In a recent EDHEC-Risk Institute position paper (Blanc-Brude, 2014), we argue that  improving long-term investors’ access to  infrastructure requires the creation of new  performance measurement tools that  can inform the asset allocation decisions  of investors in infrastructure, as well as  provide a sound basis for the calibration of  prudential regulatory frameworks. Without the development of performance measures adapted to long-term investment in illiquid assets, investors and regulators struggle to integrate assets like infrastructure debt into their respective risk and return frameworks.

In the same paper, we describe a roadmap to create long-term investment benchmarks in infrastructure. We propose to address the challenges of illiquid investment performance measurement by focusing on those underlying financial instruments that are more frequently used in the development of new infrastructure projects, for which tractable valuation models can be developed that take into account their illiquid nature and can deal with the paucity of available data.

Indeed, measuring the performance of illiquid infrastructure investments implies two significant challenges: first, illiquidity implies that only limited information can be gleaned from market prices and, second, given the large size of each individual instrument, little private data is available to any single individual investor.

Without market prices or large cash flow datasets, performance measurement is not straightforward. But even if limited information  is available for research today, it  is our premise that aiming to develop the  best possible knowledge of the performance  of long-term investment in infrastructure  — conditional on the information available  today — and allowing for the possibility  of learning as new data becomes available,  is an improvement of the current state of  complete absence of relevant performance  measures.

In this paper, following our roadmap, we focus exclusively on private project finance (PF) loans, as they constitute by far the  largest proportion of illiquid infrastructure  project debt, and are well-defined since  Basel-II, providing us with an uncontroversial  setting to model expected cash flows.

Project finance loans are also the most  relevant to long-term investors who seek  to access a type of instruments previously  unavailable to them (as opposed to  corporate bonds), since PF is a unique  form of corporate governance that creates  significant and extensive control rights for  lenders through embedded options and debt  covenants.

For example, debt covenants prohibiting  equity holders from raising more cash  through new debt or equity issuance to  service existing debt can be expected to  impact the default mechanism in infrastructure  project finance; while debt holders’  option to either restructure the debt upon  default or take over the project company,  can have a significant influence on expected  recovery rates and the risk return profile of  PF debt.

Crucially, while project finance loans are  not collateralised since the investment is  structured on a non-recourse or limited recourse  basis, they have a “tail” i.e. the  difference between the original maturity  of the project loan and the life of the  infrastructure project. The free cash flow  of the firm available during that period  acts as a form of collateral. In certain  states of the world — corresponding to a  breach of covenant — lenders have control  rights that allow them to restructure a loan  and use its tail to maximise their recovery  rate. The value of the loan’s tail, as well  as the relative size of liquidation and restructuring  costs of the project company,  can thus be expected to have a significant  impact on performance.

Because PF loans have unique characteristics,  existing loan valuation models are  inadequate because they not only fail to  take into account the effects of debt  covenants and embedded options, but also  do not incorporate the dynamic nature  of the credit risk profile, and often make  ad hoc assumptions regarding probabilities  of default and loss given default. Option based  valuation models used for corporate  securities also cannot be directly applied to  project finance loans.

If the embedded options and covenants  found in PF debt are not taken into account,  infrastructure debt valuation is likely to be  off by an order of magnitude. In this paper,  we develop an endogenous model of credit  risk in order to derive more relevant and  precise performance measures.

Finally, existing approaches typically fail to  produce the risk-return measures that are  relevant to risk management, strategic asset  allocation, and prudential regulation.

Objectives and Approach 

The objectives of this paper are:

1. to determine the most appropriate pricing model for infrastructure project finance loans;
2. to design a methodology that can be readily applied given the current state of empirical knowledge and at a minimum  cost in terms of data collection;
3. to derive the most relevant return and risk measures for long-term debt investors: expected loss, expected  recovery rates, loss given default, valueat-  risk (VaR), expected shortfall or CVaR,  duration, yield, and z-spread;
4. to define the minimum data collection requirements for infrastructure project loan valuation that can nevertheless  inform a robust and academically  validated pricing model.

In this paper, we show that the valuation of illiquid infrastructure project debt taking into account its illiquidity and the absence of market price feedback can be done using advanced, state-of-the-art structural credit risk modelling, relying on a parsimonious set of empirical inputs.

