Valeriy Zakamulin

THE CARMA INTEREST RATE MODEL

In this paper, we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This model is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provides closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.

Forecasting the Size Premium Over Different Time Horizons

In this paper, we provide evidence that the small stock premium is predictable both in-sample and out-of-sample through the use of a set of lagged macroeconomic variables. We find that it is possible to forecast the size premium over time horizons that range from one month to one year. We demonstrate that the predictability of the size premium allows a portfolio manager to generate an economically and statistically significant active alpha.

Sharpe (Ratio) Thinking About the Investment Opportunity Set and CAPM Relationship

In the presence of a risk-free asset the investment opportunity set obtained via the Markowitz portfolio optimization procedure is usually characterized in terms of the vector of excess returns on individual risky assets and the variance-covariance matrix. We show that the investment opportunity set can alternatively be characterized in terms of the vector of Sharpe ratios of individual risky assets and the correlation matrix. This implies that the changes in the characteristics of individual risky assets that preserve the Sharpe ratios and the correlation matrix do not change the investment opportunity set. The alternative characterization makes it simple to perform a comparative static analysis that provides an answer to the question of what happens with the investment opportunity set when we change the risk-return characteristics of individual risky assets. We demonstrate the advantages of using the alternative characterization of the investment opportunity set in the investment practice. The Sharpe ratio thinking also motivates reconsidering the CAPM relationship and adjusting Jensens alpha in order to properly measure abnormal portfolio performance.

Market Timing with Moving Averages: Anatomy and Performance of Trading Rules

In this paper, we contribute to the literature in two important ways. Therst contri- bution is to demonstrate the anatomy of market timing rules with moving averages. Our analysis offers a broad and clear perspective on the relationship between different rules and reveals that all technical trading indicators considered in this paper are computed in the same general manner. In particular, the computation of every technical trading indicator can be equivalently interpreted as the computation of the weighted moving average of price changes. The second contribution of this paper is to perform the longest out-of-sample testing of a set of trading rules. The trading rules in this set are selected to have clearly distinct weighting schemes. We report the detailed historical performance of the trading rules over the period from 1870 to 2010 and debunk several myths and common beliefs about market timing with moving averages.

Market Timing with a Robust Moving Average

In this paper we entertain a method of finding the most robust moving average weighting scheme to use for the purpose of timing the market. Robustness of a weighting scheme is defined its ability to generate sustainable performance under all possible market scenarios regardless of the size of the averaging window. The method is illustrated using the long-run historical data on the Standard and Poors Composite stock price index. We find the most robust moving average weighting scheme, demonstrates its advantages, and discuss its practical implementation.

SECULAR MEAN REVERSION AND LONG-RUN PREDICTABILITY OF THE STOCK MARKET: Secular Mean Reversion and Long-Run Predictability of the Stock Market

The empirical financial literature reports evidence of mean reversion in stock prices and the absence of out‐of‐sample return predictability over horizons shorter than 10 years. Anecdotal evidence suggests the presence of mean reversion in stock prices and return predictability over horizons longer than 10 years, but thus far, there is no empirical evidence confirming such anecdotal evidence. The goal of this paper is to fill this gap in the literature. Specifically, using 141 years of data, this paper begins by performing formal tests of the random walk hypothesis in the prices of the real S&P Composite Index over increasing time horizons of up to 40 years. Although our results cannot support the conventional wisdom that the stock market is safer for long‐term investors, our findings speak in favor of the mean reversion hypothesis. In particular, we find statistically significant in‐sample evidence that past 15‐17 year returns are able to predict the future 15‐17 year returns. This finding is robust to the choice of data source, deflator, and test statistic. The paper continues by investigating the out‐of‐sample performance of long‐horizon return forecasting based on the mean‐reverting model. These latter tests demonstrate that the forecast accuracy provided by the mean‐reverting model is statistically significantly better than the forecast accuracy provided by the naive historical‐mean model. Moreover, we show that the predictive ability of the mean‐reverting model is economically significant and translates into substantial performance gains.

Technical Trading Rules

This chapter reviews the most common trend-following rules that are based on moving averages of prices. It also discusses the principles behind the generation of trading signals in these rules. This chapter also illustrates the limitations of these rules and argues that the moving average trading rules are advantageous only when the trend is strong and long-lasting.

Optimal Dynamic Portfolio Risk Management

Numerous econometric studies report that financial asset volatilities and correlations are time-varying and predictable. Over the past decade, this knowledge has stimulated increasing interest in various dynamic portfolio risk control techniques. The two basic types of risk control techniques are: risk control across assets and risk control over time. At present, the two types of risk control techniques are not implemented simultaneously. There has been surprisingly little theoretical study of optimal dynamic portfolio risk management. In this paper, the author fills this gap in the literature by formulating and solving the multi-period portfolio choice problem. In terms of dynamic portfolio risk control, the solution shows that it is optimal to simultaneously control portfolio risk both across assets and over time. Using several datasets and performing out-of-sample simulations, the author demonstrates the superiority of dynamic portfolio risk control both across assets and over time. Specifically, he shows that portfolios with risk control only across assets outperform equally weighted portfolios and that portfolios with risk control both across assets and over time outperform portfolios with risk control across assets only.

A Comprehensive Look at the Empirical Performance of Moving Average Trading Strategies

Despite the enormous current interest in market timing and a series of publications in academic journals, there is still lack of comprehensive research on the evaluation of the profitability of trading rules using methods that are free from the data-snooping bias. In this paper we utilize the longest historical dataset that spans 155 years and extend previous studies on the performance of moving average trading rules in a number of important ways. Among other things, we investigate whether overweighting the recent prices improves the performance of timing rules; whether there is a single optimal lookback period in each trading rule; and how accurately the trading rules identify the bullish and bearish stock market trends. In our study we, for the first time, use both the rolling- and expanding-window estimation scheme in the out-of-sample tests; study the performance of trading rules across bull and bear markets; and perform numerous robustness checks and tests for regime shifts in the stock market dynamics. Our main results can be summarized as follows: There is strong evidence that the stock market dynamics are changing over time. We find no statistically significant evidence that market timing strategies outperformed the market in the second half of our sample. Neither the shape of the weighting function nor the type of the out-of-sample estimation scheme allows a trader to improve the performance of timing rules. All market timing rules generate many false signals during both bullish and bearish stock market trends, yet these rules tend to outperform the market in bear states.

Secular Mean Reversion and Long-Run Predictability of the Stock Market

Empirical financial literature documents the evidence of mean reversion in stock prices and the absence of out-of-sample return predictability over periods shorter than 10 years. The goal of this paper is to test the random walk hypothesis in stock prices and return predictability over periods longer than 10 years. Specifically, using 141 years of data, this paper begins by performing formal tests of the random walk hypothesis in the prices of the real S&P Composite Index over increasing time horizons up to 40 years. Even though our results cannot support the conventional wisdom which says that the stock market is safer for long-term investors, our findings speak in favor of the mean reversion hypothesis. In particular, we find statistically significant in-sample evidence that past 15-17 year returns are able to predict future 15-17 year returns. This finding is robust to the choice of data source, deflator, and test statistic. The paper continues by investigating the out-of-sample performance of long-horizon return forecast based on the mean-reverting model. These latter tests demonstrate that the forecast accuracy provided by the mean-reverting model is statistically significantly better than the forecast accuracy provided by the naive historical-mean model. Moreover, we show that the predictive ability of the mean-reverting model is economically significant and translates into substantial performance gains.