Measuring volatility with the realized range

Realized variance, being the summation of squared intra-day returns,has quickly gained popularity as a measure of daily volatility.Following Parkinson (1980) we replace each squared intra-day returnby the high-low range for that period to create a novel and moreefficient estimator called the realized range. In addition wesuggest a bias-correction procedure to account for the effects ofmicrostructure frictions based upon scaling the realized range withthe average level of the daily range. Simulation experimentsdemonstrate that for plausible levels of non-trading and bid-askbounce the realized range has a lower mean squared error than therealized variance, including variants thereof that are robust tomicrostructure noise. Empirical analysis of the S&P500index-futures and the S&P100 constituents confirm the potential ofthe realized range.realized volatility;bias-correction;high-frequency data;high-low range;market microstructure noise

Range-based covariance estimation using high-frequency data: The realized co-range

We introduce the realized co-range, utilizing intraday high-lowprice ranges to estimate asset return covariances. Using simulationswe find that for plausible levels of bid-ask bounce and infrequentand non-synchronous trading the realized co-range improves upon therealized covariance, which uses cross-products of intraday returns.One advantage of the co-range is that in an ideal world it is fivetimes more efficient than the realized covariance when sampling atthe same frequency. The second advantage is that the upward bias dueto bid-ask bounce and the downward bias due to infrequent andnon-synchronous trading partially offset each other. In a volatilitytiming strategy for S\\&P500, bond and gold futures we find that theco-range estimates are less noisy as exemplified by lowertransaction costs and also higher Sharpe ratios when using moreweight on recent data for predicting covariances.bias-correction;market microstructure noise;high-frequency date;realized co-range;realized covariance

Forecasting Sovereign Default risk with Merton’s Model

Merton's structural model for sovereigns is proven to be useful to analyze the default risk of a country. We are the first to investigate how fast CDS spreads react to changes in model inputs and outputs. CDS spread changes strongly correlate with exchange rate returns, which are an input to the model. But CDS spread changes on average react with a delay to changes in model outputs such as the distance to default, the default probability and model spreads. Hence contingency claim analysis for sovereigns provides useful predictions for CDS spreads

Measuring volatility with the realized range

Realized variance, being the summation of squared intra-day returns, has quickly gained popularity as a measure of daily volatility. Following Parkinson (1980) we replace each squared intra-day return by the high-low range for that period to create a novel and more efficient estimator called the realized range. In addition we suggest a bias-correction procedure to account for the effects of microstructure frictions based upon scaling the realized range with the average level of the daily range. Simulation experiments demonstrate that for plausible levels of non-trading and bid-ask bounce the realized range has a lower mean squared error than the realized variance, including variants thereof that are robust to microstructure noise. Empirical analysis of the S&P500 index-futures and the S&P100 constituents confirm the potential of the realized range

Residual Momentum

Conventional momentum strategies exhibit substantial time-varying exposures to the Fama and French factors. We show that these exposures can be reduced by ranking stocks on residual stock returns instead of total returns. As a consequence, residual momentum earns risk-adjusted profits that are about twice as large as those associated with total return momentum; is more consistent over time; and less concentrated in the extremes of the cross-section of stocks. Our results are inconsistent with the notion that the momentum phenomenon can be attributed to a priced risk factor or market microstructure effects

Forecasting Volatility with the Realized Range in the Presence of Noise and Non-Trading

We introduce a heuristic bias-adjustment for the transaction price-based realized range estimator of daily volatility in the presence of bid-ask bounce and non-trading. The adjustment is an extension of the estimator proposed in Christensen et al. (2009). We relax the assumption that all intra-day high (low) transaction prices are at the ask (bid) quote. Using data-based simulations we obtain estimates of the probability that a given intraday range is (upward or downward) biased or not, which we use for a more refined bias-adjustment of the realized range estimator. Both Monte Carlo simulations and an empirical application involving a liquid and a relatively illiquid S&P500 constituent demonstrate that ex post measures and ex ante forecasts based on the heuristically adjusted realized range compare favorably to existing bias-adjusted (two time scales) realized range and (two time scales) realized variance estimators

Range-based covariance estimation using high-frequency data: The realized co-range

We introduce the realized co-range, utilizing intraday high-low price ranges to estimate asset return covariances. Using simulations we find that for plausible levels of bid-ask bounce and infrequent and non-synchronous trading the realized co-range improves upon the realized covariance, which uses cross-products of intraday returns. One advantage of the co-range is that in an ideal world it is five times more efficient than the realized covariance when sampling at the same frequency. The second advantage is that the upward bias due to bid-ask bounce and the downward bias due to infrequent and non-synchronous trading partially offset each other. In a volatility timing strategy for S\\&P500, bond and gold futures we find that the co-range estimates are less noisy as exemplified by lower transaction costs and also higher Sharpe ratios when using more weight on recent data for predicting covariances

Predicting the Daily Covariance Matrix for S&P 100 Stocks Using Intraday Data - But Which Frequency To Use?

This paper investigates the merits of high-frequency intraday data when forming minimum variance portfolios and minimum tracking error portfolios with daily rebalancing from the individual constituents of the S&P 100 index. We focus on the issue of determining the optimal sampling frequency, which strikes a balance between variance and bias in covariance matrix estimates due to market microstructure effects such as non-synchronous trading and bid-ask bounce. The optimal sampling frequency typically ranges between 30- and 65-minutes, considerably lower than the popular five-minute frequency. We also examine how bias-correction procedures, based on the addition of leads and lags and on scaling, and a variance-reduction technique, based on subsampling, affect the performance

Modeling and Forecasting S&P 500 Volatility: Long Memory, Structural Breaks and Nonlinearity

The sum of squared intraday returns provides an unbiased and almost error-free measure of ex-post volatility. In this paper we develop a nonlinear Autoregressive Fractionally Integrated Moving Average (ARFIMA) model for realized volatility, which accommodates level shifts, day-of-the-week effects, leverage effects and volatility level effects. Applying the model to realized volatilities of the S&P 500 stock index and three exchange rates produces forecasts that clearly improve upon the ones obtained from a linear ARFIMA model and from conventional time-series models based on daily returns, treating volatility as a latent variable

The Effects of Federal Funds Target Rate Changes on S&P100 Stock Returns, Volatilities, and Correlations

We study the impact of FOMC announcements of Federal funds target rate decisions on individual stock prices at the intraday level. We find that the returns, volatilities and correlations of the S&P100 index constituents only respond to the surprise component in the announcement, as measured by the change in the Federal funds futures rate. For example, an unexpected 25 basis points increase of the target rate leads on average to a 113 basis points negative market return within five minutes after the announcement. It also increases market volatility during the 60-minute window around the announcement with 147 basis points. Positive surprises, meaning bad news for stocks, provoke a stronger reaction than negative surprises. Market participants also respond differently to good and bad news. In case of bad news for stocks the fact that there is a surprise matters most, whereas in case of good news the magnitude of the surprise is more important. Across sectors, Financials and IT show the strongest response to target rate surprises