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Beating the Market: The Predictive Power of Factor Premiums and the Business Cycle Jan Jongsma1
ABSTRACT
This paper tests the predictive power of a combination of three factor premiums and the business cycle for future returns of stocks. Although the strategy portfolio constructed in this paper does create a significant alpha in most cases, its Sharpe ratio does only significantly
outperform that of the market in the Eurozone. A similar strategy only making use of the three factor premiums, however, does outperform the market as well as an equally weighted portfolio in the US stock market.
Field Key Words: Investment Strategies, Factor Premiums, Business Cycle JEL classification: E44, F44, G11
This paper is submitted as a master’s thesis for the program Finance (EBM866B20). Supervisor: Prof. A. Plantinga, University of Groningen. I would like to thank Prof. Plantinga for his useful feedback. Furthermore, I would like to give my special thanks to Sibrand Drijver for his feedback and comments during the writing process.
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1 Introduction
Factor investing is a fast growing market that has become especially popular since the financial crisis of 2008. Passive smart beta strategies making use of factor investing grew from USD 50 billion in 2009 to nearly USD 500 billion worldwide at June 30 2015 (Bioy et al, 2015). Numerous academic papers have been devoted to the factors or risk premiums that seem to outperform the market over the long term (Fama and French, 1993; Carhart, 1997), even after their existence has become widely known. Other studies find that tilting a portfolio to certain asset types or sectors based on the stage of the business cycle generates excess returns (Greetham and Hartnett, 2004). Furthermore Harvey (1998) finds that the equity premium seems to be higher at business cycle troughs than it is at peaks. In this paper, I combine these two fields of study to determine whether factor premiums combined with the stage of the business cycle contain predictive power for the future returns of stocks, and in extension of this, if a portfolio based on these expected returns of stocks is able to generate excess returns.
The results of this paper could give insights into whether there is a relationship between factors and the business cycle and how these variables drive returns. In an economic way, this research could help institutional as well as private investors in their choices
regarding asset allocation and market timing.
I test the predictive powers of the factor premiums combined with the stage of the business cycle by calculating the expected return of stocks using a rolling regression and construct a portfolio of the stocks with the highest expected returns. I compare the
performance of this portfolio against three other portfolios: a market portfolio, a portfolio that uses expected return that does not take the phase of the business cycle into account, and an equally weighted portfolio.
The research covers four different economic zones, namely the Eurozone, the US, the UK and Japan. The portfolios are constructed over a period ranging from March 1992 to June 2015 using data from 1980 on. The factors I use to estimate the expected return of stocks are
value, size, momentum and low volatility during four stages of the business cycle that are
defined as reflation, recovery, overheat and stagflation.
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concludes and puts the findings in perspective of the existing literature. Finally, section 8 discusses the limitations of this paper and gives suggestions for further research.
2 Theoretical background
2.1 Factor investing
The first one to acknowledge that return is a compensation for being exposed to a certain type and amount of risk was Markowitz (1952). He finds that combining imperfectly correlated assets can help to create a portfolio with higher return per unit of risk. Using this model, Sharpe (1964) develops the first factor based framework: the Capital Asset Pricing Model (CAPM). In this framework he splits the risk of a portfolio into idiosyncratic risk, which is firm-specific risk, and systematic risk, which is market risk. The exposure of an individual stock to this systematic risk is measured by β (beta). While idiosyncratic risk can be diversified away in this model, systematic risk cannot, which is why investors are
compensated with returns for bearing this risk. Ross (1976) creates the first multifactor asset pricing model, in which he makes the expected return dependent on various macroeconomic factors. The sensitivity of the theoretical stock price to changes in each of these factors is measured by beta coefficients. The model is called Arbitrage Pricing Theory (APT), as Ross argues that an investor could use the model to calculate the theoretical stock price in order to earn arbitrage profits by buying undervalued stocks and selling overvalued ones. In time, other academics added new, non-macroeconomic, factor premiums to the CAPM, the most renowned of which are by Fama and French (1992) and Carhart (1997). The main benefit of these newfound factors is that evaluating returns and risk using factor premiums helps
separate true alpha generated by a portfolio manager from beta (Ang et al 2009). Furthermore, investing in factor premiums can help prevent problems related to traditional market cap weighting, which encourages overweighting overvalued stocks and underweighting undervalued stocks. This can lead to bubble creation (Arnott, 2011).
Bender et al (2010) distinguish three categories for factor premiums: asset class risk, style risk, and strategy risk. The asset class risk premium arises from passive investment in traditional source of risk (e.g. equities, bonds or commodities), style risk premium from the fundamental or technical characteristics of assets (e.g. size or value), and strategy risk
premium from the execution of an investment strategy (e.g. carry trade or merger arbitrage).
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Although numerous factor premiums have been identified throughout the years, no consensus has been reached yet on which factors effectively drive prices. The reason for this is that numerous factors could be the result of data mining while others are competed away after their existence became known to public (Dimson et al, 2010). To assist in selecting factor premiums, Koedijk et al (2013) provide five criteria: rationality: the factor premium must be based on a strong economic or behavioral rationale; persistence: factor premiums need to be realizing positive returns for a substantial period; implementability: the factor premium needs to be liquid, sufficiently scalable and has to be accessible at acceptable costs;
manageability: an institutional investor should be able to use a consistent strategy to benefit
from the factor, and; explainability: the factors should be understandable and easy to explain. The factor premiums for equities that satisfy all these criteria are market, size, value,
momentum, and low volatility. I will explain these concepts below.
Market: The market risk premium is the return investors receive over the risk-free rate
as a compensation for being exposed to risk. Investors’ reluctance to bear risk requires risky yields to be higher than sure yields (Hirshleifer, 1961).
Size: Small cap stocks tend to grow faster than large cap stocks (Fama and French,
1992). The rationale behind this could be that small cap stocks are less liquid and are more vulnerable to financial distress than companies with a large capitalization (Fama and French, 1993). Furthermore, these smaller stocks tend to have a lower coverage by analysts, and this low information efficiency can lead to these stocks being undervalued (Naumer, Nacken and Scheurer, 2013).
