Reading 11- LOS F (Part 2): Q3 class, only, management, company, created

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3.aig Standish, CFA, is investigating the validity of claims associated with a fund that his company offers. The company advertises the fund as having low turnover and, hence, low management fees. The fund was created two years ago with only a few uncorrelated assets. Standish randomly draws two stocks from the fund, Grey Corporation and Jars Inc., and measures the variances and covariance of their monthly returns over the past two years. The resulting variance covariance matrix is shown below. Standish will test whether it is reasonable to believe that the returns of Grey and Jars are uncorrelated. In doing the analysis, he plans to address the issue of spurious correlation and outliers.

	Grey	Jars
Grey	42.2	20.8
Jars	20.8	36.5

Standish wants to learn more about the performance of the fund. He performs a linear regression of the fund’s monthly returns over the past two years on a large capitalization index. The results are below:

ANOVA
	df	SS	MS	F
Regression	1	92.53009	92.53009	28.09117
Residual	22	72.46625	3.293921
Total	23	164.9963
	Coefficients	Standard Error	t-Stat	P-value
Intercept	0.148923	0.391669	0.380225	0.707424
Large Cap Index	1.205602	0.227467	5.30011	2.56E-05

Standish forecasts the fund’s return, based upon the prediction that the return to the large capitalization index used in the regression will be 10 percent. He also wants to quantify the degree of the prediction error, as well as the minimum and maximum sensitivity that the fund actually has with respect to the index.

He plans to summarize his results in a report. In the report, he will also include caveats concerning the limitations of regression analysis. He lists four limitations of regression analysis that he feels are important: relationships between variables can change over time, the decision to use a t-statistic or F-statistic for a forecast confidence interval is arbitrary, if the error terms are heteroskedastic the test statistics for the equation may not be reliable, and if the error terms are correlated with each other over time the test statistics may not be reliable.

Given the variance/covariance matrix for Grey and Jars, in a one-sided hypothesis test that the returns are positively correlated H₀: ρ = 0 vs. H₁: ρ > 0, Standish would:

A)   reject the null at the five percent but not the one percent level of significance.

B)   not reject the null hypothesis at either the five nor the one percent level of significance.

C)   reject the null at the one percent level of significance.

D)   need to gather more information before being able to reach a conclusion concerning significance.

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The correct answer was C)

First, we must compute the correlation coefficient, which is 0.53 = 20.8 / (42.2 × 36.5)^0.5.

The t-statistic is: 2.93 = 0.53 × [(24 - 2) / (1 - 0.53 × 0.53)]^0.5, and for df = 22 = 24 - 2, the t-statistics for the five and one percent level are 1.717 and 2.508 respectively.