Question

A security that increases in price from TZS 5000 to TZS 10000 during the year 1 and drops back to TZS 5000 during year 2. what would be the Annual holding period yields , find arithmetic mean rate of return and geometric mean rate of return

Answer 1

Formula sheet

A	B	C	D	E	F	G	H
2
3
4		Holding period return on stocks can be calculated as follows:
5
6		Annual Holding period yield = [Final Price - Initial Price] / Initial Price
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8		Year	Price	Change in Price	Annual Holding period yield
9		0	5000
10		1	10000	=D10-D9	=E10/D9
11		2	5000	=D11-D10	=E11/D10
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13		Arithmatic mean rate of return	=AVERAGE(F10:F11)	=AVERAGE(F10:F11)
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15
16		Geometric mean of returns can be calculated as follows:
17		Geometric return over n year	=[(1+R1)*(1+R2)*(1+R3)*…*(1+Rn)](1/n)-1
18		Where R1, R2 … Rn are return in year 1, 2 …n respectively.
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20		Geometric average return over 2 years	=[(1+R1)*(1+R2)](1/2)-1
21			=(((1+F10)*(1+F11))^(1/2))-1	=(((1+F10)*(1+F11))^(1/2))-1
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23		Hence Geometric average return is	=D21
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