Open Ended Questions: Please show calculations to get any credit 01. For the fol
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Open Ended Questions: Please show calculations to get any credit 01. For the following stock quotations (A,B, and C) and outstanding shares create price weighted, value weighted and equally weighted indexes and calculate rates of return? (25 points) Day 2 Day 1 Price and Quantty Price and Quantity $100 S20 $45 200 500 150 $120 S12 $25 200 1000 300 a) First find out the divisor and price weighted index for day 1 and then calculate its return for day 1? (8 points) b) Find out value weighted index for day 1 and then calculate its return for day 1? (6 points) c) Find out the equally woighted index for day 1 and then calculate its return for day 17 (6 points) d) Explain why retuns are different for the three indexes and also provide rationale why they (returns) are not the samo? (5 points)Explanation / Answer
a) A price-weighted index is a stock index in which each stock influences the index in proportion to its price per share. Adding the price of each stock in the index and dividing by the total number of stocks determines the index’s value. A stock with a higher price will be given more weight than a stock with a lower price and, therefore, will have a greater say in the index’s performance.
Index Value Day 1 = 100+20+45 / (200+500+150) = 165/850 = .194
Index Value for Day 2 = 120+12+25 /(200+1000+300) = 157/1500 = .104
Therefore Index is down by = .194-.104 / .194 = 46%
b) For a value-weighted index, the number of outstanding shares is a factor. To determine the weight of each stock in a value-weighted index, the price of the stock is multiplied by the number of shares outstanding
Day 1 : Index Value = (100x200+20x500+45x150)/ (200+500+150)
= (20000+10000+6750)/850 = 43.23
Day 2 : Index Value : 120x200+12x1000+25x300/(200+1000+300) = 24000+12000+7500/1500 = 29
Therefore Index is down by 43.23-29/43.23 = 32.9%
c)In an unweighted index, all stocks have the same impact on the index, no matter their share volume or price. Any price change in the index is based on the return percentage of each component. For example, if Stock A is up 20% i.e (120-100), Stock B is down -40% i.e (20-12)/20 and Stock C is down -44% i.e (45-25)/45 ,
therefore The index is down by 21.33%, or 20-40-44 / 3, i.e., the number of stocks in the index.
d) Returns are different as the weight are different. In price-weighted index a stock with a higher price will be given more weight than a stock with a lower price and, therefore, will have a greater say in the index’s performance. For a value-weighted index, the number of outstanding shares is a factor. The stock has more outstanding is having more say in the index. In an unweighted index, all stocks have the same impact on the index, no matter their share volume or price. Any price change in the index is based on the return percentage of each component.
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