| The return and risk of an asset are the two important issues in investment,and there are a lot of studies on the factor structure of excess return and volatility in financial research.Regarding the factor structure of excess return,the earliest proposed CAPM model illustrates the linear relationship between the excess return of an asset and the excess return of the market.Since then,a large number of factor models of returns have been proposed,such as the famous Fama-French three factors model,Fama-French five factors model and momentum factor model,etc.In factor models,the volatility of individual assets can be decomposed into idiosyncratic volatility and common factor volatility,the common factor volatility is called systematic risk.Idiosyncratic volatility is widely used in asset pricing.Based on the three-factor model,Ang et al.extracts idiosyncratic volatility from the level of individual stocks,which further shows that the higher the idiosyncratic volatility of a stock,the lower the future average return.Since then,many scholars have proved that idiosyncratic volatility is driven by a common idiosyncratic factor,which the market value-weighted average of all stocks’ idiosyncratic volatilities.But in this model,only the factor structure of idiosyncratic volatility is considered,and the time-varing structure of systematic risk is not considered.This paper finds that the risk of assets is driven by common risk factors and models them.When considering the factor model of asset volatility and return,both the return factor and the volatility factor can be observed,and the market is driven by multi-dimensional states,so that the model can describe the complexity of financial risk from multiple dimensions.On the other hand,dynamic portfolio optimization has always been a hot issue in mathematic financial research.Due to the inseparability of mean and variance,it is very difficult to theoretically find the optimal solution for dynamic portfolio optimization,especially when considering the time-varying asset returns and volatilities.Due to the time-varying mean vector and volatility matrix,it is even more difficult to solve the dynamic portfolio.However,the dynamic portfolio theory to be applied,it needs to satisfy more diverse market.Therefore,this paper mainly studies the optimization problem of dynamic investment portfolio under different volatility and return structures.In the specific model,not only the market without transaction cost is considered,but also the more realistic market with transaction cost,the market with shorting,and the time-consistent strategy is further studied.Considering the theory of dynamic portfolio optimization in different markets is conducive to the continuous updating of the theory of dynamic portfolio optimization and better application in the actual market.This paper considers the factor volatility models from two aspects.On the one hand,through the analysis of the actual data of the US stock market,it is found that the volatility of assets is driven by common risk factor,and further through the analysis of the financial data of the US stock market,it is found that common risk factor can be priced.In this regard,a new factor model of volatility is proposed.On the other hand,it is applied through time-varying models of volatility in the literature.This paper mainly focuses on the theoretical derivation and practical performance of the combinatorial optimization model under the factor model.Based on this purpose,starting from the factor model of assets and the factor model of volatility,this paper obtains the dynamic optimal semi-explicit optimal solution of the multi-period mean-variance model,and proves the efficient frontier of the optimal solution.Theoretically obtained semi-analytical optimal dynamic mean variance portfolio strategy is related to an important stochastic process.This stochastic process is called FIO in this paper.FIO does not depend on the current wealth level and investment goals of investors,but only on the market.settings related.And the relationship between FIO and the minimum variance signed martingale measure is proved theoretically.In order to make the strategy of this paper land,the simulation algorithm of FIO is given,and the relationship between CR and the optimal strategy is analyzed in the US stock market in CRSP.The empirical results show that compared with the out-ofsample efficient frontier achieved by the classical multi-period mean-variance model,the model proposed in this paper can achieve a larger out-of-sample Sharpe ratio,which is close to the out-of-sample Sharpe ratio of the classical model twice.In a market with no-shorting constraint,we consider a more complex factor structure,and believe that the systematic volatility of assets is affected by stochastic factors and obeys the stochastic volatility model,and the idiosyncratic volatility of assets is driven by CIV.In this way,the randomness of our asset’s volatility model will come from two parts,one is the driving idiosyncratic volatility,and the other is the systematic volatility.Based on this idea,we constructed relevant factor models and volatility models,applied them to the market with short selling restrictions,and obtained the dynamic optimal semi-explicit optimal solution of the multi-period mean-variance model theoretically.Know the efficient frontier of the optimal solution.Further theoretically,this strategy is extended from time-inconsistent strategy to time-consistent strategy.From an empirical point of view,this optimal strategy is used to analyze the relationship between future investment opportunities and the optimal strategy in the U.S.stock market in CRSP,and compared with the out-of-sample efficient frontier realized by the classical MMV model with multi-period mean variance.,resulting in a higher out-of-sample Sharpe ratio.Also has a higher out-of-sample Sharpe ratio than volatility without a factor structure.At the end of the paper,the theoretical properties of factor models and factor models of volatility in markets with transaction fees are investigated.Due to the transaction cost,the multi-period mean-variance objective function we obtain will be greatly complicated,which will greatly increase the difficulty in obtaining the theoretical optimal solution.In this paper,the semi-explicit dynamic optimal solution is obtained theoretically,and the efficient frontier is given.When the factor model of return and the factor model of volatility are applied to the actual market,there are enough theoretical guarantees to make the strategy fit the actual market situation as much as possible. |
