Question

The following table shows the nominal returns on U.S. stocks and the rate of inflation Nominal Return(%) 10.4 8.3 16.0 3.9 Inflation (%) Year 2010 2011 2012 2013 2014 3.5 3.0 3.8 4.6 .2 -37.2 a. What was the standard deviation of the nominal market returns? (Do not make the adjustment for degrees of freedom described in footnote 18.) (Use decimals, not percents, in your calculations. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Standard deviation b. Calculate the arithmetic 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.) Average real return

Answer 1

(a) Let the nominal returns for Year i be denoted by Xi

Average nominal return ER = (10.4+8.3+16.0+3.9-37.2)/5 = 0.28%

Standard Deviation = sqrt (Σ(Xi - ER)²/n) = sqrt ( (10.4 - 0.28)² + (8.3 - 0.28)² + (16.0 - 0.28)² + (3.9 - 0.28)² + (-37.2 - 0.28)² )/5) = 19.14 %

(b) According to Fisher Equation,

(1 + Real Rate of Return) = (1 + Nominal Rate of Return)/(1 + inflation rate)

=> Real Rate of Return = (1 + Nominal Rate of Return)/(1 + inflation rate) - 1

Calculating using the above formula -

Year	Nominal	Inflation	Real
2010	10.4	3.5	6.67
2011	8.3	3	5.15
2012	16	3.8	11.75
2013	3.9	4.6	-0.67
2014	-37.2	0.2	-37.33

Arithmetic Average Real rate of return = (6.67 + 5.15 + 11.75 - 0.67 - 37.33) /5 = -2.89%