Value investing across asset classes

The objective of this study is to derive two long-only value risk premium multi-asset strategies, as well as naive investment strategies (equal weighted investment strategy and 60/40 portfolio) which are back tested out-of-sample and evaluated for the period from January 1995 to December 2015. The obtained results exhibit superior excess return for the absolute and relative value strategies compared to the naive investment strategies, and display more effective risk-reward ratios due to better distributed returns. However, the findings emphasise concurrently that the value investing strategies should be applied as a complementary portfolio instrument in the context of dynamic asset allocation due to value phase shifts to mitigate drawdown. Moreover, the overall statistical inference presents that the most influential determinants are interest rate related factors like the inflation rate and macro-economic driven variables, such as the I.S.M. Composite Index and the oil price. The multivariate regression analysis also shows a strong dependency between the value strategy returns, stocks and commodities. ARTICLE HISTORY Received 20 September 2015 Accepted 4 June 2018


Introduction
This article investigates the robustness of two different value investing strategies that are defined as the absolute value and relative value risk premium strategies in a multi-asset allocation context. Both strategies follow the basic concept of value investing by picking those assets that are undervalued relative to their own history or within the investment universe.
The value effect for stock selection has been studied widely, but relatively low attention has been paid to value investing in the context of a multi-asset allocation combined with absolute and relative risk premium strategies. The contribution of this study is that the different multivariate regression analyses highlight the strong dependence of macro-economic and interest rate sensitive related factors, whereby the largest portfolio weights in both risk premium portfolios are allocated in equities. Thus, the asset allocation and regression analysis indicate strong asset allocation ability in a multi-asset context of both value premia strategies, considering that the value strategies increase exposure to risky asset classes during economic stress phases in which the risk premium is highest and investor sentiment is low.
The main goal of this work is to provide an in-depth analysis of the outperformance or underperformance of absolute and relative risk premium strategies in comparison with two naive investment strategies with a performance and risk analysis and also how the absolute and relative value strategy can be disentangled with respect to macro-economic, financial markets and risk specific determinants of different market regimes. Thus, the work examines the usefulness of two simple value risk premium strategies compared to the traditional equal weighted and strategic weighted portfolio (60/40 portfolio) through regime investing from the perspective of a longterm multi-asset investor.
The rest of the article is organised as follows: Section 2 reviews previous work and provides a theoretical framework, Section 3 presents the data and methodology employed, Section 4 presents the results, and Section 5 provides the conclusions.

