Section 2 - ECON 136 Financial Economics Section 2(Sep 4th...

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ECON 136: Financial Economics Section 2 (Sep 4th) Xing Huang 1 Economics Department, UC Berkeley 1 Stock Index 1.1 Review Weights Feature Rebalance Equally weighted 1 N Equal weights Yes Price weighted P i P N j =1 P i Equal shares No Market-value weighted P i M i P N j =1 P j M j Propotional shares No 1.2 Example: calculate the returns of the stock index (revised on Ch2 problem 9, BKM 8th ed) Consider the three stocks in the following table. P t represents price at time t , and Q t represents shares outstanding at time t: P 0 Q 0 P 1 Q 1 A 90 100 95 100 B 50 200 45 200 C 100 200 110 200 Calculate the rate of return on an equally weighted index, a price-weighted index and a market- value-weighted index of the three stocks for this period. Answer: R A = P 1 A P 0 A 1 = 95 90 1 = 5 90 ; R B = 1 10 ; R C = 1 10 For equally weighted index, w A = w B = w C = 1 3 For price weighted index, w A = 90 90 + 50 + 100 = 9 24 ; w B = 5 24 ; w C = 10 24 1 Thank you all very much !! 1
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For market-value weighted index, w A = 90 100 90 100 + 50 200 + 100 200 = 9 39 ; w B = 10 39 ; w C = 20 39 : Therefore, we can easily get the returns for these three index as following. R EW = 1 3 5 90 + 1 3 ( ± 1 10 ) + 1 3 1 10 = 1 48 ² 2 : 08% R PW = 9 24 5 90 + 5 24 ( ± 1 10 ) + 10 24 1 10 = 1 24 ² 4 : 17% R V W = 9 39 5 90 + 10 39 ( ± 1 10 ) + 20 39 1 10 = 1 26 ² 3 : 85% Note: There is another simpler way to calculate R PW and R V W : Because price weighted index has the same shares for all stocks, we could assume it has 1 share
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Section 2 - ECON 136 Financial Economics Section 2(Sep 4th...

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