Question

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...

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.]

Solutions

Expert Solution

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


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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...
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