Portfolio Formation Period Research Articles

Detailed study of a moving average trading rule

We present a detailed study of the performance of a trading rule that uses moving averages of past returns to predict future returns on stock indexes. Our main goal is to link performance and the stochastic process of the traded asset. Our study reports short-, medium- and long-term effects by looking at the Sharpe ratio (SR). We calculate the Sharpe ratio of our trading rule as a function of the probability distribution function of the underlying traded asset and compare it with data. We show that if the performance is mainly due to presence of autocorrelation in the returns of the traded assets, the SR as a function of the portfolio formation period (look-back) is very different from performance due to the drift (average return). The SR shows that for look-back periods of a few months the investor is more likely to tap into autocorrelation. However, for look-back larger than few months, the drift of the asset becomes progressively more important. Finally, our empirical work reports a new long-term effect, namely oscillation of the SR and proposes a non-stationary model to account for such oscillations.

Information Ratio Analysis of Momentum Strategies

In the past 20 years, momentum or trend following strategies have become an established part of the investor toolbox. We introduce a new way of analyzing momentum strategies by looking at the information ratio (IR, average return divided by standard deviation). We calculate the theoretical IR of a momentum strategy, and show that if momentum is mainly due to the positive autocorrelation in returns, IR as a function of the portfolio formation period (look-back) is very different from momentum due to the drift (average return). The IR shows that for look-back periods of a few months, the investor is more likely to tap into autocorrelation. However, for look-back periods closer to 1 year, the investor is more likely to tap into the drift. We compare the historical data to the theoretical IR by constructing stationary periods. The empirical study finds that there are periods/regimes where the autocorrelation is more important than the drift in explaining the IR (particularly pre-1975) and others where the drift is more important (mostly after 1975). We conclude our study by applying our momentum strategy to 100 plus years of the Dow-Jones Industrial Average. We report damped oscillations on the IR for look-back periods of several years and model such oscilations as a reversal to the mean growth rate.

Can the Cross-Sectional Variation in Expected Stock Returns Explain Momentum?

AbstractIt has been hypothesized that momentum might be rationally explained as a consequence of the cross-sectional variation of unconditional expected returns. Stocks with relatively high unconditional expected returns will on average outperform in both the portfolio formation period and in the subsequent holding period. We evaluate this explanation by first removing unconditional expected returns for each stock from raw returns and then testing for momentum in the resulting series. We measure the unconditional expected return on each stock as its mean return in the whole sample period. We find momentum effects vanish in demeaned returns.

Is More Always Better? Empirical Evidence on Optimal Portfolio Size

A restriction on portfolio size results in welfare losses for investors. To measure these welfare losses, we compare n-asset optimal portfolios with 26-asset optimal portfolios using the concept of proportionate opportunity cost. The original historical asset returns data are used with a VAR in generating joint returns distributions for the portfolio formation period. We find that suboptimal diversification imposes substantial costs on investors with low levels of relative risk aversion. Investors with high levels of risk aversion incur very small or no cost at all diversifying sub-optimally. We show that investors with high levels of risk aversion place most of their initial wealth in the safe asset and, therefore, few stocks are needed to achieve optimal diversification.

Relative Spurious Regression Bias in Business-Cycle Models of Stock Momentum

We investigate whether persistent macroeconomic variables can be reliably shown to predict momentum profits. We find that when predictor variables are persistent and the predictive relationship is estimated over a period that overlaps the momentum portfolio formation period, predicted returns will be positively correlated with past returns. This occurs even when returns are constructed to be serially uncorrelated and independent of the predictors. This means there will be a positive predicted return to momentum portfolios and the macroeconomic variables will appear to explain momentum profits, even when stock returns are unrelated to the macroeconomic variables. We show that the apparent ability of the business-cycle model in Chordia and Shivakumar (2002) to explain intermediate-term momentum profits comes from this effect, which we term a relative spurious regression bias. We demonstrate that results similar to those of Chordia and Shivakumar obtain when we replace their macroeconomic variables with random variables constructed to be persistent but independent of stock returns. Once the parameter estimation period is chosen to be prior to the portfolio formation period, the predictive power of the macroeconomic variables disappears and momentum is no longer explained by the business cycle model.

