Question

Consider the three stocks in the following table. P_trepresents price at time t, and Q_trepresents shares outstanding at time t. There are three time points 0, 1, and 2.

	P0	Q0	P1	Q1	P2	Q2
A	90	100	95	100	100	100
B	50	200	45	200	45	200
C	100	200	110	200	105	200

a) Form an equally weighted portfolio in stocks A, B, C at time 0 and hold it to time 1.

Calculate the portfolio return from 0 to 1.

Keep two decimal places.

b) Form an equally weighted portfolio in stocks B, C (No Stock A) at time 1 and hold it to time 2.

Calculate the portfolio return from 1 to 2.

Keep two decimal places.

Answer 1

Solution (a)

Stock	Weights	P0	Q0	Purchase Cost	P1	Q1	Sale Value	Return	Return * Weight
A	0.33	90.00	100.00	9,000.00	95.00	100.00	9,500.00	500.00	166.67
B	0.33	50.00	200.00	10,000.00	45.00	200.00	9,000.00	-1,000.00	-333.33
C	0.33	100.00	200.00	20,000.00	110.00	200.00	22,000.00	2,000.00	666.67
Portfolio Return									500.00

Return in %

Stock A = 166.67 / 9,000 * 100 = 1.85%

Stock B = -333.33 / 10,000 * 100 = -3.33%

Stock C = 666.67 / 20,000 * 100 = -3.33%

Total Portfolio Return = 1.85% (1.85% + (-3.33%) + 3.33%)

Solution (b)

Stock	Weights	P1	Q1	Purchase Cost	P2	Q2	Sale Value	Return	Return * Weight
B	0.50	45.00	200.00	9,000.00	45.00	200.00	9,000.00	-	-
C	0.50	110.00	200.00	22,000.00	105.00	200.00	21,000.00	-1,000.00	-500.00
Portfolio Return									-500.00

Return in %

Stock B = 0 / 9,000 * 100 = 0%

Stock C = -500 / 22,000 * 100 = -2.27%

Total Portfolio Return = -2.27% (0% + (-2.27%))