Question

Note the return series below and answer the following questions

CPI Year Large Stocks LT Gov Bonds US Tbills 2009 26.46% 9.49% 0.15% 2.72% 7.73% 2010 15.06% 0.14% 1.50% 2011 35.75% 2.96% 2.11% 0.06% 2012 16.00% 1.80% 0.08% 1.74% 2013 32.39% -14.69% 0.05% 1.50%

1. What is the average nominal return earned on large company stocks? (Enter percentages as decimals and round to 4 decimal places)

2. What is the average real return earned on large company stocks? (Enter percentages as decimals and round to 4 decimal places)

3. What is the average risk premium earned on large company stocks? (Enter percentages as decimals and round to 4 decimal places)

4. What is the average real risk premium earned on large company stock? (Enter percentages as decimals and round to 4 decimal places)

5. What is the average risk premium earned on the US t-bills? (Enter percentages as decimals and round to 4 decimal places)

6. What is the average rate of inflation? (Enter percentages as decimals and round to 4 decimal places)

Answer 1

In order to find the answer to all the questions let us first find the average of all the values in table.

Formula for average return is;

SumOf Returns Average Return = " NumberOf Returns

Below table shows calculation of the average returns for all :

Year	Return %
	Large Stocks	LT Gov Bonds	US T Bills	CPI
2009	26.46	-9.49	0.15	2.72
2010	15.06	7.73	0.14	1.50
2011	2.11	35.75	0.06	2.96
2012	16.00	1.80	0.08	1.74
2013	32.39	-14.69	0.05	1.50
Sum of Return	92.02	21.10	0.48	10.42
Average Return %	18.4040 %	4.2200 %	0.0960 %	2.0840 %

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1. What is the average nominal return earned on large company stocks? (Enter percentages as decimals and round to 4 decimal places)

The average return of the large company stocks is, sum of all the returns divided by no of returns.

Nominal return for any investment is it's return without adjusting for any inflation effect. As the given rates are without inflation adjustment, these are nominal returns.

Year	Large Stocks
2009	26.46
2010	15.06
2011	2.11
2012	16.00
2013	32.39

SumOf Returns Average Return = " NumberOf Returns

Sum of return of large stocks =( 26.46 + 15.06 + 2.11 + 16.00 + 32.39 ) = 92.02

Average return = 92.02 / 5 = 18.4040 %

Hence, the NOMINAL Average Return on Large company stocks is = 18.4040 %

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2. What is the average real return earned on large company stocks? (Enter percentages as decimals and round to 4 decimal places)

Real return is the rare of return an investor earns after considering the impact of inflation for that period. We are given CPI values. CPI is Consumer Price Index which is a measure of inflation.

(CPI is a weighted average of prices of predetermined basket of good and services. Any changes in CPI reflects the changes in standard of living/purchasing power indicating inflation/deflation.)

Formula to calculate real rate is;

Real Rate of Return = 1 + nominal rate 1 + inflation rate

Nominal return on Large company stock = 18.4040 %
Average inflation = 2.0840 %

Therefore,

Real Rateof Return = 1 + 0.18404 1+0.02084

Real Rateof Return = 1.18404 1-1=0.159868 1.02084

REAL Rate of return on Large Stocks =15.9868 %

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3. What is the average risk premium earned on large company stocks? (Enter percentages as decimals and round to 4 decimal places)

A risk premium is excess return which is earned on an investment over a risk free rate of return. This is additional return an investor would require in order to undertake higher risk. The risk free rate is usually the rate of return on an investment with zero risk. Theoretically there is no such investment but the govt investments are default free and hence rate on such is used as the risk free rate. For example, US T Bills rate is used as the risk free rate.

Formula to calculate risk premium = Security Return - Risk Free Rate

Nominal return on Large company stock = 18.4040 %
Average return on T Bills = 0.0960 %

Risk Premium = 18.4040 - 0.0960 = 18.3080

Risk Premium on Large stock = 18.3080 %

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4. What is the average real risk premium earned on large company stock? (Enter percentages as decimals and round to 4 decimal places)

Average real risk premium will exclude the effect of inflation.

it is calculated as - real risk premium = Security Real rate of Return - Risk Free Rate

Real return on Large company stock = 15.9868 %
Average return on T Bills = 0.0960 %

Risk Premium = 15.9868 - 0.0960 = 15.8908

REAL Risk Premium on Large stock = 15.8908 %

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5. What is the average risk premium earned on the US t-bills? (Enter percentages as decimals and round to 4 decimal places)

US T bills are backed by government and usually govt does not default hence there is no risk on these investments. Which is why this rate is usually used as risk free rate. There can no be any risk premium (excess return) on the US t bills.

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6. What is the average rate of inflation? (Enter percentages as decimals and round to 4 decimal places)

The average inflation rate as mentioned earlier is, total inflation divided by no of period.

Year	CPI
2009	2.72
2010	1.50
2011	2.96
2012	1.74
2013	1.50

Sum of return of large stocks =( 2.72 + 1.50 + 2.96 + 1.74 + 1.50 ) = 10.42

Average return = 10.42 / 5 = 2.0840 %

Hence, the average inflation rate for the 5 year period is = 2.0840%

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