Research On Calculation And Applications Of Liquidity-Adjusted VaR For Open-End Funds

Considering the importance of liquidity risk in risk management and defects of current researches on liquidity risk,the paper attempts to improve the method to cal-culate the liquidity-adjusted VaR in order to enhance the level of risk management for open-end funds.To calculate liquidity risk more accurately,we propose 3-α LVaR system and apply it to some aspects of risk management.In daily risk management,open-end fund will encounter uncertain requests of re-demption and purchase.Therefore,fund must employ optimal trading strategy to raise money for the uncertain cash outflow and maximize its expected utility,which makes liquidity risk measure based on optimal trading strategy logical.We believe trading volume consisting of two parts,that is liquidation of fund and spontaneous trading volume—stochastic trading of other traders caused by stochastic information,affects market price.There is broad information asymmetry on financial markets,traders would take advantage of trading volume and other variables to speculate possible in-formation,which provides the possibility of trading volume affecting price.In this paper,we consider two kinds of information,that is liquidity information which does not change the intrinsic value of an asset and asset information which changes the in-trinsic value.Traders will need two kinds of price compensation,one called direct price impact is instantaneous for changing current portfolios,and one called information im-pact is permanent for being at the place of information disadvantage,since they can not infer which kind of information driving the trade because of similar behavior of private information owners.Furthermore,trading volume can be still used to infer information in near future and affect market price in multiple periods,which enlarges the impact of trading volume to future prices.Thus,price process can be decomposed into three parts,that is asset information,direct price impact and information impact.To intro-duce the funding liquidity as a constraint condition,we first determine the maximum cash outflow of the fund at a given confidential level just like the way VaR is calculated,and then look for a trading strategy to meet the maximum cash outflow at another con-fidential level.At last,under certain assumptions,we build an optimization model to maximize the fund’s expected utility which integrates market risk,asset liquidity risk and funding liquidity risk.Under optimal trading strategy,the maximum loss at a given confidential level is the liquidity-adjusted VaR,and we call it 3-α LVaR because of the three confidential levels.To understand the model more clear,we analyze optimal trading strategies sepa-rately by numerical method under single-asset-and-complete-liquidation situation and multiple-assets-and-determinate-liquidation-amount situation with assumptions includ-ing nonnegative amount of assets sold at every period in any feasible strategy,linear price impact,normal distribution and specific variance-covariance structure between variables.Under single-asset situation,optimal trading strategy depends on influence of asset information,direct price impact and information impact.When the expectation of asset information dominates,amounts of asset sold will be increasing if expecta-tion is positive and decreasing if expectation is negative.When the variance of asset information dominates,amounts of asset sold will be decreasing.When direct price impact dominates,amounts of asset sold will be steady.When information impact dominates,amounts of asset sold will concentrate at any point of the liquidation period if expectation dominates,and at the beginning if variance dominates.Under multiple-assets situation,one asset’s liquidation process will depend on other asset’s parameters and the relationships between assets which makes the influence of a parameter more complicated to optimal trading strategy,as well as its own parameters.One parameter’s change will incur influence to the portfolio like the income effect and substitution effect in microeconomics and may likely lead to jump or reversion of optimal trading strategy compared with that under single-asset situation.Therefore,estimation of parameters should be as precise as possible to prevent calculation of VaR deviating largely from the real value.Based on optimal trading strategy,we propose the formula to calculate 3-α LVaR,which is still a quantile.Under assumptions like linear price impact,normal distri-bution,specific variance-covariance structure between variables and others,we calcu-late 3-α LVaR and conduct sensitivity analysis which shows 3-α LVaR is quite robust when one parameter changes,however not so robust when lots of parameters change.Compared with conventional VaR ignoring funding liquidity,3-α LVaR is more con-servative,which can be widely applied to many areas,such as portfolio selection and risk-adjusted return of capital.Finally,the paper demonstrates the calculation process of 3-α LVaR of a stock based open-end fund using high-frequency data in China’s stock market.Related pa-rameters are estimated separately by regression with pooled data model and panel data model.Given liquidation amount being 6%the value of original portfolio,3-α LVaR is bigger than VaR without liquidity 10.06%and 16.62%and VaR only considering asset liquidity 2.44%and 6.41%respectively under pooled data model and panel data model.Hence,liquidity risk is important in risk management and should be valued more when market condition is worse.Then,we calculate the investment efficiency of the origi-nal portfolio and find it very high under both data processing method compared with optimal portfolio given the same portfolio value.