In: Finance
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?
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.]
Portfolio Beta value = 0.8065
We first calculate the excess returns first
Excess returns are calculated by subtracting the risk-free value from the Rp and Rm
Year | Rp | Rm | Rf | Rp-Rf | Rm-Rf |
2000 | 18.1832 | -24.909 | 5.112 | 13.0712 | -30.021 |
2001 | -3.454 | -15.102 | 5.051 | -8.505 | -20.153 |
2002 | 47.5573 | 20.784 | 3.816 | 43.7413 | 16.968 |
2003 | 28.7035 | 9.4163 | 4.2455 | 24.458 | 5.1708 |
2004 | 29.8613 | 8.7169 | 4.2182 | 25.6431 | 4.4987 |
2005 | 11.2167 | 16.3272 | 4.3911 | 6.8256 | 11.9361 |
2006 | 32.2799 | 14.5445 | 4.7022 | 27.5777 | 9.8423 |
2007 | -41.039 | -36.048 | 4.0232 | -45.062 | -40.072 |
2008 | 17.6082 | 9.7932 | 2.2123 | 15.3959 | 7.5809 |
2009 | 14.1058 | 16.5089 | 3.8368 | 10.269 | 12.6721 |
2010 | 16.1978 | 8.0818 | 3.2935 | 12.9043 | 4.7883 |
2011 | 11.558 | 15.1984 | 1.8762 | 9.6818 | 13.3222 |
2012 | 42.993 | 27.1685 | 1.7574 | 41.2356 | 25.4111 |
2013 | 18.8682 | 17.2589 | 3.0282 | 15.84 | 14.2307 |
2014 | -1.4678 | 5.1932 | 2.1712 | -3.639 | 3.022 |
2015 | 9.2757 | 4.4993 | 2.2694 | 7.0063 | 2.2299 |
2016 | 8.5985 | 23.624 | 2.4443 | 6.1542 | 21.1797 |
For running a regression in excel, go to Data => Data analysis => Regression
We now run a regression with Rm-Rf (excess market returns) as X(independent) variable and Rp-Rf (excess portfolio returns) as Y(dependent) variable
We get the following result
Here, the X Variable 1 coefficient is the Beta value = 0.8065
Alpha = Intercept coefficient = 8.94729