Peter H. Ritchken

This commentary provides my own reflections on “Risk Transmission Across Supply Chains” by Sheridan Titman.

A firm that borrows to finance investment can exploit its lender’s inability to observe how much funds are deployed. We examine when this unobservability generates genuine agency costs, and whether and how monitoring can resolve it. We conduct comprehensive analyses on two types of investments: those that cannot shift the distribution of the underlying “states of the world”, termed the exogenous state investment, and those that can shift the distribution to be more favorable in the sense of first-order stochastic dominance (FOSD), termed the FOSD-endogenous state investments. We show that for both investment types, unobservability either leads to under-investment or has no effect. Under-investment occurs only if a high loan repayment reduces the firm’s privately optimal investment level after obtaining the loan, regardless of the investment type. We show that monitored debt, where the bank can verify that all borrowed money is invested, can mitigate this under-investment distortion only if the firm uses all debt and zero internal working capital to finance the investment. Any use of unmonitored internal working capital eliminates the value of monitoring. Our paper alerts firms to the effects of unobservable investment and provides a general diagnostic for determining when investment unobservability matters across different investment environments. For investments where the use of loan proceeds can be easily verified, our analysis shows that monitored debt provides an effective way to reduce agency costs. It also highlights the value of working capital in lowering credit spreads by reducing the lender’s exposure in default.

This paper develops a model of the term structures of nominal and real interest rates driven by state variables representing the short-term real interest rate, expected inflation, inflation’s central tendency, and four volatility factors that follow GARCH processes. We derive analytical solutions for nominal bond yields, yields on inflation-indexed bonds that have an indexation lag, and the term structure of expected inflation. Unlike prior studies, the model’s parameters are estimated using data on inflation swap rates, as well as nominal yields and survey forecasts of inflation. The volatility state variables fully determine bonds’ time-varying risk premia and allow for stochastic volatility and correlation between bond yields, yet they have small effects on the cross section of nominal yields. Allowing for time-varying volatility is particularly important for real interest rate and expected inflation processes, but long-horizon real and inflation risk premia are relatively stable. Comparing our model prices of inflation-indexed bonds to those of Treasury Inflation Protected Securities (TIPS) suggests that TIPS were significantly underpriced prior to 2004 and again during the 2008-2009 financial crisis.

We establish Markovian models in the Heath, Jarrow and Morton paradigm that permit an exponential affine representation of riskless and risky bond prices while offering significant flexibility in the choice of volatility structures. Estimating models in our family is typically no more difficult than estimating term structure models in the workhorse affine family. In addition to diffusive and jump-induced default correlations, default events can impact credit spreads of surviving firms. This feature allows a greater clustering of defaults. Numerical implementations highlight the importance of taking interest rate-credit spread correlations, credit spread impact factors and the full credit spread curve information into account when building a unified model framework that prices any credit derivative.

This paper develops and estimates an equilibrium model of the term structures of nominal and real interest rates. The term structures are driven by state variables that include the short term real interest rate, expected inflation, a factor that models the changing level to which inflation is expected to revert, as well as four volatility factors that follow GARCH processes. We derive analytical solutions for the prices of nominal bonds, inflation-indexed bonds that have an indexation lag, the term structure of expected inflation, and inflation swap rates. The model parameters are estimated using data on nominal Treasury yields, survey forecasts of inflation, and inflation swap rates. We find that allowing for GARCH effects is particularly important for real interest rate and expected inflation processes, but that long-horizon real and inflation risk premia are relatively stable. Comparing our model prices of inflation-indexed bonds to those of Treasury Inflation Protected Securities (TIPS) suggests that TIPS were underpriced prior to 2004 but subsequently were valued fairly. We find that unexpected increases in both short run and longer run inflation implied by our model have a negative impact on stock market returns.

Predictions of firm-level credit spreads based on the current spot and forward credit spreads can be significantly improved upon by using the information contained in the shape of the creditspread curve. However, the current credit-spread curve is not a sufficient statistic for predicting future out-of-sample credit spreads; predictions can be significantly improved upon by exploiting the information contained in the shape of the riskless yield curve. In the presence of credit-spread and riskless factors, other macroeconomic, marketwide, and firm-specific risk variables do not significantly improve predictions of credit spreads. These results have important implications for credit-spreads modeling.

We study the effects of disruption risk in a supply chain where one retailer deals with competing risky suppliers who may default during their production lead-times. The suppliers, who compete for business with the retailer by establishing wholesale prices, are leaders in a Stackelberg game with the retailer. The retailer, facing uncertain future demand, chooses order quantities while weighing the benefits of procuring from the cheapest supplier against the advantages of order diversification. For the model with two suppliers we show that low supplier default correlations dampens competition among the suppliers, increasing the equilibrium wholesale prices. Therefore, the retailer prefers suppliers with highly correlated default events, despite the loss of diversification benefits. In contrast, the suppliers and the channel prefer defaults that are negatively correlated. However, as the number of suppliers increases our model predicts that the retailer may be able to take advantage of both competition and diversification.