Question

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

Year	Nominal Return (%)	Inflation (%)
2010	11.7	2.2
2011	8.6	3.4
2012	15.5	2.9
2013	5.7	4.3
2014	−44.2	.3

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)-Standard Deviation of the Nominal Market Returns

Firstly, Calculate the Average Nominal Market Rate Return

Average Nominal Market Rate Return = [0.1170 + 0.086 + 0.1550 + 0.057 – 0.4420] / 5

= -0.027 / 5

= -0.0054

Secondly, Calculate the Variance of the Returns

Variance = [{0.1170 - (-0.0054)}²] + [{0.0860 - (-0.0054)}²] +[{0.1550 – (-0.0054)}²] +[{0.057 - (-0.0054)}²] + [{-0.4420 – (-0.0054)}²] / 5

= [0.014982 + 0.008354 + 0.025728 + 0.003894 + 0.190620] / 5

= 0.243577 / 5

= 0.048715

Standard Deviation = (0.048715)^1/2 or the Square Roof of 0.048715

= 0.2207

= 22.07%

“Therefore, Standard Deviation of the Nominal Market Returns = 22.07%”

(b)-Average Real Return

Firstly, calculate the Real Rate of Return for the each years Nominal rate of Return

Real Rate of Return is calculated by using the following formula

Real Rate of Return = [(1 + Nominal Rate) / (1 + Inflation Rate)] – 1

2010 = [(1+ 0.1170) / (1 + 0.022)] – 1 = 9.30%

2011 = [(1 + 0.086) / (1 + 0.034)] – 1 = 5.03%

2012 = [(1 + 0.1550) / (1 + 0.029)] – 1 = 12.24%

2013 = [(1 + 0.057) / (1 + 0.043)] – 1 = 1.34%

2014 = [{1 – (-0.4420)} / (1 + 0.0030)] – 1 = -44.37%

Therefore, Average Real Return = [9.30% + 5.03% + 12.24% + 1.34% - 44.37%] / 5

= -16.46% / 5

= -3.29% (Negative)

“Therefore, the Average Real Return = -3.29%”