In: Finance
The following six (4) questions are based on the following data:
Year | Rp | Rm | Rf |
2000 | 18.1832 | -24.9088 | 5.112 |
2001 | -3.454 | -15.1017 | 5.051 |
2002 | 47.5573 | 20.784 | 3.816 |
2003 | 28.7035 | 9.4163 | 4.2455 |
2004 | 29.8613 | 8.7169 | 4.2182 |
2005 | 11.2167 | 16.3272 | 4.3911 |
2006 | 32.2799 | 14.5445 | 4.7022 |
2007 | -41.0392 | -36.0483 | 4.0232 |
2008 | 17.6082 | 9.7932 | 2.2123 |
2009 | 14.1058 | 16.5089 | 3.8368 |
2010 | 16.1978 | 8.0818 | 3.2935 |
2011 | 11.558 | 15.1984 | 1.8762 |
2012 | 42.993 | 27.1685 | 1.7574 |
2013 | 18.8682 | 17.2589 | 3.0282 |
2014 | -1.4678 | 5.1932 | 2.1712 |
2015 | 9.2757 | 4.4993 | 2.2694 |
2016 | 8.5985 | 23.624 | 2.4443 |
When performing calculations in the following problems, use the numbers in the table as-is. I.e., do NOT convert 8.5985 to 8.5985% (or 0.085985). Just use plain 8.5985.
1. Using the basic market model regression, R p = α + β R m + ϵ, what is the beta of this portfolio? Yes, this is an opportunity to practice regression analysis. You can use Excel or other tool of choice.
2. For precision, find the portfolio beta using the excess return market model:
R p − R f = α + β ∗ ( R m − R f ) + ϵ
[Hint: compute annual excess returns first, then run regression.]
3. Using the excess return beta β ∗ from the previous problem, what is Jensen's alpha for the portfolio?
[Hint: use Equation (17.6) from Moore (2015)]
4. What is the portfolio's M2 measure?
(1) Regression Analysis between Rp and Rm
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.699678 | |||||||
R Square | 0.489549 | |||||||
Adjusted R Square | 0.455519 | |||||||
Standard Error | 14.79791 | |||||||
Observations | 17 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 1 | 3150.173 | 3150.173 | 14.38578 | 0.001769 | |||
Residual | 15 | 3284.673 | 218.9782 | |||||
Total | 16 | 6434.845 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 9.505086 | 3.906462 | 2.43317 | 0.02795 | 1.17866 | 17.83151 | 1.17866 | 17.83151 |
Rm | 0.821598 | 0.216617 | 3.79286 | 0.001769 | 0.35989 | 1.283307 | 0.35989 | 1.283307 |
From the output of regression analysis between Rp and Rm, we get β=0.821598
(2) Regression Analysis between (Rp-Ef) and (Rm-Rf)
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.706928 | |||||||
R Square | 0.499748 | |||||||
Adjusted R Square | 0.466397 | |||||||
Standard Error | 14.71172 | |||||||
Observations | 17 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 1 | 3243.244 | 3243.244 | 14.98486 | 0.001508 | |||
Residual | 15 | 3246.521 | 216.4347 | |||||
Total | 16 | 6489.764 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 8.947298 | 3.649684 | 2.451527 | 0.02696 | 1.168181 | 16.72641 | 1.168181 | 16.72641 |
Rm-Rf | 0.806506 | 0.208344 | 3.871028 | 0.001508 | 0.362431 | 1.25058 | 0.362431 | 1.25058 |
From the Regression Analysis between (Rp-Ef) and (Rm-Rf), we get β=0.806506
(3) Jensen's α = Rp - [Rf + β*(Rm-Rf)]
(Rp)avg = 15.356
(Rf)avg = 3.438
(Rm-Rf)avg = 3.683
Jensen's α = 15.356 - [3.438 + 0.806506*3.683] = 8.947
(4) M^2 = (σm/σp)*(Rp-Rf) + Rf
M^2 = (17.078/20.054)*(15.356-3.438) + 3.438 = 13.587