Value: Stocks with a low price/earnings (P/E) ratio or low price to book (P/B) ratio
tend to grow faster than their counterparts with high ratios (Fama and French, 1992). According to Fama and French (1992 and 1993), these firms tend to be in distress and thus vulnerable to economic shocks. However, De Groot and Huij (2011) find that the value risk premium is concentrated in the least distressed stocks. Other explanations are that these firms are undervalued and will mean revert back to their real value (DeBondt and Thaler, 1985) or that investors extrapolate past earnings too far in the future, leading to stocks with low past growth rate to be underpriced (Lakonishok et al, 1944).
Momentum: Stocks that have performed well in the recent past are more likely to
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the behavioral finance theories about investor herding, underreaction and overreaction and
confirmation bias.
Low-volatility: recent studies find that, on average, low-volatility stocks tend to
outperform the market (Baker et al, 2011). This contradicts the theories of Markowitz (1952) and Sharpe (1964), who argued that risk should be rewarded by a higher expected return. This anomaly can be explained by the behavioral finance theories lottery ticket effect, winner’s
curse and attention bias (Koedijk et al, 2013). Another explanation could be that individual as
well as institutional investors tend to invest more in high volatility stocks led by respectively overconfidence or mandate to beat a fixed benchmark, leaving lower-risk stocks less attractive and generating a premium (Baker et al, 2011).
2.2 Business cycles
The unavoidable cycle of prosperity and recession is identified for the first time by Clément Juglar (Schumpeter, 1939). He establishes that there is an endogenous cause for cycles instead of an exogenous one, stating that “the only cause of depression is prosperity” (Schumpeter, 1954 p.1090). He regards recessions as a natural economical phenomenon that drives all the companies with poor fundamentals out of the market and leaves only the sound ones, making recessions beneficial to economic development. Schumpeter goes even further by stating that a recession forces these sound firms to improve their organization and
introduce new technologies in order to survive, which will eventually help to overcome the recession and boost economic evolution (Dal-Pont Legrand and Hagemann, 2005). In 1939, using the ideas of Juglar, Schumpeter described the sinusoid shaped business cycle that is typical for our capitalistic system, and consists of four stages: expansion, crisis, recession and recovery.
For this paper I will use a model described in Greetham and Hartnett (2004). This model, which is similar to that of Schumpeter, identifies four different stages using the inflation rate and the output gap, which is the percentage deviation of the actual GDP output from the potential GDP output. The cycle starts with reflation, in which a decreasing output gap, excess capacity, and falling commodity prices put downward pressure on inflation and force central banks to lower the interest rates in order to stimulate the economy. This results in a higher growth rate bringing the business cycle in the recovery phase, where profits and the output accelerate, but the inflation and interest rates stay low. When capacity constraints eventually lead to a lower productivity growth and accelerating inflation, the economy enters
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sustainable growth path, even though growth stays above trend. When, subsequently, growth slows down below the trend, indicating a decelerating output gap, and inflation keeps rising, the cycle is in stagflation. This stage is characterized by low productivity, high wages, and leverage causing profits to decrease sharply. After this stage, the economy will slowly move to the reflation stage again. This is visualized in Figure 1 below.
Figure 1. Defining four business cycle phases using the inflation and output gap cycle
2.3 Factor investing and the business cycle
Advocates of the efficient market hypothesis state that the price of a security reflects all public information about its value. Numerous academic papers investigate the possibility of gaining positive returns by using market timing. Carhart (1997) finds that mutual funds trade too often and hurt performance while doing so,while Sharpe (1975) states that for timing strategies to outperform a buy and hold strategy in the period of 1934 to 1972, an investor needed a predictive accuracy of 74%. Jeffrey (1984) finds that there is more to be lost than to be gained practicing market timing. Furthermore, Barber and Odean (2000) find that, as a result of timing decisions, individual investors on average underperform the market cap-weighted benchmark by 1.1% per year and the relevant factor corrected benchmark by 3.7% per year.
Despite the arguments of these authors who suggest that buy and hold strategies cannot be outperformed by timing, much research has been dedicated to investing through the business cycle in order to outperform the market. Peláez (2015) constructs a Recession
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four different asset classes risk premiums through the business cycle in the United States. They find that in each stage of the business cycle, explained in the section above, one of the four assets outperforms the others. They also find a relationship in equity performance between industries in the different business cycles. For example, Oil & Gas and
Pharmaceuticals tend to perform well relative to the market during stagflation while these categories lack the market during recovery.
Looking at the topic of asset style risk premiums through the business cycle, a considerable amount of research has been conducted, although the authors do not
consequently use the same model for estimating the phases of the business cycle. In fact, even the number of phases and definitions of a business cycle or stage differ between the various papers. Kwag and Lee (2006) use the business cycle stages contraction and expansion, defined and calculated by the National Bureau of Economic Research (NBER) during the period of 1960 to 2001. They test the relative performance of value stocks during these economic stages and find that value stocks outperform growth stocks and the market index in both economic conditions. This outperformance was greatest during contraction. Chordia and Shivakumar (2002) also divide the business cycle into the contraction and expansion stages, using the NBER database to test momentum profits through the business cycle from 1926 to 1994. They find that the profits differ significantly between the two states with relative monthly momentum profits of 0.53% during the expansionary periods and -0.72% during contraction periods, although the -0.72% is not statistically significant. These findings are at odds with those of Griffin et al (2003), who test the performance of momentum stocks during the business cycle using GDP growth. They divide GDP growth in four equal regimes ranking from low to high, and find that momentum profits are positive and significant in all regimes, although the size of the profits hardly differs between them. Switzer (2010) investigates the factor premium size during recessions and recoveries by comparing the relative performance of small cap stocks to large cap stock using NBER’s peak and trough categories during the period of 1926 to 2010. He finds that small cap firms generate relatively high returns in the year following a through. However, their premium is negative over the year prior to a peak and onset of a recession. Furthermore, the size premium for US stocks is 2.03% per month over the entire period of 1926 to 2010. Arshanapalli et al (2004) examine if the factor
premiums value, size and momentum are related to the probability of a recession in the period of 1961 to 2002. They use the Experimental Recession Index (XRI) by NBER, which
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value and momentum. Evidence for a link between recession risk and size premium is weak,
which might be explained by the fact that the size premium has diminished over the recent years, according to the authors. Liew and Vassalou (2000) test if the relationship between factors and the business cycle also work the other way around. They test if value, size and
momentum premiums can predict future GDP growth. They find that the size and value
premiums possess predictive abilities having positive and significant coefficients of similar magnitude. However, they did not find any evidence for predictive properties of the
momentum premium. Finally, Cooper and Priestly (2009) find evidence that the output gap is a good predictor for stock returns in G7 countries and US excess bond returns.
