Question

QUESTIONS Use the following information to answer the next three questions: Stock 12/31/18 Closing Price 12/31/19 Closing Price 630 180 Stock X had a 3:1 split immediately after closing on 12/31/18. Find the value of a price weighted index on 12/31/18. W 90 295 250 330 None of the above Click Save and submit to save and submit. Click Save All Answers to save all answers. Save All Answc

Answer 1

Question 3: Given the split-ratio is 3:1, the stock price of X immediately after the split becomes $630/3 = $210. Hence, the value of the price-weighted index on Dec 31, 2018 is calculated as the sum of the stock prices that forms the index divided by the number of stocks. Here, it is $(210 + 75 + 45)/3 = $110. The correct choice is None of the above.

Question 4: On Dec 2019, the price-weighted index is again calculated as the sum of the stock prices that forms the index divided by the number of stocks. In this case, it is $(180 + 80 + 55)/3 = $105. Hence, the change in the value of index over 2018-19 is $(105 - 110)/$110 = -0.0455.

Question 5: Calculating the returns for each of the stocks,

1. For stock X, price changes from $210 to $180. Hence, returns is $(180 - 210)/$210 = -0.1429
2. For stock Y, price changes from $75 to $80. Hence, returns is $(80 - 75)/$75 = 0.0667
3. For stock Z, price changes from $45 to $55. Hence, returns is $(55 - 45)/$45 = 0.2222

Using the formulae for the percentage change in equally weighted index using geometric mean returns, we've if r is the required change in the index,

$r = \sqrt[3]{(1+r_X)(1+r_Y)(1+r_Z)}-1$

On putting in the values,

$r=\sqrt[3]{(1-0.1429)(1+0.0667)(1+0.2222)}-1=0.0377$

Hence, the correct choice is 0.0377.