Theoretical framework
The initial foundations of value investing were established by Graham and Dodd (1934) in their book Security Analysis. Following this book, Stattman (1980), as well as Rosenberg, Reid, and Lanstein (1985) demonstrated that low price-to-earnings (P/ E) ratios generate superior positive returns in the long-term. These studies provide the most frequently discussed explanation for the outperformance of certain stocks (Hammond, Leibowitz, & Siegel, 2001). Fama and French (2012) found consistent risk premia in individual stocks. Fama and French (1996) documented the link between value and expected stock returns, while Gerakos and Linnainmaa (2012) showed the high correlations between past returns and the book value of stocks. Barberis, Shleifer, and Vishny (1998), as well as Hong and Stein (1999), investigated the under-reaction phenomenon and justified capital market inefficiencies with shortterm under-reaction of market participants when processing information. Lakonishok, Shleifer, and Vishny (1994) demonstrated similar results based on the cash-flow-toprice ratio. Basu (1977) referred to the P/E ratio anomaly by observing that stocks with low P/E ratios outperform stocks with high P/E ratios. Litzenberger and Ramaswamy (1979) discovered a strong positive relationship between dividend yields (D.Y.) and expected returns of common stocks. Asness, Ilmanen, Israel, and Moskowitz (2015) concluded that value investing is most effective with multiple value variables. They also showed that securities revert to their fundamental fair values (mean-reversion), and that the success of the value premium can even exist in efficient markets.
Numerous studies have used different valuation metrics for stocks. The key figures in this context are D.Y. (Fama & French, 1989;Blitz & Vliet, 2008); P/E ratio and book-to-price ratio (Fama & French, 1992;Fama & French, 1993;Lakonishok et al., 1994). Cochrane (2011) showed that yield describing future returns is a 'pervasive phenomenon' and it has been applied by Leibowitz, Bova, and Kogelman (2014) to a range types of bonds. Fama and French (1998) identified that returns on equity are well forecasted using D.Y. Value effects in a multi-asset context have also been found for commodities, bonds and currencies. For commodities, the value effect was tested by Erb and Harvey (2006) and Richard and Krinsky (1995). Meese and Rogoff (1983), Rogoff (1996) and Cheung, Chinn, and Pascual (2003) confirmed the previous observation for currencies, while Cochrane and Piazzesi (2005), Duffee (2002), Dai and Singleton (2002) as well as Ilmanen (1995) and Altman (1968) did the same for bonds.
In terms of commodities, the roll yield is predominantly used as the valuation metric. However, for bonds, the yield to maturity and traditional financial ratios such as E.B.I.T.D.A. and market value of its equity/total liabilities are the most used valuation measures. The real bond yield is also a possible value measurement. For currencies, valuation is assessed by using the difference between interest rates of the countries, as well as the purchasing power parity (P.P.T.). The deviation from P.P.T. is a possible value measurement as long as prices converge to P.P.T. (Israel & Moskowitz, 2012). Asness, Moskowitz, and Pedersen (2013) showed that there is a significant value premium in different asset classes and a high correlation between different value strategies. However, Zhang (2005) and Cochrane (1996), both proponents of the E.M.H., provided one explanation, which connects assets with low valuation to higher risk and this needs to be compensated with an excess return. Market participants are compensated with an appropriate risk premium, which is usually reflected in times of economic stress (Fama & French, 1992;Zhang, 2005). Campbell, Hilscher, and Szilagyi (2011) and also Novy-Marx (2012) argued that history shows different results, because of the high correlation between the value of a company and the reported profitability, which challenges the distress argument. Behavioural finance theory shows the link between long-term returns and book-to-market value measures, which was documented by Hirshleifer and Subrahmanyam (1998), as well as Hong and Stein (1999), and La Porta (1996).
In summary, according to French (1992, 1993) value strategies generate superior returns due to the increased underlying risk of value strategies. Lakonishok et al. (1994) and Haugen (1995) have identified that value strategies work because investors make systematic errors in their forecasts or because investors are uncomfortable with holding value stocks.

Sample data and back testing specification
The empirical back test is designed to meet the requirements of a global diversified multi-asset portfolio. Thus, the portfolios consist of an investment universe of eight assets, including equities (M.S.C.I. World; M.S.C.I. Emerging Markets), fixed income securities (U.S. Treasury Bonds), R.E.I.T.s (F.T.S.E. N.A.R.E.I.T.), commodities (Gold; S&P G.S.C.I.) and currencies (J.P.Y./U.S.D.; E.U.R./U.S.D.), which are the most liquid currencies. All data are denominated in U.S. dollars, whereby all indices are net total return indices. The data history ranges from December 1992 to December 2015. The back test period is sufficient as it contains a minimum of two business cycles. Thus, the monthly return time series R i are computed with a discrete computed rate of return, with P i ; t as the price of asset i at time t; as follows: The discrete compound rate of return starts in January 1995 and ends in December 2015. The z-score is computed with a starting lag length of 24 months, thus the gathered raw data ranges from December 1992 to acquire an observation back testing period of 20 years. All indices are net total return indices denominated in U.S. dollars. Moreover, the assets are easily tradable. For generating buy or sell signals by detecting whether an asset is undervalued or overvalued, the following value factor metrics are used (also known as value risk premia): earnings yield for equities; D.Y. for real estates; yield to maturity for fixed income instruments; real exchange rate for currencies; rolling yield or treasury yield for commodities.
The trading signals detection for currency value risk premia are based on O.E.C.D. fair value real exchange rates. For equities, the earnings yield is the reciprocal value of the P/E ratio. The PE, the D.Y. and yield to maturity are sourced from Bloomberg and DataStream. The positive or negative roll yield for commodities is produced as a result of rolling future positions into new future positions. The O.E.C.D. valuation calculation for currencies uses the real effective exchange rate, which is compounded as follows: where the real effective exchange rate, REER; for country i is the sum of trade weighted, s j ; real exchange rate (RER) for the trade partner in country j: The exchange rates are in natural logarithms. The real exchange rate (RER) for country j is an adjustment of nominal bilateral exchange rates (NER) with domestic price (DP) and foreign prices ðFP) calculated as follows: The price earnings ratios, PE, of index i are defined as the sum of index shares weighted average price earnings ratio, in which S is the weight factor for index shares, P is the price of the index i and 12M FWD EPS is the 12-month-forward earnings for the index i; calculated as follows: where the 12-month forward EPS (EPS1FD12) is calculated as follows: where M is the number of months to the end of the current fiscal year. Note that the current fiscal year will be FY1 if the date is before FY1 year end and FY2 if the date is after FY1 year end. F1 is the consensus earnings forecast for the current fiscal year and F2 is the consensus earnings forecast for the next fiscal year. The dividend yield, DY for index i is calculated as the index shares weighted average dividend per share price ratio, in which S is the weight factor for index shares, P is the price of the index i in the denominator and 12M DVD=Share is the gross dividend per share over the prior 12 months for the index i; calculated as follows: 1 The commodity roll yield, CRY for index i is the difference of the calculated R, discrete returns of the commodity excess return index i and the commodity spot index i; defined as: Then, the return of the excess return index is the sum of the change in spot price and the roll yield. Gold is a hedge instrument against inflation and the government bond yield is directly affected by changes in interest rates based on changes in inflation. Thus, the U.S. treasury yield is defined as the value factor for gold.

