Question: The single-index model (SIM) is possibly the simplest asset pricing model that we use in finance to measure the tradeoff between the systematic risk and

The single-index model (SIM) is possibly the simplest asset pricing model that we use in finance to measure the tradeoff between the systematic risk and return
of a stock. Mathematically the SIM could be expressed as rit − rf = αi + βi(rmt − rf ) + εit, (1) where rit is the (simple) return for security i at time t, rmt is the market return at
time t, rf is the risk-free rate, and εit is the error term. The coefficient βi measures the systematic risk that firm i is facing.

(a) Using the data in “table ” below, please estimate αi and βi via OLS regression in Excel.
(b) Explain the estimated βi in words.

-date rf rm Jan-08 0.0326 -0.0609 Feb-08 0.0210 -0.0349 Mar-08 0.0170 -0.0030 Apr-08 0.0140 0.0449 May-08 0.0145 0.0098 Jun-08 0.0185 -0.0878 Jul-08 0.0187 Aug-08 0.0166 Sep-08 0.0172 -0.0960 Oct-08 0.0085 -0.1679 Nov-08 0.0049 -0.0826 Dec-08 0.0007 0.0162 Jan-09 0.0008 -0.0885 Feb-09 0.0027 -0.1136 Mar-09 0.0028 0.0878 Apr-09 0.0022 0.0997 May-09 0.0016 0.0579 Jun-09 0.0013 -0.0026 Jul-09 0.0017 0.0754 Aug-09 0.0019 0.0296 Sep-03 0.0014 0.0347 Oct-09 0.0010 Nov-10 0.0013 Dec-10 0.0016 Jan-11 0.0015 Feb-11 0.0015 Mar-11 -0.0057 0.0145 -0.0178 Nov-09 0.0006 0.0605 Dec-09 0.0006 0.0161 Jan-10 0.0008 -0.0382 Feb-10 0.0010 0.0293 Mar-10 0.0013 0.0596 Apr-10 0.0016 0.0148 May-10 0.0017 -0.0852 Jun-10 0.0016 -0.0517 Jul-10 0.0017 0.0741 Aug-10 0.0016 -0.0522 Sep-10 0.0013 0.0893 Oct-10 0.0016 0.0369 0.0008 0.0599 0.0251 0.0306 0.0014 0.0006 Apr-11 0.0007 0.0269 May-11 0.0005 -0.0147 Jun-11 0.0005 -0.0183 Jul-11 0.0002 -0.0212 ri -0.0843) -0.1656 0.0434 0.0049 -0.0070 -0.0286 -0.0651 0.0610 -0.0220 -0.1634 -0.0945 -0.0386 -0.1204 -0.0556 0.1375 0.1029 0.0311 0.1379 -0.0105 0.0480 0.0434 0.0781 0.0606 0.0364 -0.0755 0.0174 0.0216 0.0427 -0.1552 -0.1081 0.1217 -0.0907 0.0435 0.0890 -0.0529 0.1049 -0.0064 -0.0415 -0.04485 0.0209 -0.0351 0.0396 0.0538 -0.0292 -0.0643 0.0699 -0.03943 0.0149 0.1375 0.0748 0.0164 Aug-11 0.0010 -0.0568 Sep-11 0.0002 -0.0721 Oct-11 0.0002 0.1059 Nov-11 0.0001 -0.0033 Dec-11 0.0001 0.0096 Jan-12 0.0002 0.0426 Feb-12 0.0006 0.0407 Mar-12 0.0008 0.0312 Apr-12 0.0008 -0.0075 May-12 0.0009 -0.0629 Jun-12 0.0007 0.0400 0.0480 Jul-12 0.0010 0.0125 -0.0366 0.0197 0.0458 -0.0344) Aug-12 0.0010 Sep-12 0.0010 0.0244 Oct-12 0.0009 -0.0199 Nov-12 0.0009 0.0029 -0.0673 Rss:120.00.10 0.0070 0.0034 -0.0074 -0.0884

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