A fund has changed managers twice during the past 10 years. An analyst wishes to measure whether either of the changes in managers has had an impact on performance. The analyst wishes to simultaneously measure the impact of risk on the fund’s return. R is the return on the fund, and M is the return on a market index. Which of the following regression equations can appropriately measure the desired impacts? A) R = a + bM + c1D1 + c2D2 + c3D3 + å, where D1 = 1 if the return is from the first manager, and D2 = 1 if the return is from the second manager, and D3 = 1 is the return is from the third manager. B) R = a + bM + cD + å, where D = 1 if the return is from the first manager, 2 if the return is from the second manager, and 3 if the return is from the third manager. C) The desired impact cannot be measured. D) R = a + bM + c1D1 + c2D2 + å, where D1 = 1 if the return is from the first manager, and D2 = 1 if the return is from the third manager.
d…right?
Gotta be D for this one!
Correct… The effect needs to be measured by two distinct dummy variables. The use of three variables will cause collinearity, and the use of one dummy variable will not appropriately specify the manager impact.
Nice question. I almost got trapped by A.
is there a rule that 2 is the max, 3 causes collinearity? it says 2 changes, implying 3 managers, and thus 3 dummies?
pacmandefense Wrote: ------------------------------------------------------- > is there a rule that 2 is the max, 3 causes > collinearity? it says 2 changes, implying 3 > managers, and thus 3 dummies? Yes, there is. With 3 managers, using three dummies will actually create a situation where the estimates for each beta coefficient will not exist. If your matrix algebra is up to par, it results in an inconsistent beta matrix since a column of ones is always included for the intercept term. There has to be some sort of a base condition, and if one of the other conditions occurs then the corresponding dummy adds/subtracts from the base value. N conditions -> N-1 dummies.
bM is the average on the market. a = excess return of manager 3 c1 = excess return over (a + bM) of manager 1 c2 = excess return over (a+bM) of manager 2
wyantjs Wrote: ------------------------------------------------------- > pacmandefense Wrote: > -------------------------------------------------- > ----- > > is there a rule that 2 is the max, 3 causes > > collinearity? it says 2 changes, implying 3 > > managers, and thus 3 dummies? > > > Yes, there is. With 3 managers, using three > dummies will actually create a situation where the > estimates for each beta coefficient will not > exist. If your matrix algebra is up to par, it > results in an inconsistent beta matrix since a > column of ones is always included for the > intercept term. There has to be some sort of a > base condition, and if one of the other conditions > occurs then the corresponding dummy adds/subtracts > from the base value. N conditions -> N-1 dummies. thanks. knew the rule. had a lapse.
Let me rephrase. I shouldn’t say inconsistent because the matrix equation actually will have an infinite number of solutions as there will be a linear dependence relation among some combination of columns. More appropriately, the coefficient matrix will not be invertible, will not lead to a unique solution, and your computer program will likely (hopefully) break down.