How to construct a bond volatility index and extract market information

Volatility indices, based upon the methodology of the Cboe volatility index (VIX), serve as measures of near-term market uncertainty across asset classes. They are constructed from out-of-the-money put and call premia using variance swap pricing. Volatility indices for fixed income markets are of particular importance, as they allow inferring market expectations about discount factors and credit premia, which have repercussions on all assets and the broader economy. There is a step-by-step construction plan for building a bespoke index for any rates market with liquid futures and options. Such a volatility index supports asset management in two ways. First, it is a valid basis for portfolio risk management and volatility targeting. Second, it can be used for extracting forward-looking market information, including changing probability quantiles for prices and rates, probabilities of certain extreme events, and the skewness of expectations.

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Realistic volatility risk premia

The volatility risk premium compensates investors for taking volatility risk. Conceptually it is based on the difference between options-implied and expected realized volatility. In equity markets this premium should be positive in the long run and fluctuate overtime depending on the market’s willingness to pay for protection against future changes in price volatility. In practice, measuring the premium overtime is challenging, particularly because expected realized volatility is not known. Using recent realized volatility as a proxy can be highly misleading. However, a realistic estimate can be constructed by considering the trade-off between timeliness and noise ratio of recent price changes and the long-term mean reversion of volatility. This “realistic” volatility risk premium has been positively correlated with subsequent daily volatility index future returns.

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The importance of volatility of volatility

Options-implied volatility of U.S. equity prices is measured by the volatility index, VIX. Options-implied volatility of volatility is measured by the volatility-of-volatility index, VVIX. Importantly, these two are conceptually and empirically different sources of risk. Hence, there should also be two types of risk premia: one for the uncertainty of volatility and for the uncertainty of variation in volatility. The latter is often neglected and may reflect deep uncertainty about the structural robustness of markets to economic change. A new paper shows the importance of both risk factors for investment strategies, both theoretically and empirically. For example, implied volatility and “vol of vol” typically exceed the respective realized variations, indicating that a risk premium is being paid. Also, high measured risk premia for volatility and “vol-of-vol” lead to high returns in investment strategies that are “long” these factors.

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VIX term structure as a trading signal

The VIX futures curve reflects expectations of future implied volatility of S&P500 index options. The slope of the curve is indicative of expected volatility and uncertainty relative to volatility and uncertainty priced in the market at present. Loosely speaking, a steeply upward sloped VIX futures curve should be indicative of present market complacency, while an inverted downward sloped curve should be indicative of present market panic and capitulation. In both cases the slope of the curve would serve as a contrarian indicator for market directional positions. An empirical analysis for 2010-2017 suggests that an inverted VIX curves has had a significant positive relation with subsequent S&P500 returns. Normal VIX curves, however, did not have significant predictive power, possibly because a market can stay complacent longer than it can panic.

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Using VIX for forecasting equity and bond returns

Over the past 25 years the relation between implied equity volatility (VIX) and market returns has been non-linear. When VIX was low there was no meaningful relation. However, when volatility increased above average higher equity and lower bond returns followed. This is evidence for “flight to quality“, where investors pay a rising premium for safe and liquid assets as volatility increases. Fear of redemptions, liquidity constraints, and deteriorating market intermediation are plausible causes of this effect.

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The information value of VIX

Two recent papers help understanding the information value of the implied volatility index for the S&P 500 stock index (VIX). An ECB paper de-composes VIX into measures of equity market uncertainty and risk aversion, e.g. the quantity and price of risk. Risk aversion in particular has been both a driver of monetary policy and an object of its effect. Meanwhile, a Fed paper emphasizes that the implied volatility of VIX (“vol of vol”) is a useful measure of tail risk prices and a predictor of tail risk hedges’ returns.

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