Calculate the arithmetic mean return and the geometric mean


1. Refer to the table below. The table below shows the annual returns (in percentages) for 2 major market indices. For each index, calculate the arithmetic mean return and the geometric mean return of full-year returns from 2005-2015. What is the relationship between the arithmetic and geometric mean returns?

 

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

Nasdaq
Composite Index

1.37

8.59

50.0

-31.5

-21.1

-39.3

85.6

39.6

21.6

22.7

39.9

Dow Jones
Industrial Average

-0.61

3.15

25.3

-16.8

-7.1

-6.2

25.2

16.1

22.6

26.0

33.5

2. (i) Estimate the stock beta for a company. Select a publicly traded company (preferably large firms) and download the monthly closing prices for 5 years into Excel.

Choose a market index (e.g. S&P 500) and download the monthly closing values for 5 years into Excel. Calculate the monthly returns for the selected company and the market index. Using the regression function in Excel, regress the stock return on the market index return.

(ii) Compare and contrast the stock beta you estimated with two other sources (e.g. Yahoo! Finance, CNBC, etc.)

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Financial Management: Calculate the arithmetic mean return and the geometric mean
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