Question

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

Answer 1

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%