# Equilibrium Returns

Equilibrium returns are estimated using the Capital Asset Pricing Model (CAPM). CAPM assumes that an asset’s return in excess of the risk-free rate is proportional to the asset’s sensitivity to the non-diversifiable risk of the market (this sensitivity is also referred to as Beta).

The CAPM postulates that systematic risk cannot be removed through diversification; however, idiosyncratic risk is diversifiable. Therefore, when markets are in equilibrium, investors are only compensated for systematic risk and should seek to remove all idiosyncratic risk through diversification.

The expected return of an asset is a function of that asset’s sensitivity to the market portfolio, the expected return of the market portfolio, and the expected return of a risk-free asset. Global diversified asset class indices are typically used as a proxy for the market portfolio. The WPA provides the option to use the [Windham-defined Global Market Portfolio](#the-windham-global-market-portfolio) or a user-specified market portfolio. 

The equilibrium return is calculated as the risk-free rate plus the beta of a given asset multiplied by the overall risk premium of the equity market. Users can specify market assumptions and the risk-free rate in the Parameters box on the Return Estimation screen or in the market assumptions field of the Home tab (Summary Ribbon).

### Beta

Beta is the measure of security price volatility relative to a market portfolio, i.e. the component of an asset’s risk that cannot be diversified away. As a proxy, the WPA defaults to using the [Windham-defined Global Market Portfolio](#the-windham-global-market-portfolio) as a starting point, however, users may also specify their own market portfolio composition. Beta is then calculated using regression analysis. A beta greater than one means the return of an asset will be more volatile than the market portfolio, while a beta of less than one means it will be less volatile.

## The Windham Global Market Portfolio

We suggest using a global market capitalization weighted portfolio. The following are estimates of a market cap weighted portfolio of stock, bonds, and commodities used in the WPA.

| Asset Class                    | Weights |
| ------------------------------ | :-----: |
| U.S. stocks                    |  34.7%  |
| Foreign stocks (developed)     |  13.6%  |
| Emerging markets stocks        |   6.0%  |
| Global bonds                   |  43.4%  |
| Global real estate (developed) |   1.1%  |
| Commodities                    |   1.3%  |

{% hint style="info" %}
These market weights were updated on January 31, 2025.
{% endhint %}

Windham Labs' capitalization weighted global market portfolio is our view on a proxy for the global equilibrium allocation of investable risky assets. To create this portfolio, we first identify seven asset classes: U.S. stocks, foreign stocks (Non-U.S. developed markets), emerging markets stocks, global bonds, global real estate (developed markets), and commodities. We then used the sources below to value each of these asset classes:

* For **stocks**, we used the market capitalization for MSCI USA, MSCI World ex-US, and MSCI Emerging Markets.
* For **bond** markets, we use Bloomberg Barclays Global Aggregate (Hedged) Index.
* For **global real estate**, we use FTSE NAREIT Global.
* For **commodities**, we refer to [Zdoeswijk, Lam, Swinkles 2017](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2978509) and use their global market portfolio value, the commodity allocation, and the Bloomberg Commodity Index total return to extrapolate data since 2017 (base year).
* To avoid overlapping data, we do not treat **hedge funds** as an asset class.
* We exclude **private equity** considering its relative small size to global equities and lack of direct access.


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