Posts Tagged ‘volatilidad


Paper: Volatilidad y largo plazo

Are Stocks Really Less Volatile in the Long Run?


According to conventional wisdom, annualized volatility of stock returns is lower over long horizons than over short horizons, due to mean reversion induced by return predictability. In contrast,we find that stocks are substantially more volatile over long horizons from an investor’s perspective. This perspective recognizes that parameters are uncertain, even with two centuries of data, and that observable predictors imperfectly deliver the conditional expected return. Mean reversion contributes strongly to reducing long-horizon variance, but it is more than offset by various uncertainties faced by the investor, especially uncertainty about the expected return. The same uncertainties reduce desired stock allocations of long-horizon investors contemplating target-datefunds.

Link al Paper


Finanzas 101: Modelar la volatilidad

El blog Quantitative Research and Trading propone una serie de posts sobre volatilidad y pricing de opciones. Asi mismo, linkea una presentación la cual vale la pena mirar.

En esta primera entrega ofrece algunos conceptos claves sobre volatilidad como este:


Mean Reversion vs. Momentum
A puzzling feature of much of the literature on volatility is that it tends to stress the mean-reverting behavior of volatility processes.  This appears to contradict the finding that volatility behaves as a reinforcing process, whose long-term serial autocorrelations create a tendency to trend.  This leads to one of the most important findings about asset processes in general, and volatility process in particular: i.e. that the assets processes are simultaneously trending and mean-reverting.  One way to understand this is to think of volatility, not as a single process, but as the superposition of two processes:  a long term process in the mean, which tends to reinforce and trend, around which there operates a second, transient process that has a tendency to produce short term spikes in volatility that decay very quickly.  In other words, a transient, mean reverting processes inter-linked with a momentum process in the mean.  The presentation discusses two-factor modeling concepts along these lines, and about which I will have more to say later.



Paper: Diversificación de la Volatilidad

The Hazards of Volatility Diversification

Recent research advocates volatility diversification for long equity investors. It can even be justified when short-term expected returns are highly negative, but only when its equilibrium return is ignored. Its advantages during stock market crises are clear but we show that the high transactions costs and negative carry and roll yield on volatility futures during normal periods would outweigh any benefits gained unless volatility trades are carefully timed. Our analysis highlights the difficulty of predicting when volatility diversification is optimal. Hence insitutional investors should be sceptical of studies that extol its benefits. Volatility is better left to experienced traders such as speculators, vega hedgers and hedge funds.

Link al Paper



Falkenblog tiene un post donde comenta este paper.


Volatilidad a la VIX

A partir de hoy, la CBOE aplicara la metodología utilizada en el VIX a opciones de ciertas acciones (Apple, Amazon, IBM, Google, Goldman Sachs). Cortita y al pie, pero muy util.



Finanzas 101: VIX

No es el primer post que linkeamos explicando el VIX, pero creo tampoco sera el ultimo. En este caso, Credit Writedowns explica porque hay que estar checkeando el VIX de forma diaria.


So, as you can see, the VIX is much more valuable than the financial news ever explains. It’s not just a measure of volatility or fear. It is a moving prediction of the future. That’s why stock analysts get very afraid of a rising VIX. It’s a warning signal of things to come.



Paper: Volatilidad implícita y poder predictivo

Do Implied Volatilities Predict Stock Returns?

Using a complete sample of US equity options, we find a positive, highly significant relation between stock returns and lagged implied volatilities. The results are robust after controlling for a number of factors such as firm size, market value, analyst recommendations and different levels of implied volatility. Lagged historical volatility is – in contrast to the corresponding implied volatility – not relevant for stock returns. We find considerable time variation in the relation between lagged implied volatility and stock returns.

Link al Paper


Paper: Instrumentos de volatilidad como hedge

Using Volatility Instruments as Extreme Downside Hedges

“Long volatility” is thought to be an effective hedge against a long equity portfolio, especially during periods of extreme market volatility. This study examines using volatility futures and variance futures as extreme downside hedges, and compares their effectiveness against traditional “long volatility” hedging instruments such as out-of-the-money put options. Our results show that CBOE VIX and variance futures are more effective extreme downside hedges than out-of-the-money put options on the S&P 500 index, especially when reasonable actual and/or estimated costs of rolling contracts have taken into account. In particular, using 1-month rolling as well as 3-month rolling VIX futures presents a cost-effective choice as hedging instruments for extreme downside risk protection as well as for upside preservation.

