volatility

volatility - UNIVERSITY OF ESSEX DEPARTMENT OF ECONOMICS...

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Unformatted text preview: UNIVERSITY OF ESSEX DEPARTMENT OF ECONOMICS EC372 Economics of Bond and Derivatives Markets Volatility 1. What is volatility and why does it matter? In the context of this note, volatility means the ‘standard deviation of the rate of return on an asset’. The asset will be an company’s stock or a share price index, the application being to the S&P 500 index. The variance is defined as volatility-squared, i.e., the ‘squared standard deviation of the rate of return on an asset’. Volatility and variance have a time dimension: conventionally the unit is one year, and values are quoted as percentages. Volatility and variance are thus indices of the variability of an asset’s rate of return. Volatility matters because it is a determinant of many financial decisions and hence of security prices. For example: mean-variance portfolio selection requires the variances (and covariances) of asset returns; option price formulae are functions of, among other variables, the underlying asset’s volatility. More generally, but less precisely, volatility reflects the stability or otherwise of asset prices – volatility increases at times of unease in financial markets, dramatically so during crises. 2. Explicit versus implicit volatility By construction volatility is a ‘summary statistic’ based on the probability distribution of an asset’s rate of return. But what is the source of the probability distribution? In finance, probabilities appear in two distinct ways: (i) as a way of expressing investors’ beliefs about asset prices, and hence rates of return – call these ‘belief’ probabilities 1 ; (ii) as a reflection of the absence of arbitrage opportunities, i.e. ‘risk-neutral’ or ‘martingale equivalent’ probabilities. Remember that the absence of arbitrage opportunities is equivalent to the existence of risk-neutral probabilities. In principle, measures of volatility can be ‘backward-looking’ (what volatility was ) or ‘forward- looking’ (what volatility is forecast to be ). Although types (i) and (ii) could be either, measures assumed to be based on belief probabilities are almost always backward-looking, those for risk- neutral volatility being constructed as forward-looking. While there exist circumstances in which the belief probabilities would result in the same value of volatility (and variance) as the risk-neutral probabilities, there is no guarantee that the required circumstances hold. Indeed, empirical evidence suggests that there may be significant differences between the two. 2 Hence, a distinction should be made (but is often overlooked) between volatility obtained from belief probabilities and risk-neutral probabilities....
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volatility - UNIVERSITY OF ESSEX DEPARTMENT OF ECONOMICS...

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