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# Bodie EOC Question 8

#### agattik

##### New Member
I would like to propose two changes to the solution proposed in file R10.P1.T1.Bodie:
• The variances for the return are given in an arbitrary and unspecified dimension (e.g. "881" where the unit would be percent-squared i.e. per-ten thousand or base points). It would be much more correct to divide the percentages by 100 to have no-dimension values in the calculation and provide the unit in the result (e.g. 8.81%)
• For question c, the solution claims there is no arbitrage opportunity, but as the problem provides the excess returns, there is no justification for subtracting the risk-free return a second time when calculating the Treynor, therefore there is an arbitrage opportunity by selling A and shorting C.

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#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @agattik Excellent feedback, I agree! (although I think you mean the final could be "e.g., 8.81 %^2" ?). In regard to the arbitrage solution, I think the problem is that it's not obvious that the given return assumptions--i.e., the E[R(i)] = 10%, 12% and 14%--are given as gross returns; Bodie's problem obviously intends for the assumption to be that the excess returns are 8%, 10% and 12% so that the Treynor ratios are all equal to 1.0. Thanks!

#### agattik

##### New Member
Thanks David, I agree with you on what the intent of the exercise appears to be, but the way it's formulated states explicitly that "Ri is the excess return for security i." and (from the table) "E(Ri) = 10%, 12%, 14% for A, B, and C.". Therefore I don't see how we could logically compute Treynor ratios based on excess returns of 8%, 10%, and 12%.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@agattik I agree, both symbols are R(i). It's a mistake; we'll report to publisher/Bodie (cc: @Nicole Seaman ) and update here if/when we get feedback.