asymmetric volatility

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Traders and Investors Club Asymmetric Volatility and Leverage Effect

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Presentation about Volatility Trading Techniques at London Traders & Investors Club

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Page 1: Asymmetric Volatility

Traders and Investors Club

Asymmetric Volatility and Leverage Effect

Page 2: Asymmetric Volatility

Introduction

1) THEORY AND DEFINITIONS

2) VOLATILITY PROXY AND LOG-RETURNS

3) STOCHASTIC VOLATILITY

3A) STOCHASTIC VOLATILITY CHARTS: GOLD,CRUDE OIL,FTSE and EURO vs DOLLAR

Page 3: Asymmetric Volatility

Leverage Effect

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)

Page 4: Asymmetric Volatility

Leverage Effect2)”Volatility of stocks tends to

increase when the price drops” (F. Black)

3)”Negative correlation between past returns and future volatility”(J.P. Bouchaud)

Page 5: Asymmetric Volatility

Types of Volatility

Actual Historical

Volatility over a specified period but with the last observation on a date in the past

Page 6: Asymmetric Volatility

Types of Volatility

Actual Future

Volatility over a period starting at the current time and ending at a future date

(options’ expiration date)

Page 7: Asymmetric Volatility

Types of Volatility

Implied

Volatility observed from historical prices of options

(Black-Scholes model)

Page 8: Asymmetric Volatility

Types of Volatility

Stochastic Volatility

Tendency of volatility to revert to some long-run mean value (GARCH family models, Chen model, Heston model, etc)

Page 9: Asymmetric Volatility

Proxy for VolatilityTrue volatility cannot be observed because it

is very difficult to separate:

- market-wide factors (systematic variables) - stock-specific factors (idiosyncratic

variables).

Therefore, log-normal returns are usually employed as a proxy for the true volatility.

Page 10: Asymmetric Volatility

Log-Normal Returns

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

Page 11: Asymmetric Volatility

Log-Normal Returns

Rt = ln (Pt / Pt-1)

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.

Page 12: Asymmetric Volatility

Stochastic Volatility

GARCH Model: GARCH (Generalised Autoregressive Conditional Heteroskedasticity) it assumes that the randomness of variance process varies with variance.

Page 13: Asymmetric Volatility

Stochastic VolatilityThe GARCH variance is a weighted average of 3

different variables:

1) Long run average volatility

2) Forecasted volatility values calculated in previous period

3) New information not available when the previous forecast was made

Page 14: Asymmetric Volatility

Crude Oil Futures Market

.01

.02

.03

.04

.05

.06

.07

07M07 08M01 08M07 09M01 09M07 10M01

Conditional Standard Deviation

Page 15: Asymmetric Volatility

News Impact Curve – CL1

.000

.004

.008

.012

.016

.020

.024

-25 -20 -15 -10 -5 0 5 10 15 20 25

Z

SIG

2

Page 16: Asymmetric Volatility

Residuals – Crude Oil

0

10

20

30

40

50

60

70

80

90

-2.50 -1.25 0.00 1.25 2.50 3.75

Series: Standardized ResidualsSample 1/03/2007 3/01/2010Observations 795

Mean -0.016696Median -0.009076Maximum 3.618355Minimum -3.375965Std. Dev. 0.998636Skewness -0.079619Kurtosis 3.092973

Jarque-Bera 1.126280Probability 0.569418

Page 17: Asymmetric Volatility

Gold Futures Market

.008

.012

.016

.020

.024

.028

07M07 08M01 08M07 09M01 09M07 10M01

Conditional Standard Deviation

Page 18: Asymmetric Volatility

News Impact Curve – Gold

.00

.01

.02

.03

.04

.05

-25 -20 -15 -10 -5 0 5 10 15 20 25

Z

SIG

2

Page 19: Asymmetric Volatility

Residuals - Gold

0

40

80

120

160

200

-4 -2 0 2 4

Series: Standardized ResidualsSample 1/03/2007 3/01/2010Observations 795

Mean -0.025197Median 0.011170Maximum 4.780058Minimum -5.287299Std. Dev. 1.001487Skewness -0.315884Kurtosis 5.191299

Jarque-Bera 172.2805Probability 0.000000

Page 20: Asymmetric Volatility

FTSE 100

.00

.01

.02

.03

.04

.05

.06

07M07 08M01 08M07 09M01 09M07 10M01

Conditional Standard Deviation

Page 21: Asymmetric Volatility

News Impact Curve – FTSE100

.000

.004

.008

.012

.016

.020

-25 -20 -15 -10 -5 0 5 10 15 20 25

Z

SIG

2

Page 22: Asymmetric Volatility

Residuals – FTSE100

0

10

20

30

40

50

60

70

80

90

-3.75 -2.50 -1.25 0.00 1.25 2.50

Series: Standardized ResidualsSample 1/02/2007 3/01/2010Observations 801

Mean -0.010717Median 0.035188Maximum 3.253203Minimum -4.090106Std. Dev. 0.993679Skewness -0.367643Kurtosis 3.571112

Jarque-Bera 28.92990Probability 0.000001

Page 23: Asymmetric Volatility

Euro vs Dollar

.002

.004

.006

.008

.010

.012

.014

.016

07M01 07M07 08M01 08M07 09M01 09M07 10M01

Conditional Standard Deviation

Page 24: Asymmetric Volatility

News Impact Curve – Eur vs Dol

.0000

.0001

.0002

.0003

.0004

-25 -20 -15 -10 -5 0 5 10 15 20 25

Z

SIG

2

Page 25: Asymmetric Volatility

Residuals – Euro vs Dollar

0

20

40

60

80

100

-3.75 -2.50 -1.25 0.00 1.25 2.50 3.75

Series: Standardized ResidualsSample 1/01/2007 2/26/2010Observations 825

Mean -0.004203Median -0.014799Maximum 4.468386Minimum -3.666132Std. Dev. 0.992727Skewness 0.021811Kurtosis 3.562993

Jarque-Bera 10.96096Probability 0.004167

Page 26: Asymmetric Volatility

VIX

1 29 57 85 1131411691972252532813093373653934214494775055335615896176456737017297577850

10

20

30

40

50

60

70

80

90

Series1

Page 27: Asymmetric Volatility

Crude Oil 10 years Impact Curve

.000

.001

.002

.003

.004

.005

.006

.007

-25 -20 -15 -10 -5 0 5 10 15 20 25

Z

SIG

2

Page 28: Asymmetric Volatility

ConclusionsThe analysed markets present strong

evidence of leverage effect processes

The financial crises “re-shaped” many markets that were usually considered NOT TO BE LEVERAGED (Currency markets, Crude Oil , Gold, commodity markets)

Page 29: Asymmetric Volatility

ConclusionsIn leveraged markets returns drop much

more quickly than “normal markets”

Asymmetric volatility can be used to scale trades and re-enforce short or long positions

Asymmetric volatility is often used in options and futures strategies both for speculating and hedging purposes