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You have been provided with the following data relating to five companies. Company Book Value Market Value Returns Year 1 Year 2 2000 4% 3% 2000 -5% 6% Arneb 2000 Betelgeuse 2500 Chalawan 2000 +5 Deneb 2500 -5 Eltanin 5000-5 2500 -10% 8% 2000 4% -3% 5000 15% 12% You have been asked to fit a Barra-style model with three factors: a market factor, a small-minus-big factor (using a natural log scale for market size) and a book to market ratio factor (without logs). You are to estimate the model by weighting all five companies equally. (a) Write down the first two rows (corresponding to Arneb and Betelgeuse) of a factor loading matrix for this proposed model. [2] (b) Determine a set of coefficients ha, ho, ho, hd, he such that the small-minus-big factor return for the Barra-style model in each year is given by: SMB factor return = ha x Arneb return + hy x Betelgeuse return the x Chalawan return + hd x Deneb return the x Eltanin return [3] Let R denote the matrix of historic returns covering 30 time periods, the first two columns of which are listed at the start of the question. A colleague has calculated that: You have been provided with the following data relating to five companies. Company Book Value Market Value Returns Year 1 Year 2 2000 4% 3% 2000 -5% 6% Arneb 2000 Betelgeuse 2500 Chalawan 2000 +5 Deneb 2500 -5 Eltanin 5000-5 2500 -10% 8% 2000 4% -3% 5000 15% 12% You have been asked to fit a Barra-style model with three factors: a market factor, a small-minus-big factor (using a natural log scale for market size) and a book to market ratio factor (without logs). You are to estimate the model by weighting all five companies equally. (a) Write down the first two rows (corresponding to Arneb and Betelgeuse) of a factor loading matrix for this proposed model. [2] (b) Determine a set of coefficients ha, ho, ho, hd, he such that the small-minus-big factor return for the Barra-style model in each year is given by: SMB factor return = ha x Arneb return + hy x Betelgeuse return the x Chalawan return + hd x Deneb return the x Eltanin return [3] Let R denote the matrix of historic returns covering 30 time periods, the first two columns of which are listed at the start of the question. A colleague has calculated that

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