Gerry Tsoukalas

Optimal Credit Swap Portfolios

This paper formulates and solves the selection problem for a portfolio of credit swaps. The problem is cast as a goal program that entails a constrained optimization of preference-weighted moments of the portfolio value at the investment horizon. The portfolio value takes account of the exact timing of protection premium and default loss payments, as well as any mark-to-market profits and losses realized at the horizon. The constraints address collateral and solvency requirements, initial capital, position limits, and other trading constraints that credit swap investors often face in practice. The multimoment formulation accommodates the complex distribution of the portfolio value, which is a nested expectation under risk-neutral and actual probabilities. It also generates computational tractability. Numerical results illustrate the features of optimal portfolios. In particular, we find that credit swap investment constraints can have a significant impact on optimal portfolios, even for simple investment objectives. Our problem formulation and solution approach extend to corporate bond portfolios and mixed portfolios of corporate bonds and credit derivatives. This paper was accepted by Wei Xiong, finance.

Dynamic Portfolio Execution

We analyze the optimal execution problem of a portfolio manager trading multiple assets. In addition to the liquidity and risk of each individual asset, we consider cross-asset interactions in these two dimensions, which substantially enriches the nature of the problem. Focusing on the market microstructure, we develop a tractable order book model to capture liquidity supply/demand dynamics in a multi-asset setting, which allows us to formulate and solve the optimal portfolio execution problem. We find that cross-asset risk and liquidity considerations are of critical importance in constructing the optimal execution policy. We show that even when the goal is to trade a single asset, its optimal execution may involve transitory trades in other assets. In general, optimally managing the risk of the portfolio during the execution process affects the time synchronization of trading in different assets. Moreover, links in the liquidity across assets lead to complex patterns in the optimal execution policy. In particular, we highlight cases where aggregate costs can be reduced by temporarily overshooting one’s target portfolio.

Large-Scale Loan Portfolio Selection

We consider the problem of optimally selecting a large portfolio of risky loans, such as mortgages, credit cards, auto loans, student loans, or business loans. Examples include loan portfolios held by financial institutions and fixed-income investors as well as pools of loans backing mortgage- and asset-backed securities. The size of these portfolios can range from the thousands to even hundreds of thousands. Optimal portfolio selection requires the solution of a high-dimensional nonlinear integer program and is extremely computationally challenging. For larger portfolios, this optimization problem is intractable. We propose an approximate optimization approach that yields an asymptotically optimal portfolio for a broad class of data-driven models of loan delinquency and prepayment. We prove that the asymptotically optimal portfolio converges to the optimal portfolio as the portfolio size grows large. Numerical case studies using actual loan data demonstrate its computational efficiency. The asymptotically optimal portfolio’s computational cost does not increase with the size of the portfolio. It is typically many orders of magnitude faster than nonlinear integer program solvers while also being highly accurate even for moderate-sized portfolios.

Is Operating Flexibility Harmful under Debt

We study the inefficiencies stemming from a firm’s operating flexibility under debt. We find that flexibility in replenishing or liquidating inventory, by providing risk-shifting incentives, could lead to borrowing costs that erase more than one-third of the firm’s value. In this context, we examine the effectiveness of practical and widely used covenants in restoring firm value by limiting such risk-shifting behavior. We find that simple financial covenants can fully restore value for a firm that possesses a midseason inventory liquidation option. In the presence of added flexibility in replenishing or partially liquidating inventory, financial covenants fail, but simple borrowing base covenants successfully restore firm value. Explicitly characterizing optimal covenant tightness for all these cases, we find that better market conditions, such as lower inventory depreciation rate, higher gross margins, or increased product demand, are typically associated with tighter covenants. Our results suggest that ...

Does Crowdfunding Benefit Entrepreneurs and Venture Capital Investors

Problem definition: We study how a new development in entrepreneurship—crowdfunding—interacts with more traditional financing sources such as venture capital investors (VCs) and bank financing. Aca...