Principle of Asset Allocation

Question 1

How can we improve the quality of inputs in MVO to resolve the problem of GIGO

Answer 1

We can use the reverse optimization - instead of starting with expected returns (and the other inputs) and deriving optimal portfolio weights, start with what we assume to be “optimal” portfolio weights from the global market portfolio and derive the expected returns consistent with those weights.

Question 2

Describe what role the black litterman extension does to the reverse optimization

Answer 2

Black Litterman is an extension of reverse optimization. After that we have calculated the implied returns from the global market portfolio, we can adjust the implied returns to reflects the investor views on future returns.

Question 3

How can we address the GIGO and highly concentrated allocation issues

Answer 3

We can address by adding more constraints to the model per example, in terms of maximum weights from one asset class.

Resample MVO can also help to address those problems. here are the best guesses of inputs (based on all the combination of inputs to create the portfolios on the efficient frontier), here are lots of variations around those best guesses (made by Monte Carlo), and here is the average of the asset allocations to get to a 5% expected portfolio return

Question 4

Discuss the use of Monte Carlo simulation to evaluate the robustness of an asset allocation.

Answer 4

• Monte Carlo Simulation can be use to address the limitation of MVO as a single period model and the issues of taxes and portfolio rebalancing in a multi period. When investor wants to add money or withdraw money, it will create cash flow interim that will change expected path of returns in the porfolio. This can be address by using a Monte Carlo Sim.
• Can also be use to show the different outcome/possibility of returns in the portfolio to identify the risk tolerance of the client.

Question 5

Describe how we can identify the optimal allocation for less liquid asset classes (real-estate, private debt, etc)

Answer 5

Exclude illiquid asset classes when running an MVO, but use them to meet separately set target asset allocations.

Include the illiquid asset classes in MVO and model the inputs of the specific (not asset class) investments you plan to use (i.e., the risk estimate will be based on both nonsystematic and systematic).

Include the illiquid asset classes in MVO using highly diversified asset class inputs, recognizing that the actual investments made may have different characteristics. The input estimates for this approach are normally made using reported alternative investment indexes. Such indexes are usually not pure representations of the asset class but include characteristics of other asset classes as well. This violates the requirement that asset classes be mutually exclusive and biases the reported correlations upward.

Question 6

What is marginal contribution to portfolio risk and how do we calculate it

Answer 6

MCTR is the change in portfolio total risk for a small change in asset allocation

MCTR = (beta of asset class with respect to the portfolio) * (total portfolio risk as measured by standard deviation)

Question 7

How do we calculate the absolute contribution to total risk

Answer 7

weight of assets i * MCTR

Question 8

How can we tell that we achieved the optimal asset allocation to each asset class :

Answer 8

When the ratio of excess return to MCTR is equal for all asset class and that it is equal with the Sharpe Ratio.