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федеральное государственное автономное образовательное учреждение высшего образования

"Национальный исследовательский университет

"Высшая школа экономики"

негосударственное образовательное учреждение высшего образования

"российская экономическая школа"(институт)

выпускная квалификационная работа

Прогнозирование доходности рынка акций на основе технического агрегированного индекса

Бакалаврская программа

Совместная программа по экономике НИУ ВШЭ и РЭШ

Автор:

М. В. Буробин

Научный руководитель:

О. К. Шибанов

Москва, 2019 г.



Аннотация

рынок акция фоновый макроэкономический

Большинство научных работ опираются на фундаментальные и макроэкономические переменные для прогнозирования рынка акций. Тем не менее, недавние исследования показали способность технических индикаторов прогнозировать рынок акций США, несмотря на общее мнение о том, что технические индикаторы не являются статистически значимыми переменными для предсказания доходности рынка акций. В связи с этим, мы проанализировали способность тех технических переменных, которые использовались в предыдущих работах, предсказывать доходности других рынков. Мы проанализировали фондовые рынки Великобритании и Южной Кореи и показали, что ни один из технических индексов, созданных с использованием метода частичных наименьших квадратов, главной компоненты и равных весов, а также ни один из 14 отдельных технических индикаторов не является хорошим предсказателем доходности рынка акций.



Abstract

Most academic papers rely on fundamental and macroeconomic variables to forecast equity risk premium. Yet, recent studies showed the ability of technical indicators to forecast equity risk premium in the US despite the overall consensus view that technical variables cannot predict equity risk premium at a significant level. Therefore, it was in our interest to investigate the ability of those technical indicators employed by authors of previous works to forecast equity risk premium outside the US. We analyzed UK and South Korea stock markets and showed that none of the technical indices created using partial least squares, principal component and equal weights methods as well as none of 14 individual technical indicators could be utilized to forecast equity risk premium.



Table of Contents

• 1. Introduction
• 2. Data
• 3. Construction of TECH PLS, TECH PC and TECH EW
• 4. Predictive models
• 5. Results
• 6. Conclusion
• Literature review



1. Introduction

A variety of studies were made to forecast stock market returns using any sort of macroeconomic and fundamental variables. For example, one of the most popular works on fundamental variables used to forecast equity risk premium include dividend yield (Campbell and Yogo, 2006), dividend payout ratio (Campbell and Shiller, 1988), and book-to-market ratio (Pontiff and Schall, 1998), while the main macroeconomic variables could be represented with nominal interest rates and interest rate spreads (Campbell, 1987), consumption-wealth ratio (Lettau and Ludvigson, 2001), and stock market volatility (Guo, 2006). However, Welch and Goyal (2008) showed that most of the fundamental and macroeconomic variables fail to forecast equity risk premium in the US stock market in the out-of-sample analysis.

While relatively little attention was paid to technical indicators as a tool to forecast equity risk premium, technical analysis could be used to achieve better forecasting power. In practice, many traders and investors use technical indicators to forecast the direction of the equity market as well as individual stocks' performance. Technical indicators is very popular tool to forecast short-term equity returns comparing to fundamental analysis that is usually used to forecast longer time periods. While fundamental analysis is based on identifying the true value of the company's share price, many fundamental-focused investors would have to wait a lot until the fair value is reflected in the stock price: it could take a month or even a year for this reflection to take place.

Furthermore, if we want to forecast the direction of the equity market in a week or a couple of months, technical analysis is a good choice for this goal, while many fundamental variables such as dividend yield, price-to-earnings ratio, and price-to-book ratio don't adjust that rapidly as those are partially based on company's earnings and therefore could not be used to forecast equity risk premium for short time periods in most of the cases.

A few papers also showed the impact of technical analysis on equity returns among individual and institutional investors. For example, Arvid et al (2014) showed that technical analysis led to lower returns for individual investors by isolating the trading strategy from other factors. However, Smith et al (2013) concluded that the net effect of technical analysis on the management of institutional equity-related portfolios has been beneficial. On average, the consensus still remains that technical analysis could not be used as a good tool to forecast equity returns.

