 28.7953 0.0000
MktPrem^2 -5.72122 1.21812 -4.69675 0.0000
USD 0.245772 0.0985563 2.49372 0.0126
LT_Treas_Ret 0.0226059 0.0642462 0.351864 0.7249
IntSpreadCh 0.00059129 0.00127048 0.465407 0.6416
Comm_Ret -0.0691549 0.0319066 -2.16741 0.0302
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.259039 6 0.0431732 148.74 0.0000
Residual 0.632177 2178 0.000290256
-----------------------------------------------------------------------------
Total (Corr.) 0.891217 2184
R-squared = 29.0658 percent
R-squared (adjusted for d.f.) = 28.8704 percent
Standard Error of Est. = 0.0170369
Mean absolute error = 0.0120907
Durbin-Watson statistic = 2.07562 (P=0.0386)
Lag 1 residual autocorrelation = -0.038326
Multiple Regression - WX - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: WX - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.000615505 0.000639382 0.962657 0.3357
MktPrem 1.06512 0.0997996 10.6726 0.0000
MktPrem^2 -3.99967 3.64708 -1.09668 0.2728
USD -0.422298 0.181553 -2.32603 0.0200
LT_Treas_Ret -0.0822848 0.120082 -0.68524 0.4932
IntSpreadCh 0.000493799 0.00215488 0.229154 0.8187
Comm_Ret -0.0173343 0.0663799 -0.261137 0.7940
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.0508058 6 0.00846764 25.58 0.0000
Residual 0.29789 900 0.000330989
-----------------------------------------------------------------------------
Total (Corr.) 0.348696 906
R-squared = 14.5702 percent
R-squared (adjusted for d.f.) = 14.0007 percent
Standard Error of Est. = 0.0181931
Mean absolute error = 0.0134085
Durbin-Watson statistic = 2.04127 (P=0.2672)
Lag 1 residual autocorrelation = -0.0249089
Multiple Regression - Z - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: Z - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT 0.0000528488 0.00071892 0.0735114 0.9414
MktPrem 0.931624 0.0583569 15.9643 0.0000
MktPrem^2 -1.17159 2.20373 -0.531639 0.5950
USD 0.582542 0.1783 3.26721 0.0011
LT_Treas_Ret 0.0327446 0.116229 0.281725 0.7782
IntSpreadCh -0.000021435 0.00229844 -0.00932589 0.9926
Comm_Ret -0.0359003 0.0577228 -0.621943 0.5340
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.265972 6 0.0443286 46.66 0.0000
Residual 2.06905 2178 0.000949978
-----------------------------------------------------------------------------
Total (Corr.) 2.33502 2184
R-squared = 11.3905 percent
R-squared (adjusted for d.f.) = 11.1464 percent
Standard Error of Est. = 0.0308217
Mean absolute error = 0.0212074
Durbin-Watson statistic = 1.9564 (P=0.1541)
Lag 1 residual autocorrelation = 0.0216827
Multiple Regression - GM - risk_free
Multiple Regression Analysis
-----------------------------------------------------------------------------
Dependent variable: GM - risk_free
-----------------------------------------------------------------------------
Standard T
Parameter Estimate Error Statistic P-Value
-----------------------------------------------------------------------------
CONSTANT -0.000169821 0.000420681 -0.40368 0.6864
MktPrem 0.973485 0.034148 28.5078 0.0000
MktPrem^2 0.250218 1.28953 0.194038 0.8461
USD 0.0214131 0.104333 0.205238 0.8374
LT_Treas_Ret -0.0613192 0.0680121 -0.901592 0.3673
IntSpreadCh 0.00169181 0.00134495 1.2579 0.2084
Comm_Ret -0.0427583 0.0337769 -1.2659 0.2055
-----------------------------------------------------------------------------
Analysis of Variance
-----------------------------------------------------------------------------
Source Sum of Squares Df Mean Square F-Ratio P-Value
-----------------------------------------------------------------------------
Model 0.269288 6 0.0448813 137.98 0.0000
Residual 0.708462 2178 0.000325281
-----------------------------------------------------------------------------
Total (Corr.) 0.97775 2184
R-squared = 27.5416 percent
R-squared (adjusted for d.f.) = 27.342 percent
Standard Error of Est. = 0.0180356
Mean absolute error = 0.0134747
Durbin-Watson statistic = 2.18953 (P=0.0000)
Lag 1 residual autocorrelation = -0.0947941
Appendix B – Autocorrelation Data
[pic]
Appendix C – Screen Overviews
1) Five-day Sum of Residuals
2) 30-Day Sum of Residuals
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- why are most people poor
- test to see what career fits you
- best products to see online
- synonym for likely to happen
- most likely thesaurus
- what values are most important to you
- likely to recommend
- likely to recommend scale
- covid vaccine most likely to succeed
- more likely to synonyms
- vehicles most likely to 300k
- how to see connections to db2 db