# Asset-liability Optimization

Learn how to think about asset-liability matching analysis in portfolio construction.

Investors who manage portfolio assets from a surplus perspective often use asset-liability optimization. This framework is simply a variation of the theoretical foundations used in asset-only optimization.

We consider a fund's liabilities as an embedded short position with a weight of -100%, which corresponds to a funding ratio of 1. Therefore, all optimal portfolios are derived in terms of its surplus efficiency. Unless the liabilities are independent of each of the assets in the portfolio, the asset weights that form the portfolios along the efficient frontier net of liabilities will differ from those that we obtain when we ignore liabilities. This fact, precludes us from approaching portfolio optimization sequentially.

In the Windham Portfolio Advisor, we can set up a case file to perform asset-liability optimization intuitively.

## Adding a Liability Instrument

Suppose we have a portfolio of U.S. stocks and U.S. bonds. Add the fund's proxy for the liability instrument, in this example we will use U.S. inflation-linked Treasuries as our liability instrument.

You can extend the framework to include more than one liability instrument, in this example we consider a single instrument.

#### Classify liability instruments as Overlay

Next, we would need to define the liability instrument as an *Overlay *in the Define Portfolios screen. Unlike assets, overlay instruments are not considered by the optimizer when enforcing the sum of weights portfolio constraint.

## Expected Return, Risk, and Correlations

Select and configure your return and risk models on the respective screens in the WPA.

## Using Optimization Constraints to Define the Asset-Liability Framework

To modify an asset-only optimization framework to include liabilities, we would need to add the liabilities instrument as a negative asset. In this example for a fully-funded plan, we specify the lower and upper bound constraints for the optimizer to -100% as shown below in the Constraints screen.

If a fund is underfunded by 5%, then we would specify the embedded short position with a weight of -105% instead; or if a fund is overfunded by 5%, then specify the embedded short position with a weight of -95%.

Other constraints and elements of the optimization set up would be similar to that of an asset-only exercise.

## Optimize

Now, we are ready to optimize. Head over the Parametric Optimization screen and construct your portfolio. The outcomes of the optimizations would now account for the liability instrument (or portfolio).

Results in subsequent exposure to loss and risk budget screens now describes its analytics as a surplus of liabilities.

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