Size, Value and Equity Premium Waves Tuesday, 14 August, 2018

A new financial research paper has been published and is related to:

#25 - Small Capitalization Stocks (Size) Premium
#26 - Value (Book-to-Market) Anomaly

Author: Herskovic, Kind, Kung

Title: Size Premium Waves

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3220825

Abstract:

This paper examines the link between microeconomic uncertainty and the size premium across different frequencies in an investment model with heterogeneous firms. We document that the observed time-varying dispersion in firm-specific productivity can account for a large size premium in the 1960's and 1970's, the disappearance in the 1980's and 1990's, and reemergence in the 2000's. Periods with a large (small) size premium coincide with high (low) microeconomic uncertainty. During episodes of high productivity dispersion, small firms increase their exposure to macroeconomic risks. Our model can also explain the strong positive low-frequency co-movement between size and value factors, but a negative relation with the market factor.

Notable quotations from the academic research paper:

"The relation between firm size and expected stock returns has varied signifi cantly over time in waves. Banz (1981) documented a size premium whereby firms with small market capitalizations earn higher expected returns than large ones before 1975, and that this size e ffect cannot be explained by market betas. The size e ffect subsequently vanished starting in the early 1980s to the late 1990s, before reemerging after 2000.

We also observe that measures of microeconomic uncertainty, such as the cross-sectional dispersion in plant- and firm-level total factor productivity (TFP), sales, and payouts, exhibit similar low-frequency patterns as the size premium.

size premium waves

Figure 1 illustrates that microeconomic uncertainty is strongly positively correlated with the size premium. In this paper, we demonstrate how persistent variation in microeconomic uncertainty can potentially rationalize the observed size premium waves.

To this end, we build a dynamic partial equilibrium production model with heterogeneous firms. The model has several distinguishing features. First, firms are subject to persistent idiosyncratic and aggregate TFP shocks with time-varying second moments. The second moment shocks to the idiosyncratic component capture time-varying cross-sectional dispersion in idiosyncratic productivity (microeconomic uncertainty) while the second moment shocks to the aggregate component capture fluctuations in macroeconomic uncertainty. Second, firms face quadratic adjustment costs and operating costs. Third, the representative household has recursive utility de fined over aggregate streams of consumption.

We find that our calibrated model produces a realistic size premium and captures the salient dynamics of the size premium across diff erent frequencies. Namely, the model generates a countercyclical size premium and reproduces the low-frequency wave patterns, including a large spread during 1960-1980, a disappearance between 1980-2000, and resurgence post-2000. The mean-reverting idiosyncratic TFP shocks helps to generate a negative relation between firm market capitalization and expected returns in the stationary distribution.

Small firms are those that have received a recent history of negative idiosyncratic shocks. Due to mean reversion, the shorter-term payouts of small fi rms therefore constitute a smaller share of aggregate payouts relative to their longer-term payouts. With a similar logic, the payout shares of large firms have the opposite pattern. Consequently, small firms are more exposed to aggregate long-run risks than large firms, which gives rise to a quantitatively signi ficant size premium.

The low-frequency fluctuations of the size premium in the model are driven by the persistent volatility process for idiosyncratic TFP shocks. When TFP dispersion is high, small fi rms are subjected to a larger history of negative idiosyncratic shocks that increases their exposure to longrun risks relative to periods with low TFP dispersion. As a result, the size premium is larger during periods of higher TFP dispersion. In the data, we find a very strong association between TFP dispersion and the size premium at low frequencies, consistent with the model predictions. Calibrating the idiosyncratic volatility process to our empirical measure, we show that our model can provide a quantitatively relevant account of the observed size premium waves.

equity premium

micro and macro uncertainity

The equity premium is strongly correlated with macroeconomic uncertainty, as measured by the realized volatility of consumption growth, output growth, and TFP, but negatively related to microeconomic uncertainty at low frequencies. The correlation between the equity premium and macroeconomic uncertainty is 0.76, while the correlation between the equity premium and microeconomic uncertainty is -0.64 (See Figures 3 & 4).

The model also generates signifi cant equity and value premia, inline with the observed magnitudes in the data. Persistent shocks to aggregate productivity growth are a source of long-run risk that help to generate a sizable equity premium when coupled with recursive preferences. Persistent second moment shocks to aggregate productivity growth generate a countercyclical equity premium.

equity premium

The size an value premia are strongly positively related at low frequencies (i.e., correlation of 0.66), but they are both negatively related with the equity premium at low frequencies (correlation between the size premium and the equity premium is -0.62 and the correlation between the value premium and the equity premium is -0.50). Figure 2 provides a visual depiction of these relations.