However, recent studies that contributed to equity risk premium forecasting using technical indicators implemented by Neely et al (2014) and Qi Lin (2017) turned out to be surprising for us and for existing consensus view regarding technical indicators and their ability to forecast equity risk premium. Neely et al (2014) showed in his paper that technical index based on 14 individual technical indicators widely used by traders and investors could be a significant predictor of the equity risk premium in the US market. They found that technical indicators have statistically significant out-of-sample forecasting power, which is higher than the forecasting power of fundamental and macroeconomic indicators. On top of that, Qi Lin (2017) showed that another index based on the same technical indicators from Neely et al (2014) could produce significant forecasting power in the US and China stock markets that is higher than Neely et al (2014) proposed.

Therefore, it was in our interest to check the ability of technical indicators to forecast equity risk premium outside the US and China using the approach of previous authors as their results turned out to be surprising. This paper investigates the ability of technical indicators to forecast equity risk premium for FTSE 100 and KOSPI that are taken as a benchmark for UK and South Korea equity markets respectively.

The rest of the paper is organized as follows. We describe the data in section 2. In section 3, we describe the construction of 3 technical indices that are used to forecast equity risk premium. In section 4, we describe the predictive model. In section 5, we present the results of out-of-sample predictive regression for TECH PLS, TECH PC, TECH EW and 14 technical indicators from Neely et al (2014) for UK and South Korea markets. Section 6 concludes.

2. Data

In this section, we will present data used to forecast equity risk premium as well as underlying methods of technical indices construction. As in Neely et al (2014), we used 14 technical indicators based on three popular trading strategies.

The first strategy is based on the momentum rule, which generates a buy signal if the adjusted closing price of the equity index at the end of the current month (t₀) is higher than its level m months ago. If the price level at the end of the current month (t₀) is lower than m months ago, our strategy generates a sell signal. Similar to Neely et al (2014) we used a binary variable for this strategy, which takes the value of 1 in case of a buy signal and value of 0 in case of a sell signal. We derived the trading signal mathematically with the following equation:

, (1)

Where is the adjusted closing price at the end of the current month (t), while is the adjusted closing price at the end of month t-m, where m takes the values of 9 and 12, following Neely et al (2014). We use the same designations of MOM(9) and MOM (12) as Neely et al (2014) suggested.

Our second trading strategy is based on a moving average rule that helps traders and investors to reduce the noise that contained in price fluctuations, therefore moving averages help us to better identify the trend that the index is following. The general idea of many trading strategies based on a moving average rule is to look at the relation between the short moving average and long moving average. As short moving average is based on a smaller sample, it is more sensitive to price fluctuations of the underlying asset. If a short moving average crosses the longer one from downside up and is now trading above the longer MA, it represents a very bullish signal for traders and investors. Similar, if short MA crosses the longer one from upside down, it represents a very bearish signal. Taking this into consideration, similar to Neely et al (2014), we employ a trading strategy that generates a buy signal when the shorter moving average is trading higher than a longer MA and generates a sell signal when the opposite is true. This could be written down with the following equation:

, (2)

and

, (3)

Where m = s,l and s,l are the length of short and long moving averages respectively. Obviously, s < l. Following Neely et al (2014), we will designate these signals as MA(s,l) and will compute buy or sell signals for s = 1,2,3 and l = 9,12. Finally, we derived six indicators which are used afterward to predict equity risk premium for UK and South Korea markets. These indicators are: MA(1,9), MA(1,12), MA(2,9), MA(2,12), MA(3,9), MA(3,12).

Our third trading strategy is based on the on-balance volume rule. The volume could play an important role in equity risk premium forecasting as price increase/decrease sometimes does not carry valuable information itself. For example, if changes in the index price were accompanied by low volumes during that period of time, changes in the price could have been driven by an unexpected big bid/offer and low market liquidity pushing the price in any direction. In this case, price fluctuations do not matter much. However, if price increase/decrease was accompanied by higher than average volumes, this change may reveal new expectations of investors that may have started to price new information learned about the market. Therefore, on-balance-volume should be used as another useful technical measure. On-balance-volume is calculated by multiplying the volume traded during the given period of time by the binary variable that takes the value of 1 if the adjusted closing price of the market index is higher than the price in the previous month and -1 otherwise. To generate a buy or sell signal using the on-balance-volume measure, OBV onwards, we use a two-step procedure. Firstly, we calculate the moving average of the OBV for different periods. We use a period of 1,2,3 months for short moving averages and 9, 12 months for long moving averages. After constructing 5 moving averages at each time step, we generate a buy or sell signal by comparing each of the short moving averages with each of the long MAs. Similar to usual MA trading strategy, we call on a buy if shorter MA is trading above the longer one and call on a sell otherwise. We use a binary variable that takes the value of 1 in case of a buy signal and 0 in case of a sell signal. Equations for all three steps that are used in this trading strategy are presented below:

