variables. Coefficients capture this association numerically and can be computed validly as long as the variances of the two variables and the covariance between them are finite and constant.” Statement 2: “If the correlation between two variables is -1, then if one variable increases by one unit, the other will always decrease by one unit, regardless of the initial value of the first variable.” As the discussion continued, Diaz mentioned that he was trying to determine the relationship between U.S. stock market returns and short-term interest rates. For this, he had calculated the correlation coefficient between annual returns to a U.S. market index and annual interest rates using data of the past twenty years. However, when Thomas reviewed his calculations, he made the following comment: Statement 3: “Your data set includes three observations that can clearly be termed as outliers. Hence, to make sure that the sample correlation is a reliable measure of the true population correlation, you need to recalculate it after removing the effect of the outliers.”

Level II of CFA®Program Mock Exam 1 – Solutions (AM)FinQuiz.com © 2019 - All rights reserved. Thomas continued by making the following statement about correlation analysis: Statement 4: “While determining the relationships between international market returns and the initial dollar investment made, on the one hand, and between initial investment and risk, on the other, I found out that there was a strong positive relationship between return and risk. This shows that investing in high risk investments will yield higher returns.” Diaz just invested 2% of BED’s portfolio in high-yield U.S. corporate bonds. When Thomas asked him why he did so, Diaz stated there was a high positive and significant correlation between short-term interest rates and bond yields and that U.S. interest rates were expected to decrease. However, when Thomas performed his own calculations, he stated that the correlation, though high and positive, was not significant and hence, the strategy may prove to be unfruitful. Even so, Diaz gathered the following information to estimate the regression equation for the bond yield and interest rates. Exhibit 1 Regression analysis with interest rates as the independent variable Covariance between interest rates and bond yields0.000586Variance of interest rates0.000956 Variance of bond yields0.000765 Average short-term interest rate5.50% Average bond yield6.78% After estimating the regression equation, Diaz tested the slope coefficient for significance. Although he knew the method of testing, he did not know how changes in the values of key inputs affected the ultimate conclusion. When he asked Thomas about it, he made the following comments: Statement 5: “If you decrease the level of significance from 5% to 1%, the probability of Type 1 error will decrease and the probability of Type 2 error will increase.” Statement 6: “Smaller standard errors lead to tighter confidence intervals but if the standard error is incorrectly calculated the probability of Type 1 error will increase.”

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