Value risk premia and naive investment strategies
The most comprehensive measure to quantify, identify and select undervalued assets in the investment universe is the standardisation of value risk premia with the aid of a z-score. A large positive (negative) z-score indicates that the asset is episodically expensive (cheap). Mathematically, the z-score for risk premium i is the difference between the current value of the risk premium, X i ; and the mean value of the risk premium, l i ; divided by the standard deviation of the risk premium, r i ; as follows: All computed z-score time-series for the absolute and relative value risk premia strategies are calculated with an extending window, starting with a minimum sample size of 24 months to compound the first sample mean and standard deviation. Additionally, both value risk premium portfolios are rebalanced at the beginning of every month according to the specific strategy signal generation at the end of the previous month, t À 1:

Absolute value risk premium strategy
The absolute risk premium strategy selects those assets that are historically undervalued within a predetermined range of standardised yield movements. The risk premium z-score ranges from 0.0 to 1.5, which identifies those assets that are historically cheap based on the current high risk premium value for asset i: For example, for equities, this means concurrently that the current PE ratio is relatively low compared to its own history and evaluated with a high earnings yield. If there is no risk premium within the determined z-score range, the portfolio is fully invested in the money market, as follows: If N; which is the number of assets selected from the investment universe, is zero, the strategy is invested fully in the money market. N can be a maximum of eight, which means that the whole investment universe is currently undervalued; where the weight, w; for asset i at the time t is a function of the calculated z-score value of the risk premium for asset i at time t À 1 (out-of-sample), denoted as Zscore i;tÀ1 : Moreover, the portfolio weights are always equally allocated to the number of selected undervalued assets. The absolute value risk premium strategy portfolio return, PðRÞ Abs: ; is calculated as the sum of weighted asset returns of the selected assets.
where w is the weight for asset i and R is the return for asset i: Since the absolute value risk premium strategy does not take into account the preference of selected assets, the portfolio can be invested in all assets.

Relative value risk premium strategy
The relative risk premium strategy considers the cross-sectional examination of scaled yield movements by investing in the three assets that are most undervalued in comparison to the other assets in the investment universe. Thus, there is the preference to invest in the maximal three assets that are most undervalued in comparison. The weight, w; for the selected asset i at time t is fixed at one third, whereby the signal generation process always takes the three assets with the highest cross z-score values, denoted as CrossZscore i Rank 1À3 ;tÀ1 ; without taking into account the overall z-score level. This implies that N is always equal to three assets, as follows: where the CrossZscore i;tÀ1 is the z-score cross, the calculated z-score of risk premiums at time t. The relative value risk premium strategy portfolio return, PðRÞ Rel: ; is also calculated as the sum of the weighted asset returns of the selected assets i; as follows: where w is the weight for asset i and R is the return for asset i.

