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Key points

• Infrastructure debt spreads are reported directly in the primary and secondary markets.
• A risk factor model of credit spreads is estimated for all available price information at each point in time.
• A mark-to-market spread for each debt instruments to be priced at each point in time is estimated.

Unlike unlisted equity investment for which only prices are observable, infrastructure debt spreads are reported directly in the primary and secondary markets. As is the case for the valuation of equity investments, a risk factor model of credit spreads is estimated for all available price information at each point in time.

Next, the estimated risk premia that explain observed spreads are used to compute a mark-to-market spread for each debt instruments to be priced at that time, given their individual factor loading.

Spreads are obtained from primary and secondary market sources and regressed against individual asset factor loadings (betas) to estimate individual factor prices ($\begin{array}{l}\hat{\lambda_k}\end{array}$) in the cross section, at that point in time. Thus, we have:

where $\begin{array}{l}\omega_i\end{array}$ is the measurement noise introduced when estimating $\begin{array}{l}E({s_i})\end{array}$. In other words, following the APT equation (Modern Approach:3), we can write spreads at time $\begin{array}{l}t\end{array}$ as a function of factor loading and factor prices plus some measurement error.

Using a range of statistical techniques (e.g. Bayesian regressions) the value of $\begin{array}{l}\lambda_i\end{array}$ can be estimated for observable transactions at time $\begin{array}{l}t\end{array}$ (the cross section of transactions).

Estimated $\begin{array}{l}\hat{\lambda_k}\end{array}$ then gives us new estimates of spread  $\begin{array}{l}\hat{s_{i}}\end{array}$ for all assets $\begin{array}{l}j\end{array}$ in the relevant period in accordance with their individual betas, including those assets for which no transaction prices were available at the time, so that:

Hence, our approach consists of predicting the prices of risk factors that apply to assets with certain characteristics even though they have not been traded in the relevant period.

## Choice of Risk Factors for Private Infrastructure Debt

The following systematic five key risk factors are used by EDHECinfra to estimate the a model of the expected returns using observable market prices as inputs, as well as several control (dummy) variables that account for sector and business model specific effects.

Factor NameFactor DefinitionFactor Interpretation
SizeOutstanding Face ValueLarger instruments tend to have lower spreads confirming a known stylised fact from the empirical literature on credit spreads (See Strahan 2005 on the non-price characteristics of loans. By this hypothesis, lenders extend larger debt instruments to lower credit risks).
MaturityMaturity

Instruments with longer maturity are more sensitive to interest rate movement attract positive risk premia and higher spread for infrastructure corporates, but also lower risk premia for infrastructure project finance loans. This is also in line with long-standing finding in the empirical literature on spreads, including project finance loans.

Credit RiskProbability of DefaultHigher credit risk as estimated by our borrower-specific credit risk model commands positive positive risk premia and higher spread.
Short Term Rates3-Month interest rate Likewise, controlling for other effects, movements in short-term interest rates impact risk premia
TICCS® Business RiskMerchant, Regulated or Contracted control variablesControlling for business risk families as defined in TICCS® shows that merchant companies systematically attract higher risk premia i.e. expected returns are higher in riskier segments of the infrastructure market.
TICCS® Sector Industrial activity superclass or class control variablesLikewise, a few sectors are found to have systematically higher or lower expected returns even after controlling for the effect of the factors described above e.g. renewable energy projects have systematically lower returns (or higher prices) even for similar size, profits, leverage. etc.