Future Excess Returns to High R&D Firms and Firm Size

Prior research documented that high R&D intensity firms generate future positive excess returns. We explore the magnitude of future excess returns to small and large capitalization firms within the high R&D intensity group. Our inquiry is motivated by arguments in the innovation literature that technical and commercial uncertainty associated with R&D is larger for small than large R&D firms. Using data over the period 1975 to 2005, we find average excess returns over the three-year post portfolio formation period of 6.40% for the high R&D intensity portfolio. However, the excess returns are 7.15% and 3.15% for the small and large high R&D intensity firms, respectively. Small firms constitute only 8.57% of the total market value of the high R&D intensity portfolio, while large firms constitute 78.20%. Taken together, the results suggest that the large magnitude of future excess returns to small high R&D intensity firms do not imply large gains for investors. We also find that the spread in uncertainty (future profitability) between large and small firms within high R&D intensity firms is larger (smaller) than the spread in low and non-R&D firms, suggesting that uncertainty (future profitability) is disproportionately high (low) for small, high R&D firms. These results suggest that the larger magnitude of future excess returns to small, high R&D intensity firms are likely due to greater risk associated with them.

In this issue

In this issue

Evaluating a news‐aware quantitative trader: The effect of momentum and contrarian stock selection strategies

AbstractWe study the coupling of basic quantitative portfolio selection strategies with a financial news article prediction system, AZFinText. By varying the degrees of portfolio formation time, we found that a hybrid system using both quantitative strategy and a full set of financial news articles performed the best. With a 1‐week portfolio formation period, we achieved a 20.79% trading return using a Momentum strategy and a 4.54% return using a Contrarian strategy over a 5‐week holding period. We also found that trader overreaction to these events led AZFinText to capitalize on these short‐term surges in price.

Return‐based investment strategies in the New Zealand stock market: momentum wins

PurposeThe purpose of this paper is to examine the profitability of return‐based investment strategies in the New Zealand stock market; 16 such strategies are examined for the period from January 1995 to December 2004.Design/methodology/approachThe paper shows that, at the end of each month of the sample period, every security is ranked in ascending order using their past J‐month formation period cumulative return (J=3, 6, 9 and 12). Then these securities are allocated to three groups; group 1 represents the loser portfolio, while group 3 represents the winner portfolio. Finally, equally weighted average returns of winner and loser portfolios are calculated over the next K‐month holding period (K=3, 6, 9, and 12). The statistical significance of the returns earned from buying winners and shorting losers is tested in order to determine the profitability of proposed strategies.FindingsThe findings in this paper show that a strong momentum effect, rather than a reversal effect, is present in this market. For example, the strategy, which is based on a six‐month portfolio formation period and a six‐month holding period, generates a monthly return of 1.14 per cent. These strategies are most profitable when they are based on formation and holding periods of three‐to‐six months. Further analyses reveal that the profits generated by such investment strategies cannot be explained by either the small firm effect or the January effect.Originality/valueThe main implication of this paper shows that buying past winners and selling past losers is profitable in the short to medium run in New Zealand.

The Opportunity Cost of Being Constrained by the Type of Asset: Bonds Only or Stocks Only

I explore investors' welfare losses when they restrict themselves to invest in either stocks only or bonds only, but not in both. The restriction gives investors sub-optimal asset allocations that result in welfare losses. To measure these welfare losses I compare “only stock indices and Treasury bills” optimal portfolios and “only bond indices and Treasury bills” optimal portfolios with “stock and bond indices and Treasury bills” optimal portfolios using the concept of proportionate opportunity cost along with various CRRA utility functions. The original historical asset returns data set is used with a VAR in generating joint returns distributions for the portfolio formation period. I show that for investors with low levels of risk aversion welfare losses do not exceed 1.8% of initial wealth when they invest sub-optimally. For investors with medium and high levels of relative risk aversion, suboptimal portfolios of only one type of assets, stocks only or bonds only, along with Treasury bills, give expected utility about as high as optimal portfolios that include both types of assets, stocks and bonds.