1) On-balance volume (OBV) calculation (Granville, 1963):

2) Moving average of the on-balance volume:

3) Generation of a buy or sell signal based on MA of OBV:

,

We then computed monthly trading signals for s = 1,2,3 and l = 9, 12 and came up with 6 technical indicators: VOL(1,9), VOL(1,12), VOL(2,9), VOL(2,12), VOL(3,9), VOL(3,12).

We used past prices and volume data taken from Thomson Reuters DataStream tool for the maximum available period of time. As for the UK market represented by FTSE 100, we used monthly and daily prices and monthly volume data since October 1986 to construct 14 technical indicators used further in our predictive models. Despite price data was available for earlier periods, we still had to use it since Oct 1986 as volume data started to be tracked only since the end of 1986. To create 6 simple moving averages, we used daily data of FTSE 100 adjusted closing prices that already account for dividends and stock splits, while we used monthly data for the construction of the rest 8 technical indicators. We arrived at a monthly equity risk premium values by deducting the 1M UK interest rate nominated in local currency from the log return of FTSE 100. After accounting for all lags occurred after the construction of technical indicators, we used data spanning from Nov 1992 and arrived at first predictive results in Dec 1995. Similar to FTSE 100, to forecast equity risk premium in South Korea, we used daily and monthly data of adjusted closing prices for KOSPI and monthly volume data since Jan 1990. Despite price and volume data was available since the beginning of 1984, we used data starting from 1990 due to earlier unavailability of short-term interest rates needed to calculate equity risk premium. We finally used data on 3M interest rate nominated in local currency spanning from 1991 to 2019. After accounting for all lags, we came up with the data for TECH PLS, TECH EW, TECH PC and 14 technical indicators starting from Jan 1996 and made the first prediction using our regression forecast on Jan 1999.



3. Construction of TECH PLS, TECH PC and TECH EW

As Qi Lin (2017) proposed, each technical indicator should capture some latent information that is relevant for equity risk premium forecasting. This appears because each of 14 technical indicators is based on past prices and volume data but due to different methods of construction captures information and expectations about the future events that are already priced-in differently. Hence, if we add these 14 technical indicators all together into a single model, it should forecast equity risk premium better. However, it could struggle from overfitting. To address this issue, the principal component method could be used as Neely et al (2014) proposed. However, Qi Lin (2017) showed that the PC method is not the best way of getting relevant information as PC will contain not only relevant latent factors but idiosyncratic error components as well. It was one of our interests to check whether the first principal component is a good indicator of equity risk premium forecasting, therefore we constructed TECH PC based on initial 14 technical indicators by taking the first principle component.

However, Qi Lin (2017) suggested using TECH PLS in the predictive model to arrive at stronger out-of-sample results than those of Neely et al (2014). Qi Lin (2017) finally showed that TECH PLS is a significant predictor of US and China equity risk premium and significantly outperforms TECH PC. In order to address the concern of data snooping, it was of our interest to validate results reported by Qi Lin (2017). Therefore, we used TECH PLS to forecast equity risk premium for FTSE 100 and KOSPI. Following Qi Lin (2017), we used a similar methodology to construct TECH PLS. Overall, PLS stands for Partial Least Squares method and was initially suggested as a useful tool by Kelly and Pruitt (2015) to forecast equity returns. Partial Least Squares method is made of two OLS regressions and could produce sufficient forecasting power when both time dimension and cross-sectional dimension become large. We use this two-step procedure to construct TECH PLS. According to Qi Lin (2017), in the first step for each technical indicator, , we run N time series OLS regression on equity risk premium () for each month t₀. We used last 60 months data to find the regression coefficients. This regression allowed us to extract true but not observable drivers of each technical indicator to future stock returns. The regression itself is presented below:

, t = 1, 2, …, T,

Where T = 60, as we run a regression based on the last 60 months data. Using the following regression, we came up with sensitivity coefficients for the period spanning from Nov 1992 to Mar 2019. We then used T cross-sectional regression that is represented with the following equation:

where N = 14 as we run a cross-sectional regression on 14 technical indicators at each time step. Finally, we came up with TECH PLS values at each month starting from Nov 1992 and ending in Mar 2019.

