Econometrics of Volatility

94 Pages·2017·1.35 MB·English

by  Arora, Siddharth

Econometrics of Volatility
Siddharth Arora
[email protected]
Mathematical Institute, University of Oxford
Hilary Term, 2017
Course Outline
• Session I – Basics of volatility, estimating volatility
• Session II – ARCH, GARCH modelling approaches
• Session III – Value at Risk (VaR), Technical analysis
These lecture notes are based on the material prepared by J Taylor and P McSharry
It is good to have an end to journey toward; but it is the journey that matters, in the end – E. Hemingway
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Volatility
• Volatility is a measure of the variability of the price of a financial
instrument over time.
• Historical volatility is calculated from the time series of past market
prices.
• For example, one could calculate the daily returns and then use the
standard deviation of these returns as a measure of the historical
volatility.
Fragility is the quality of things that are vulnerable to volatility - N.N. Taleb 3
Annualized volatility
• In order to create a standard, it is common practice to estimate an
annualized measure of volatility.
• This is a useful approach as the annualized volatility can then be
directly compared with the annualized return for that particular
instrument.
• If we are subjected to high volatility, we would expect a high level
of return.
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Volatility and direction
• Volatility does not covey any information about the likely direction
of price changes.
• It focuses on the dispersion of returns since the standard deviation is
computed using the squares of the returns.
• Negative and positive returns have the same effect on the volatility
measure.
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Volatility and risk
• Two instruments with different volatilities may have the same
expected return.
• In this sense, volatility warns us about the size of fluctuations that
we might expect.
• A financial instrument with higher volatility will have larger swings
in values over a given period of time and can therefore be said to be
more risky.
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Risk and Reward
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Volatility sizing
• Many investors will wish to construct a portfolio of financial
instruments.
• In order to ensure that each asset in the portfolio represents an
equal level of risk, the volatility can be used to infer appropriate
weights.
• This is the motivation behind the 60%-40% split for equities and
bonds since equities typically have a higher level of volatility.
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Retirement
• A rule of thumb for the split between equities and bonds is to invest
your age in bonds and the remainder in equities.
• This way, the overall portfolio becomes less volatile as your
approach retirement.
• When saving for retirement, high volatility results in a wider
distribution of possible final portfolio values.
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Trading
• Traders attempt to time the market in order to perform better than a
buy and hold long-term strategy.
• Volatility presents opportunities to buy assets cheaply and sell when
overpriced.
• Volatility is particularly important for mean-reversion strategies
which rely on fluctuations in prices over relatively short periods of
time.
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