Does Time Variation in Systematic Risk Affect the Profitability of Contrarian Investment Strategies?

Recent empirical studies seem to suggest that contrarian strategies make substantial profits that may be inconsistent with informationaly efficient markets. This paper examines whether the detection of contrarian profits is sensitive to the definition of abnormal returns and the duration of the formation and testing periods and investigates the effect of well-known monthly seasonals on the empirical results. Furthermore, in view of recent evidence that beta risk is not constant, the paper employs a procedure that allows for time-variation in systematic risk, and also examines whether abnormal returns of contrarian strategies are normal compensation for changes in risk between portfolio formation and portfolio testing period. No empirical evidence on contrarian profits exist so far for the Athens Stock Exchange, an emerging market for which one would expect more return predictability. To anticipate the results, we find that longer horizon contrarian strategies are more profitable than shorter horizon strategies. However, contrarian profits are very sensitive to the specification of abnormal returns, i.e. when we allow beta risk to vary over time most of the profits from contrarian strategies disappear. Furthermore, even for the case where we do detect arbitrage profits the results indicate that they may be due to changes in market risk.

Contrarian and Momentum Strategies in the Indian Capital Market

The study attempts to evaluate if there are any systematic patterns in stock returns for the Indian market. The empirical findings reveal that there is a reversal in long-term returns, once the short-term momentum effect has been controlled by maintaining a one year gap between portfolio formation period and the portfolio holding period. A contrarian strategy based on long-term past returns provides moderately positive returns. Further, there is a continuation in short-term returns and a momentum strategy based on it provides significantly positive payoffs. The results in general are in conformity with those for developed capital markets such as the US.

Do International Diversification Benefits Continue Beyond the Portfolio Formation Period in a Small Market? Evidence for New Zealand Before and During the Asian Crisis

This research examines whether international diversification benefits achieved in an initial portfolio formation period continue to be realised in subsequent evaluation periods and in the face of a major market disturbance. A NZ-only efficient frontier is used as a base investment from which off-shore unit trusts are added. Off-shore unit trusts considered are from Australia, Hong Kong, Japan and Great Britain. The analysis is conducted over a six-year period which includes the recent Asian crisis. It is found that diversification reduced the impacts of the crisis, and that the traditional, full covariance portfolio formation model performed better than three simpler models.

Optimal Diversification: Is It Really Worthwhile?

Executive Summary. Recent research has demonstrated that the Markowitz efficient frontier is fuzzy and may consist of many statistically indistinguishable frontiers. Therefore, it opens the possibility that an efficient portfolio developed by mean-variance analysis may not be any more efficient than a naively diversified portfolio. Using an efficiency test developed by Gibbons, Ross, and Shanken (1989), we find evidence to support that an efficient portfolio is statistically more efficient than a corresponding naively diversified portfolio when the portfolio formation period is the same as the period used for testing the efficiency difference. However, no evidence is found to support that an efficient portfolio is statistically more efficient than a corresponding naively diversified portfolio when the portfolio formation period differs from the test period. Thus, in practical terms, efficient portfolios may not be superior to naively diversified portfolios in a statistical sense.

Do UK Security Analysts Over-react?

Abstract Consensus analysts' earnings per share forecasts have become increasingly accessible in recent years and such measures have been widely adopted by academics as proxies for the market's expectations of earnings. Some US studies have suggested that analysts, in revising earnings forecasts, are prone to over-reaction. This study tests for evidence of over-reaction in revisions of the consensus earnings per share forecasts of UK companies reported by the Institutional Brokers Estimate System. For a series of periods, portfolios of companies attracting high and low revisions of earnings forecasts are constructed. We then compare the subsequent earnings forecast of the companies which attracted high revisions in the portfolio formation period with those of the companies which attracted low revisions in the portfolio formation period. We also compare actual changes in annual earnings with forecast changes in annual earnings. Both analyses suggest that UK analysts are prone to under-reaction, a finding w...