Naive investment strategies
For comparison reasons, there are two naive investment strategies. The first naive investment strategy is the equal weighted investment strategy, which allocates the weights of asset i in the portfolio equally. Since the investment universe includes eight assets, the single w is the weight for asset i and it is 12.5% over time, as follows: The equal weighted strategy portfolio return, PðRÞ Equ: is also calculated as the sum of the weighted asset returns of assets i; as follows: where R is the return for asset i. The strategic weighted strategy portfolio return, PðRÞ Strat: ; is also calculated as the sum of the weighted asset returns of assets i; as follows: where R MSCI World is the return for of M.S.C.I. World and R US Treas: is the yield for of US Treasury Bonds. The strategic weighted investment strategy has a static strategic allocation of 60 percent in equities (MSCI World) and 40 percent in fixed income securities (U.S. Treasury Bonds).

Performance and risk measurements
The first risk-adjusted measure is Jensen's Alpha (also known as ex post alpha) that estimates how much the strategy risk premium forecasting ability contributes to the strategy returns. The formula is as follows: where R F is the one-period risk free interest rate, b i E R M ð ÞÀ R F is the Capital asset pricing model, b i is the measure of risk as the systematic measure and E R M ð Þ is the expected one-period return on the market portfolio that consists of an investment in each asset in the market in proportion to its fraction of the total value of all assets in the market.
The maximum drawdown (M.D.D.) in percentage is calculated to determine which of the strategies suffers the greatest loss. The M.D.D. is computed as follows: where Max i;t 0 eð0;TÞ is the largest drop of the price from the running maximum up to time T, P i;t is the price of the portfolio i at time t, when the portfolio is bought, and P i;t 0 is the price of the portfolio i at the time t 0 ; when the portfolio is sold. Besides volatility, the second widely adopted risk measure is the Value at Risk (VAR) and the related Conditional Value at Risk (CVaR). The historical VaR is calculated as follows: with N as the number of standard deviations, which depends on the specified confidence level. Furthermore, r is the estimated daily standard deviation expressed as a proportion of price or value and ffiffiffiffiffiffiffiffiffi ffi Days p is the square root of the number of days used for the VaR analysis. The expected shortfall (E.S.), otherwise known as the Conditional Value at Risk (CVaR), is as an alternative risk tool to the VaR that is more sensitive for fat tail frequency distributions. ES is the integral of the VaR for a given confidence level: with X as a random variable, a as the confidence level (for instance 1%), and VaR as the Value at Risk. One additional important risk measure is the Tracking Error, denoted as TE, which is formally the standard deviation of the difference among the portfolio relative to the benchmark. Hence, it is computed as the standard deviation of active returns, as follows: with R P as the return from the portfolio and R B as the return from the benchmark, n is the number of periods. The compound performance and risk measurements are connected to the well-known Sharpe ratio and Information Ratio. The ex post Sharpe ratio is as follows: with R P as the portfolio return, R F as the risk-free rate and r P as the standard deviation of the portfolio. Since the Sharpe ratio considers the portfolio volatility in the denominator, the Information ratio is used to quantify the excess return over the specific risk taken to the benchmark. Thus, the ex post Tracking Error (TE) is in the denominator as follows: 3.3. Determinants of risk premium investment strategies 3.3.1. Binary market stress indicator and independent sample data The binary market stress indicator is the mean of all z-score calculated indices that displays the market stress, which contains the following components: 1. The M.S.C.I. World Index that illustrates the equity market stress (also including a mean-reversion anchor character). 2. The City Eco Surprise G10 index represents the economic stress expected from market participants in G10 countries. This is an index that measures the degree of surprise in the release of global economic data with a daily frequency for the G10 countries. 3. The T.E.D. Spread is used to summarise the stress in financial markets. It is calculated as the gap between the three-month L.I.B.O.R. and the three-month Treasury bill rate. 4. The default risk with the credit conditions is measured by the credit spread between Baa rated corporate bonds and U.S. Treasury bonds.. 5. The V.I.X. index shows the implied risk expected by the S&P 500 market. For all gathered data, the z-score with an extending window is calculated. In phases of market stress, the binary indicator switches from 1 to 0, and vice versa. Thus, an indicator value of one means there is no market stress measured by the mean of the z-scores of the underlying components at that time t. The observation period ranges from 2001 to the end of 2015.

