Chapter 8, Problem 1OR

Summary Introduction

To discuss: The annual average return and standard deviation.

Introduction:

In financial context, return is seen as percentage that represents the profit in an investment.

Explanation of Solution

Determine the annual average returns of MM fund:

Annual average returns can be computed by dividing sum of returns and number of years considered.

$\begin{array}{c}\text{Annual average returns}\left(\overline{\text{r}}\right)={\displaystyle \sum _{\text{i=1}}^{\text{n}}\frac{\left(\text{ Returns}\left({\text{R}}_{\text{i}}\right)\right)}{\text{n}}}\\ \text{=}\frac{76+16.6-34.9+39.6}{4}\\ =\frac{97.3}{4}\\ =24.325\%\end{array}$

Hence, the annual average return of MM fund is 24.325%

Determine the expected return of Market index SP:

$\begin{array}{c}\text{Annual average returns}\left(\overline{\text{r}}\right)={\displaystyle \sum _{\text{i=1}}^{\text{n}}\frac{\left(\text{ Returns}\left({\text{R}}_{\text{i}}\right)\right)}{\text{n}}}\\ \text{ =}\frac{26.5+15.1+2.1+16}{4}\\ =\frac{59.7}{4}\\ =14.925\%\end{array}$

Hence, the annual average return of Market index SP is 14.925%.

Therefore, annual average return of MM fund is better than the annual average return of Market index SP over the given period of time.

Determine the money at the end of 2012 in MM fund:

It is calculated by multiplying the investment with the value attained by adding one with annual average return of MM fund.

$\begin{array}{c}\text{Money at the end of 2012 }=\text{Investment }\times \left(1+\text{Return}\right)\\ \text{=1,000}\times \left(1+0.24325\right)\\ =1,000\times 1.24325\\ =\text{1,243}\text{.25 }\end{array}$

Hence, the money at the end of 2012 in MM fund is $1,243.25.

Determine the money at the end of 2012 in Market index SP:

It is calculated by multiplying the investment with the value attained by adding one with annual average return of Market index SP.

$\begin{array}{c}\text{Money at the end of 2012 }=\text{Investment }\times \left(1+\text{Return}\right)\\ \text{=1,000}\times \left(1+0.14925\right)\\ =1,000\times 1.14925\\ =\text{1,149}\text{.25}\end{array}$

Hence, the money at the end of 2012 in MM fund is $1,149.25.

Compute standard deviation of MM fund:

Year	Return	Average return	Return - Average return	(Return - Average return)^2
2009	76.00%	24.325%	51.68%	0.2670
2010	16.60%	24.325%	-7.73%	0.0060
2011	-34.90%	24.325%	-59.23%	0.3508
2012	39.60%	24.325%	15.28%	0.0233
Total				0.6471

Computation of standard deviation:

The standard deviation of MM fund should be calculated as follows:

$\begin{array}{c}{\text{σ}}_{\text{MF}}\text{=}\sqrt{{\displaystyle \sum _{\text{i}\text{=}\text{1}}^{\text{n}}\frac{{\left(\text{Return}-\text{Average return}\right)}^{\text{2}}}{\left(\text{Number of years}-\text{1}\right)}}}\\ =\sqrt{\frac{0.6471}{4-1}}\\ =\sqrt{0.2157}\\ =0.464435\end{array}$

Hence, the standard deviation of MM fund is 46.44%

Compute standard deviation of Market index SP:

Year	Return	Average return	Return - Average return	(Return - Average return)^2
2009	26.50%	14.925%	11.58%	0.0134
2010	5.10%	14.925%	-9.83%	0.0097
2011	2.10%	14.925%	-12.83%	0.0164
2012	16.00%	14.925%	1.08%	0.0001
Total				0.0396

Computation of standard deviation:

The standard deviation of Market index SP should be calculated as follows:

$\begin{array}{c}{\text{σ}}_{\text{MF}}\text{=}\sqrt{{\displaystyle \sum _{\text{i}\text{=}\text{1}}^{\text{n}}\frac{{\left(\text{Return}-\text{Average return}\right)}^{\text{2}}}{\left(\text{Number of years}-\text{1}\right)}}}\\ =\sqrt{\frac{0.0396}{4-1}}\\ =\sqrt{0.0132}\\ =0.1149\end{array}$

Hence, the standard deviation of Market index SP is 11.49%

Therefore, MM fund is more volatile than Market index SP according to the value of standard deviation.