Consider the following realized annual returns: Year End Market Realized Return

Question

Consider the following realized annual returns:

Year End

Market Realized Return

Microsoft Realized Return

1996

21.2%

88.3%

1997

30.3%

56.4%

1998

22.3%

114.6%

1999

25.3%

68.4%

2000

-11.0%

-62.8%

2001

-11.3%

52.7%

2002

-20.8%

-22.0%

2003

33.1%

6.9%

2004

13.0%

9.2%

2005

7.3%

-0.9%

Suppose that you want to use the 10 year historical average return on Microsoft to forecast the expected future return on Microsoft. Required: Calculate the 95% confidence interval for your estimate of the expected return

Year End

Market Realized Return

Microsoft Realized Return

1996

21.2%

88.3%

1997

30.3%

56.4%

1998

22.3%

114.6%

1999

25.3%

68.4%

2000

-11.0%

-62.8%

2001

-11.3%

52.7%

2002

-20.8%

-22.0%

2003

33.1%

6.9%

2004

13.0%

9.2%

2005

7.3%

-0.9%

Explanation / Answer

Microsoft Realized Return

Hence average annual rate = 18.50%( Rounded to 2 decimal places)

Taking this average will be the expected future return

Using the annual return to calculate Standard deviation in excel:
=STDEV(P9;P18) where  P9;P18 are the annual returns
We get standard deviation as 51.45%


Confidence interval = mean +- Standard deviation*z value
z value at 95%= 1.96
Hence confidence interval = [18.50%+(1.96*51.45)] , [18.50%-(1.96*51.45)]
=119.34% to -82.34%

Year End Market Realized Return

Microsoft Realized Return

1996 21.20% 88.30% 188.30% 1997 30.30% 56.40% 156.40% 1998 22.30% 114.60% 214.60% 1999 25.30% 68.40% 168.40% 2000 -11.00% -62.80% 37.20% 2001 -11.30% 52.70% 152.70% 2002 -20.80% -22.00% 78.00% 2003 33.10% 6.90% 106.90% 2004 13.00% 9.20% 109.20% 2005 7.30% -0.90% 99.10% =product of all yearly rates 5.455184598 5.45518^(1/10)= 1.184897942

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