In turn, following the roadmap defined in  Blanc-Brude (2014), the data required to  evaluate the performance of illiquid infrastructure  project debt can provide the basis  for a reporting standard for long-term  investors, which can also be used to  populate a centralised database, thus  addressing the scattered nature of existing  empirical observations, and allowing for the  ongoing monitoring of the performance of  long-term infrastructure investments.

As for any security, the valuation of project  finance loans consists of modelling or  observing cash flows and deriving their  present value. However, available empirical  observations are limited in time (for example  a project may have a 30 year life but we  cannot realistically collect more than 10  years of cash flows) and in the cross-section  (each country only has so many operating  toll roads or power plants relying a given  contractual and financial structure).

Thus, we devise a two-step modelling  process: first, we model the cash flows  of generic types of financing structures  that are commonly found in infrastructure  project financing.

Thus, by partitioning the investable universe  of infrastructure projects into tractable  cash flow models characterised by well-documented  parameters — such as initial  leverage, amortisation profile, and typical  average debt service cover ratio throughout  the project lifecycle — we can identify  reasonably homogenous families of  project structures, which we can be  considered to correspond to a single  underlying cash flow process.

Second, given a generic cash flow model,  we build a valuation model to derive  the relevant return and risk measures.  This model takes into account the fact that  illiquid markets with large transaction costs  — as is the case of infrastructure project  debt — do not lead to the formation of  unique prices, or valuation measures, but  instead that the value of the same asset  must lie within a range determined by the  characteristics and preferences of individual  investors.

Thus, our methodology also determines  “arbitrage bounds” or limits on possible  valuations for illiquid infrastructure debt  which asset values can be expected to lie.

Next, we describe each step in more details,  before presenting our main results.

Cash Flow Model 

The task of projecting future cash flows  to project finance lenders first requires to  determine the future free cash flows to the  project company before deriving cash flows  to lenders.

The free cash flows of the project company  — often referred to as the Cash Flow  Available for Debt Service or CFADS — is  private information and not easily observed.  Instead, we focus on the Debt Service  Coverage Ratio (DSCR), which is typically  monitored and recorded by infrastructure  PF lenders. Indeed, knowledge of the distribution  of the DSCR at each point in time,  combined with the Base Case Debt Service,  which is also easily observable at the time  of financial close, can be used to infer the  expected value and volatility of the CFADS  of a typical infrastructure project.

In this paper, we focus on two generic  project types, which embody a large number  of real-world infrastructure projects and  their associated debt securities. We define  two families of DSCR dynamics called 1)  merchant infrastructure and 2) contracted  infrastructure.

Merchant infrastructure refers to those  projects that generate revenue by selling  their output or service in a market, and  hence are exposed to market risks, while  contracted infrastructure projects receive  a contracted revenue stream in exchange  for providing a pre-agreed output or service,  and bear little to no market risk.

Examples of merchant infrastructure  projects may include a power plant that  sells electricity at market prices or a road  collecting tolls from users. Examples of  contracted projects may include schools  and hospitals that receive a fixed payment  from a government entity upon the  satisfactory delivery and maintenance of  an infrastructure, or an energy project  financed on the back of take-or-pay  purchase agreement.

These two project types have different  underlying business risk, and as a consequence,  they are financially structured in  different manners. Merchant infrastructure  projects are generally structured with a  rising mean DSCR, and a longer tail. A rising  DSCR implies that lenders get paid faster  than the equity owners, and a longer tail  increases the value of lenders’ security. In  other words, lenders demand an increasing  mean DSCR and a longer tail to protect  themselves against a higher and increasing  DSCR volatility, which results from higher  revenue risk.

In contrast, contracted projects are structured  with a flat DSCR and shorter tails,  as lenders demand less protection against  default due to lower expected underlying  revenue risk.  Of course, other generic project financial  structures exist, even though they tend to  be a combination of these two types, e.g.  shadow toll roads collect a volume-based  income paid typically by a government.

For each generic type, we initially model  the CFADS of a generic project financing  structure, using typical values for initial  leverage, tail length, contracting periods,  etc. and reasonable parameter estimates  of the DSCR. In due course, once enough  empirical observations become available,  DSCR parameters can be updated using  Bayesian inference techniques as suggested in Blanc-Brude (2014) and detailed in Blanc-  Brude and Hasan (2014).