Estimation models and market regimes
The different estimation models and statistical inference analyses extend the previous robustness investigation to consider the possible impact of macroeconomic and capital market determinants of previous back tested risk premium strategies. One group is formed with macroeconomic factors, the second group with financial market factors and the third one with risk specific factors. The first estimation model with macro-economic factors, R i;macro ; is as follows: Moreover, the second regression model, R i;market ; contains the financial market factors as independent variables to determine the most significant exogenous variables that explain the risk premium portfolio returns according to the different asset classes, as follows: Subsequently, the third multivariate estimation model incorporates the risk specific factors, R i;risk ; to examine whether the strategies react sensitively to turbulent markets, as follows: where R i is the portfolio return of the value risk premium strategy i in time period t: The different factors K represent the different independent variables. The betas b i are the factor loadings for strategy i on the factors K and describe the level of movement in strategy i as a result of a unit of movement in the different factors K (slope); a is a constant and is also referred to as the intercept of the regression line; e i is the strategy specific factor called the error term. In detail, K UTS is the U.S. Treasury yield curve. K UI is the year on year U.S. C.P.I. inflation rate; K ISM is the change in the I.S.M. composite index (I.S.M.), K CEU is the change in the currency rate E.U.R./U.S.D.; K OPR is the change in the oil price and; K EURI is the risk-free yield in form of the money market yield. L MSCIW is the change in the world stock market (MSCI World); L USB is the US bond market ( The multivariate regression analysis for financial market factors and risk factors are also investigated for different market regimes by multiplying the different independent market variables with the market stress indicator value (binary: 1 or 0) for a stress(-free) market environment. Both conditions can be computed as follows: and where IV i; t;stressÀfree is the independent variable i at time t in a market stress-free condition and IV i; t;stress is the independent variable i at time t in a market stress situation. BMSI t is the binary stress indicator index and IV i; t is the independent variable i at time t. After computation of every independent variable for different market situations, there is an N Â M matrix of independent variables, where N represents the number of observations and M is the number of market stress-free independent variables, denoted with plus, and market stress independent variables, denoted with minus. Therefore, every market situation can be investigated independently by regressing the matrix including all independent variables for different regimes towards the risk premium strategy portfolio returns.

