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# Shadow Assets, Shadow Liabilities, and Illiquidity

Learn how to construct a portfolio to account for illiquidity in the Windham Portfolio Advisor.
Investors rely on liquidity to implement strategic asset allocation decisions, rebalancing decisions, and other portfolio construction processes to meet demands for cash, etc.
To account for the impact of liquidity, investors should attach a shadow asset to liquid asset classes and a shadow liability to illiquid asset classes in a portfolio. This modeling approach enables investors to use liquidity to increase a portfolio's expected utility while accounting that illiquidity subverts from preserving a portfolio's expected utility.
These shadow allocations allow investors to address illiquidity within a single, unified framework of expected return and risk.
In the Windham Portfolio Advisor, we can structure the use of shadow assets and shadow liabilities similar to how we would think about overlays.

## Adding a Shadow Asset and Shadow Liability Instrument

Once you have selected the core asset classes in your portfolio, you can add proxy instruments to represent a Shadow Asset and Shadow Liability. In our example, we simply pick two unused cash instruments as proxies for these shadow instruments.
Adding shadow asset and shadow liability instruments
Use any instrument in our database to proxy shadow instruments. Their time series data become irrelevant as typically in these analyses, we would be using views to document expected returns, risk, and correlation. Underlying data of the shadow proxies are irrelevant.
Once these proxies are added, customize their display name to notate on screen that they would serve as placeholders (proxies) for a shadow asset and a shadow liability in the portfolio.

#### Classify shadow instruments as Overlay

Next, we would need to define the shadow asset and shadow liability instruments as an Overlay in the Define Portfolios screen. Unlike assets, overlay instruments do not require funding (think of forward or futures) so the optimizer does not consider this as part of the sum of weights constraint.

## Expected Return, Risk, and Correlations

In the risk and return screen of the WPA, enter your estimates of expected return and risk for the shadow asset and shadow liability as views. We can assume that correlation coefficients for the shadow asset and shadow liability are zero.
For the known asset classes, you can use one of our models to copy estimates over into the views column or import your own!

## Using Optimization Constraints to Define the Framework

We would have to define groups and constraints to describe the mathematical relationships between asset classes, the shadow asset, and the shadow liability.

### Define Groups

In the Constraints screen, we will need to define a few groups to reflect the analytical framework.
Start by defining groups in the Constraints screen
We would need to define the following groups
 Group Constituents Liquid Assets U.S. Equities, Foreign Developed Market Equities, Emerging Market Equities, Treasury Bonds, U.S. Corporate Bonds, and Commodities. Illiquid Assets Real Estate Shadow Asset Shadow Asset Shadow Liability Shadow Liability Shadow Instruments Shadow Asset, and Shadow Liability
Defining a group is as simple as following the wizard steps on the Constraints screen. For example, to define a group of Liquid Assets
1. 1.
Select Manage a group of assets
2. 2.
In the Define a group text input bar, enter a group name: Liquid Assets
3. 3.
Select the new group in the list, and
check the corresponding instruments on the right panel that would be a part of that group.
Defining the necessary groups
You can repeat this exercise for the groups outlined in the table above.

### Setting up the Constraints

Next, we will need to define a few constraints to set up the shadow liquidity framework. We would need to specify the following
\begin{aligned} \text{Allocation to Liquid Assets}&=\text{Allocation to Shadow Asset} \\ \text{Allocation to Illiquid Assets}&=\text{Allocation to Shadow Liability} \end{aligned}
These relationships are defined as constraints in an optimization framework. The constraint equations above can be specified by creating group ratio constraints and following the on-screen fields. You can repeat this for illiquid assets after adding the first liquid assets relationships.
Example of creating the relevant group ratio constraint
Finally, we would need to specify that the allocation to the shadow asset and shadow liability must equal to the funding level of the portfolio. Assuming that we are working with a fully-funded long-only portfolio (allocations sum to 100%), we would need to specify the following relationship
$\text{Allocation to Shadow Asset}=1.00 - \text{Shadow Liability}$
Or, to put it simply, Shadow Instruments = 100%. Specify this using a group constraint for the group Shadow Instruments as defined earlier.
Our collection of constraints to reflect these relationships would look like
Summary of constraints for modeling liquidity

## 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 liquidity.
Optimal Allocations accounting for Liquidity

## Further Reading

A good point of departure for understanding how to account for illiquidity and modeling the expected return and risk of shadow assets and liabilities, please refer to the following sources literature:
1. 1.
W. Kinlaw, M. Kritzman, D. Turkington. 2017. "Illiquidity," in A Practitioner's Guide to Asset Allocation, Wiley Finance.
2. 2.
W. Kinlaw, M. Kritzman, D. Turkington. 2013. "Liquidity and Portfolio Choice: A Unified Approach, " Journal of Portfolio Management, Vol. 39, No. 2
3. 3.
A. Lo, C. Petrov, and M. Wierzbicki. 2003. "It's 11pm - Do You Know Where Your Liquidity Is? The Mean-Variance Liquidity Frontier," Journal of Investment Management, Vol. 1, No. 1.
4. 4.
P.A. Samuelson. 1998. "Summing Up on Business Cycles: Opening Address," in Beyond Shocks: What Causes Business Cycles. Federal Reserve Bank of Boston.