Once the future CFADS distribution is  known, projecting cash flows to debt holders  is possible if the debt schedule is also known.  But while one debt “base case” schedule is  determined at financial close and is known  ex ante, we know that restructurings or  “work outs” following a breach of covenant  are common in project finance, which can  change the debt schedule. Thus, we need to  model these changes in the debt schedule  to be able to determine total cash flows to  lenders in all possible states of the world.

To take into account these potential  changes in the debt schedule, we model the  debt renegotiation process to determine  the outcome of restructuring after either  a technical (covenant-driven) or a hard  default (of payment). With technical  defaults, lenders can only try to maximise  the recovery rate of the original debt  given the tail, whereas hard defaults give  them more options, including exiting the  relationship with original equity investors  and taking over or selling the project or its  debt.

The new debt service is determined by taking  into account what each party would lose in  the absence of a workout. In our dynamic  renegotiation model, if there is no space  for renegotiation upon a hard default, the  project is taken over by lenders (which may  seek a new equity investor). Conversely,  restructuring must take place as long as  the value of either debt or equity postrestructuring  is higher than in the absence  of renegotiation i.e. as long as lenders can  get more than their exit value and equity  holders more than nothing, a new debt  schedule is agreed and maximises recovery  in the tail.

Valuation Model 

Thus, given a model of expected cash flows  taking into account the conditional distribution  of the DSCR at time t and the  outcome of renegotiations between debt  and equity holders upon technical and hard  defaults, we can determine the cash flows to  project finance lenders in every future state  of the world.

To value these cash flows, we take a  so-called structural approach. Structural  models present the advantage of calculating  the value of firm’s securities as a function  of their fundamentals. Credit risk measures,  such as the probability of default, loss given  default, value-at-risk &c are determined by  an explicit mechanism corresponding to a  value threshold, instead of being exogenously  specified.

In project finance, the thresholds that  lead to credit events are well defined as  a function of the DSCR and monitored,  that is, observable, which is a substantial  improvement on most structural credit  models applied to regular corporate debt.  In particular, we show that distance to  default can be expressed as a function of  the distribution of the DSCR.

Most cash flow discounting models use  a risk premium to be added to the time value of money (the risk-free rate) in order  to compute a value. However, in structural  models of credit risk, the heterogeneity  of investors’ preferences is incorporated  through risk-adjusted or risk-neutral probabilities.  For risk-averse investors, risk-neutral  probabilities penalise future cash flows by  decreasing their expected value under the  equivalent risk-neutral measure.

That is, instead of discounting actual  expected cash flows at a premium to the  risk-free rate, they are decreased under the  risk neutral measure and then discounted at  the risk-free rate. The more risk-averse an  investor, the higher the premium demanded  for each unit of risk, and the lower  the expected value under the risk-neutral  probability measure.

This technique is routinely used in option  pricing models: the required price of risk  (and the risk-neutral probabilities) are  determined such that the expected present  value of the risky asset’s cash flows under  the risk-neutral measure is equal to the  observed market price of a portfolio with  an equivalent payoff.

In the absence of market prices however,  as is the case with illiquid infrastructure  debt, there is no unique value to which  the discounted risk-adjusted cash flows  should correspond. Instead, incorporating  investors’ risk preferences to determine the  value of expected cash flows leads to a  range of values, since the required price of  each unit of risk must depend on individual  investors’ unique circumstances, including  regulatory requirements, the diversification  level of the existing portfolio or the  structure of their liability.

In this case, we argue that the required  price of one unit of risk (the required Sharpe  or reward-to-risk ratio) should always lie  in an approximate arbitrage band of [0; 2]  that rules out investments that are either  too risky for any investor to take, or too  attractive not to be arbitraged away despite  the illiquidity of these instruments.

The lower limit of the band corresponds to  an investor that requires no premium above  the risk-free rate for bearing the risks in PF  loans. This could be the case for risk-neutral  investor. The upper limit corresponds to an  investor that requires a premium of 200  basis points for bearing each unit of risk (one  standard deviation of the DSCR) taken in a  PF loan.

The combination of both cash flow and  valuation models allows us to evaluate  the performance of project finance loans  from the perspective of different individual  investors.

Finally, the value of expected cash flows  under the risk-neutral measure can be  determined using the Black-Cox decomposition,  which divides a security’s cash  flows into four components: 1) its payout  at maturity, 2) its payout if the debt  reorganises at a lower boundary i.e. default,  3) its payout if the debt is restructured at  an upper boundary i.e. refinancing, 4) its  payout before reaching any of these boundaries

The present value of these four payouts  determines the total value of a project  finance loan at each point in its life given  all the paths that the debt cash flows can  take in different states of the world.

