Abstract:
Portfolio theory assumes that investors accept risk. This means that
in the equal rate of return on the two assets, the assets were chosen
that have a lower risk level. Modern portfolio theory is accepted by
investors who believe that they are not cope with the market. So
they keep many different types of securities in order to access the
optimum efficiency rate that is close to the rate of return on market.
One way to control investment risk is establishing the portfolio
shares. There are many ways to choose the optimal portfolio
shares. Among these methods in this study we use loss functions.
For this, we choose all firms from the year 2011 to the end of 2015
that had been a member in the Tehran Stock Exchange. The results
of this research show that the likelihood functions have the best
performance in Forecasting the optimal portfolio allocation problem.
Machine summary:
Model selection generally involves the evaluation of forecasts of volatility within loss functions, which are classified as either direct or indirect by Patton and Sheppard [15].
Indeed, Han- sen and Lunde [13] and Patton [16] demonstrate that noise in the volatility proxy renders certain di- rect loss functions incapable of ranking forecasts consistently in the univariate setting.
For example, Engle and Colacito [8] evaluate the forecasting performance in terms of portfolio return variance, while Fleming et al.
Engle and Colacito [8] and Patton and Sheppard [15] have demonstrated that the portfolio variance is minimised when the correct forecast is applied; a result that links the portfolio variance with robust statistical loss functions (Berker [4]).
This paper extends the previous literature by considering the role played by loss functions in ex-ante multivariate volatility model selection, where forecasts from these models will subsequently be used in mean–variance portfolio optimisation.
In doing so, it will assess the ability of a range of loss functions to discriminate between volatility forecasting models where the intended use of the forecasts is a portfolio optimisation problem.
These results show that QLK outperforms MSE and MAE, and MAE is not a robust loss function for multivariate volatility forecast evaluations.
This paper has investigated the performances of a range of loss functions for selecting models to be applied in a subsequent portfolio allocation problem.
, On loss functions and ranking forecasting performances of multivariate volatility models.