Question

1. We have the following information for the XYZ stock:

Year Annual Return

2014 10%

2015 -15%

2016 15%

2017 20%

a. Calculate the arithmetic average annual return.

b. Calculate the geometric average annual return.

c. Calculate the standard deviation of the returns.

d. If $1000 is invested in the stock at the start of 2014, how much will it become by year-end 2017?

2.An investor invested $1000 in a mutual fund at the start of 2009. At year-end 2017, this investment grew to $3500. How much is the geometric annual return during this holding period?

Answer #1

XYZ stock price and dividend history are as follows:
Year
Beginning-of-Year Price
Dividend Paid at Year-End
2015
$
104
$
2
2016
115
2
2017
90
2
2018
105
2
An investor buys three shares of XYZ at the beginning of 2015,
buys another one shares at the beginning of 2016, sells one share
at the beginning of 2017, and sells all three remaining shares at
the beginning of 2018.
a. What are the arithmetic and geometric average
time-weighted rates...

XYZ stock price and dividend history are as follows: Year
Beginning-of-Year Price Dividend Paid at Year-End 2015 $ 106 $ 5
2016 101 5 2017 89 5 2018 94 5 An investor buys three shares of XYZ
at the beginning of 2015, buys another two shares at the beginning
of 2016, sells one share at the beginning of 2017, and sells all
four remaining shares at the beginning of 2018. a. What are the
arithmetic and geometric average time-weighted rates...

XYZ stock price and dividend history are as follows:
Year
Beginning-of-Year Price
Dividend Paid at Year-End
2007
$ 340
$ 6
2008
$ 350
$ 6
2009
$ 330
$ 6
2010
$ 335
$ 6
An investor buys 3 shares of XYZ at the beginning of 2007, buys
another 2 shares at the beginning of 2008, sells 1 share at the
beginning of 2009, and sells all 4 remaining shares at...

XYZ stock price and dividend history are as follows:
Year
Beginning-of-Year Price
Dividend Paid at Year-End
2015
$
116
$
4
2016
123
4
2017
105
4
2018
110
4
An investor buys four shares of XYZ at the beginning of 2015,
buys another two shares at the beginning of 2016, sells one share
at the beginning of 2017, and sells all five remaining shares at
the beginning of 2018.
a. What are the arithmetic and geometric average
time-weighted rates...

The annual returns on the stock of a firm during the last four
years are provided below.
___________________________________
Year Return
___________________________________
2016
–0.10 (or –10%)
2017
0.10 (or 10%)
2018
0.15 (or 15%)
2019
0.25 (or 25%)
__________________________________
a) Find the holding period return of the stock over the
four-year period.
b) Compute the arithmetic average return of the stock over the
four-year period.
c) Calculate the geometric average return of the...

The annual returns on the stock of a firm during the last four
years are provided below.
___________________________________
Year Return
___________________________________
2016
–0.10 (or –10%)
2017
0.10 (or 10%)
2018
0.15 (or 15%)
2019
0.25 (or 25%)
__________________________________
a) Find the holding period return of the stock over the
four-year period.
b) Compute the arithmetic average return of the stock over the
four-year period.
c) Calculate the geometric average return of the...

5. Consider the rate of return of stocks ABC and XYZ.
Year
rABC
rXYZ
1
20%
30%
2
12
12
3
14
18
4
3
0
5
1
−10
a. Calculate the arithmetic average return on these stocks over
the sample period.
b. Which stock has greater dispersion around the mean
return?
c. Calculate the geometric average returns of each stock. What
do you conclude?
d. If you...

Consider the following realized annual returns: Year End Index
Realized Return Stock A Realized Return 2006 23.6% 46.3% 2007 24.7%
26.7% 2008 30.5% 86.9% 2009 9.0% 23.1% 2010 -2.0% 0.2% 2011 -17.3%
-3.2% 2012 -24.3% -27.0% 2013 32.2% 27.9% 2014 4.4% -5.1% 2015 7.4%
-11.3% The average annual return on the Index from 2006 to 2015 is
closest to: 8.75% 7.10% 9.75% 4.00%

The following data is provided for a market 500 Index: Year
Total return Year Total return 2000 16.0% 2010 2.0% 2001 8.0% 2011
3.0% 2002 -3.0% 2012 3.0% 2003 1.0% 2013 4.0% 2004 5.0% 2014 5.0%
2005 21.0% 2015 4.0% 2006 43.0% 2016 3.0% 2007 4.9% 2017 3.5% 2008
-7.0% 2018 4.5% 2009 0.1% 2019 5.8% Calculate the last 10 -year
arithmetic average annual rate of return on the market Index.
3.78%
2.69%
0.37%
3.93%

The following data is provided for a market 500 Index: Year
Total return Year Total return 2000 16.0% 2010 2.0% 2001 8.0% 2011
3.0% 2002 -3.0% 2012 3.0% 2003 1.0% 2013 4.0% 2004 5.0% 2014 5.0%
2005 21.0% 2015 4.0% 2006 43.0% 2016 3.0% 2007 4.9% 2017 3.5% 2008
-7.0% 2018 4.5% 2009 0.1% 2019 5.8% Calculate the 20 -year
geometric average annual rate of return on the market Index.
5.91%
3.32%
3.77%
0.28%

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