Question

The data is for stock ZZZ; price and dividend history are as follows:

Year     Beginning-of-Year Price          Dividend Paid at Year-End

2015               $118                                       $3       

2016                126                                          3       

2017                110                                          3       

2018                115                                          3       

What are the arithmetic and geometric average time-weighted rates of return for the investor?

	A.	Arithmetic mean is 2.09% and the geometric average is 1.70%
	B.	Arithmetic mean is 2.09% and the geometric average is 1.90%
	C.	Arithmetic mean is 2.39% and the geometric average is 1.70%
	D.	Arithmetic mean is 2.09% and the geometric average is 1.90%

Answer 1

Answer: Option (A)

Year(i)	Beginning Price	Ending Price #	Capital Gain^	Dividend	Total Return	Returns(Ri)		(1+Ri)
2015	$        118	$        126	$             8	$             3	$          11	9.32%		1.0932
2016	$        126	$        110	$        (16)	$             3	$        (13)	-10.32%		0.8968
2017	$        110	$        115	$             5	$             3	$             8	7.27%		1.0727
2018	$        115	NA	NA	$             3
					Sum	6.28%	Product	1.0517

# Ending Price of 2015 will become the Beginning Price of 2016

^Capital Gain = Ending Price - Beginning Price

Total Return = Dividnd + Capital Gain

Return = Total Return / Beginning Price

Note: Return for the year 2018 is not considered as Year End Price is not given (Due to which Capital Gain Computation is not available)

Arthematic Mean = Sum of Observations / No. of Observations

Arthematic Mean = 6.28 / 3

Arthematic Mean = 2.09%

Geometric Mean = [((1 + R1) × (1 + R2) × ... × (1 +Rn))^(1/n)] - 1

Geometric Mean = [((1 + 0.0932)(1 - 0.1032)(1 + 0.0727))^(1/3)] - 1

Geometric Mean = [(1.0517)^(1/3)] - 1

Geometric Mean = 1.017- 1

Geometric Mean = 1.7%