Considering the findings above, it is interesting to investigate the predictive power of the combination of risk premiums and the business cycle for returns of single stocks. To test this I build a model that calculates the expected return for each next month, based on the risk premiums and the business cycle, and I construct a portfolio based on these expected returns. The factors used in this model are the style risk premiums: value, momentum and low
volatility. Size is not included as it is an endogenous factor for return in a regression. The
strategy portfolio that results from this is compared to three benchmarks: a market portfolio, a portfolio based on the risk premiums but not on the business cycle, and an equally weighted portfolio. My hypotheses are therefore:
H1a: A portfolio based on risk premiums and the business cycle phases is able to outperform the market portfolio.
H1b: A portfolio based on risk premiums and the business cycle phases is able to outperform a portfolio that is only based on risk premiums.
H1c: A portfolio based on risk premiums and the business cycle phases is able to outperform an equally weighted portfolio.
3 Methodology
3.1 Goal
As stated in the previous section, the aim of this paper is to find if the expected risk premiums value, momentum and low-volatility combined with the business cycle have
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the factor premiums with estimated factor betas found in a rolling regression. This will be explained later from section 3.4 onwards.
3.2 Estimating the business cycle
I use the direction of the inflation gap cycle and the output gap cycle to define in what stage of the business cycle the economy is located each month. To make the model
implementable in real life the inputs of the model cannot be forward looking. Because of this, one cannot simply draw a line at the moment one of the cycles changes direction. I use the procedure described in Figure 2 to estimate the direction of the inflation cycle, based on only backward looking input data.
Figure 2. Procedure to estimate the direction of the inflation cycle
To describe this procedure mathematically, I define the following set of equations:
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Where 𝑧𝑡 is the directional signal of the inflation cycle at time t, 𝐼𝐿𝑗𝑡 is the inflation label of
economic zone j in month t, 𝐼𝑗𝑡 is the inflation in economic zone j in month t, 𝜎𝑗𝑡 is the lagged
12-month standard deviation of the lagged 12-month moving average of the inflation cycle in economic zone j at time t, n=12 and 𝛼 is a parameter to improve the fit of the formula.
Parameter 𝛼 is estimated in the in-sample period for each economic zone in a way that the signals have an optimal fit. This parameter can be changed when the characteristics of the series change (e.g. two-way volatility). However, in the data used for this paper, changing the parameters during the out-of-sample period is not necessary.
As is stated in Figure 2, there is a change of direction after two signals point in the same direction. This has a slightly negative effect at the fit of the cycle compared to a direct change of direction after one signal, but it prevents numerous false direction changes which could prevent a significant amount of transaction costs. The graphs containing the results can be found in Appendix A.
The procedure used for calculating the output gap cycle resembles that of the inflation cycle, as is shown in Figure 3 below.
Figure 3. Procedure to estimate output gap cycle.
To describe this procedure mathematically, I define the following set of equations:
11 𝐺𝐿𝑗𝑡 = { 3 𝑖𝑓, 𝑤𝑡+ 𝑤𝑥 = 2 2 𝑖𝑓, 𝑤 + 𝑤𝑥= −2 𝐺𝐿𝑗,𝑡−1, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝑗 = 1, … ,4, 𝑡 = 1, … , 𝑇, max 𝑥 < t| |𝑤𝑥| = 1 (4)
Where 𝑤𝑡 is the directional signal of the output gap cycle at time t, 𝐺𝐿𝑗𝑡 is the output
gap label of economic zone j in month t, 𝐺𝑗𝑡 is the output gap in economic zone j in month t, 𝜎𝑗𝑡 is the lagged 4-quarter standard deviation of the lagged 4-quarter moving average of the output gap cycle in economic zone j at time t, n=4 and 𝛼 is a parameter to improve the fit of the formula. Again, 𝛼 can be changed to improve the fit after characteristics of the series change on a structural basis, although it is not necessary for data in the out-of-sample period used in this paper. When the model indicates a change of direction, the first month of the quarter is selected. The results of this can be found in Appendix B.
To translate the direction of the inflation gap cycle and the output gap cycle into a phase of the business cycle, the labels of a specific month can be entered in formula (5) to arrive at the business cycle phase of this month.
𝑃𝑗𝑡 = |𝐼𝐿𝑗𝑡+ 𝐺𝐿𝑗𝑡| – 2 𝑗 = 1, … ,4, 𝑡 = 1, … , 𝑇 (5) Where, 𝑃𝑗𝑡 is the business cycle phase at moment t in economic zone j and can take the value of 1,2,3 or 4, 𝐼𝐿𝑗𝑡 is the inflation label in month t and 𝐺𝐿𝑗𝑡 is the output gap label of
economic zone j in month t.
3.3 Sample periods
The total period of the model ranges from March 1982 to June 2015 and is divided into two sample periods. The in-sample period ranges from March 1982 to February 1992 and will only serve the purpose of estimating regression parameters. This ten-year period is chosen because in this range all economic zones have experienced all four business cycle phases for at least one month. The out-of-sample period ranges from March 1992 to June 2015. This is the period of which I build a portfolio based on the expected returns found with a rolling regression of historical returns and factors, which will be explained in the next section.