Results 

Here, we report results for a typical investor  requiring a Sharpe ratio of 1 to invest  in illiquid infrastructure debt and typical  parameters detailed in chapter 4.

A low but dynamic risk profile

We find that the debt of both types of  generic infrastructure projects discussed in  this paper — merchant and contracted —  exhibit highly dynamic risk profiles.

In the case of merchant infrastructure  projects, the probability of both technical  and hard defaults (PD), and of hard  defaults only (Moody’s definition) shown  on figure 1, goes down sharply post  construction, while expected loss (EL) and  extreme losses (VaR,cVaR) tend to rise  throughout the loan’s life. Similarly, in the  case of contracted infrastructure projects,  while PD stays almost constant during the  loan’s life, the severity of losses increase  with time.  The diverging trends in the distribution  of defaults and losses are a consequence  of restructurings upon defaults. Even if  defaults are concentrated in a certain period  of time, debt restructuring can spread losses  over the entire life of the project. Hence,  losses tend to increase with time, as the  cumulative number of defaults (and hence  restructurings) accrue losses near the end  of loan’s life. However, part of the losses  suffered during the loan’s life are , recovered  in the loan’s tail, thus reducing the overall  expected loss.  Indeed, risk levels are found to be relatively  low and recovery relatively high. While EL  never rises above 2%, VaR and CVaR while  they increase towards the end of the loan’s  life as the value of the tail is exhausted,  never reach levels higher the 6% and 10%  respectively, while expected recovery rates  are always in the 80% to 100% range, as  shown on figure 2.

IMAGE: (P24 Fig 1), (P24 Fig 2)

Hard default frequencies match reported averages

The different aspects of the projects’ risk  profile can largely be explained by their  DSCR profiles, tail values, and the costs of  exit relative to the cost of renegotiation for  lenders.

The rising DSCR profile of merchant infrastructure  implies that the project’s likelihood  of default decreases faster in time. If a  loan survives the first few years after the  construction stage, the increasing mean  DSCR more than offsets the increasing  DSCR volatility, making it less likely that  the project will default in the future. For  contracted infrastructure, flat DSCR profile  implies that the probability to default barely  changes in time, though it stays at a very  low level due to lower DSCR volatility.

Moreover, when using Moody’s definition  of default in project finance — by which  each loan is only allowed to default once (Moody’s, 2013) — we find marginal default  frequencies in line with reported empirical  estimates, trending downwards from just  under 2% at the beginning of the loan’s life  to almost zero after ten years, in the case  of merchant infrastructure, and flat at 0.5%  for contracted projects.

While Moody’s (2013) does not explicitly  differentiate between merchant and  contracted projects, its main sample is  effectively dominated by merchant or  part merchant projects, yielding the oftreported  decreasing PD profile reproduced  here on page 32; while in a separate study  focusing on PPPs — effectively contracted  infrastructure — Moody’s report very low  PD in the range predicted by our model.

Low credit risk and high recovery

The loss profiles for the two DSCR families  shown on figure 2 are similar insofar  as expected losses (EL) are very low and  then increase towards the maturity of the  loan, but differ in terms of the behaviour  of extreme losses. Extreme losses (VaR  and cVaR) increase almost linearly towards  the maturity of the loan for contracted infrastructure projects, but stay relatively  constant near the loan’s maturity for  merchant projects.

The increasing EL for both DSCR families  is a consequence of cumulative haircuts  received upon hard defaults in all the prior  periods. The increasing VaR and cVaR in the  case of flat DSCR family are due to a lower  tail value, and constant leverage in time, the  combination of which implies that near the  loan’s maturity the remaining value of the  project may not be sufficient to offset losses,  making defaults more severe.

Figure 3 shows the evolution of the loss  given default (LGD) i.e. one minus the  recovery rate, as a function of time.  Recovery rates are very high (always above  85%).

For merchant infrastructure (rising DSCR),  LGD decreases in time, as the distribution  of losses does not change much during  the loan’s life. For contracted infrastructure  however (flat DSCR), the LGD first increase,  and then decrease.

