Question

1.$ Sarah makes a value weighted portfolio of three securities. At time the prices of Apple, Walmart, and Netflix are $70, $20, and $100. The shares outstanding are 83, 71, and 84, with time 1 prices of $80, $10, and $120. What is the percent change in a value weighted index of these shares from time 0 to time 1?

2. Joe invest $10000 to construct an equally weighted portfolio of three securities. At time 0 the prices of IBM, Exon, and Costco are $80, $30, and $125. At time 1, the prices are $90, $70, and $130. After rebalancing to keep equal weights in each company at time 1, how many shares do you hold of each stock?

Answer 1

1) The value of index at time 0 = price of apple in time 0 *number of shares of apple +price of walmart in time 0 *number of shares of Walmart+price of Netflix in time 0 *number of shares of Netflix

=70*83+20*71+100*84

=15630

The value of index at time 1 = price of apple in time 1 *number of shares of apple +price of walmart in time 1 *number of shares of Walmart+price of Netflix in time 1 *number of shares of Netflix

=80*83+10*71+120*84

=17430

Percentage change in value weighted index is given by

((Value of index at time 1-Value of index at time 0)/Value of index at time 0)*100

=((17430-15630)/15630)*100

=11.516%

2) for a equally weighted portfolio amount invested in each stock = $10000/3 = $3333.33

at time =0

Number of shares of IBM= Amount invested in IBM/ Price of IBM= 3333.33/80= 41.67 shares

Number of shares of Exon= Amount invested in Exon/ Price of Exon= 3333.33/30= 111.11 shares

Number of shares of Costco= Amount invested in Costco/ Price of Costco= 3333.33/125= 26.67 shares

The value of index at time 1 = price of IBM in time 1 *number of shares of Costco +price of Exon in time 1 *number of shares of Exon+price of Costco in time 1 *number of shares of Costco

=41.67*90+111.11*70+26.67*130

=14995.1

for a equally weighted portfolio amount invested in each stock = $14995.1/3 = $4998.367

at time =1

Number of shares of IBM to be held after rebalancing= Amount invested in IBM/ Price of IBM= $4998.367/90= 55.54 shares

Number of shares of Exonbe held after rebalancing= Amount invested in Exon/ Price of Exon= $4998.367/70= 71.41 shares

Number of shares of Costcobe held after rebalancing= Amount invested in Costco/ Price of Costco= $4998.367/130= 38.45 shares

(therefore number of shares to be bought for IBM = 55.54-41.67= 13.87 shares

therefore number of shares to be Sold for exon = 111.11-71.41= 39.70 shares

therefore number of shares to be bought for Costco = 38.45-26.67= 11.78 shares

Note: it is assumed that shares can be bought in decimals. )