Optimization – Efficient Frontier, Black Litterman

In an effort to improve the portfolios performance there are different methodologies to assist the investor in determining the optimal allocations to funds in the portfolio. Some of the most commonly used methods are linear optimization, Markowitz Efficient Frontier and Black-Litterman.

Linear optimization provides options in addition to the traditional tasks of maximizing return and minimizing volatility. For example, linear optimization can be used to allocate among the funds to minimize the drawdown or downside risk of the portfolio. Markowitz Efficient Frontier is an intuitive and easy to use model that is best fit when the funds historically have had a normal distribution and the funds are expected to perform similarly in the future. However, linear optimization and Markowitz Efficient Frontier are models that rely on historical returns. When a fund’s future performance is believed to be different than the fund’s past performance the Black-Litterman optimization may be a good choice due to the relative and absolute views used to enter expected performance.

All of these optimization methodologies allow for minimum and maximum allocation constraints that keep allocations within investment policy requirements.

  • Linear Optimizer – as the name suggests, this optimization methodology is focused on a single performance or risk measurement to solve for the allocations to the underlying funds that maximizes the performance measurement or minimizes the risk measurement.

Solvers calculate the selected statistics for the portfolio within the constraints set for the individual underlying assets. Then the allocations are changed and the selected statistic is calculated. Through multiple iterations an optimizer solves for the top portfolios for the selected criteria.

  • Markowitz Efficient Frontier – a mean variance optimization methodology that for a selected level of risk determines the highest return or for a target return determines the lowest risk by allocating among the underlying funds. Inputs needed to create optimal portfolios are the expected returns, variances for all assets and covariance between all of the underlying funds in the portfolio. The inputs are calculated from the funds’ historical returns. As such the start and end dates used for the optimization are important factors in the outcome of the optimization. Depending on the investment horizon for the portfolio it may be appropriate to use a subset of the available data to determine the optimal allocations.
  • Black-Litterman – like Markowitz Efficient Frontier, is a mean variance optimization methodology but allows the input of relative and/or absolute return assumptions.

Market Capitalization of the asset classes in the portfolio is used to attempt to address over allocating to a single asset class. The Black-Litterman approach was originally used for global equities, bonds and currencies, where the market capitalization can fairly easily be determined. However, when using the approach with other asset classes the market capitalization might not be possible to ascertain. One suggestion for using Black-Litterman with a portfolio of hedge funds would be to use the fund’s AUM as a proxy for the market capitalization.

Views allow assumptions about future expected performance to be used in lieu of the funds’ historical performance to determine the optimal allocation. The views can take two forms; relative and absolute.
• The absolute view is a forecast of a funds future performance. Figure 33
• A relative view is a statement that a fund or group of funds will outperform another fund or group of funds. Figure 34

Figure 33: Black-Litterman Absolute View
Figure 34: Black-Litterman Relative View

Investors who are required to select and monitor investment managers should develop a basic understanding of investment statistics. Quantitative tools can provide you with good insight that you can use in your qualitative interviews with managers and when monitoring your investments.