IMAGE: (P24 Fig 3)

This increase in LGD for the flat DSCR family  arises from the increasing severity of losses  near the maturity of the loan as observed  in figure 2: mean EL, VaR, and cVaR all  increase linearly towards to maturity of  the loan. Hence, LGD, which is affected  by the full distribution of the losses and  not just by mean losses, increases in time  as we approach the period of the most  severe losses. As we move through time,  expected losses continue to increase due to  the more extreme losses getting nearer, but  also decrease due to the potential losses  that now lie in the past and were not  realised. At some point, the latter effect  dominates and LGD begin to decrease.

Value is driven by lenders’ exit option and monitoring

Importantly, the size of losses for both  DSCR families is primarily influenced by  lenders’ exit value net of exit costs. Exit  costs determine the aggregate loss of value  (debt+equity) if the debt owners take over  the project company upon a hard default  and do not renegotiate with the original  equity investors.

The higher the exit costs, the lower the value  that lenders can obtain by taking over the  project company after a hard default, and  the lower their bargaining power in negotiations  with original equity holders.

This is primarily a consequence of the  unsecured nature of project finance debt,  which makes the value of project company  strongly dependent on the owners’ ability to  run it. In the absence of expertise required  to run the project company, the lenders  are likely to be forced to offer concessions  to equity holders to benefit from their  ability to run the firm. Hence, lenders may  have to suffer losses even in otherwise low  risk projects like contracted infrastructure  because replacing the equity owners upon  a hard default, while it is in their power, can  be very costly in some cases.

As a consequence, ongoing monitoring of  the SPE conducted is required of lenders  in project in order to avoid ever having to contemplate exercising their option to exit,  in particular, technical default triggers (e.g.  a low DSCR or loan-life cover ratio) allow  lenders to intervene and maximise their  recovery rates long before more expensive  options to restructure, sell or liquidate the  SPE ever arise.

A DSCR-driven yield profile

The yield curve for both types of project  debt is driven by two forces: the increasing  severity of losses towards the end of the  loan’s life pushes up the yield since the  discounted value of expected cash flows  is further reduced, while the sequential  resolution of uncertainty as maturity  approaches pulls it down. The actual yield  curve shown on figure 5 balances the two  effects.

IMAGE: (P24 Fig 5)

Initially the yield goes up as we get closer to  the region where larger losses are likely to  be accrued and the first effect dominates.  However, as we move past this region, the  probability of default during the remaining  life of the loan goes down and expected  recovery goes up: at one point the yield  starts to decrease, as the second effect  begins to dominate. In the case of rising  DSCR projects, for which PD decreases  more sharply and losses are more evenly  distributed, uncertainty is resolved faster,  and the yield begins to go down sooner in  the project lifecycle.

A credit vs. duration risk trade-off

Finally, we also illustrate how the ability to  reschedule debt upon technical and hard  default creates a trades off between credit  risk and duration risk. That is, to reduce  the credit losses upon default, investors  have to extend the maturity of their loan  further in the tail, and have to bear a higher  interest rate risk due to a higher duration.  This trade-off can be quantified, as shown  on figure 4, and may help determine the  optimal debt schedule for an investor with  a given aversion to credit and interest rate  risks.

IMAGE: (P24 Fig 4)

Next Steps: Data Collection and Portfolio Construction 

Thus, with a parsimonious set of inputs  that consists of the parameters of the  DSCR distribution across different types of  generic projects, the base case debt schedule  and a number of variables defined in the  covenants at financial close, infrastructure  project finance loans can be valued at any  point in time, and their risk/return profile  can be constructed spanning the entire life  of the loan.

In other words, by partitioning the infrastructure  project finance universe into a  parsimonious set of tractable cash flow  models, which can be calibrated using  available data in due course, we can  create the building blocks thanks to which  the systematic performance of different  exposures to infrastructure debt can be  identified, and later portfolio (benchmark)  construction can take place.

In this paper, we deliver the first three  steps of the roadmap defined in Blanc-  Brude (2014) with respect to infrastructure  debt investment: defining the most relevant  underlying financial instrument, designing a valuation framework that is adapted to its  private and illiquid nature, and the determination  of a standard for data collection and  investment performance reporting in infrastructure  investment.

Next steps include active data collection  to better calibrate our model of DSCRt  dynamics, before moving to the portfolio  level of the analysis, towards long-term  investment benchmark in infrastructure  debt.