A value premium arises due to the combination of the asymmetric capital adjustment costs and operating costs, in a similar spirit as Zhang (2005). Firms with high book-to-market ratios have large stocks of capital, but have experienced a recent history of negative idiosyncratic shocks. Therefore, such firms have strong incentives to disinvest due to the low marginal product of capital and high operating costs, but the presence of capital adjustment costs prevents them from selling off their unproductive capital rapidly, which exposes high book-to-market (value) fi rms more to adverse aggregate shocks than low book-to-market (growth) firms. In particular, discouraging aggressive disinvestment policies prevents fi rms with large capital stocks from increasing payouts financed through capital sales in response to negative idiosyncratic shocks. The operating costs that are proportional to the capital stock of the firm reduce the funds available for payouts, especially for large fi rms. Therefore, these investment frictions imply that high book-to-market fi rms have low payout shares today, but higher payout shares at longer horizons due to mean reversion. Therefore, value firms are more exposed to long-run risks than growth firms, thereby generating a sizable value premium. The low-frequency fluctuations of the value premium are driven by the persistent idiosyncratic volatility process."


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SSRN Platform Upgrade Friday, 10 August, 2018

We would like to share an announcement from SSRN (Social Science Research Network) as we link a lot from Quantpedia to a research papers hosted on www.ssrn.com.

"SSRN Platform Upgrade Server Outage this Weekend

We wanted to let you know about a planned outage to SSRN this weekend, which will mean you will not be able to access the site during this period.

The outage will take place from 9am EST Friday 10th August until 9am EST Monday 13th August. Please ensure you download any papers you need before this planned site maintenance.

This outage is to improve the robustness and performance of the platform going forward.

Thank you,
SSRN Team

"

A New Filter Fields in Quantpedia Screener Tuesday, 7 August, 2018

As we mentioned several days ago, we have started a really fruitful cooperation with QuantConnect (see our blog post). With the company’s resources and extensive database of historical data, combined with a backtesting engine, QuantConnect was able to start systematically backtesting strategies from our database. So we can finally start showing you out-of-sample backtests for some of our strategies ...

Now we are adding a new field into our Screener so that you are now able to filter strategies with QuantConnect code, charts and statistics:

Screener

There are two more fields we are also adding into our Screener subpage:

Free/Premium field allows you to screen and display only Free or Only Premium strategies out of our database ...

And Papers field allows you to screen and display only strategies with/without any related research papers ...

The QUANTPEDIA Team

 

An Extensive Test of Market Timing Strategies in the Gold Market Monday, 6 August, 2018

Authors: Bartsch, Baur, Dichtl, Drobetz

Title: Investing in the Gold Market: Market Timing or Buy-and-Hold?

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3202658

Abstract:

While the literature on gold is dominated by studies on its diversification, hedging, and safe haven properties, the question “When to invest in gold?” is generally not analyzed in much detail. We test more than 4,000 seasonal, technical, and fundamental timing strategies for gold. While we find large gains in economic terms relative to the buy-and-hold benchmark for several strategies, the results are robust to data-snooping biases only for selected technical trading strategies. These superior technical trading strategies outperform the buy-and-hold benchmark because they shift out of the gold market following a prolonged trend of negative gold market returns. We verify that the outperformance is not driven by a systematic reaction to the broader market environment and conclude that our results point to the presence of behavioral biases inducing gold market trends.

Notable quotations from the academic research paper:

"The question when to invest in gold has received remarkably little attention, while most research focuses on the diversification, hedging, and safe haven properties of gold. This study aims to close this gap by analyzing if an active investor can beat a passive buy-and-hold strategy by timing the gold market. For our evaluation period from January 1990 to December 2015, our back-test results for more than 4,000 different seasonal, technical, and fundamental trading strategies reveal that significant excess returns were possible.

To construct a comprehensive collection of market timing strategies, we build either on the economic properties of gold or incorporate the findings regarding previously surveyed anomalies in gold prices. In this section, we describe the strategies, rules, and variables used to predict gold returns.

