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Traders and Investors Club<br />Asymmetric Volatility and Leverage Effect<br />
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Introduction<br />1) THEORY AND DEFINITIONS<br />2) VOLATILITY PROXY AND LOG-RETURNS<br />3) STOCHASTIC VOLATILITY<br />3A) STOCHASTIC VOLATILITY CHARTS: GOLD,CRUDE OIL,FTSE and EURO vs DOLLAR<br />
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Leverage Effect<br />1)“ Negative returns seemed to be more important predictors of volatility than positive returns. Large prices declines forecast greater volatility than similarly large prices increases” (R. Engle)<br />
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Leverage Effect<br />2)”Volatility of stocks tends to increase when the price drops” (F. Black)<br />3)”Negative correlation between past returns and future volatility”(J.P. Bouchaud)<br />
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Types of Volatility<br />Actual Historical<br />Volatility over a specified period but with the last observation on a date in the past<br />
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Types of Volatility <br />Actual Future<br /> Volatility over a period starting at the current time and ending at a future date (options’ expiration date)<br />
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Types of Volatility<br />Implied<br />Volatility observed from historical prices of options<br /> (Black-Scholes model)<br />
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Types of Volatility<br /> Stochastic Volatility<br /> Tendency of volatility to revert to some long-run mean value (GARCH family models, Chen model, Heston model, etc) <br />
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Proxy for Volatility<br />True volatility cannot be observed because it is very difficult to separate:<br /> - market-wide factors (systematic variables) <br /><ul><li>stock-specific factors (idiosyncratic variables). </li></ul>Therefore, log-normal returns are usually employed as a proxy for the true volatility.<br />
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Log-Normal Returns<br />The log-normally distribution of data allows for a more accurate estimation of the return sensitivity for a given change in the information set available in the market for any given time period<br />
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Log-Normal Returns<br />Rt = ln (Pt / Pt-1)<br />Where Rt denotes the log - return at time t for the asset price , Pt denotes the price at time t whilst Pt-1 represents the price at time t-1.<br />
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Stochastic Volatility<br />GARCH Model: GARCH (Generalised Autoregressive Conditional Heteroskedasticity) it assumes that the randomness of variance process varies with variance. <br />
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Stochastic Volatility<br />The GARCH variance is a weighted average of 3 different variables: <br />1) Long run average volatility<br />2) Forecasted volatility values calculated in previous period<br />3) New information not available when the previous forecast was made<br />
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Conclusions<br />The analysed markets present strong evidence of leverage effect processes<br />The financial crises “re-shaped” many markets that were usually considered NOT TO BE LEVERAGED (Currency markets, Crude Oil , Gold, commodity markets)<br />
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Conclusions<br />In leveraged markets returns drop much more quickly than “normal markets”<br />Asymmetric volatility can be used to scale trades and re-enforce short or long positions<br />Asymmetric volatility is often used in options and futures strategies both for speculating and hedging purposes<br />
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