We also constructed TECH EW index, where EW stands for “Equal Weights”. As we have 14 technical indicators, at each month we weighted each indicator with 1/14 and add the weighted results all together to construct a single TECH EW index. We then used TECH EW to compare the predictive results with those of TECH PC and TECH PLS.

4. Predictive models

Following Qi Lin (2017), we used a similar univariate regression model to forecast equity risk premium for the next period:

,

where is the equity risk premium in the next period and TECH is one of the technical indices in the current month (TECH PLS, TECH PC or TECH EW). We then also compare the results of the univariate predictive model based on each of three technical indices with univariate regressions based on each of 14 individual technical indicators. On top of that, we compare each of the predictive results with the average excess return, which is somewhat different from the excess return proposed by Qi Lin (2017). Qi Lin (2017) calculated excess return (HA) from the beginning of the sample up to the current month, however, we used last 36 months to calculate average equity risk premium at each time step. Finally, to compare the results of the predictive models, we employed Campbell and Thomson (2008) statistic:

,

where is the realized equity risk premium in the next period, is the predicted equity risk premium by the model and HA is a rolling average calculated as discussed above. This measure could take values in the range and indicates that the model outperforms the average equity risk premium if is positive. Campbell and Thomson (2008) argued that if is higher than 0.5% for monthly equity risk premium forecasts, then the results are significant. We will use this benchmark in the discussion of our results in the next section.

Qi Lin (2017) showed that TECH PLS performs well in out-of-sample tests for US and China aggregate stock markets with TECH PLS for US stock market of 8.8%, which is significantly higher than those of TECH PC and TECH EW, which take values of 0.22% and 0.43% respectively. As for the Chinese stock market out-of-sample forecasts, TECH PLS generates of 2.337%, while TECH PC and TECH EW fails to outperform TECH PLS with of -0.225% and 0.408% respectively. Overall, Qi Lin (2017) results showed that TECH PLS is one of the most powerful tools to forecast equity risk premium across US and China stock markets, however, the results may be different on other developed and emerging markets. To address the concern of data snooping, we analyzed another one developed and one emerging market, UK and South Korea respectively and came to a conclusion that results may be different this time.

5. Results

We analyzed the UK and South Korean stock markets and came to the conclusion that TECH PLS fails to outperform the average return for the last 36 months. On top of that, none of the predictors including three aggregated indices and 14 technical indicators showed positive . This came in contrast with the results of Neely et al (2014) and Qi Lin (2017) that showed strong performance of their indices based on of 0.5% benchmark proposed by Campbell and Thomson (2008). Our results indicate that neither of indices: PLS or PC could be a significant predictor for any given stock market and that previous results work only in the US, China or maybe some other markets, however, the approach is not universal.

UK stock market

UK stock market had a negative equity risk premium for the period from 1987 until 2019 of -0.08% with standard deviation of 4.4%. 1^st percentile stood at -11.32%, while 99^th percentile was at 8.1%. The negative equity risk premium of -0.08% may have influenced our results given that it should be positive in a base case scenario. It occurs because investors who are willing to take an additional risk by investing in equities rather than risk-free bonds should be compensated by higher average returns when investing in the stock market. However, equity investors on average lost to bond investors as equity risk premium was negative for the observable timeframe.