3.4 Estimating the expected returns
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regressions, which means that the regression might give more accurate estimates each month as the estimation window becomes larger. This rolling regression is defined in equation (6). For this regression I define sets θ𝑡 = {1, … , 𝑡} and θ𝑃𝑡= {𝑡 ∈ θ𝑡|𝑃} for a given P at time t, with horizon T at 30-06-2015.
𝑟𝑖𝑞 = 𝛼𝑖𝑡+ ∑3𝑗=1𝛽𝑖𝑗𝑡∗ 𝑓𝑖𝑗,𝑞−1+ 𝜀𝑖𝑞 𝑞 ∈ θ𝑃𝑡, 𝑖 = 1, … , 𝑛, 𝑡 = 1, … , 𝑇 (6)
Where 𝑟𝑖𝑞 is the realized return of stock i in month q, 𝑓𝑖𝑗,𝑞−1 is factor j of stock i in month q-1, 𝑃𝑡 is the phase of the business cycle in month t, and 𝜀𝑖𝑞 is the error term of
expected return of stock i at time q that cannot be explained by the regression. Note that 𝑃𝑡 is known at time t.
After all 𝛽𝑖𝑗𝑡s are estimated, the expected return of each following month can be calculated by multiplying the 𝛽̂𝑖𝑗𝑡with the factors 𝑓𝑖𝑗𝑡. This gives the formula:
𝐸𝑅𝑖,𝑡+1 = 𝛼̂𝑖𝑡+ ∑3𝑗=1𝛽̂𝑖𝑗𝑡∗ 𝑓𝑖𝑗𝑡 𝑖 = 1, … , 𝑛, 𝑡 = 1, … , 𝑇 (7)
The following numerical example will provide some insight into how this formula works. Assume that at time t for stock i the estimated 𝛼̂𝑖𝑡 is 0.003 and the estimated factor
betas 𝛽̂𝑖𝑗𝑡 for the factors value, momentum and volatility are respectively 0.045, 5.126 and -1.040. Furthermore, suppose that the lognormal price to book ratio is 1.340, the momentum factor is 0.031, and the 24-month volatility is 0.056. In this case, the expected return of stock i for month t+1 is 0.043 or 4.3%. In section 4.2 I describe how the factors for value,
momentum and volatility are derived.
3.5 Building the strategy portfolio
For this thesis I use a long-only approach despite the arguments for a long-short combination. Some of these arguments, stated by Koedijk et al (2014), are that market exposure could be eliminated and the risk premium could be captured better using a long-short strategy. However, a considerable amount of institutional investors, such as pension funds, are bound by investment guidelines that restrict the amount of leverage or short positions (Koedijk et al, 2014), making the long-only approach the better option for this thesis.
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top-quintile with the highest expected returns logically get the largest percentage and vice versa. The formula to calculate these weights is:
𝜔𝑖𝑡 =𝑘𝑛𝑡∑−𝑘𝑖𝑡𝑘+1 𝑗𝑡 𝑛
𝑗=1 𝑖 = 1, … , 𝑛, 𝑡 = 1, … , 𝑇 (8)
Where 𝜔𝑖,𝑡 is the weight of stock i in month t, 𝑘𝑖𝑡 is the rank of stock i month t, and 𝑘𝑛𝑡 is the total amount of ranks or stocks in month t. To prevent liquidity problems, the
amount of capital allocated to a single stock cannot be greater than 5% of the volume of that stock in that specific month. This means that only stock with an available volume and price in
datastream can be bought by the strategy. Capital that cannot be allocated to stocks as a
results of these liquidity restrictions are invested in a 3-month T-bill of the economic zone for that specific month.
The value of the strategy portfolio in each month is then calculated by:
𝑉𝑡 = ∑𝑛𝑖=1𝜔𝑖𝑡∗ 𝑉𝑡−1∗ 𝑒𝑅𝑖𝑡− 𝑇𝐶 ∗ ∑𝑖=1𝑛 |𝜔𝑖𝑡 ∗ 𝑉𝑡−1− 𝜔𝑖,𝑡−1∗ 𝑉𝑡−2| 𝑡 = 1, … , 𝑇 (9)
Where 𝑉𝑡 is the value of the strategy portfolio in month t, 𝜔𝑖𝑡 is the weight of stock i at the beginning of month t, 𝑅𝑖𝑡 is the lognormal return of stock i in month t, and 𝑇𝐶 is the transaction costs expressed as a fraction of the transaction.
For determination of transaction costs I use the paper High-Frequency Trading and the
Execution Costs of Institutional Investors (Brogaard et al, 2014). They find that in the period
between 2003 and 2011 the average trading costs for institutional investors were between 12 and 20 bps for FTSE 250 stocks. Since I use a uniform transaction for all investment
universes and time periods, I stay on the safe side and select 20 bps for the transaction costs.
