A Portfolio Strategy With Transactions Costs

The core issue of the finance is efficient allocation of resources,and it will be finished by transaction in the market.Markowitz(1952) proposed mean-variance analysis method which measured the risk of stock return,and it was the prelude to the study of modern finance. Sharpe(1964) proposed the capital asset pricing model (CAPM) which is based on the mean-variance analysis,and it is a perfectly theoretical model.It can explain why different securities have different returns.In order to improve the practicality of the model,economists are committed to relax its strict assumptions after the CAPM was proposed.Many correctional model have been proposed now.Merton(1973) proposed the intertemporal capital asset pricing model(ICAPM) by correcting single-cycle limitation of CAPM.Breeden (1979) proposed a consumption-oriented capital asset pricing model(CCAPM).The market without transaction costs is an important assumption in Merton(1973)’s research.However,the transaction costs are the essential characteristics of some economic theories.At the same time,they exist in the real world.Therefore,this paper further study the portfolio problem with transaction costs on the basis of the relevant research.The object of the research is the investors’ long-term investment dynamic strategy,the data are difficult to obtain.This paper considers fund companies’ investment strategies as viable investment strategies.The data come from annual reports,semi-annual reporst,quarterly reports of13fund companies.Finally,we build a investment strategy from April2004to December2012,and it is a total of442weekly data.Taking into account the consistency and availability of data,we only study two assets,namely the risky asset and the risk-free asset.Thus,weekly investment strategy is a radio about the risky asset and the risk-free asset.This paper selected weekly returns of SSE Composite Index and. risk-free assets from RESSET financial research database as weekly returns of the market and risk-free assets.Firstly,according to transaction costs model we obtain a certain transaction range which is the optimal ratio of investing in the risky asset.Then following this criterion,we can obtain the adjusted portfolio strategy by changing the ratio outside the range to inside.Then,we obtain the descriptively statistical analysis of the weekly market returns,weekly risk-free returns,the unadjusted portfolio returns and the adjusted portfolio returns.We need find the sequence of mean,variance,kurtosis, skewness and other statistics,and preliminary analysis statistical properties of returns.Secondly,we analysis between the unadjusted portfolio returns and the adjusted portfolio returns.We compare the unadjusted portfolio returns and the adjusted portfolio returns by fitting the CAPM and portfolio effects of four performance evaluation(cumulative return,Sharpe ratio,Treynor performance measure,Jensen’s measure).The research found the adjusted portfolio returns are all better than the unadjusted portfolio returns.Moreover,we further study the nature of the adjusted portfolio returns.First,we test the adjusted portfolio returns.According to tests’results,we use GARCH or TARCH model.Second,we consider information of the bear market or bull market on investment strategy. We analysis the adjusted portfolio returns by the conditional CAPM.Third,we use GARCH or TARCH model based on the conditional CAPM. The research found the adjusted portfolio returns better fit AR(2)-GARCH (1,1)model.However,when we consider with CAPM the adjusted portfolio returns better fit AR(1)-GARCH(1,1)-TARCH model.Finally,the research found real returns of China’s stock market is not too large considering the transaction costs.Thus,the strategy we maintain a certain percentage of the risky asset and risk-free asset is better.This strategy can obtain high returns in a bull market,and it can withstand market risks in bear market.The further study have two directions.First,if we can get complete data of investment institutions,we can draw a more accurate conclude. In addition,according to these data we can get deeper information and research more.Second,the range of investment ratio may change if the initial value of the transaction costs model varies. The initial value we recearch is used by most scholars.However,we need further research the impact of the initial value of the transaction costs model.