Question

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

Year	Nominal Return (%)	Inflation (%)
2012	0.4	7.4
2013	-17.0	7.5
2014	-15.0	8.0
2015	-43.0	12.3
2016	67.8	7.9
2017	28.5	4.5

a. What was the standard deviation of the market returns? (Use decimals, not percents, in your calculations. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

b. Calculate the average real return. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places)  

Answer 1

Answer:-

Average nominal return = (0.4-17-15-43-+67.8+28.5 / 6 )= 21.7/6 = 3.61 or 0.03616

Variance = (0.4-3.61)^2 + (-17-3.61)^2 + (-15-3.61)^2 + (-43-3.61)^2 + (67.8-3.61)^2 + (28.5-3.61)^2 /6

= 10.3041 + 424.7721 + 346.3321 + 2172.4921 + 4120.3561 + 619.5121/6

= 7693.7686 /6

= 1282.2947

So standard deviation = √ variance

SD = √1282.2947

SD = +- 35.81%

(B) Average Real return = (1.004/1.074-1) + (-1.17/1.075-1)+(-1.15/1.08-1)+(-1.43/1.123-1)+(1.678/1.079-1)+(1.285/1.045-1)

= -0.065 + 2.088+-2.64+-2.27+0.55+0.2296

= -2.1074