3.6 Market portfolio
Because the investment universes of each economic zone used in this thesis contain numerous stocks that have characteristics such as small capitalization and insolvency, which are not common in the regular benchmarks (e.g. S&P500 and the Eurostoxx50), I create a market portfolio for each economic zone as a benchmark. These market portfolios are built by giving each stock a weight according to their market capitalization:
𝜔𝑖𝑡 = 𝑀𝑉𝑖𝑡
∑𝑛𝑖=1𝑀𝑉𝑗𝑡 𝑖 = 1, … , 𝑛, 𝑡 = 1, … , 𝑇 (10)
Where 𝜔𝑖,𝑡 is the weight of stock i in month t, and 𝑀𝑉𝑖𝑡 is the market value of stock i
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3.7 Isolating the business cycle effect
To isolate the business cycle effect of the strategy, I build a portfolio using the same methodology without the business cycle restriction and compare it to the normal strategy portfolio. The formula to estimate the betas of this new portfolio without the business cycle can be described as:
𝑟𝑖𝑞 = 𝛼𝑖𝑡+ ∑3 𝛽𝑖𝑗𝑡∗ 𝑓𝑖𝑗,𝑞−1+
𝑗=1 𝜀𝑖𝑞 𝑞 ∈ θ𝑡, 𝑖 = 1, … , 𝑛, 𝑡 = 1, … , 𝑇 (11)
Where 𝑟𝑖,𝑞 is the realized return in month q, 𝑓𝑖𝑗,𝑞−1 is factor j of stock i in month q-1,
and 𝜀𝑖𝑡 is the error term of expected return of stock i at time t that cannot be explained by the regression. After all 𝛽𝑖𝑗s are estimated, the expected return can be calculated by multiplying
the 𝛽̂𝑖𝑗𝑡with the factors 𝑓𝑖𝑗𝑡. This gives the formula:
𝐸𝑅𝑖,𝑡+1 = 𝛼̂𝑖𝑡+ ∑3 𝛽̂𝑖𝑗𝑡∗ 𝑓𝑖𝑗𝑡
𝑗=1 𝑖 = 1, … , 𝑛, 𝑡 = 1, … , 𝑇 (12)
After the expected returns are calculated, the stocks from the top-quintile will be selected again each month and weighted according the linear decreasing percentage method described in 3.5.
3.8 Equally weighted portfolio
An outperformance of a strategy can be caused by its deviation in weighting stocks relative to the market (Bolognesi and Zuccheri, 2013). To rule out that this is the case with the strategies used in this paper, I build an equally weighted portfolio and see how it performs against the market and the strategies with and without the business cycle. The equally weighted portfolio can be constructed by allocating 1𝑛 to each stock in each month, thus dividing the holdings equally over all available equities.
3.9 Performance measurement
To measure the performance of the different strategies and compare them with each other, I use the compound annual growth rate (CAGR), maximum drawdown (MDD), Sharpe ratio (S) and information ratio (IR).
The CAGR of a portfolio measures the mean annual growth rate of a portfolio and can be calculated with the formula:
𝐶𝐴𝐺𝑅𝑝𝑡2 = (𝑉𝑉𝑡1𝑡2) 1 𝑌
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Where 𝑉𝑡1 is the value of the portfolio at time t1 and Y is the number of years between
t1 and t2 portfolio.
I define drawdown as 𝐷𝐷𝑝𝑡 = | max
𝑞≤t 𝑉𝑝𝑞
𝑉𝑝𝑡 − 1| for 𝑡 = 1, … , 𝑇, and MDD is a measure of
risk defined by the maximum loss from a peak to a trough of a portfolio calculated by:
𝑀𝐷𝐷𝑝𝑡=
max
𝑞 ≤ t 𝐷𝐷𝑝𝑞 (14)
Where 𝑀𝐷𝐷𝑝𝑡 is the maximum drawdown of portfolio p at time T and 𝑉𝑝𝑡 is the value of portfolio p at time t.
The Sharpe ratio measures the return per unit of risk and can be calculated by: 𝑆𝑝 = 𝑟𝑝𝜎−𝑟𝑓
𝑝 (15)
Where 𝑆𝑝 is the Sharpe ratio of portfolio p, 𝑟𝑝 is the return of portfolio p, 𝑟𝑓 is the
relevant risk-free rate, and 𝜎𝑝 is the standard deviation of the returns of portfolio p.
The information ratio measures the ability of a strategy or manager to generate excess returns compared to his benchmark and is calculated by:
𝐼𝑅𝑝= 𝑟𝑝−𝑟𝑚𝜎
𝑝−𝑚 (16)
Where 𝐼𝑅𝑝 is the Information ratio of portfolio p, 𝑟𝑝 the return of portfolio p, 𝑟𝑚 the
return of the benchmark, which is the market portfolio in this thesis, and 𝜎𝑝−𝑚 is the tracking error of the portfolio which is the standard deviation of the difference between the returns of the portfolio and those of the benchmark.
Finally, I use the Carhart four-factor model to find the four-factor alpha of the portfolios. The four factor alpha and betas are found by the formula:
𝑟𝑝𝑡− 𝑟𝑓𝑡= 𝛼𝑖𝑇+ 𝛽𝑖𝑇∗ 𝑅𝑀𝑅𝐹𝑡+ 𝑠𝑖𝑇∗ 𝑆𝑀𝐵𝑡+ ℎ𝑖𝑇∗ 𝐻𝑀𝐿𝑡+ 𝑤𝑖𝑇∗ 𝑊𝑀𝐿𝑡+ 𝜀𝑖𝑡
t=1, …, T (17) Where 𝑟𝑝𝑡 is the return of portfolio p at time t, 𝑟𝑓𝑡 is the risk-free rate at time t, 𝑅𝑀𝑅𝐹𝑡 market premium over the risk-free rate at time t, 𝑆𝑀𝐵𝑡, 𝐻𝑀𝐿𝑡 and 𝑊𝑀𝐿𝑡 are the returns on
16
difference between the return of the portfolio and the risk free rate at time t that cannot be explained by the combination of the alpha and factor premiums.
4 Data and descriptives
4.1 Investment universe
For this study, I investigate the returns of the strategy in the data of the following economic zones: Eurozone, US, UK and Japan. The investment universe for the US consists of all US stocks listed at the NYSE and Nasdaq. For the Eurozone all stocks from Eurozone countries of the datastream constituent list ‘Europe ex UK’ are used. For the United Kingdom I use all British stocks listed at the FTSE. For Japan I take all Japanese stocks listed at the TSE. The datastream constituent lists used for collecting the stock data only contain stocks that are currently active. To prevent survivorship bias in this thesis, I added delisted stocks from the datastream ‘Dead stock’ constituent lists of the four economic zones used. Stocks are removed from the universe after the month they become delisted. The table below shows characteristics of the number of the stocks in the economic zones during the period of 31-3-1992 to 30-06-2015, which is the period in which the strategy is active.
