can anyone comment on CFAI Book 3, page 268, exercise # 1, where they say that "we would lower sharpe ratio if we combined corner ptfl 4 and 5).
I did that math before reading the solution and my sharpe is exactly the same (0.424) as the one of combining the tangency ptfl with risk-free asset.
The weights I got for the corner ptfls 4 and 5 (assuming the expected return of 6.5%) were 54.6% and 45.4%, which gave me the same linear approximation of the recommended ptfl’s standard deviation of 9.9%, therefore resulting in the same sharpe.
I don’t understand , tigas. CP 4 obviously has the highest Sharpe of all the CP’s . CP 5 has the next highest . Any linear combination of CP 4 and CP 5 must have a LOWER Sharpe than CP 4. The solution involving t-bills preserves the Sharpe at the highest level , i.e. at the level of CP 4. Can you check your calculations again? How can you get a Sharpe higher than CP 4 if you use a linear combination of CP 4 and CP 5 which has a lower Sharpe?
Maybe it is a stretch to say the S.d. of a linear combination of CP 4 and CP 5 would be a weighted sum of the s.d. of each CP. You would be ignoring correlation ( i.e. setting it to zero ) which would not be correct. A t-bill has no s.d. ( theoretically very low ) , so it is different from a C.P. in that it offers very low risk footprint.
given it is a corner portfolio there should be no correlation. Even the books calculate the sd as the weighted sum. given the weights of 54.6% and 45.4% - the sd is more than 9.9% -> it is 9.93% or thereabouts and the sharpe comes out as 0.4224. (not 0.424). it looks like a rounding issue to me.
yes guys, there was precisely that, a rounding issue. I got s SD of 9.94 (above 9.9) and a sharpe of 0.4225, just below 0.424. many thanks once again tigas