Optimal Reciprocal Reinsurance under VaR or TVaR Constraint

Most existing researches on optimal reinsurance contract are based on an insurer’s viewpoint. However, the optimal reinsurance contract for an insurer is not necessarily to be optimal for a reinsurer. Hence, this study aims to develop the optimal reciprocal reinsurance which satisfies the benefits of both the insurer and reinsurer. Additionally, due to legislative restriction or risk management requirement, the wealth of insurer and reinsurer are frequently imposed upon a VaR (Value-at-Risk) or TVaR (Tail Value-at-Risk) constraint. Therefore, this study develops an optimal reciprocal reinsurance contract which maximizes the common benefits (evaluated by weighted addition of expected utilities) of the insurer and reinsurer subject to their VaR or TVaR constraints. Furthermore, for avoiding moral hazard problem, the developed contract is additionally restricted to a regular form or incentive compatibility (both indemnity schedule and retained loss schedule are continuously nondecreasing).

Hedging with an Edge: Parametric Currency Overlay

We propose an optimal currency hedging strategy for global equity investors using currency value, carry, and momentum to proxy for expected currency returns. A benchmark risk constraint ensures the overlay closely mimics a fully hedged portfolio. We compare this with naïve and alternative hedges in a demanding out-of-sample test, with transaction and rebalancing costs and margin requirements. Other hedging methods generally reduce risk but at a cost. Some tend to short currencies with high returns and all incur substantial costs with frictions, mostly margin requirements and equity rebalancing costs. The proposed strategy uses predictable returns to reduce this cost. It produces a statistically significant 17% gain in Sharpe ratio and an annualized Jensen-α of 0.93% versus a fully hedged benchmark. Notably, most of the implementation costs of the strategy would be incurred by the benchmark anyway. This reduces its marginal cost and highlights a specific synergy of integrating hedging with speculation. This paper was accepted by Gustavo Manso, finance.

DYNAMIC MEAN-VARIANCE PORTFOLIOS WITH RISK BUDGET

We study a dynamic mean-variance portfolio selection problem subject to possible limit of market risk. Three measures of market risk are considered: value-at-risk, expected shortfall, and median shortfall. They are all calculated in a dynamic consistent sense. After applying the technique of delta-normal approximation, we can explicitly solve for the optimal solution and calculate the economic loss brought by the risk budget constraint. With the analytical results obtained, influential factors of economic loss are then explored by which some guidelines on trading practice are proposed. The guidelines are independent of risk measures, and are valuable to both institutions and regulators, for they suggest that an institutional investor would spontaneously obey good investment discipline to avoid potential impact of risk constraint. This result meets the purpose of external regulation from the perspective of market discipline.