A remarkable feature of the table above is that all economic zones contain the least amount of stocks in the last month of the sample. This suggests that in recent years the amount of mergers, acquisitions and delistings was higher than the IPO’s. Doidge, Karolyi and Stulz (2015) confirm this for the US stock market.
4.2 Factors and return data
For all of these stocks, I extract the total return index over a period of 31-3-1980 to 30-06-2015 to calculate the lognormal returns and the factors momentum and volatility. The momentum factor in month t is calculated by the average returns of month t-13 to t-1, the month between t-1 and month t is skipped to prevent microstructure issues (Liew and
Vassalou, 2000; Griffin and Martin, 2003). The volatility factor is calculated by simply taking
Eurozone US UK Japan # of stocks at 31-3-1992 1854 3825 1262 1974 # of stocks at 30-06-2015 1159 3685 436 1867 Median # of stocks 1905 5549 1367 2365 Maximum # of stocks 2341 6870 1618 2552 Minimum # of stocks 1159 3685 436 1867
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the 24-months trailing standard deviation. Furthermore, I extract the monthly volume by turnover, price, market value, and price-to-book (PB) ratio for all stocks. The PB values are made lognormal by LN(PB) when PB>0. If PB<0 it will be set to 0. This is done to mute extreme swings in PB values (e.g. when book values are close to zero). I use the total return index on 3 month T-bills as a proxy for risk-free rate. These are measured by the JP Morgan 3-month cash index for each individual economic zone. I extract the 𝑆𝑀𝐵𝑡, 𝐻𝑀𝐿𝑡 and 𝑊𝑀𝐿𝑡 from the website of Kenneth French2. For the Eurozone and the UK I use the European
factors, as there are no separate UK factors, for the US I take the North American factors and for Japan the Japanese factors. The 𝑅𝑀𝑅𝐹𝑡 is calculated by subtracting the risk-free rate from
the market portfolio return each month. To estimate the stages of the business cycle through the time frame of the research I use proxies for the output gap and inflation. For each of the economic zones I take the quarterly figures of the Oxford Economics Output Gap. The monthly inflation is calculated from the Consumer Price Index of the countries/economic zones. Since the inflation data of the Eurozone is not available for the period 03-1980 to 12-1990, I estimate the inflation rate for this period by:
𝐼𝐸𝑡 = ∑ 𝜔𝑗𝑡∗ 𝐼𝑗𝑡 𝑡 = 03 − 1980, . . , 12 − 1990 (18) Where 𝐼𝐸𝑡 is the estimated Eurozone inflation, 𝜔𝑗𝑡is the weight of the GDP of country j at time t relative to the total GDP of the Eurozone, and 𝐼𝑗𝑡 is the inflation of country j at time t.
All data described above is extracted from datastream, unless stated otherwise.
4.3 Descriptive statistics of the portfolio returns
Table 2 shows the descriptive statistics of the monthly returns for the four portfolios in each economic zone. The Jarque-Bera test statistic is large and significant, which means that the returns are not normally distributed. In each economic zone the kurtosis of the market is lower than the other three portfolios, indicating that the probability distribution of the other portfolios is less flat than that of the market. Furthermore, the skewness of the strategy and the strategy without business cycle is larger than that of the market portfolio in all zones except the Eurozone. This means that these portfolios are more skewed to the right, indicating more positive extremes, relatively speaking.
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Table 2. Descriptive statistics of portfolio returns
Market Strategy
Strategy without business cycle
Equally
weighted Market Strategy
Strategy without business cycle
Equally
weighted Market Strategy
Strategy without business cycle
Equally
weighted Market Strategy
Strategy without business cycle Equally weighted Min -0.177 -0.126 -0.133 -0.157 -0.175 -0.212 -0.209 -0.180 -0.145 -0.177 -0.194 -0.177 -0.197 -0.172 -0.185 -0.166 Q1 -0.027 -0.003 0.006 0.017 -0.017 -0.002 0.016 0.022 -0.016 -0.011 0.007 0.013 -0.033 -0.015 -0.002 0.015 Median 0.012 0.011 0.011 0.013 0.015 0.020 0.022 0.016 0.011 0.008 0.013 0.008 0.003 0.006 0.005 0.004 Q3 0.047 0.038 0.036 0.037 0.038 0.051 0.055 0.041 0.034 0.040 0.040 0.027 0.040 0.043 0.046 0.042 Max 0.233 0.170 0.189 0.164 0.116 0.338 0.285 0.233 0.109 0.278 0.283 0.215 0.141 0.252 0.255 0.243 N 279 279 279 279 279 279 279 279 279 279 279 279 279 279 279 279 Skewness 0.164 -0.128 0.110 -0.414 -0.790 0.580 0.360 -0.164 -0.531 0.564 0.439 -0.046 -0.091 0.342 0.300 0.234 Kurtosis 1.112 1.445 1.656 1.668 1.596 3.697 2.458 2.418 0.769 3.090 3.006 4.113 0.564 0.903 0.679 0.696 Jarque Bera 42.680 28.853 21.551 28.598 51.933 21.293 9.437 5.179 70.932 14.880 8.963 14.493 69.364 56.543 66.790 64.252 P-value Jarque Bera 0.000** 0.000** 0.000** 0.000** 0.000** 0.000** 0.004** 0.038* 0.000** 0.000** 0.006** 0.000** 0.000* 0.000* 0.000* 0.000* *statistically significant at a 5% level, **statistically significant at a 1% level
Eurozone US UK Japan
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5 Results
5.1 Market and strategy portfolio
The performance of the market and strategy portfolio for all economic zones are shown in Table 3 below. As can be seen, in all zones the CAGR of the strategy is higher than that of the market. Furthermore, the Sharpe ratio is higher in each zone, meaning that the return per unit of risk is higher for the strategy than for the market. In section 5.3 I will check if this difference is also significant. A remarkable result is the CAGR of the strategy portfolio in the US with its 21.22%. This seems to be an extremely high result for a trading strategy as it means that each dollar invested in 1992 becomes over 89 times as much in 2015.
