1. Suppose you have 5-year annual data on the excess returns on a fund manager’s portfolio (“fund ABC”) and the excess returns on a market index (where is the return on fund ABC, is the risk-free rate and is the return on the market index):
Year t Excess return on fund ABC
Excess return on market index
1 14.0 16.0
2 32.0 21.7
3 11.6 6.0
4 21.2 16.2
5 17.4 11.0
(a) What is the estimated alpha ( ) for Fund ABC?
(b) Given the data in question (a), what is the estimated beta ( ) of Fund ABC?
(c) Suppose that the unbiased estimator of the standard deviation of the disturbance (s) is 5.1. What is the nearest value to the standard errors of the estimated CAPM alpha ( ) of Fund ABC
(d) The estimated alpha ( ) and beta ( ) of a rival fund, Fund DEF, are 2.3 and 3.1, respectively. If the expected market risk premium is 12%, what would we expect the excess return of Fund DEF to be
2. You are told that the return of a stock is unrelated to the movement in the market, (i.e. the stock has zero systematic risk). You calculated the beta and its standard deviation using 40 quarterly observations on the stock’s return and found out that its beta is 0.355 and the standard deviation is 0.20. Write down the null and alternative hypotheses to test the claim and test the hypothesis against a two-sided alternative.
3. You are estimating the following econometric model under the restriction that β3 + β4 = 1. A regression carried out on a sample of 120 quarterly observations produces the value of 145.45 for restricted residual sum of squares and a value of 109.50 for the unrestricted residual sum of squares. Perform the test on this restriction and state your conclusion.
yt = β1 + β2×2 + β3×3 + β4×4 + ut
4. You have estimated the following model. Calculate the t-statistics for parameters and compare them with the R2 statistics. Do you see any problem with this estimation? If you see a problem, how would you go about addressing it?
yt = 0.75 + 0.252x2t – 0.751x3t; R2 = 0.96 ;
se(constant) = 0.355; se(x2t ) = 0.150 and se(x3t) = 0.690
5. In a regression model with two explanatory variables and a sample of 50 observatuibs, the estimated errors produce a correlation coefficient of 0.4. Calculate D-W (Durbin-Watson) test statistic and test for the absence of autocorrelation in the error terms. Make sure that you state the null and alternative hypotheses.