Robustness of value risk premium investment strategies
Naive investment strategies (Table 1) show the highest degree of left skewness. Moreover, Figures 1-4 emphasise the strong leptokurtic shape of all return distributions. The absolute value risk premium strategy provides the largest kurtosis. The descriptive statistics clarify that the value risk premium strategy returns are better distributed compared to naive investment strategies, with less fat tails on the left side of the return distributions (Backhaus, Zhakanova, & Fiedler, 2016). In particular, the absolute value risk premium strategy provides evidence of consistent positive returns.
Additionally, Table 2 illustrates that the value risk premium investment strategies outperform all compared strategies over a period of 20 years. These findings are also confirmed by the average annualised total returns of 8.38% and 7.54%, respectively. Thus, on an average yearly basis, the relative and absolute value risk premium strategies outperformed the strategic weighted portfolio by 2.02% and 1.23%, and also generated annualised excess returns of 4.56% and 3.75% compared to the equal    The largest return of the relative value risk premium strategy could be generated before the financial crisis from year 2006 to 2008 by mainly investing in stocks (M.S.C.I. World and M.S.C.I. Emerging Markets) and gold. The weightings ( Figure 5) prove that the preference of undervalued markets is relatively stable over time by mainly investing in stocks and gold. Only when gold was relatively overvalued did the dollar represent a preferred portfolio weight. In particular, during the subprime  crises, the R.E.I.T.s were undervalued and, thus, would have had a major weight in the portfolio. Figure 6 shows that the portfolio is better diversified than the other value risk premium strategies. The strategy is mainly invested in stocks, such as M.S.C.I. World and M.S.C.I. Emerging Markets, U.S. Treasuries, commodity index, as well as in currencies, such as E.U.R./U.S.D. and partly J.P.Y./U.S.D. The strategy also proves a risk prevention character with a lag by being fully invested in the money market in 2009 and, thus, generating the highest returns in comparison.
The absolute value risk premium strategy could generate superior annual total returns between the years 2002 and 2008, ranging between 15% and 30% per year.
Moreover, in the period from 1997 to 2001, the strategic weighted investment strategy outperformed all other strategies (Figure 7). However, the simulation shows that the diversification effect is not sufficient to avoid losses across all economic cycles.
Nevertheless, both value risk premium strategies also generated a negative alpha for a minimum of seven years. The value risk premium strategy annual returns fluctuated every two to three years with extraordinary returns and mitigated risk behaviour in accordance with the performance of the other benchmarks (Figures 8 and 9).
Moreover, it is clear that the performance of the value risk premium strategies is relatively poor in the years after the crises, with minimum annual returns and partial underperformance compared to the naive investment strategies, which is a primary indication of distorted signal generation in times of expansive monetary policy.  The last conspicuous key figure is Jensen alpha, with M.S.C.I. World monthly log returns as market returns. Although the relative value risk premium strategy achieves higher returns, the Jensen's alpha for the absolute value risk premium strategy is higher with 4.73% (Table 2). Overall, the value risk premium strategies show extraordinary robust returns over time with a lagging risk mitigation character, whereby   both strategies highlight the importance of dynamic asset allocation due to superior selection quality. Volatility steadily increases ( Figure 10) after the financial crisis in 2008 and reaches its peak in the middle of 2011. Later, the volatility decreases to a level in the range between 5% to 12% in 2015 for all strategies. Moreover, the relative value risk premium strategy has a higher volatility compared to the absolute value risk premium strategy and naive investment strategies (Table 2). Moreover, the rolling volatility of the equal weighted strategy is higher than the strategic weighted, which again highlights that the investor will not be compensated for equal allocation.
In different periods (Figure 11), the value premium strategies perform better, which emphasises the better quality selection of assets. These findings are confirmed by the average drawdown that is similar to the naive investment strategies, which again emphasises the slight risk mitigation character (Table 2). Furthermore, by examining the Tracking Error, it is clear that the allocation and thus the specific risk compared to the measured benchmark is widening across the strategies.
Combining the performance and risk measurements, the quality effects of selecting the value risk premium exposure in the multi-asset context generate better risk-adjusted returns, measured by the information ratios of 0.17 and 0.06, as  well as the negative values for both naive investment strategies. However, the Sharpe ratios provide evidence that the strategic weighted portfolio provides a slightly better risk-return trade off compared to the value risk premium strategies due to the proportionally lower volatility. The strong divergence of the Value-at-Risk (V.a.R.) and E.S. at 99% confidence among the strategies supports the previous findings (Table 1). Thus, by applying the value risk premium strategies, the investor will be fairly compensated with robust risk-adjusted returns for accepting to take more risk over time due to selection quality and slight risk prevention characteristics. Moreover, the findings emphasise that value investing strategies should be applied as a complementary portfolio instrument in the context of dynamic asset allocation.

Binary market stress indicator results
The Binary Market Stress Indicator (Figure 12) illustrates the market stress indicator. In particular, the longest stress duration is displayed from mid-2008 until mid-2009. Moreover, there are frequent periods in the more recent years, where the indictor switches in a stress environment; for example, this can be observed mid-2010, from mid-2011 until 2012, at the end of 2014 and the end of 2015. It is obvious that the market regime after the financial crisis was characterised by increasing market stress due to the banking crises, oil turmoil, the decrease in global economic growth and higher volatility among global financial markets.