Seasonal trading strategies:

Baur (2013) provides evidence for monthly seasonality in the gold market, with positive and statistically significant gold returns limited to the months September and November. Similar results are shown by Qi and Wang (2013) for the Chinese gold market and Naylor, Wongchoti, and Ith (2015) for U.S. gold ETF returns. To exploit this monthly anomaly, an investor could follow a simple strategy that invests in gold in September and November and reverts to holding cash in the remaining months. Although this strategy is supported by economic intuition, e.g., by the increased wedding season gold jewelry demand in India, the strategy itself is merely mechanic. Therefore, to address the concern that this strategy has simply been ‘mined’ from the data, we follow Dichtl and Drobetz (2014) and implement a more comprehensive approach: Each month, an investor can either be invested 100% in the gold market, or 100% in cash. In this vein, we obtain 212 = 4,096 different monthly seasonal allocation strategies, labeled from SEA0 to SEA4095, where SEA stands for seasonal.

Technical trading strategies:

Moskowitz, Ooi, and Pedersen (2012) find time series momentum in monthly returns of several liquid instruments, including gold futures. Therefore, we include monthly technical trading strategies based on moving average and momentum indicators in our empirical analyses. We invest in the gold market if the short moving average is above the long moving average and revert to holding cash otherwise. The short index for the moving average is set to 𝑠 = 1, 2, 3 and the long index to 𝑙 = 9, 12, which results in six moving average strategies. We also set 𝑠 = 1 and 𝑙 = 10, 24, 36, 48 to cover some other parameterizations that are popular in the literature and among investors. Overall, we employ ten different moving average strategies. We invest in gold if the gold market exhibits positive time series momentum. Otherwise, an allocation is taken in the cash market. Following Moskowitz, Ooi, and Pedersen (2012), we set π‘š = 1, 3, 6, 9, 12, 24, 36, 48 months.

Fundamental trading strategies:

Building on the economic properties of gold, a lot of researchers identify several fundamental factors that serve as predictors of future gold returns by affecting either the demand and supply of gold or market participants’ expectations thereof. To construct tradeable strategies based on these fundamental factors, we first estimate a simple linear regression model for each predictor variable (11 predictors in total) for forecasts of the spot price of gold. We also exploit the simple mean of all individual forecasts (𝑀𝐸𝐴𝑁) as another potential market timing strategy. We also consider a “kitchen sink” forecast (𝐾𝑆𝐹), which incorporates all available predictor variables simultaneously in a multivariate regression model.

performance of strategies

We measure the performance of our market timing strategies in terms of mean absolute returns and mean risk-adjusted excess returns, or Sharpe ratios (Sharpe, 1994), over the evaluation period. Table 3 lists the five best market timing strategies for each of the three strategy groups, i.e., seasonal trading strategies, technical trading strategies, and fundamental trading strategies.

Overall, while the results in Table 3 already provide a first indication which strategies perform well compared to the buy-and-hold strategy, these analyses neither test for statistical significance nor account for the data-snooping problem.

However, because all timing strategies are tested on the same data set, the observed outperformance may simply result from chance and not due to any robust relationship. To account for this data snooping bias, we apply a multiple testing framework and find that only a limited number of technical trading strategies show a statistically significant outperformance relative to the buy-and-hold strategy.

To assess the statistical significance of performance relative to buy-and-hold, while controlling for data snooping, we use Hansen’s (2005) SPA-test to all three types of strategies. In each test, the strategies are compared with the performance of the buy-and-hold benchmark. Accordingly, the first test considers all 4,095 different monthly seasonal trading strategies,12 the second test all 18 technical trading strategies, and the third test all 15 fundamental trading strategies. The SPA-test results are presented in Table 4.

test SPA

To further examine the characteristics of these superior technical trading strategies, we verify their long-term market timing ability using a conditional market model and preclude that their excess returns are compensation for crash risk, i.e. periods of persistent negative returns. Moreover, we find that the outperformance of these strategies is not driven by different economic and financial regimes. We thus conclude that the superiority of those timing strategies comes from the presence of behavioral biases in the gold market. As pointed out by Hurst, Ooi, and Pedersen (2013), trends emerge if market participants initially underreact to new information, possibly due to anchoring or conservatism. Trend-following strategies, such as time series momentum or moving-average rules, capitalize on the subsequent price changes, since the market price only gradually incorporates the full effect of the news. Once a trend has started, a delayed over-reaction may even exacerbate the trend, e.g., due to herding behavior, feedback trading, or biased self-attribution."


