# Multi-goal Optimization

Investors are often must decide whether to consider absolute return and risk, or relative return and risk. Sophisticated investors, however, employ optimization in an attempt to be sensitive to both. Many address this duel concern of absolute and relative return and risk by constraining the asset weights in the optimization process, which is time-consuming and produces sub-optimal portfolios.

Imagine for a moment, a new approach. An approach that allows investors to simultaneously consider absolute and relative performance, yields a higher expected return, in a more efficient process. Here at Windham Labs, we offer an innovative optimization technique: Multi-goal Optimization.

Multi-goal Optimization combines mean-variance analysis, which characterizes assets and portfolios by their expected absolute return and standard deviation, with tracking errorâ€”which gives a measurement of the volatility of relative returns. This technique allows investors to identify efficient allocations that consider both absolute and relative performance. Rather than producing an efficient frontier in two dimensions, Multi-goal Optimization produces an efficient surface in three dimensions: expected return, standard deviation, and tracking error.

## Benefits of Multi-goal Optimization

Multi-goal optimization typically yields an expected result that is superior to constrained mean-variance optimization.

• For a given expected return, multi-goal optimization produces a portfolio with a lower standard deviation and less tracking error

• For a given standard deviation, multi-goal optimization produces a portfolio with a higher expected return and less tracking error

• For a given tracking error, multi-goal optimization produces a portfolio with a higher expected return and lower standard deviation

Higher expected return, lower standard deviation, less tracking error

Multi-goal Optimization not only identifies allocations that are efficient based simultaneously on expected absolute and relative performance, but also estimates return distributions in both absolute and relative dimensions. Analysis of joint-probability distributions generated by Multi-goal Optimization allow the investor to minimize the likelihood of failing to achieve an absolute target, while at the same time underperforming a benchmark.

The traditional approach of imposing allocation constraints on the mean-variance optimization process is an inefficient way to address performance goals. Multi-goal Optimization, which encompasses both absolute and relative measures of risk in an unconstrained optimization process, typically produces a superior solution through a more efficient process.

# Video Presentation

To help visualize this concept, play the video presentation below

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