Portfolio Allocation for Bayesian Optimization

Bayesian optimization with Gaussian processes has become an increasingly popular tool in the machine learning community. It is efficient and can be used when very little is known about the objective function, making it popular in expensive black-box optimization scenarios. It uses Bayesian methods to sample the objective efficiently using an acquisition function which incorporates the model's estimate of the objective and the uncertainty at any given point. However, there are several different parameterized acquisition functions in the literature, and it is often unclear which one to use. Instead of using a single acquisition function, we adopt a portfolio of acquisition functions governed by an online multi-armed bandit strategy. We propose several portfolio strategies, the best of which we call GP-Hedge, and show that this method outperforms the best individual acquisition function. We also provide a theoretical bound on the algorithm's performance.Comment: This revision contains an updated the performance bound and other minor text change

Portfolio Allocation and Alternative Structures of the Standard Reinsurance Agreement

This paper examines how insurance companies participating in delivery of crop insurance would change patterns of portfolio allocation across reinsurance funds in reaction to the 2005 Standard Reinsurance Agreement. The returns of insurance companies under the SRA are calculated using a simulation model. An heuristic allocation rule is introduced in order to imitate portfolio allocation strategies of participating companies. The main conclusion of the analysis is that the bulk of changes in portfolio allocations are likely to be caused by the introduction of "retained net book quota share" reinsurance rather than adjustments in the cession limits and retention requirements for the Assigned Risk Fund.crop insurance, portfolio allocation strategies, reinsurance funds, Standard Reinsurance Agreement, Risk and Uncertainty,

Portfolio allocation: Getting the most out of realised volatility

Recent advances in the measurement of volatility have utilized high frequency intraday data to produce what are generally known as realised volatility estimates. It has been shown that forecasts generated from such estimates are of positive economic value in the context of portfolio allocation. This paper considers the link between the value of such forecasts and the loss function under which models of realised volatility are estimated. It is found that employing a utility based estimation criteria is preferred over likelihood estimation, however a simple mean squared error criteria performs in a similar manner. These findings have obvious implications for the manner in which volatility models based on realised volatility are estimated when one wishes to inform the portfolio allocation decision.Volatility, utility, portfolio allocation, realized volatility, MIDAS

Portfolio allocation in transition economies

Designing an investment strategy in transition economies is a difficult task because stock-markets opened through time, time series are short, and there is little guidance how to obtain expected returns and covariance matrices necessary for mean-variance portfolio allocation. Also, structural breaks are likely to occur. We develop an ad-hoc investment strategy with a flavor of Bayesian learning. An observation is that often an extreme event will herald a new state of the economy. We use this observation to re-initialize learning when unlikely returns materialize. By using a Cornell benchmark, we are able to show the usefulness of our strategy for certain types of re-initializations.mean-variance allocation; portfolio choice; transition economies

Pricing Illiquid Assets

The present paper investigates the portfolio allocation decisions of an investor with infinite horizon when available financial assets differ in their degrees of liquidity. A model with risk neutral agents allows us to endogenously determine the liquidity premium. With risk averse agents, we develop a nontrivial portfolio allocation problem, which enables us to calculate the demand for an illiquid asset for any given yield premium. We calibrate and numerically simulate both models. Reasonable parameter values imply a liquidity premium of 1.7% for the risk neutral case. In the portfolio allocation problem we find that a reasonable amount of illiquidity can cause a substantial drop of demand for the asset. We are also able to calculate the price discount at which an agent would be indifferent between immediate sale and waiting for a buyer with a fundamentally justified price.

Risk Aversion and Intertemporal Substitution in the Capital Asset Pricing Model

When tastes are represented by a class of generalized preferences which -- unlike traditional Von-Neumann preferences -- do not confuse behavior towards risk with attitudes towards intertemporal substitution, the true beta of an asset is, in general, an average of its consumption and market betas. We show that the two parameters measuring risk aversion and intertemporal substitution affect consumption and portfolio allocation decisions in symmetrical ways. A unit elasticity of intertemporal substitution gives rise to myopia in consumption-savings decisions (the future does not affect the optimal consumption plan), while a unit coefficient of relative risk aversion gives rise to myopia in portfolio allocation (the future does not affect optimal portfolio allocation). The empirical evidence is consistent with the behavior of intertemporal maximizers who have a unit coefficient of relative risk aversion and an elasticity of intertemporal substitution different from 1.

Intra-Daily FX Optimal Portfolio Allocation

We design and implement optimal foreign exchange portfolio allocations. An optimal allocation maximizes the expected return subject to a Value-at-Risk (VaR) constraint. Based on intradaily data, the optimization procedure is carried out at regular time intervals. For the estimation of the conditional variance from which the VaR is computed, we use univariate and multivariate GARCH models. The result for each model is given by the best intradaily investment recommendations in terms of the optimal weights of the currencies in the risk portfolio.Optimal portfolio selection; Value-at-risk; GARCH models; Foreign exchange markets