We made forecasts for the equity risk premium in the UK stock market using several different approaches. First of all, our main interest was to forecast equity risk premium using the so-called TECH PLS index proposed by Qi Lin (2017) as it showed strong performance in the US stock market and was a significant predictor at 0.5% benchmark proposed by Campbell and Thomson (2008). We calculated that the average of TECH PLS stood at 0.01. Median for TECH PLS was 0, 1^st percentile was -0.36 and 99^th percentile was 0.37. Standard deviation for the sample of observations was 0.16. As Qi Lin (2017) stated, TECH PLS should be a positive predictor of the equity risk premium. Intuitively, this is absolutely correct as TECH PLS is based on 14 technical binary variables that take the value of 1 if the strategy proposes to BUY and 0 to sell. Therefore, the higher the value of TECH PLS the higher our conviction that the market should rise in the next period implying positive beta in the univariate regression model. However, our results came in contrast to the base case scenario as our model produced the average beta for the observable period of -0.05%. While the beta was negative from 1995 until 2004 most of the time, it rapidly turned to be positive from 2004 until 2011, then again negative until 2016 and positive for the rest of the period (graph in the appendix). The peak of the TECH PLS regression coefficient came in the 2008 crisis indicating that the PLS approach captures information differently in various market conditions. Furthermore, it shows that in the crisis TECH PLS predicts equity risk premium better than in basic market conditions. As we already mentioned, average PLS regression coefficient came at -0.05%, however, if we exclude the 2008 financial crisis timeframe to capture usual market performance, the coefficient will be even lower implying the poorer performance of the index to forecast equity risk premium in normal times. Our analysis also showed that for the full sample stood at -7.9% implying that TECH PLS fails to outperform average equity risk premium benchmark. We also constructed floating and cumulative indicators (graph in the appendix) to capture in different market conditions. Most often floating that we calculated based on LTM was negative, while being positive only three times for a short period of time: during the 2008 financial crisis, 2012-2013 and in 2017. Cumulative also indicates poor performance of TECH PLS by being negative from 1997 until 2019. Overall, we used all available data for the UK stock market and showed that TECH PLS is not a good predictor for the equity risk premium.

Secondly, it was in our interest to analyze other indices such as TECH PC and TECH EW for the UK stock market. As Neely et al (2014) proposed, TECH PC could be a significant predictor of the monthly equity risk premium for the US stock market, however, we did not find similar evidences for the UK market. We calculated that the average of TECH PC stood at -0.04. Median for TECH PC was -0.58, 1^st percentile was -1.23 and 99^th percentile was 2.12. Standard deviation for the sample of observations was 1.21. In contrast to TECH PLS, TECH PC regression coefficient was positive and stood at 0.22%. Overall, this at least indicates the right relationship between the independent and dependent variables. PC coefficient was positive most of the time, while it was negative for the longest time in a row during the 2008 financial crisis and later years of market recovery. However, cumulative average for the full sample stood at -10.3% that is below the 0 baseline and lower than of TECH PLS. Therefore, TECH PC on average predicts the equity risk premium poorer than TECH PLS for the UK stock market.

We also used TECH EW to forecast equity risk premium. We calculated that the average of TECH EW stood at 0.6. Median for TECH EW was 0.64, 1^st percentile was 0 and 99^th percentile 1. Standard deviation for the sample of observations was 0.31. We used TECH EW which is calculated using the equal weights for each of technical indicators to compare the results of both of TECH PLS and TECH PC to TECH EW. If for TECH EW is higher than for TECH PLS and TECH PC, it means that methods used in the construction of TECH PLS and TECH PC create poorer results than just simple weighting by 1/14. After our analysis, we came to the conclusion that TECH EW regression coefficient was negative and the lowest among all three TECH indices and stood at -0.52%. You can refer to the fluctuations of the TECH EW regression coefficient during different market conditions in the graph in appendix. Average for the full sample was negative and stood at -9.6% that is lower than for TECH PLS but higher than for TECH PC. Similar to TECH PC , TECH EW had extremely low during the same timeframe. If we exclude this timeframe, we will arrive at of -6.9%. This is still below 0 and therefore TECH EW is not a good predictor of the equity risk premium, however, it is higher than the overall of TECH PLS.

We also made 14 univariate regression models using 14 individual technical indicators. The best results in terms of was for MA(3,12), a technical indicator which generates the value of 1 indicating a BUY signal when the short moving average calculated based on last 3 months data is higher than the long moving average calculated based on LTM data, and generating 0 otherwise. We calculated that the average of MA(3,12) stood at 0.66. Median for MA(3,12) was 1, 1^st percentile was 0 and 99^th percentile 1. Standard deviation for the sample of observations was 0.47. The average regression coefficient was at 0.01%, slightly above 0. While the worst performance showed VOL(3,12) with at -11.8%.

