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The following table shows the nominal returns on Brazilian stocks and the rate of inflation. Year Nominal Return (%) Inflation (%) 2012 0.2 6.9 2013 -16.0 7.0 2014 -14.0 7.5 2015 -42.5 11.8 2016 67.3 7.4 2017 28.0 4.0 a. What was...

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Finance

The following tableshows the nominal returns on Brazilian stocks and the rate ofinflation.

YearNominal Return(%)Inflation(%)
20120.26.9
2013-16.07.0
2014-14.07.5
2015-42.511.8
201667.37.4
201728.04.0

a.What was the standard deviation of the market returns?

b. Calculate theaverage real return

Answer & Explanation Solved by verified expert
4.3 Ratings (678 Votes)

a). Standard deviation of the nominal returns = {[(nominal return - average)^2]/n}^0.5

where n = number of observations = 6

Standard deviation = 35.32%

b). Real return r = (nominal return - inflation)/(1+inflation)

Average real return = sum of real returns/number of observations = - 2.91%

Calculations are, as follows:

Formula r = (n-i)/(1+i)
Year Nominal Return n (%) Inflation i (%) (n-A)^2 Real return r (%)
2012 0.20% 6.90%            0.001320 -6.27%
2013 -16.00% 7.00%            0.039336 -21.50%
2014 -14.00% 7.50%            0.031803 -20.00%
2015 -42.50% 11.80%            0.214678 -48.57%
2016 67.30% 7.40%            0.402802 55.77%
2017 28.00% 4.00%            0.058403 23.08%
Sum 23.00%            0.124724 -17.48%
Average 3.83% Standard deviation 35.32% -2.91%

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Transcribed Image Text

The following tableshows the nominal returns on Brazilian stocks and the rate ofinflation.YearNominal Return(%)Inflation(%)20120.26.92013-16.07.02014-14.07.52015-42.511.8201667.37.4201728.04.0a.What was the standard deviation of the market returns?b. Calculate theaverage real return

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