Figure 4. Performance of the four portfolios in the Eurozone
5.2 Strategy without business cycle and equally weighted portfolio
Table 4 below shows the performance of the strategy without the business cycle restriction and the equally weighted performance. All CAGRs, Sharpe ratios, and Information ratios of the strategy without the business cycle portfolios are higher than the strategy portfolios for each of the economic zones. This indicates that the business cycle does not add value in estimating expected returns of stocks and might even destroy value. Furthermore, Table 4 shows that the CAGRs, Sharpe ratios, and Information ratios of the equally weighted portfolio are lower than that of the strategy and the strategy without the business cycle. This might indicate that the outperformance of these two strategies compared to the market portfolio is not exclusively caused by their alternative weighting. In section 5.3 I check if these
differences between the Sharpe ratios are statistically significant. A graph showing the 0 2 4 6 8 10 12 14 16 18 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 M illi o ns
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Table 3. Performance of the market and strategy portfolio
Market Strategy Market Strategy Market Strategy Market Strategy
Annualized return (CAGR) 03-1992- 06-2015 7.68% 12.18% 9.82% 21.22% 8.41% 9.84% 2.37% 6.31%
Max Drawdown -54.53% -42.97% -50.29% -48.08% -42.34% -55.89% -54.97% -67.65%
Sharpe ratio (1 month) 0.058 0.165 0.119 0.217 0.073 0.071 0.025 0.070
Sharpe ratio (1 year) 0.210 0.610 0.436 0.833 0.266 0.261 0.087 0.249
Information ratio (1 month) - 0.108 - 0.206 - 0.026 - 0.088
Information ratio (1 year) - 0.407 - 0.811 - 0.098 - 0.316
Japan
This table presents the performance of the market and strategy portfolio in the four economic zones. The market portfolio is constructed by simply giving each stock a weight of its market capitalization divided by the total market capitalization of the investment universe. This procedure is described in equation (10).
For the construction of the strategy portfolio the exposure to the factors value, momentum and low-volatility for each stock are calculated given the phase of the business cycle using a rolling regression described in equation (6). After this procedure the expected returns of each month t+1 can be calculated for all stock by multiplying the factor exposures with the factor values of month t, this is described in equation (7). The strategy portfolio is constructed by giving the stocks in the top-quintile of these expected returns a linear decreasing weight according to their rank in the quintile, described by equation (8). Both portfolios are rebalanced at the end of each month.
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Table 4. Performance of the strategy without business cycle and equally weighted portfolio
Strategy without business cycle Equally weighted Strategy without business cycle Equally weighted Strategy without business cycle Equally weighted Strategy without business cycle Equally weighted
Annualized return (CAGR) 03-1992- 06-2015 12.71% 10.45% 24.38% 15.48% 11.94% 7.17% 7.33% 5.26%
Max Drawdown -40.72% -52.19% -41.06% -50.04% -57.48% -56.10% -66.27% -61.25%
Sharpe ratio (1 month) 0.159 0.123 0.253 0.188 0.096 0.047 0.078 0.061
Sharpe ratio (1 year) 0.590 0.453 0.982 0.703 0.356 0.171 0.279 0.218
Information ratio (1 month) 0.110 0.072 0.266 0.155 0.062 -0.034 0.110 0.078
Information ratio (1 year) 0.414 0.270 1.061 0.595 0.234 -0.125 0.396 0.278
This table presents the performance of the strategy without business cycle and the equally weighted portfolio in the four economic zones. For the construction of the strategy without business cycle portfolio the exposure to the factors value, momentum and low-volatility for each stock are calculated using a rolling regression, described in equation (11). After this procedure the expected returns of each month t+1 can be calculated for all stock by multiplying the factor exposures with the factor values of month t, as is described in equation (12). The strategy portfolio is constructed by giving the stocks in the top-quintile of these expected returns a linear decreasing weight according to their rank in the quintile. This is described in equation (8).
The equally weighted portfolio is constructed by simply giving each stock in the investment universe an equal weight. Both portfolios are rebalanced at the end of each month.
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development of the four portfolios in the Eurozone can be found in Figure 4. All other graphs can be found in Appendix D.
5.3 Comparing Sharpe ratios
To be able to compare the different portfolios, I test if the 1-month Sharpe ratios differ significantly. To do this, I use the studentized time series bootstrap method described in Ledoit and Wolf (2008). The results are displayed in the graph below.
As can be found in the Table 5, there are only two economic zones with statistical differences between 1-month Sharpe ratios. In the Eurozone, the Sharpe ratio of the strategy portfolio, the strategy without business cycle portfolio and the equally weighted portfolio differ significantly from that of the market portfolio. This indicates that they significantly outperform the market. The strategy portfolio also significantly differs statistically from the equally weighted portfolio, which indicates that the difference in Sharpe ratios between the strategy portfolio and the market portfolio is not exclusively caused by its alternative weighting.
The US shows a statistically significant difference between Sharpe ratios of the strategy without business cycle portfolio and the other portfolios on a 5% level. This means that it significantly outperforms the market and that this outperformance is not exclusively caused by its alternative weighting. More importantly, however, it shows that in the US the addition of the business cycle results in a lower Sharpe ratio and thus less explanatory power.
Furthermore, there are no significant differences between the other Sharpe ratios, which tells us that the business cycle does not add any significant value here on the market and the strategy without the business cycle.