While making the analysis, we created 14 individual technical indicators, which could be divided into 3 groups: those based on Moving Average rule, Momentum strategy, and On-Balance-Volume. The best was for the Moving Average group, which stood at -8.37% (simple average of six ), while the worst was for on-balance-volume with at -10%, implying that on-balance-volume indicators on average lowered for our technical indices.

South Korea stock market

South Korea stock market had a negative equity risk premium for the period from 1991 until 2019 of -0.21% with a standard deviation of 7.6%. 1^st percentile stood at -17.96%, while 99^th percentile was at 19.47%. As well as in the UK market, negative equity risk premium of -0.21% may have influenced our results given that it should be positive in a base case scenario. The results for the South Korea stock market are more enigmatic as equity risk premium was lower on average for the observable period than in the UK market, however, the volatility of equities was higher with a standard deviation of 7.6% in South Korea vs 4.4% in the UK.

To analyze South Korea equity market, we also employed three technical indicators, TECH PLS, TECH PC and TECH EW as well as built 14 univariate regressions based on each of 14 technical indicators. Average for TECH PLS stood at - 0.02, median was 0, 1^st percentile -0.88, while 99^th percentile was at 0.71 and standard deviation of 0.3. Despite regression coefficient for TECH PLS was above 0 at 0.12% indicating the right relationship between the indicator and equity risk premium, was -14.8% much lower than of TECH PC and TECH EW. for TECH PC and TECH EW were at -7.5% and -8.2% respectively. On top of that, for TECH PLS was the lowest across three technical indices as well as 14 individual technical indicators implying that TECH PLS is the worst predictor of equity risk premium across 17 constructed instruments for South Korea equity market.

TECH PC had an average of 0, median of -0.39, 1^st percentile of -1.44, 99^th percentile 1.83 and a standard deviation of 1.24. The regression coefficient for TECH PC was negative at -0.11% implying a reverse relationship between TECH PC and equity risk premium. Regression coefficient across different market timeline is showed in the appendix. for TECH PC was negative and stood at -7.5% with big drops in 2014 and 2017. TECH EW regression coefficient was positive at 1.22% with at -8.2%.

Again on-balance-volume group of variables had the lowest average of -11.15%, while the best group was moving averages with of -9.17%. The best indicator across 14 constructed was MA(1,12) with at -8.05%, while the worst was VOL(1,12) with at -12.7%.



6. Conclusion

Following recent studies that forecasted equity risk premium using technical indicators, we analyzed UK and South Korea stock markets and came to a conclusion that none of the technical indicators including those of TECH PLS, TECH PC and TECH EW as well as 14 individual technical indicators could be used as a tool to forecast equity risk premium. These results came in contrast to the conclusions of previous works by Neely at el (2014) and Qi Lin (2017). Despite the study of Qi Lin (2017) showed a much better performance of TECH PLS than any other technical index as well as any fundamental or macroeconomic variable in out-of-sample tests for both the US and China stock markets, hinting that TECH PLS could be a significant predictor across many markets, we regret to inform that the PLS approach does not work in the UK and South Korea.



Literature review

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Campbell, J. Y., M. Yogo. 2006. Efficient tests of stock return predictability. Journal of Financial Economics 81 27-60.

Campbell, J. Y., S. B. Thompson. 2008. Predicting the equity premium out of sample: Can anything beat the historical average? Review of Financial Studies 21 1509-1531.

Goyal, A., I. Welch. 2008. A comprehensive look at the empirical performance of equity premium prediction. Review of Financial Studies 21 1455-1508.

Granville, J. 1963. Granville's New Key to Stock Market Profits. Prentice-Hall, New York.

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Appendix

1. Summary table for the UK stock market:

Full sample	Average	Median	1st percentile	99th percentile	St.dev
Equity risk premium, %	-0.08%	0.34%	-11.32%	8.10%	4.4%
TECH PLS*	0.01	0.00	-0.36	0.37	0.16
TECH PC*	-0.04	-0.58	-1.23	2.12	1.21
TECH EW*	0.60	0.64	0	1	0.31
MA(1,9)	0.65	1.00	0	1	0.48
MA(1,12)	0.65	1.00	0	1	0.48
MA(2,9)	0.65	1.00	0	1	0.48
MA(2,12)	0.65	1.00	0	1	0.48
MA(3,9)	0.64	1.00	0	1	0.48
MA(3,12)	0.66	1.00	0	1	0.47
MoM(9)	0.68	1.00	0	1	0.47
MoM(12)	0.69	1.00	0	1	0.46
VOL(1,9)	0.56	1.00	0	1	0.50
VOL(1,12)	0.57	1.00	0	1	0.50
VOL(2,9)	0.49	0.00	0	1	0.50
VOL(2,12)	0.47	0.00	0	1	0.50
VOL(3,9)	0.49	0.00	0	1	0.50
VOL(3,12)	0.49	0.00	0	1	0.50
*data from Oct 1992
Otherwise data from Oct 1987

