MODspartan
New Member
Hi all,
I'm having some trouble (read: a lot of trouble) with example 11.3 in the Bodie reading. I cannot seem to get the calculations working out to the values in table 11-2, in particular the weights for the APT portfolio and for the Treynor-Black procedure.
For example, in the second row of the table the reading has w(beta) = 1 when alpha_active = 1%, Residual SD = 4, and beta_active = 2. The index risk premium = 7, index SD = 20, and index Sharpe is 0.35. But from the Treynor-Black equations I get the weight to put in the active portfolio as:
w_0 = (1/4^2) / (7 / 20^2) = 3.57 = w(beta = 0) [according to the table]
w_a = 3.57 / [1 + 3.57(1 - 2)] = -1.38 != w(beta)
I think it boils down to what Bodie means by w(beta = 0) and w(beta).
Treynor-Black Equations for ref
w_0 = (alpha_active / var(e_active)) / (E(R_m)/Var(R_m))
w_active = w_0 / [ 1 + w_0(1-beta_active) ]
I'm having some trouble (read: a lot of trouble) with example 11.3 in the Bodie reading. I cannot seem to get the calculations working out to the values in table 11-2, in particular the weights for the APT portfolio and for the Treynor-Black procedure.
For example, in the second row of the table the reading has w(beta) = 1 when alpha_active = 1%, Residual SD = 4, and beta_active = 2. The index risk premium = 7, index SD = 20, and index Sharpe is 0.35. But from the Treynor-Black equations I get the weight to put in the active portfolio as:
w_0 = (1/4^2) / (7 / 20^2) = 3.57 = w(beta = 0) [according to the table]
w_a = 3.57 / [1 + 3.57(1 - 2)] = -1.38 != w(beta)
I think it boils down to what Bodie means by w(beta = 0) and w(beta).
Treynor-Black Equations for ref
w_0 = (alpha_active / var(e_active)) / (E(R_m)/Var(R_m))
w_active = w_0 / [ 1 + w_0(1-beta_active) ]