Link al Paper


Hedgeate un black swan…

Risk.Net tiene un post donde introduce un nuevo desarrollo de CBOE: un instrumento que permite tomar posiciones frente a eventos de baja probabilidad (tail events).

“The skew index will offer the chance to take hedging or speculative positions on the skew of S&P 500 Index options, and consequently on the investors’ perception of forthcoming tail events such as extreme losses,” explained Shalen.

Skew reflects the fact that implied volatilities on options vary with strike levels, and is driven by supply and demand dynamics in the equity derivatives market. Historically, investors have purchased out-of-the-money puts to hedge their equity positions and sold out-of-the-money calls for premium. As a result, volatility for low strikes has increased, while volatility for high strikes has decreased.

If market participants expect a crisis, they would be more likely to buy put protection, which all things being equal would contribute to an increase in skew. Market participants could therefore take long positions in the index to hedge against future expectations of a tail event. Those who feel expectations of a crisis are overplayed could decide to short the index.

Shalen says the new product shows no correlation with market volatility, and any rise in the index is associated with the perception of correlated jumps in index stocks that occur during market crises.

En la nota se cita el siguiente paper de Peter Carr Towards a Theory of Volatility Trading (2002)


un poquito de leverage…

CSS Analytics tiene un post donde muestra la relación entre fundamentals y análisis técnico vía el Efecto Apalancamiento.

The “leverage effect”  and subsequent theory originated from early studies done by Fisher Black (of Black-Scholes fame). Black  found  that stock volatility tended to rise when stock prices went down and that volatility fell when prices went up. The economic rationale behind this effect is rooted in the firm’s capital structure. As a stock rises, the percentage of equity to debt rises, and the firm becomes less risky since the debt holders claims to the company value are more limited. Conversely, as the stock falls, the percentage of equity to debt falls, and the increased share of debt holder claims make the firm’s equity more risky. Thus a falling stock price should lead to an increase in future volatility.


Well most educated finance students understand first of all the principle of balance sheet leverage: when you add debt to the balance sheet, a given % increase in sales has a disproportionately larger increase in the % increase in earnings because you are netting out a fixed interest cost. If we all agree that 1) the market tends to discount future GDP and hence revenues, and 2) that firm value is also a function of earnings growth and total earnings, then the firms that will experience the greatest percentage change in firm value when the market forecasts a recovery should mathematically be the most leveraged firms.

This affects the technical trader in many ways whether you trade short-term or not. It means that the biggest winning stocks will have strong velocity relative to volatility (think sharpe ratio) only while the market is rising. When the market peaks, in fact, their velocity relative to volatility will have peaked at extraordinary levels. At this point the firm’s debt to equity is often at unsustainable  levels–leaving it vulnerable to the largest proportionate changes in firm leverage–and hence future volatility/downside risk.


Paper: spread como proxy de riesgo

Is There a Distress Risk Anomaly? Corporate Bond Spread as a Proxy for Default Risk

Although financial theory suggests a positive relationship between default risk and equity returns, recent empirical papers find anomalously low returns for stocks with high probabilities of default. The authors show that returns to distressed stocks previously documented are really an amalgamation of anomalies associated with three stock characteristics — leverage, volatility and profitability. In this paper they use a market based measure — corporate credit spreads — to proxy for default risk. Unlike previously used measures that proxy for a firm’s real-world probability of default, credit spreads proxy for a risk-adjusted (or a risk-neutral) probability of default and thereby explicitly account for the systematic component of distress risk. The authors show that credit spreads predict corporate defaults better than previously used measures, such as, bond ratings, accounting variables and structural model parameters. They do not find default risk to be significantly priced in the cross-section of equity returns. There is also no evidence of firms with high default risk delivering anomalously low returns.

Link al Paper

Fun & Finance


Fun & Finance Rollover

"It is hard to be finite upon an infinite subject, and all subjects are infinite." Herman Melville

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July 2020



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