2. Regression coefficients and for UK stock market

	Beta, %	R^2 (OOS)
TECH PLS*	-0.05%	-7.89%
TECH PC*	0.22%	-10.30%
TECH EW*	-0.52%	-9.61%
MA(1,9)	-0.24%	-9.58%
MA(1,12)	-0.62%	-8.23%
MA(2,9)	-0.03%	-9.36%
MA(2,12)	-0.22%	-8.56%
MA(3,9)	-0.25%	-9.44%
MA(3,12)	0.01%	-5.03%
MoM(9)	0.10%	-8.61%
MoM(12)	-0.37%	-11.17%
VOL(1,9)	-0.80%	-8.04%
VOL(1,12)	-0.78%	-7.96%
VOL(2,9)	-0.02%	-11.10%
VOL(2,12)	0.18%	-10.64%
VOL(3,9)	0.13%	-10.20%
VOL(3,12)	-0.10%	-11.81%

3. Summary table for South Korea stock market:

Full sample	Average	Median	1st percentile	99th percentile	St.dev
Equity risk premium, %**	-0.21%	-0.22%	-17.96%	19.47%	7.6%
TECH PLS*	(0.02)	0.00	-0.88	0.71	0.30
TECH PC*	0.00	-0.39	-1.44	1.83	1.24
TECH EW*	0.54	0.57	0	1	0.32
MA(1,9)	0.57	1.00	0	1	0.50
MA(1,12)	0.58	1.00	0	1	0.49
MA(2,9)	0.57	1.00	0	1	0.50
MA(2,12)	0.58	1.00	0	1	0.49
MA(3,9)	0.56	1.00	0	1	0.50
MA(3,12)	0.58	1.00	0	1	0.49
MoM(9)	0.58	1.00	0	1	0.49
MoM(12)	0.59	1.00	0	1	0.49
VOL(1,9)	0.51	1.00	0	1	0.50
VOL(1,12)	0.52	1.00	0	1	0.50
VOL(2,9)	0.49	0.00	0	1	0.50
VOL(2,12)	0.47	0.00	0	1	0.50
VOL(3,9)	0.52	1.00	0	1	0.50
VOL(3,12)	0.52	1.00	0	1	0.50
Note: *from 1996 until 2019
** from 1991 until 2019
otherwise from 1987 until 2019

4. Regression coefficients and for South Korea stock market:

	Beta, %	R^2 (OOS)
TECH PLS	0.12%	-14.80%
TECH PC	-0.11%	-7.50%
TECH EW	1.22%	-8.19%
MA(1,9)	0.45%	-9.02%
MA(1,12)	0.72%	-8.05%
MA(2,9)	0.84%	-8.88%
MA(2,12)	0.20%	-9.14%
MA(3,9)	-0.18%	-8.88%
MA(3,12)	-0.59%	-11.02%
MoM(9)	0.16%	-10.24%
MoM(12)	0.42%	-11.93%
VOL(1,9)	0.78%	-12.68%
VOL(1,12)	0.85%	-12.28%
VOL(2,9)	0.05%	-11.07%
VOL(2,12)	0.78%	-11.11%
VOL(3,9)	1.28%	-8.88%
VOL(3,12)	1.97%	-10.91%

5. UK stock market, PLS regression coefficient:



6. UK stock market, PC regression coefficient:

7. UK stock market, EW regression coefficient:

8. UK stock market, PLS regression :



9. UK stock market, PC regression :

10. UK stock market, EW regression :

11. South Korea stock market, PLS regression coefficient:



12. South Korea stock market, PC regression coefficient:

13. South Korea stock market, EW regression coefficient:



14. South Korea stock market, PLS regression :

15. South Korea stock market: PC regression :

16. South Korea stock market: EW regression :

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