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1 Short Selling Stock Indices On Signals From Implied Volatility Index Changes: Evidence From Quantile Regression Based Techniques D. E. Allen, A. K. Singh, R. J. Powell and A. Kramadibrata Edith Cowan University

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2 Reading Questions 1. Explain what short selling is. What is the difference between naked and covered short selling 2. How does the SECs rule 201 impact on short selling? 3. What are the IOSCO (2009) recommendations with regard to short selling? 4. Are there any significant differences between engaging in short selling in the cash market or in the related derivatives market on the same instrument? 5. What is quantile regression? 6. How do quantile regressions differ from OLS regressions? 7. Explain what kernel quantile regressions are. 8. What are Random Forest techniques? 9. Explain the difference between making point forecasts and the use of prediction intervals as adapted in this chapter. 10. How is the inclusion of transaction costs likely to affect the results reported in the chapter?

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Introduction Changes in implied volatility derived from options on two indices: the S&P500 and the FTSE100. Leverage effect: Increases in volatility are linked with falls in stock prices and vice-versa. Forecasting future interval volatility estimates using historical volatility with quantile regression and machine learning techniques. Trading strategy based on the forecasted interval estimates of the two volatility indices. 3

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Introduction Long Position: Purchase of a security or asset in the belief that its price will subsequently rise and then selling it when it happens. Short Position: Selling a security or asset in the belief that its price will subsequently decrease and then buying it when it happens. Covered Short Selling Already have a position in the security intended to be shorted Naked Short Selling Shorting a security that is not possessed by the trader. 4

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Introduction IOSCO (2009) four broad principles in relation to short selling: The First Principle: Short selling should be subject to appropriate controls to reduce or minimise the potential risks that could affect the orderly and efficient functioning and stability of financial markets. The Second Principle: Short selling should be subject to a reporting regime that provides timely information to the market or to market authorities. The Third Principle: Short selling should be subject to an effective compliance and enforcement system. The Fourth Principle: Short selling regulation should allow appropriate exceptions for certain types of transactions for efficient market functioning and development 5

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Quantile Regression Quantile regression (Koenker and Basset, 1978) gives quantile relationships for different quantiles of the conditional distribution of the dependent variable. Quantile regression is modelled as an extension of OLS The median quantile in quantile regression is estimated by the minimization of sum of absolute errors. Other quantiles are estimated by minimizing the sum of asymmetrically weighted sum of absolute errors. Optimization problem: Outliers do not bias estimates at other quantiles 6

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Quantile Regression-Interval Estimates Quantile regression can be used to build an interval prediction using extreme quantiles as the boundary intervals. For example, 1% and 99% quantile estimates give us an interval estimate for our prediction and the value is expected to lie between these two boundary estimates. This interval estimate can be used to predict the extreme loss or extreme gain in stock returns or indices. 7

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Kernel Quantile Regression Kernel Quantile Regression, is an evolving quantile regression (Takeuchi I, et. al., 2006; Ll Youjuan, et. al., 2007) technique in the field of non linear quantile regressions. It is more effective than linear quantile regression. It uses kernel functions to model the dependence and allows to model both gaussian and non gaussian data. Kernel quantile regression can be used to forecast value at risk, using past return levels as a training set (Wang, 2009). 8

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Quantile Regression Forests Random forests provide inference about the conditional mean of the distribution in a random forest regression. Quantile Regression Forests (Meinshausen, 2006) gives a nonparametric and accurate way of estimating conditional quantiles of high dimensional predictor variables. Random forests, is a ensemble of trees of n independent variables. The weighted distribution (not the mean) of observed response variables gives the conditional distribution for quantile regression forests. 9

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Data & Methodology Use of the level of implied volatilities changes transformed into returns from the FTSE-100 and S&P- 500 volatility indices to decide the position of a directional trade in their respective underlying price indices (FTSE-100 and S&P-500). Last 4 years daily logarithmic returns-January-2007 to October 2010 Two interval estimate predictions- [1%,99%] and [5%,95%] Independent Variables-Last six days returns Dependent Variable-Present day return. 10

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Trading Strategy Interval estimates used to predict the directional change (1,-1) If (l t,u t ) represents an interval estimate for time t If l t+1 l t +T and u t+1 u t where T is a threshold (5% in present case) then -1 If l t+1 l t and u t+1 u t then 1 If l t+1 >l t, u t+1 >u t and if l t+1 -l t >u t+1 -u t then -1else 1 Total return with direction estimates is given by 11

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Results Trading Strategy Returns Year200820092010 [1%-99%][5%-95%][1%-99%][5%-95%][1%-99%][5%-95%] QR-54.2255-23.846939.532715.22916718.2909111.51107 KQR-24.9358-46.241929.411430.9178518.496923.37544 QRF-46.9848-36.191120.14434-5.99551-0.14102-1.26365 Actual hold out return -36.648242723.539854517.022388286 12 Table 1: Returns observed with trading strategy applied on FTSE-100 price index Trading Strategy Returns Year200820092010 [1%-99%][5%-95%][1%-99%][5%-95%][1%-99%][5%-95%] QR-62.7601-61.912213.9815420.32935-11.596.456039 KQR-41.5446-56.459415.5371430.6224720.8883218.41588 QRF-44.5796-51.73698.04066716.19486-4.9252514.55047 Actual hold out return -48.5895230324.985118486.66617096 Table 2: Returns observed with trading strategy applied on S&P-500 price index

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Conclusion Kernel based quantile regression methods appear to generate the greatest returns in our hold out sample periods and dominate buy and hold returns. The chapter demonstrates that quantile regression based interval estimates can be used for deciding short and long positions in the market. The empirical exercise also shows that the implied volatility indices can be used as an indicator of the performance of the underlying price index. 13

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