In applying efficient frontier analysis for an investor who uses both taxable and tax-advantaged accounts, the mean-variance optimization: A) cannot simultaneously determine both the weights in the available assets and their location in the various accounts, but it can be done in a step-wise fashion. Usually the weights are determined first and then the locations. B) would simultaneously determine both the weights in the available assets and their location in the various accounts. C)cannot simultaneously determine both the weights in the available assets and their location in the various accounts, but it can be done in a step-wise fashion. Usually the locations are determined first and then the weights.
c)
Answer:B (I’m still trying to understand…) Kaplan explanation: The mean-variance optimization should optimally allocate assets and determine the optimal asset location for each asset. Substitution of adjusted returns would allow the process to be done in one step. LOS 10.i: Demonstrate how taxes and asset location relate to mean-variance optimization. Ideally, the efficient frontier of portfolios should be viewed on an after-tax basis. Furthermore, because the tax status of an investment depends on the type of account it is held in, the same asset could appear on the efficient frontier in both taxable and nontaxable forms. For example, an investor holds both stocks and bonds in both taxable and tax-exempt accounts. In this case, there are four different assets that could appear on the efficient frontier. Of course, the optimization process would have to be constrained to account for limits on the amount of funds that can be placed in tax-advantaged accounts and the type of assets that can be allocated to them. The mean-variance optimization should optimally allocate assets and determine the optimal asset location for each asset. Accrual equivalent after-tax returns would be substituted for before-tax returns, and after-tax risk would be substituted for before-tax risk.
ok. now it comes back. rather than use the before tax returns and do the optimization - use the after tax returns.
So R1 on a tax exempt account would remain R1 even after. But R2 on a taxable account with a tax of T would become a return of R2(1-T) on the taxable. now use R1 and R2(1-T) to do your optimization.
Thanks Cpk.
What you are suggesting is a step-wise approach: 1) find after tax returns, 2) do the optimization to find the weights. This is not the same as what the answer provided by Kaplan recommends. your explanation here still rhymes more with answer C.
Their suggestion focuses combining steps 1 and 2 when doing the optimization process. One could, for instance, take a bootstrapping approach in order to find the most tax-efficient allocation.
^ Good explanation!