Anders B. Trolle

The Term Structure of Interbank Risk

We infer a term structure of interbank risk from spreads between rates on interest rate swaps indexed to the London Interbank Offered Rate (LIBOR) and overnight indexed swaps. We develop a tractable model of interbank risk to decompose the term structure into default and non-default (liquidity) components. From August 2007 to January 2011, the fraction of total interbank risk due to default risk, on average, increases with maturity. At short maturities, the non-default component is important in the first half of the sample period and is correlated with measures of funding and market liquidity. The model also provides a framework for pricing, hedging, and risk management of interest rate swaps in the presence of significant basis risk.

Keep it Simple: Dynamic Bond Portfolios Under Parameter Uncertainty

We empirically investigate the importance of parameter uncertainty to bond investors. Using a Bayesian approach, we quantify the expected utility loss due to parameter uncertainty from following seemingly optimal dynamic portfolio strategies. Expected utility losses are increasing in the number of term structure factors and the complexity of the risk premium specification. Even with long data sets to estimate parameters, an investor with typical risk aversion is better off following a portfolio strategy implied by a misspecified but parsimonious model than a correctly-specified but difficult-to-estimate three-factor affine model with time-varying risk premia.

On the Relation between Linearity-Generating Processes and Linear-Rational Models

We review the notion of a linearity-generating (LG) process introduced by Gabaix (2007) and relate LG processes to linear-rational (LR) models studied by Filipovic, Larsson, and Trolle (2017). We show that every LR model can be represented as an LG process and vice versa. We find that LR models have two basic properties which make them an important representation of LG processes. First, LR models can be easily specified and made consistent with nonnegative interest rates. Second, LR models go naturally with the long-term risk factorization due to Alvarez and Jermann (2005), Hansen and Scheinkman (2009), and Qin and Linetsky (2017). Every LG process under the long forward measure can be represented as a lower dimensional LR model.

The Price of Interest Rate Variance Risk and Optimal Investments in Interest Rate Derivatives

Recent research on unspanned stochastic variance raises the possibility that interest rate derivatives constitute an important component of optimal fixed income portfolios. In this paper, I estimate a flexible dynamic term structure model that allows for unspanned stochastic variance on an extensive data set of swaps and swaptions. I find that variance risk is predominantly unspanned by bonds, and that the price of risk on the unspanned variance factor is significantly larger in absolute value than the prices of risk on the term structure factors. Consequently, Sharpe ratios on variance sensitive derivatives are about three times larger than Sharpe ratios on bonds or short-term bond futures. These findings are corroborated by an analysis of the Treasury futures market, where the variance risk premium is estimated with a model independent approach. I then solve the dynamic portfolio choice problem for a long-term fixed income investor with and without access to interest rate derivatives and find substantial utility gains from participating in the derivatives market.

Market Structure and Transaction Costs of Index CDSs

Despite a regulatory effort to promote all-to-all trading, the post-Dodd-Frank index-CDS market remains two-tiered. Dealer-to-client trades have higher transaction costs than interdealer trades. The difference is entirely explained by the higher, largely permanent, price impact of client trades. However, transaction costs of interdealer trades vary significantly across trading protocols. Mid-market matching and workup -- both characterized by execution risk -- incur the smallest costs. Dealer-to-client trades typically execute well inside the spread quoted on the interdealer limit order book. Thus, clients who value immediacy could not improve execution with marketable interdealer orders. This may explain the endurance of the two-tiered market structure.

Fed funds futures variance futures

We develop a novel contract design, the fed funds futures (FFF) variance futures, which reflects the expected realized basis point variance of an underlying FFF rate. The valuation of short-term FFF variance futures is completely model-independent in a general setting that includes the cases where the underlying FFF rate exhibits jumps and where the realized variance is computed by sampling the FFF rate discretely. The valuation of longer-term FFF variance futures is subject to an approximation error which we quantify and show is negligible. We also provide an illustrative example of the practical valuation and use of the FFF variance futures contract.