Allocating the Tracking Error for the Multi-Asset-Class Fund by Reconciling Bottom-Up Model with Top-Down Model
In the management of benchmarked funds, managers can incur tracking errors (TEs) in the attempt to create alphas. Our work focuses on a multi-asset-class fund that is constrained not only by a limit on the portfolio's TE, but also by the limits on the asset classes' TEs. We are interested in finding the optimal TE utilized by each asset class, so that the portfolio achieves the maximum expected alpha without violating the TE limits. (The optimal TEs are depicted as the blue dots in the graph.) This problem, if mis-specified, can lead to a mis-allocation of TEs to the asset classes. (The green dot, which is far away from the blue dots, shows a mis-allocation of TEs.) We find that the key for a successful reconciliation is to approximate the correlation structure of each pair of asset classes by an affine function (shown as the grey plane). Our method proves successful in determining a more optimal use of TEs by asset classes. (The outcome of our method is shown as the pink dots, which are much nearer to the blue dots.)
The Hybrid Pareto Distribution, Implied Risk-Neutral Density and Option Pricing
This study develops a new European option pricing model based on the Extreme Value Theory (EVT). In particular, we propose to use Hybrid Pareto (HP) distribution to model loss distribution under the risk-neutral probability measure, and derive closed-form pricing formulas for call and put options. Using the S&P 500 index data, we compare the goodness of fit of our model and a benchmark model in which losses are assumed to follow the Generalized Extreme Value (GEV) model proposed by Markose and Alenton (2011). The results show that our proposed HP model can improve the fit over the GEV model for at-the-money options with 30 days to expiration.
Optimal Entry, Exit and Stop-Loss Levels for Pairs Trading Strategies with an Application to Technology Hardware, Storage & Peripherals Sector
In this study, we develop a pairs trading strategy with optimal entry, exit, and stop-loss levels. The strategy involves selecting pairs of stocks and selecting optimal levels for entering and exiting the trade. We apply the cointegration method to find the combination of stocks and then model them with the Ornstein–Uhlenbeck process to find the probability and expected time to reach exit or stop-loss level. With a transaction cost and a cost of holding short position, we derive the expected total payoff function per one trade cycle of the strategy. The optimal values are obtained by maximizing the expected total payoff function per trade cycle. The stocks in Technology Hardware, Storage & Peripherals sector are selected in our study. The backtesting results of our strategy are compared with a benchmark model. The empirical results show that our strategy gains more cumulative return than the benchmark in total testing period from 2004 to 2019. However, the number of trades during the testing period is quite small so the robustness of the higher performance is not clear. Our analysis suggests that the entry, exit, and stop-loss levels are increasing in the volatility of the spread, and are decreasing in the speed of reversion of the spread, and the cost of holding short positions.
A Reinforcement Learning Model for Lending Problems with Limited Budget and Insufficient Data
Traditional lending policy requires sufficient data for making lending decisions, therefore, some small companies could not access to the fund. In this study, we propose a decision making model that can decide whether to accept or reject a sequence of unfamiliar loan applications while having a limited budget. Our model does not have any knowledge about the incoming loans, therefore, it can predict the default probability with low accuracy at the beginning. The model can learn by observing the outcomes of the accepted loans. The model’s budget increases every time the model accepts a fully paid loan and decreases when the model accepts a defaulted loan. The objective of our model is to maximize the final budget. By using the reinforcement learning method, we propose a decision making model that takes the current budget and model accuracy into consideration when making decisions. Based on simulated data, the results show that our model yields a better performance compared to a traditional default prediction model. For the real data, our model performs well in some type of loans.
Bank Characteristics and Financial Contagion through Interbank Liability and Market Channels
In this research, we model the systemic risk in a banking system using an equilibrium approach where banks in the financial system are risk averse and aim for optimal illiquid asset holdings. Contagion can occur through interbank lending and changes in the asset price. We show that in the face of financial contagion, the incomplete financial system, such as a ring topology, that keeps banks with greater risk aversion coeffcients away from loss can amplify a fire-sale effect as they contribute low level of demands toward the market and act as poor buyers. In contrast, in a highly interconnected financial system such as complete and star topologies, banks with greater risk aversion coeffcients, instead, become more useful as shock absorbers and thus, soften a fire-sale effect. On the other hand, the incomplete financial system, such as a ring topology, that keeps banks with low risk aversion coeffcients away from loss can help soften a fire-sale effect as they are able to contribute high level of demand toward the market. In contrast, a highly interconnected financial system, such as complete and star topology, instead, renders banks with low risk aversion coeffcients less supportive as potential buyers as they reduce their demand more intensely due to the transmitted loss, and hence amplifying the fire-sale effect. Our results thus highlight that the same risk averse banks that contribute to resilience under certain financial systems may function as significant sources of fire-sale effect under others.