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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jeconom.2005.01.004 Byline: Eric Ghysels (a), Pedro Santa-Clara (b), Rossen Valkanov (b) Abstract: We consider various mixed data sampling (MIDAS) regressions to predict volatility. The regressions differ in the specification of regressors (squared returns, absolute returns, realized volatility, realized power, and return ranges), in the use of daily or intra-daily (5-min) data, and in the length of the past history included in the forecasts. The MIDAS framework allows us to compare regressions across all these dimensions in a very tightly parameterized fashion. Using equity return data, we find that daily realized power (involving 5-min absolute returns) is the best predictor of future volatility (measured by increments in quadratic variation) and outperforms models based on realized volatility (i.e. past increments in quadratic variation). Surprisingly, the direct use of high-frequency (5min) data does not improve volatility predictions. Finally, daily lags of 1-2 months are sufficient to capture the persistence in volatility. These findings hold both in- and out-of-sample. Author Affiliation: (a) Department of Economics, University of North Carolina, Gardner Hall, CB 3305, Chapel Hill, NC 27599-3305, USA (b) Department of Finance, The Anderson School, University of California, 110 Westwood Plaza, C5.19, Los Angeles, CA 90095-1481, USA

We consider various mixed data sampling (MIDAS) regressions to predict volatility. The regressions differ in the specification of regressors (squared returns, absolute returns, realized volatility, realized power, and return ranges), in the use of daily or intra-daily (5-min) data, and in the length of the past history included in the forecasts. The MIDAS framework allows us to compare regressions across all these dimensions in a very tightly parameterized fashion. Using equity return data, we find that daily realized power (involving 5-rain absolute returns) is the best predictor of future volatility (measured by increments in quadratic variation) and outperforms models based on realized volatility (i.e. past increments in quadratic variation). Surprisingly, the direct use of high-frequency (5min) data does not improve volatility predictions. Finally, daily lags of 1-2 months are sufficient to capture the persistence in volatility. These findings hold both in- and out-of-sample. JEL classification: C22; C53; G12 Keywords: Volatility forecasting; MIDAS; High-frequency data; Model selection

A study analyzing the returns from stock markets is presented. The relationship between the average returns and average variance based on conditions is examined. It is observed that the returns are directly proportionate to the risks in the stock markets.

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jfineco.2004.03.008 Byline: Eric Ghysels (a), Pedro Santa-Clara (b), Rossen Valkanov (b) Abstract: This paper studies the intertemporal relation between the conditional mean and the conditional variance of the aggregate stock market return. We introduce a new estimator that forecasts monthly variance with past daily squared returns, the mixed data sampling (or MIDAS) approach. Using MIDAS, we find a significantly positive relation between risk and return in the stock market. This finding is robust in subsamples, to asymmetric specifications of the variance process and to controlling for variables associated with the business cycle. We compare the MIDAS results with tests of the intertemporal capital asset pricing model based on alternative conditional variance specifications and explain the conflicting results in the literature. Finally, we offer new insights about the dynamics of conditional variance. Author Affiliation: (a) Kenan-Flagler Business School, McColl Building, Suite 4100, University of North Carolina, Chapel Hill NC 27599-3490, USA (b) The John E. Anderson Graduate School of Management, University of California at Los Angeles, Los Angeles, CA 90095-1481, USA Article Note: (footnote) [star] We thank Michael Brandt, Tim Bollerslev, Mike Chernov, Rob Engle, Shingo Goto, Amit Goyal, Campbell Harvey, David Hendry, Francis Longstaff, Nour Meddahi, Eric Renault, Matt Richardson, Neil Shephard, and seminar participants at Barclays Global Investors, Centro de Estudios Monetarios y Financieros (Madrid), Emory University, the Global Association of Risk Professionals, Instituto Tecnologico Autonomo de Mexico (Mexico City), Instituto Superior de Ciencias do Trabalho e da Empresa (Lisbon), the Centre Interuniversitaire de Recherche en Analyse des Organisations Conference on Financial Econometrics (Montreal), Lehman Brothers, London School of Economics, Morgan Stanley, New York University, Oxford University, University of Cyprus, University of North Carolina, and University of Southern California for helpful comments. We especially thank an anonymous referee whose suggestions greatly improved the paper. Arthur Sinko provided able research assistance.

A foreign exchange diffusion model is presented using discrete data. Financial markets need not be complete with this model.

A paper on interest rate caps and swaptions reveals that four factors influence swaption prices. Research results indicate that prices for long-term swaptions are overvalued.

Using more than one factor in models of American swaptions can increase savings significantly in the exercise of the swaptions .

A novel approach for dynamic portfolio selection is presented. The proposed method, which is similar to Markowitz paradigm, mechanically manages and optimizes portfolios.

The article examines the difference in returns under Republican and Democratic presidencies. Stock market excess return is lower under Republican presidents than under Democratic ones. Business-cycle variables do not explain the differences, and no election-date influences are observed; hence, the issue is still an economic puzzle.

The positive correlation between market returns and average stock variance is examined.