III. LongProblems. (85%) I. . Let res denote the return in month t on a managed
ID: 3321755 • Letter: I
Question
III. LongProblems. (85%) I. . Let res denote the return in month t on a managed portfolio P. Consider the regressions where rMi is the return on the S&P; index, ra is a riskless rate of interest, and 0 otherwise Consider the following results obtained when the above regressions are estimated for two actively managed portfolios, A and B, using ten years of monthly data. Each estimated coefficient is shown (as a decimal, not a percent) along with its t-statistic (below in parentheses) Rexression I Portfolio A 0.030 1.11 -0.010 1.03 0.55 (3.50) (31) (0.70) (30.7) (3.85) Portfolio B 0.015 111 0.013 1.12 0.15 (2.60) (32.7) 2.10) (314) (0.50) What is "market timing"? How can one test for its presence using one of the above regressions (I In performance evaluation, what is the usual interpretation of a finding that the (Jensen Given the above regression evidence, is the usual interpretation of that you gave in p.nt b.more a. or II). Which of portfolios A and B, if either, appears to exhibit significant market timing ability? measure) in regression I is significantly greater than zero? uppropriate for portfolio A or for portfolio B (choose one)? Exnlain vour reasoninoExplanation / Answer
(a) Market timing is when you invest when the market rate is low and withdraw when the market rate for the portfolio is high. We can test for its presence fromthe regression, since the regression models help predict in which month my returns will be high so I can cash in on it. Regression model II appears to exhibit significant market timing ability as it does its prediction using more variables and hence it factors in more variables for prediction and hence its resdiction will be more accurate
(b) The usual interpretation tha alpha in regression I is significantly greater than zero is that what holds true for a sampe of observation might not be tru for the population as a whole due to chance factos, So the significance of the coeff alpha indicates that with what confidence it will predict in the same way for the whole population. So, while testing significance if alpha is greater than zero there is a significant relationship between the dependent and the independent variable at the population level
(c) This interpretation is more appropriate for portfolio B as their are more variables involved and we need to know the significance of each coeff. when projecting to the population so that we eliminate the unnecessary variables and make the equation simpler to handle