Question

Problem 5-14 Price-Weighted Indexes (L04, CFA2) The following three defense stocks are to be combined into a stock index in January 2016 (perhaps a portfolio manager believes these stocks are an appropriate benchmark for his or her performance): Price Shares (millions) 530 230 330 1/1/16 $ 62 1/1/18 $ 81 Douglas McDonnell Dynamics General International Rockwell - 34 1/1/17 $ 66 28 52 42 63 68 ces a. Calculate the initial value of the index if a price-weighting scheme is used. Index value b. What is the rate of return on this index for the year ending December 31, 2016? For the year ending December 31, 2017? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) 2016 return 2017 return

Answer 1

To calculate the initial value of the index as per price-weighted method we would need to add up the Prices of all 3 stocks on 01/16 - $62, $34 and $63 and divide each individual stock price with the sum of all 3 stocks. Please refer to the table below -

	Price on 1/1/16	Weights	Weight * Price
Doughlas McDonnel	$                 62.00	38.99%	$                 24.18
Dynamics General	$                 34.00	21.38%	$                   7.27
International Rockwell	$                 63.00	39.62%	$                 24.96
TOTAL	159.00	Index Value	$                 56.41

	Price on 1/1/16	Weights	Weight * Price
Doughlas McDonnel	62	=F11/$F$14	=F11*G11
Dynamics General	34	=F12/$F$14	=F12*G12
International Rockwell	63	=F13/$F$14	=F13*G13
TOTAL	=SUM(F11:F13)	Index Value	=SUM(H11:H13)

Return % for 2016 -

Lets calculate the difference between the price on 01/01/16 and 01/01/17 first for each stock and then use the weights to calucate the weighted difference per share and then sum it up. Divide that sum with the weighted index value we calculated for 01/01/16 i.e. $56.41. Thus, the return for 2016 is -7.24%

	Doughlas McDonnel	Dynamics General	International Rockwell
2016 Difference	4	-6	-11
Weights	38.99%	21.38%	39.62%
Weighted Difference	1.56	-1.28	-4.36

Total Return	Percentage Return
-4.08	-7.24%

Return % for 2017 -

Holdings the weights constant the Index Price on 01/01/17 is $52.33. Applying the same concept as earlier we arrive at th below return for 2017. Thus, the return for 2017 is 29.01%

	Doughlas McDonnel	Dynamics General	International Rockwell
2017 Difference	15	14	16
Weights	38.99%	21.38%	39.62%
Weighted Difference	5.85	2.99	6.34

Total Return	Percentage Return
15.18	29.01%