BUSF_A01.qxd

CAPM: an example of beta estimation

Estimation of market factors

Year Index Return Return deviation Return variance

(1) (2) (3) (4) (5)

pmt rmt= rmt−Sm (rmt−Sm)^2

1998 218

1999 230 0.055 (0.001) 0.0000

2000 248 0.078 0.022 0.0005

2001 250 0.008 (0.048) 0.0023

2002 282 0.128 0.072 0.0052

2003 297 0.053 (0.003) 0.0000

2004 288 (0.030) (0.086) 0.0074

2005 290 0.007 (0.049) 0.0024

2006 320 0.103 0.047 0.0022

2007 356 0.113 0.057 0.0032

2008 371 0.042 (0.014) 0.0002

0.557 0.0234

Sm==0.056, Var rm==0.0023

Estimation of beta of Ace plc

Covariance

Year Share price Return Return deviation with market

(1) (2) (3) (4) (5)

£pit rit−Si (rit−Si)(rmt−Sm)

1998 1.09

1999 1.20 0.101 (0.002) 0.0000

2000 1.33 0.108 0.005 0.0001

2001 1.40 0.053 (0.050) 0.0024

2002 1.80 0.286 0.183 0.0132

2003 1.99 0.106 0.003 (0.0000)

2004 1.81 (0.090) (0.193) 0.0166

2005 1.98 0.094 (0.009) 0.0004

2006 2.25 0.136 0.033 0.0016

2007 2.55 0.133 0.030 0.0017

2008 2.80 0.098 (0.005) 0.0001

1.025 0.0361

Si==0.103, Cov(i, M) ==0.0036

Since:

bi=Cov(i, M)

Var rm

0.0361

10

1.025

10

pit−pit− 1

pit− 1

0.0234

10

0.557

10

pmt−pmt− 1

pmt− 1

Solution

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