On a given day, stock market prices respond to information about the
general economy and therefore, it may be expected that the returns
for an individual company may be correlated with the overall
performance of the market.
That is, a nonzero covariance between
the
x
and
y
observations is realistic.
The task of interest is to obtain a confidence interval estimate for the
difference between the mean return for the company and the mean
return for the market portfolio.
The differences are generated as:
i
i
i
y
x
d

=
for
i = 1, 2, . . . , 20
The sample mean and standard deviation of the differences were
calculated as:
0.173

=
d
and
1.391
=
d
s
The negative value for
d
says that the sample mean for the
company returns is less than the sample mean for the market returns.
This does not imply that this is the case for the population – the
population means are unknown.
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View Full DocumentEcon 325 – Chapter 8
5
For the purpose of the exercise, set the confidence level to 0.95.
A 95% interval estimate is:
n
s
t
d
d
c
±
An illustration of the tdistribution critical value
c
t
is below.
PDF of
)
19
(
t
tc
0
tc
Area = 0.95
Upper Tail Area = 0.05 / 2
= 0.025
Lower Tail Area = 0.025
To lookup the critical value from the Appendix Table for the
tdistribution select the degrees of freedom
(
n

1
) = 19, and set the
upper tail area to 0.025.
To check the method, with Microsoft Excel select Insert Function:
TINV(0.05, 19)
This returns the answer:
2.093
=
c
t
Econ 325 – Chapter 8
6
By using the numerical results, the 95% interval estimate for the
difference in population mean returns for the company and the
market is calculated as:
20
1.391
2.093
0.173
⋅
±

This gives the lower and upper limits:
[
0.48
0.82
,

]
h
Note that the interval contains the value zero (the lower limit is
negative and the upper limit is positive).
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 Fall '10
 WHISTLER
 Normal Distribution, Variance, confidence interval estimate, interval estimate

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