Research On Black-Litterman Based Optimal Pension Asset Allocation Models

The pension is the most important component of the social security system of aging people.Due to the increasing trend of population aging and social factors as well as economic factors,Chinese pension insurance system has been facing a serious of difficulties on pension payment in recent years.Under the double pressure of the demographic transition and the funds shortage,China gradually opens up the investment and operation on pensions as a way to maintain the sustainable operation on the pension.Chinese started the allocation of the pension asset lately,the research and practice on the allocation of the pension asset is still in its initial stage,which is a brand new attempt.The research on asset allocation and investment strategy and the application of asset allocation theory on the pension investment,can not only enriches the research results of financial markets and asset allocation theory applied to Chinese capital market,but also provides valuable investment suggestions on optimizing pension investment operations.Therefore,there is a great theoretical value and practical significance of the study on asset allocation strategy of Chinese pensions,the improvement on the returns from the pension investment which preserves and increases the value of pension assets as well as reduces the pension payment risks caused by the population aging.Under the framework of the modern portfolio theory,this paper focuses on the optimization of asset allocation of the pension.Firstly,associating the VARMA(vector auto-regressive moving average)model with the GARCH(generalized auto-regressive conditional heteroskedasticity)model and the BL(Black-Litterman)model,this paper establishes VARMA-GARCH-BL(V-G-BL)asset allocation model.According to the characteristics of long investment period of pension asset allocation,the V-G-BL model is improved on the vital parts such as the risk estimation,the income prediction and the viewpoint matrix,which establishes different V-G-BL pension asset allocation model that respectively considers time-varying covariance,long-term income prediction,and macroeconomic factors.Furthermore,expanding and popularizing the V-G-BL pension asset allocation model under CVaR risk measurement.Finally,a numerical example based on the historical data of our country is analyzed to conclude theoretical and empirical results.The main research contents of this paper are as follows:(1)For the problem of transforming the short-term covariance to the long-term covariance,a V-G-BL pension asset allocation model which considers the time-varying covariance is proposed.The BL model combines the equilibrium returns of assets with the opinions of investors,and then obtains the estimation of the expected returns from the assets,and finally the mean-variance model is used to obtain the decisions in the asset investment.The market equilibrium return of an asset is normally calculated by inverse optimization,and the covariance matrix of an asset is the key of the inverse optimization calculation.The decision of the asset allocation has a long duration,but due to the limited scanty historical data of the asset,the calculation of the long-term covariance matrix directly through historical data will cause the problem of insufficient sample data,which leads to the failure of covariance matrix estimation.The common solution is to directly model monthly data of the asset returns to obtain the monthly covariance matrices,and then obtain the covariance matrix of other deadlines by accumulating the monthly covariance matrices.However,the covariance matrix of the asset returns tends to show the feature of dynamic changing,because of the strong auto-correlation of the most asset returns.Therefore,the long-term covariance matrix obtained directly by accumulating the monthly covariance matrices is somewhat problematic.In order to better obtain the long-term covariance matrix through the short-term covariance matrix,this paper first establishes a VARMAGARCH model for the asset returns,and based on this model to obtain an effective transformation method from the short-term covariance matrix to the long-term covariance matrix,finally constructs a V-G-BL asset allocation model that considers time-varying covariance.The effectiveness of the V-G-BL model considering time-varying covariance is verified by actual data.Comparative analysis found that the pension asset allocation model that considering time-varying covariance outperforms other models without considering the time-varying covariance.(2)For the accumulated errors caused by rolling prediction of the short-term income,a V-G-BL pension asset allocation model considering long-term income prediction is proposed.In the mean-variance model,the main parameters that affect the final asset allocation decision are the asset return and the covariance matrix,and there are studies have found that the asset allocation decisions are more sensitive to the asset return,a small change in return may cause a dramatic change in the final investment decision.Although improving from the mean-variance model,the BL model weakens some sensitivity of the investment decisions on asset returns,when the asset return forecasting is used to construct the viewpoint matrix,the asset allocation decision is greatly influenced by the accuracy of asset return forecasting.Pension asset allocation has the characteristics of long investment period,and asset return is often modeled through short-term data,which leads to the need to obtain the forecasting value of long-term asset return through the rolling forecasting of short-term asset return.However,rolling forecasting will cause error accumulation and reduce the accuracy of asset return forecasting.In order to avoid the error accumulation problem of rolling forecasting,this paper first uses the direct forecasting method to forecast the closing price of assets in the future,and indirectly obtains the long-term asset return by directly forecating the long-term closing price.In order to get more accurate effect on the asset return forecasting,this paper introduces the deep learning model into the asset return forecasting,and constructs the V-G-BL pension asset allocation model considering the long-term asset return forecasting.Finally,the effectiveness of the V-G-BL pension asset allocation model considering the long-term asset return forecasting is verified by actual data.Comparative analysis found that the pension asset allocation model that considering the viewpoint of long-term asset return forecasting outperforms other models without considering the viewpoint of long-term asset return forecasting.(3)In view of the driving and impact of the macroeconomic environment on the changes of long-term returns of assets,a V-G-BL pension asset allocation model considering the macroeconomic factors is proposed.Merrill Lynch Investment Clock connects the economic cycle with the asset rotation and the sector allocation strategies,divides the economic cycle into different phases based on the inflation and economic growth in each period,and portrays the performance of major asset classes in the market at different phases.As a result,different asset allocation policies are adopted and different investment weights are given to the major asset classes in different economic cycles’ phase.The investment period of pension asset allocation is long,and the driving and impact of macroeconomic environment on the change of longterm asset return will be stronger.Therefore,it is necessary to take macroeconomic factors into account in the process of asset allocation to improve the effect of asset allocation.This paper starts with modeling with the macroeconomic factors and divides the economic cycle and monetary cycle based on macroeconomic indicators.Through the analysis of the economic cycles,dividing the economic cycle states into three states:the economic stability period,the economic transition period and the economic overheating period.Through the analysis of monetary cycle,dividing the monetary cycle into the monetary easing period and monetary deflation period.The statistical analysis of the economic cycle and the monetary cycle reveals the statistical pattern of the asset returns at different cycle states.Based on the performance of the stock,bond and monetary asset returns at different states of the economic cycle and monetary cycle,constructing the subjective opinion of investors at different economic cycles and monetary cycles.Based on the analysis of economic cycle and monetary cycle,this paper constructs a V-G-BL pension asset allocation model considering macroeconomic factors,and verifies the effectiveness of the model through actual data.Comparative analysis found that the asset allocation model considering the economic cycle and monetary cycle outperforms the comparison models.(4)Aiming at the deficiency of risk measurement on the covariance matrix,a V-G-BL pension asset allocation model under CVaR risk measurement is proposed.In the traditional mean-variance asset allocation model,the standard deviation and covariance are used to measure the risk of an asset portfolio,but there are two shortcomings.The variance only describes the degree of deviation,but not shows the direction of deviation or reflects the potential loss in the investment.Conditional Value at Risk(CVaR)solves this problem more effectively and has become a more common standard in finance.This paper introduces the CVaR risk measure into the BL model in order to improve the BL model,gives the calculation method of the BL model based on the CVaR risk measure,and constructs the V-G-BL pension asset allocation model considering the CVaR risk measure.The effectiveness of the V-G-BL model under CVaR risk measure is verified by the actual data.Comparative analysis found that the asset allocation model incorporating the CVaR risk measure outperforms pension asset allocation comparison model based on covariance matrix risk measure.