Question

The table below gives the annual total returns on Global Balanced Index Fund from 1999 to 2008. The returns are in the local currency. Use the information in this table to answer the following questions:

Table 1: Global Balanced Index Fund Total Returns, 1999-2008
Year	Return
1999	50.21%
2000	-2.18%
2001	12.04%
2002	26.87%
2003	49.90%
2004	24.32%
2005	45.20%
2006	-5.53%
2007	-13.75%
2008	-39.06%

1. (5.0 pts) Calculate the mean absolute deviation (MAD).

Calculation of MAD for Germany Index Total Returns, 1999-2008
Year	Return
1999	50.21%
2000	-2.18%
2001	12.04%
2002	26.87%
2003	49.90%
2004	24.32%
2005	45.20%
2006	-5.53%
2007	-13.75%
2008	-39.06%

2. (4.0 pts) Calculate the variance.

Solution

Calculation of Variance for Germany Index Total Returns, 1999-2008
Year	Return
1999	50.21%
2000	-2.18%
2001	12.04%
2002	26.87%
2003	49.90%
2004	24.32%
2005	45.20%
2006	-5.53%
2007	-13.75%
2008	-39.06%

                       

           

                                                                                   

3. (2.0 pts) Calculate the standard deviation.

Solution

           

3. (4.0 pts) Calculate the semi variance (the average squared deviation below the mean), a measure of downward risk.

Solution:

Answer 1

a)

Year	Return	abs deviation
1999	50.21%	0.35408
2000	-2.18%	0.16982
2001	12.04%	0.02762
2002	26.87%	0.12068
2003	49.90%	0.35098
2004	24.32%	0.09518
2005	45.20%	0.30398
2006	-5.53%	0.20332
2007	-13.75%	0.28552
2008	-39.06%	0.53862
	mean	MAD
	14.80%	24.50%

mean = 14.80%

MAD = 24.5%

b)

Year	Return	abs deviation	error^2
1999	50.21%	0.35408	0.125373
2000	-2.18%	0.16982	0.028839
2001	12.04%	0.02762	0.000763
2002	26.87%	0.12068	0.014564
2003	49.90%	0.35098	0.123187
2004	24.32%	0.09518	0.009059
2005	45.20%	0.30398	0.092404
2006	-5.53%	0.20332	0.041339
2007	-13.75%	0.28552	0.081522
2008	-39.06%	0.53862	0.290112
	mean	MAD	Variance
	14.80%	24.50%	0.089684

variance = sum of error^2 / (n-1)

= 0.089684

c)

standard deviation = sqrt(variance) =

0.299474

d)

Return	Return less than mean
-39.06%	-39.06%
-13.75%	-13.75%
-5.53%	-5.53%
-2.18%	-2.18%
12.04%	12.04%
24.32%
26.87%	semi variance
45.20%	0.035624473
49.90%
50.21%

formulas used in Excel

Year	Return	abs deviation	error^2
1999	0.5021	=ABS(B2-$B$13)	=C2*C2
2000	-0.0218	=ABS(B3-$B$13)	=C3*C3
2001	0.1204	=ABS(B4-$B$13)	=C4*C4
2002	0.2687	=ABS(B5-$B$13)	=C5*C5
2003	0.499	=ABS(B6-$B$13)	=C6*C6
2004	0.2432	=ABS(B7-$B$13)	=C7*C7
2005	0.452	=ABS(B8-$B$13)	=C8*C8
2006	-0.0553	=ABS(B9-$B$13)	=C9*C9
2007	-0.1375	=ABS(B10-$B$13)	=C10*C10
2008	-0.3906	=ABS(B11-$B$13)	=C11*C11
	mean	MAD	var	sd
	=AVERAGE(B2:B11)	=AVERAGE(C2:C11)	=SUM(D2:D11)/(9)	=SQRT(D13)