# 1.4.2 Equity risk premia

**Key points**

**Standard approaches**in public markets consist of estimating risk factor loadings (*betas*) first, then risk factor prices (*lambdas*). This is the standard Fama-McBeth approach used to develop numerous factor models.With private, illiquid assets, factor loadings can be estimated using a bottom-up approach and the firm's financials and other relevant and observable characteristics.

Next, using realised secondary market transactions or a well-defined listed proxy, observable

**expected returns (e.g. deal IRRs) can be decomposed into time series of risk factor premia**.Finally, once risk factor premia have been estimated for each valuation date,

**a firm-specific, mark-to-market risk-premia**can be computed for any private asset for which factor loadings (e.g. financials) are observable at that time.The

*Infra*Metrics® model uses**5 key risk factors**(Size, Profits, Investment, Leverage and Term) and a range of control variables to estimate the price of systematic risk factors in the private infrastructure equity market.

## Standard Approach in Public Markets

The premise that a limited number of factors explains the majority of investment risk found in financial securities makes the development of robust and persistent factor models of returns an important part of investment risk management.

With frequent trading and observable prices and returns, factor models can be used to decompose portfolio risk according to common factor exposures and to assess how much of the portfolio's returns are attributable to each common factor exposure.

The standard approach in both academic and industry factor models is the two-step regression method put forward by Fama and McBeth (1973).

In a first step, asset returns are regressed against one or more factor time series to determine factor exposures or

*betas*.In a second step, the cross-section of portfolio returns is regressed against factor exposures at each time step, to give a time series of risk premia coefficients for each factor. Fama and McBeth then average each factor coefficient to get a time series of factor prices (

*lambdas*).

Hence, the authors' approach consists of estimating two sets of coefficients, since both the asset betas or factor loadings *and* the market prices of each risk factor in the APT pricing equation are unknown and must be estimated using time series of asset prices/returns. Once individual factor loadings have been estimated over time, factor prices (*lambdas*) are estimated in the cross-section of returns given estimated asset betas.

This is possible because individual security prices are observable over time in sufficiently long time series as well as in the cross section in sufficiently large numbers. Fama and McBeth use the two dimensions of the data available to estimate first the betas and then the lambdas of the APT framework.

_{Fama, E.F. & MacBeth, J.D. (1973). Risk, Return, and Equilibrium: Empirical Tests. }_{Journal of Political Economy}_{, 81(3), 607–636. }_{http://www.jstor.org/stable/1831028}_{ }