Chapter 10, Problem 1CE

To determine

To calculate: The mean monthly return and annual return for Janus Fund.

Answer to Problem 1CE

Solution:

The mean monthly return is $\underset{\_}{1.27}$ and the annual return is $\underset{\_}{15.24}$.

Explanation of Solution

Given:

The provided table is shown below:

Month	Janus	S&P	Large Growth	Month	Janus	S&P	Large Growth
MAY 2013	1.33	2.34	2.63	NOV 2011	-0.8	-0.22	-1.06
APR 2013	3.01	1.95	1.25	OCT 2011	14.17	10.93	11.78
MAR 2013	4.26	3.75	3.19	SEP 2011	-10.38	-7.03	-8.45
FEB 2013	1.54	1.36	0.65	AUG 2011	-7.94	-5.43	-6.67
JAN 2013	4.8	5.18	4.75	JUL 2011	-2.81	-2.03	-1.27
DEC 2012	1.8	0.91	0.52	JUN 2011	-1.21	-1.67	-1.5
NOV 2012	0.56	0.58	1.95	MAY 2011	-1.07	-1.13	-1.27
OCT 2012	-1.87	-1.85	-3.01	APR 2011	3.67	2.96	2.91
SEP 2012	1.84	2.58	2.3	MAR 2011	-0.24	0.04	0.37
AUG 2012	2.77	2.25	3.27	FEB 2011	4	3.43	3.27
JUL 2012	2.11	1.39	0.47	JAN 2011	2.38	2.37	1.83
JUN 2012	2.8	4.12	2.6	DEC 2010	4.93	6.68	5.54
MAY 2012	-7.19	-6.01	-7.37	NOV 2010	-1.18	0.01	1.08
APR 2012	-0.94	-0.63	-0.7	OCT 2010	3.65	3.8	4.62
MAR 2012	2.32	3.29	3.37	SEP 2010	9.31	8.92	10.81
FEB 2012	5.33	4.32	5.34	AUG 2010	-4.22	-4.51	-4.72
JAN 2012	6.45	4.48	6.31	JUL 2010	6.02	7.01	6.73
DEC 2011	0.43	1.02	-1.14	JUN 2010	-3.92	-5.23	-5.62

Formula used:

$\overline{x}=\frac{{\displaystyle \sum x}}{n}$

Calculation:

Use the above table for Janus Fund and the formula for mean:

$\overline{x}=\frac{{\displaystyle \sum x}}{n}$

Therefore,

$\begin{array}{c}\overline{x}=\frac{\left[\begin{array}{l}1.33+3.01+4.26+1.54+4.8+1.8+0.56-1.87+1.84+2.77+2.11+2.8\\ -7.19-0.94+2.32+5.33+6.45+0.43-0.8+14.17-10.38-7.94-2.81\\ -1.21-1.07+3.67-0.24+4+2.38+4.93-1.18+3.65+9.31-4.22+6.02-3.92\end{array}\right]}{36}\\ =\frac{45.71}{36}\\ \approx 1.2697\\ \approx 1.27\end{array}$

Thus, the mean monthly return is approximately $1.27$.

To get annual return, multiply the mean monthly return by 12

$\begin{array}{c}\text{Annual return}=12\left(\overline{x}\right)\\ \approx 1.27\left(12\right)\\ \approx 15.24\end{array}$

Thus, the annual return is approximately 15.24.