Merlene Olonga, who is studying financial modelling, has been given an assignment by her tutor. She is required to calculate the covariance matrix using the single index model (SIM) and then check the accuracy of the SIM covariance matrix against the Markowitz matrix. Merlene’s input (see Table 4.8) contains returns for four companies over the past eight years, as well as the market returns for the same period.

Table 4.8 Year Company 1 Company 2 Company 3 Company 4 Market 1 7.6% 14.4% 20.3% 19.7% 17.2%

2 −3.4% 8.7% 33.6% 8.8% 9.1%

3 23.7% 28.1% 5.9% −3.1% 10.8%

4 11.3% 15.7% 4.6% 16.2% 9.5%

5 −7.8% 8.5% 9.4% 21.5% 8.9%

6 10.5% 1.7% −3.2% 29.7% 5.7%

7 25.9% 13.8% 28.5% −4.3% 13.3%

8 20.1% 9.2% 15.9% 12.6% 11.8%

(Answer:

Covariance matrix (using SIM) Covariance matrix (using Markowitz)

0.01710 0.00116 0.00232 −0.00149 0.01484 0.00397 −0.00101 −0.00744 0.00116 0.00678 0.00206 −0.00132 0.00397 0.00596 −0.00003 −0.00560 0.00232 0.00206 0.01778 −0.00264 −0.00101 −0.00003 0.01582 −0.00646

−0.00149 −0.00132 −0.00264 0.01607 −0.00744 −0.00560 −0.00646 0.01402