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Predictability of Betting-Against-Beta Factor Sunday, 29 July, 2018

A new financial research paper has been published and is related to:

#77 - Beta Factor in Stocks
#78 - Beta Factor in Country Equity Indexes

Author: Hedegaard

Title: Time-Varying Leverage Demand and Predictability of Betting-Against-Beta

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3194626

Abstract:

The leverage aversion theory implies that returns to the betting-against-beta (BAB) strategy are predictable by past market returns: An outward shift in investors' aggregate demand function simultaneously increases market prices and increases the expected future BAB return. I confirm the prediction empirically and  find that the BAB strategy performs better in times when and in countries where past market returns have been high. I construct timing-strategies that are long BAB half the time and short BAB half the time, based on past market returns, and show that these timing strategies have realized strong historical performance.

Notable quotations from the academic research paper:

"In the Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner (1965), the risk of an asset is measured by its market beta and the expected return on an asset is proportional to its beta such that the relation between beta and expected returns, the security market line (SML), has a slope equal to the equity risk premium and an intercept equal to the risk-free rate. Empirically, Black et al. (1972) fi nds that the SML is too flat, and Black (1972) and Frazzini and Pedersen (2014) (FP hereafter) suggest that the at SML is due to leverage constrained investors.

Instead of applying leverage, constrained investors obtain an expected return higher than the expected return on the market by over-weighting high-beta stocks and under-weighting low-beta stocks in their portfolios, thereby lowering future risk-adjusted returns on high-beta stocks and increasing future risk-adjusted returns on low-beta stocks. FP construct a betting-against-beta (BAB) portfolio that goes long low-beta assets, leveraged to a beta of one, and short high-beta assets, also leveraged to a beta of one. The leverage aversion theory in FP predicts that the SML should be too flat on average and that the BAB factor should have a positive average return, which FP also find empirically.

I show that according to the leverage aversion theory, a shift in investors' aggregate demand function moves the economy to a new equilibrium in which both prices and expected returns on the BAB factor have changed. The eff ect of an outward shift in investors' demand function on the expected BAB return is theoretically ambiguous, since there are two opposing e ffects:

First, holding expected returns constant, constrained investors become more constrained and increase the over-weight to high-beta stocks, such that the expected return on the BAB factor increases.

Second, since prices increase and expected returns decline for markets to clear, the improvement in utility of over-weighting high-beta stocks decline, such that investors become less constrained and the expected BAB return declines.

Thus, if investors become more constrained following an outward shift in their demand functions, the shift leads to an increase in the expected BAB return, but if investors become less constrained it leads to a decrease in the expected BAB return.

It seems natural that investors become more constrained following an outward shift in their demand functions, and I show that empirically high past market returns forecast high future BAB returns and that daily market returns are negatively correlated with contemporaneous BAB returns. I demonstrate this for both U.S. BAB returns and international BAB returns, as well as for BAB factors formed from country indices.

I show that past market returns predict future BAB returns using both regressions, sorts, and by constructing a trading strategy. First, regressing BAB returns on contemporaneous and lagged market returns shows that daily BAB returns have a strong negative correlation with daily market returns and that past market returns positively predict future BAB returns. Second, sorting BAB returns on past market returns shows that realized BAB returns are higher following high past market returns. I demonstrate this e ffect for both the United States as well as for a sample of 23 other countries. Third, I construct BAB-timing strategies that take a position in the BAB factor in a given country proportional to the past 12 month market return of that country. Across the 24 international countries, the BAB timing strategies have generated positive alpha to a two-factor model with the market and BAB in all but 2 countries, and the alpha is signi ficant in 12 of the 24 countries.

Further, the variation in expected BAB returns coming from past returns is not only a time series e ffect, it is also a cross sectional e ect. I show that past market returns help explain cross-country di fferences in future BAB returns. Sorting countries based on their past market return shows that future BAB returns are higher in countries for which the past market return was higher than the cross-country average market return, and future BAB returns are lower in countries for which the past market return was below the cross-country average.

I also test the predictability of BAB using country indices. Here, the BAB strategy goes long country indices with a low beta to a global index and short indices with a high beta to a global index. FP show that the BAB strategy generates positive excess returns in a region of 13 developed countries, and extending their results I show that the BAB strategy also generates positive returns in a region of 25 emerging countries. Further, I show that in each region the returns on the BAB strategy are predictable by past returns on a cap-weighted index of the countries in the region."


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