# sol_hw1 - University of Hong Kong Department of Economics...

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1 University of Hong Kong Department of Economics and Finance FINA 2802C Investment and Portfolio Analysis First Semester: 2007-2008 Dr. Kam-Ming Wan Answers to Problem Set 1 (1) a. I0 = (Px0 + Py0 + Pz0)/3 = 73.33, I1 = (Px1 + Py1 + Pz1)/3 = 81.67. r = (I1 - I0)/I0 = 11.37% b. 81.67 = (55 + 65 + 125/3)/new divisor, new divisor = 1.98. c. I2 = (Px2 + Py2 + Pz2)/1.98 = 89.39. d. Any divisor should be fine, so use divisor 1. Use I = (Px*Qx + Py* Qy + Pz*Qz)/1, then, I0 = 47000, I1 = 55000, I2 = 63700. r1 = (I1 - I0)/I0 = 17.02%, r2 = (I2 - I1)/I1 = 15.82%. If you use different divisor, the index level may be different, however, the return should be the same. (2) a. Day 1: the divisor is three (D 1 =3), the Dow Jones Industrial Average (DJIA) = (12+23+52)/3 =29; Day 2: D 2 =3 as there is no stock split, DJIA = (10+22+55)/3 =29; Day 3: 2-1 reverse stock split for stock B, D 3 = 3.7586 =(10+44+55)/29, DJIA = (14+46+52)/ 3.7586 = 29.798; Day 4: 2-1 stock split for stock C, D 4 = 2.8861 =(14+46+52/2)/29.798, DJIA = (13+47+25)/2.8861 = 29.4517; Day 5: D 5 = 2.8861, DJIA = (12+45+26)/2.8861 = 28.7587; b. As the DJIA is price weighted, when companies have a stock split, their prices decline, and therefore their weight in the DJIA is reduced even though they may be large and important.

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