Estimation model results and its implications
The goodness of fit of both macro-economic estimation models is 41% and 48%, respectively, indicating that 41% of the absolute value risk premium strategy return variability is explained by macro-economic factors, which are significant at a confidence level of 95%. Thus, the significant p-values are U.S. Inflation rate, I.S.M. Composite Index, the currency factor (E.U.R./U.S.D.), as well as the change in oil price. Hence, the absolute value risk premium strategy has the U.S. Inflation rate significant with a negative sign in the factor loading. Thus, these factors indicate that positive economic growth leads to positive returns, whereby a high inflation reflects an overheating economy, meaning that a reaction from the central bank involving hiking interest rates is expected. The multivariate macroeconomic factor regression analysis demonstrates a very high and significant beta at 0.4 and at 0.6 for the currency factor. Moreover, the inference shows that if the I.S.M. Composite Index increases, the return of both value risk premium strategies also increases. Additionally, the statistical outcome proves that if the dollar depreciates against the euro, the return of the strategy rises, as observed in the financial crisis of 2008. Moreover, if the oil price increases, the value of both value risk premium strategy returns also increase due to the significant factor loadings ( Table 3).
The multivariate financial market factor regression analysis demonstrates the highest R 2 of 72% for the absolute value risk premium strategy (without market regime computation) and simultaneously a high dependency between the strategy return and the significant mix of asset classes, including stocks and commodities. Thus, the inference illustrates that the strategy return increases if stocks and commodities prices grow. Moreover, gold is the most significant (lowest p-values) positive factor loading, which confirms the macro-economic regression analysis. The relative value risk premium multivariate regression analysis with financial market factor has the highest R 2 of 98%, with the determinants of stocks, bonds, gold and furthermore, for regime investigations E.U.R./U.S.D. currency pair and R.E.I.T.s. The findings show that Bonds, E.U.R/U.S.D. and R.E.I.T.s are negatively characterised determinants of the strategy. When the absolute value risk premium strategy returns increase, the value of the returns for these determinants decreases taking into account the market condition for the last two determinants (Tables 4 and 5).
The goodness of fit for the risk factor regressed estimation model are at the lowest level by comparing with all estimation models at 31% and 38%, including significant factors such as credit spreads, the V.I.X. Index and the Citi Eco Surprise Index.     Therefore, for both strategies, the most significant risk factor is the V.I.X. Index, which indicates that the value of the strategy returns increases when the V.I.X. Index level decreases. The credit spread is only significant in negative market conditions with a negative factor loading. Thus, if the credit conditions deteriorate in a stressed market environment, the absolute value risk premium strategy return increases, which emphasise the strong correlation between stock markets and the value risk premia strategies (Tables 6 and 7).
Overall, the different multivariate regression analysis (with and without different market regimes) emphasise, besides the strong correlation to stocks, the strong dependence of macro-economic and interest rate sensitive related factors: dollar, credit spreads, bonds, commodities (including gold) or the Citi Eco Surprise Index.

Conclusion
In this article, two different variations of multi-asset value risk premium investment strategies, such as the absolute and relative value risk premium investment strategy, are initially compared to the naive investment strategies by constructing portfolios. All strategies were back tested from January 1995 to December 2015.
The findings emphasise the quality effects of selecting the value risk premium exposure in the multi-asset context that generates better risk-adjusted returns measured by Information ratio, with 0.17 for the relative value risk premium strategy and 0.06 for the absolute value risk premium strategy compared to negative values for both naive investment strategies. However, the Sharpe ratios provide evidence that the strategic weighted portfolio provides a better risk-return trade off compared to the value risk premium strategies.
The findings of different multivariate regression analyses highlight the strong dependence of macro-economic and interest rate sensitive related factors, whereby the largest portfolio weights in both risk premium portfolios are allocated in equities. Therefore, the asset allocation and regression analysis indicate the strong asset allocation ability in a multi-asset context of both strategies, considering that the strategies increase exposure to risky asset classes during economic stress phases in which the risk premium is highest and investor sentiment is low.
Thus, the findings emphasise that by applying the value risk premium strategies, it is clear that investors will be fairly compensated with robust risk-adjusted returns for accepting to take more risk over time due to selection quality and slight downside prevention character, whereby the relative risk premium strategy provides a better diversification over time. Nevertheless, the findings emphasise that the value investing strategies should be applied as a complementary portfolio instrument in the context of dynamic asset allocation due to value phase shifts for optimal portfolio construction and mitigates drawdown. Note 1. Gross and net dividend amounts are assumed to be the same when only one is reported.