A Research On The Relationship Between Forecast Precision And The Performance Of The Portfolio Constructed Using Treynor—Black Model

There are more and more investors engaged in active portfolio management since1980 when Grossman and Stiglitz proposed the famous effective market paradox based on the cost of information and the fact that market arbitrage opportunity exists.The inefficiency of the market makes it possible for portfolio managers to make profits which is larger than their cost.It encourages investors to dig for information and make the market more efficient and accurately reflect the price.Treynor and Black(1973)proposed a mathematical model for security selectionan,and it's an efficient model of implementing active investment strategy,where the investor believes he has information that can be used to predict the abnormal returns(Alpha)of some securities.The model form a optimal risky portfolio(A)based on the forecasts of security analyst on stock's alpha values(abnormal returns),then combine it with the negative market index portfolio(M)to get the optimal portfolio.The Treynor—Black(TB)model is based on the single index model.It doesn't take transaction costs into consideration,and there is no restrictions on investment ratio and short selling.The weight of each stock in the portfolio is determined based on the forecasts of security analyst on stock's alpha values.when the weight is positive,buy the stock,and sell when negative.The performance of the portfolio optimally constructed based on the TB model critically depends on the forecasting ability of the security analyst.In this paper,we study the relationship between the prediction accuracy of security analysts and performance of the portfolio optimally constructed based on their forecasts using the margin trading shares as our sample.We firstly estimate beta values of stocks,using ordinary least square(OLS)method based on historical data.Then we can forecast stock's alphas on the basis of this,and the forecast values will be adjusted under different precision.Finally,the optimal portfolio is constructed based on the adjusted alpha values using the TB model.By comparing the performance of the optimal portfolio with the passive portfolio,the following aspects are studied:(1)The relationship between forecasting ability of the security analysts and the performance of the portfolio optimally constructed based on the TB mode.The conclusion shows that the performance of the optimal portfolio is better and better than the benchmark portfolio as forecast precision improves.(2)The relationship between the number of stocks included in the optimal portfolio and the performance of the optimal portfolio.The result shows that when the window size(T)and the forecast precision of analysts are fixed,the performance of the optimal portfolio is better and better than the benchmark portfolio as the number of stocks included in the optimal portfolio increases.(3)The relationship between the window size(T)and the performance of the optimal portfolio.The result shows that the longer the rolling forecast window period,the smaller the standard deviation of the portfolio,the greater the Sharp ratio and the M~2,and the better the performance of the optimal portfolio.(4)If the TB model has practical significance when the forecast precision of the analyst is very low.The result shows that even when the precision is as low as 0.005,the window size(T)is only 24,we can still use 10 stocks to construct a portfolio which is better than the benchmark portfolio.Even with a half portion of noisy analysts,the Sharp ratio of the optimal portfolio is still greater than the benchmark portfolio,indicating that the performance of the optimal portfolio is better than the benchmark portfolio.