Equilibrium Returns

Using the Capital Asset Pricing Model for estimating 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. A basket of large stock and bond indices is typically used as a proxy for the market portfolio. The WPA uses either the Windham-defined Global Market Portfolio or a-user specified market portfolio. (See “Market Portfolio Weights” for more information on the Windham Global 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 on the Summary Ribbon.


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. The market portfolio typically consists of a basket of large stock and bond indices that are designed to approximate the global market. As a proxy, the WPA offers the Windham-defined Global Market Portfolio (see “Market Portfolio Weights” for more information). Users may also specify their own market portfolio. Beta is then calculated using regression analysis. A beta greater than one means the return of the security will be more volatile than the market portfolio, while a beta of less than one means it will be less volatile. Beta is also used in calculating the Equilibrium Returns for an asset.

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 for constructing the Windham’s Global Market Portfolio

Asset Class


U.S. stocks


Foreign stocks


Emerging market stocks


U.S. bonds


Foreign bonds


U.S. real estate


Foreign real estate




These market weights were updated on February 1, 2020; the asset values were based on research as of August 1, 2019.

Windham’s capitalization weighted global market portfolio is intended to represent the world’s equilibrium allocation of risky assets. To create this portfolio, we first defined nine asset classes: US Equity, Foreign Equity, Emerging Equity, US Bonds, US Real Estate, Foreign Real Estate, and Commodities. We then used the sources below to value each of these asset classes

  • For equity markets, we used the World Federation of Exchanges total world market capitalization

  • We valued fixed income markets by total value of outstanding issues reported by the Bank of International Settlements

  • We relied on Prudential Real Estate Investors' research to measure the size of the global real estate markets

  • We valued global commodity markets by referring to the production based methodology used by the S&P GSCI Commodity Total Return Index.

  • To avoid overlapping data, we did not treat hedge funds as an asset class

  • Private equity was excluded due to its relatively small in size in relation to global equities