Estimating Volatility of the Selected Security

SYNOPTIC ABSTRACT

We consider two competing pairs of random variables (X, Y₁) and (X, Y₂) satisfying linear regression models with equal intercepts. The model which connects the selection between two regression lines with the selection between two normal populations, proposed by Gangopadhyay et al. (2013) for estimating regression coefficients of the selected regression line, is described. This model is applied to a problem in finance which involves selecting security with lower risk. It is assumed that an investor being risk averse always chooses the security with lower risk (or, volatility) while choosing one of two securities available to him for investment, and further, is interested in estimating the risk of the chosen security. We construct several estimators and apply the theory to real data sets. Finally, graphical representation of the results is given.

KEY WORDS AND PHRASES:

• Regression coefficient
• estimation after selection
• volatility
• risk averse
• squared error loss

Acknowledgments

We gratefully thank the editor and the reviewers for their detailed and excellent comments, which improved the quality of the article.