Question

In: Finance

The following table shows the nominal returns on Brazilian stocks and the rate of inflation. Year...

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 the standard deviation of the market returns?

b. Calculate the average real return

Solutions

Expert Solution

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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