Volatility: forecasting the unobservable

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If you want to take investment risk for a spin, you should definitely allocate some of your hardly-sweated savings on your favorite stock – better starting with a broad stock index tracker, a.k.a. ETF, and then moving to the next level of individual stocks, if you like hot and spicy foods. Ultimately, investment risk is an experience you want to live as fully as possible, so once you’ve chosen your favorite stock (or index tracker) don’t go out surfing, stay home and enjoy your trading session. Unfortunately, it turns out you won’t experience risk on a sunny day, for risk shows up unexpectedly and you don’t necessarily see it coming beforehand. The weather forecast might report the perfect condition for surfing, though your highly-paid and PhD-endowed risk manager might not be as accurate as you may expect.

On financial markets risk is measured by volatility which, as an approximation, is the standard deviation of the change in your stock price in one year and by and large is a measure of the uncertainty about the returns provided by the stock. Typical values of volatility, quoted by market wizards, range from 20% to 40% per annum. Though, since you monitor your investment on a daily basis, you’re more likely to be interested in daily changes. To estimate volatility of a stock price empirically, we observe stock prices at fixed intervals of time (e.g. daily, weekly, monthly, quarterly) and we need to choose an appropriate length to get a meaningful estimate. It seems the most recent 90 to 180 days are a good compromise when you want to measure it. Another rule of thumb is to set the observation period equal to the time period it is to be applied. Volatility typically tells you how much you can expect to lose on a single normal day, it doesn’t tell you how extreme the adverse swing can actually be. More advanced and sophisticated approaches have been devised, involving GARCH models, to estimate how much you can lose on a bad day down on your losing streak. Value-at-Risk (or more friedly VaR) is one such measure and provides you with a reasonable loss you might incur in on a stormy day with a margin of uncertainty, clearly.

Though, the exact alchemy of VaR calculation (using a GARCH model) is beyond the scope of this post on volatility, your economics correspondent on the opposite side of the ocean has provided readers of such respectable web issue with an update on volatility (see below) regarding the S&P 500 index as of July 30, 2014 (volatility as the standard deviation of returns has been 16.3% since July 31, 2009) adding VaR as a reassuring bottom-line of losses you may incur on a blustery business day on the markets.

Garch estimated volatilities S&P 500


Risk managers like to think of VaR as an extreme measure of volatility that should tell you, on average, the maximum loss you can suffer with a predefined interval of confidence, usually chosen to be 95% or 99%. That is on average your worst loss should not exceed VaR levels more than 1% or 5% of days. In the chart above the blue line shows S&P’s 500 index daily percent changes and the black line below it is the estimate of VaR on a given day: ideally adverse swings should not cross the black line more than 1% (in this case the confidence level is 99%), but in this case daily returns exceed VaR estimates 2.5 times (or 2.5%).

Remember when you took out that fine BMW brochure but then you set it aside because your favorite broker gave you better advice on the investment thrill of choosing a stock instead for a bigger and pricier Porsche with the reassuring remark of a better risk management model with optimized VaR levels?

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