5.4 Carhart alphas
Table 6 shows the results of the four-factor Carhart model evaluation for all sixteen portfolios. As becomes clear from the table, all strategies without business cycle and almost all strategy portfolios create a significant positive four-factor alpha higher than the equally weighted portfolio. This means that these portfolios have an outperformance against the market
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Table 5. P-values difference in sharpe ratios between portfolios (T-stat is in parentheses)
Market Strategy Strategy without business cycle
Equally weighted
Market Strategy Strategy without
business cycle Equally weighted Market - -Strategy 0.002** (3.408) -0.063 (2.184)
-Strategy without business cycle 0.012* (2.916) 0.692 (0.431) -0.018** (3.087) 0.007** (2.872) -Equally weighted 0.022* (2.313) 0.031* (2.664) 0.211 (1.239) -0.103 (1.854) 0.283 (1.131) 0.008** (2.857)
-Market Strategy Strategy without
business cycle Equally weighted Market Strategy
Strategy without
business cycle Equally weighted Market - -Strategy 0.703 (0.413) -0.192 (1.420)
-Strategy without business cycle 0.950 (0.058) 0.262 (1.164) -0.103 (1.823) 0.476 (0.686) -Equally weighted 0.497 (0.712) 0.775 (0.308) 0.241 (1.233) -0.263 (1.205) 0.568 (0.606) 0.152 (1.553)
-*statistically significant at a 5% level, *-*statistically significant at a 1% level
This table presents the p-values of the difference in Sharpe ratios between the portfolios within each economic zone. The p-values are calculated using the studentized bootstrap method described by Ledoit and Wolf (2014). The market portfolio is constructed by simply giving each stock a weight of its market capitalization divided by the total market capitalization of the investment universe. This procedure is described in equation (10). For the construction of the strategy portfolio the exposure to the factors value, momentum and low-volatility for each stock are calculated given the phase of the business cycle using a rolling regression described in equation (6). After this procedure the expected returns of each month t+1 can be calculated for all stock by multiplying the factor exposures with the factor values of month t, this is described in equation (7). The strategy portfolio is constructed by giving the stocks in the top-quintile of these expected returns a linear decreasing weight according to their rank in the quintile, described by equation (8). For the construction of the strategy without business cycle portfolio the exposure to the factors value, momentum and low-volatility for each stock are calculated using a rolling regression, described in equation (11). After this procedure the expected returns of each month t+1 can be calculated for all stock by multiplying the factor exposures with the factor values of month t, as is described in equation (12). The strategy portfolio is constructed by giving the stocks in the top-quintile of these expected returns a linear decreasing weight according to their rank in the quintile. This is described in equation (8). The equally weighted portfolio is constructed by simply giving each stock in the investment universe an equal weight. All portfolios are rebalanced at the end of each month.
Eurozone
UK
US
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Table 6. Evaluation of the portfolio returns using the Carhart four-factor model
Market Strategy
Strategy without
business cycle Equally weighted Market Strategy
Strategy without
business cycle Equally weighted
Alpha 0.000* 0.451** 0.613** 0.466* 0.000* 0.905** 1.191** 0.555** RMRF 1.000** 0.624** 0.661** 0.682** 1.000** 0.878** 0.882** 0.817** SMB 0.000* 0.468** 0.607** 0.550** 0.000* 1.078** 1.016** 0.750** HML 0,000 0.107* -0,083 -0,034 0.000** -0,039 -0.123* 0,05 WML 0.000** -0.049 -0.101** -0.163** 0.000** -0,038 -0.105** -0.155** R² 1,000 0,743 0,695 0,812 1,000 0,842 0,840 0,875 P-value F-statistic 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 Market Strategy Strategy without
business cycle Equally weighted Market Strategy
Strategy without
business cycle Equally weighted
Alpha 0,000 0,311 0.436* 0,074 0.000** 0.288* 0.408** 0.187** RMRF 1.000** 1.120** 1.178** 0.901** 1.000** 1.028** 1.112** 0.989** SMB 0.000** 1.189** 1.338** 0.928** 0,000 0.886** 1.001** 0.822** HML 0,000 -0.263** -0.299** -0,086 0,000 0.249** 0.144** 0.277** WML 0.000** -0,078 -0,0389 -0.107** 0,000 -0,045 -0,015 -0.110** R² 1,000 0,691 0,726 0,824 1,000 0,900 0,948 0,983 P-value F-statistic 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000
*statistically significant at a 5% level, **statistically significant at a 1% level
Eurozone US
UK Japan
25
6 Robustness
For the model to be consistent in predicting returns, it should also indicate which stocks will perform worst in each month. To test this, I construct the strategy and the strategy without the business cycle in the same way as described in section 3, only this time I select the bottom-quintile instead of the top-quintile of expected returns. If the model is consistent, these portfolios should underperform the market portfolio.
Table 7 shows that both bottom quintile strategies underperform the market in the Eurozone, UK and Japan which is consistent with the model. In the US the strategies outperform the market but underperform the strategies using the top-quintile. However, the bottom-quintile strategies in the US still underperform the equally weighted portfolio, this indicates that their outperformance relative to the market might simply be caused by their alternative weighting method.
For consistency reasons, I perform a Carhart four-factor model evaluation for the bottom quintile portfolio. The results of this are displayed in Table 8. As becomes clear from the table, only the US strategy portfolio has a significant alpha, indicating that the other portfolios do not outperform the market, and thus confirming the predictive power of the model described in this paper.
7 Conclusion
This paper investigates whether the risk premiums value, momentum and volatility have predictive power for estimating expected return. The first hypothesis states that a portfolio that uses the ex-ante risk premiums combined with the state of the business cycle can outperform the market portfolio. I find that although the strategy generates a positive four-factor alpha in the Eurozone, US and Japan. However, its Sharpe ratio does only differ significantly from that of the market in the Eurozone. This means I have to reject hypothesis H1a for the US, UK and Japan.
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Table 7. Performance of bottom quintile portfolios
Strategy Strategy without
business cycle Strategy
Strategy without
business cycle Strategy
Strategy without
business cycle Strategy
Strategy without business cycle
CAGR 03-1992- 06-2015 3.17% 2.62% 13.96% 9.85% 3.38% 3.49% 1.97% 1.31%
Max Drawdown -55.78% -68.42% -53.80% -63.34% -77.24% -84.75% -78.92% -80.90%
Sharpe ratio (1 month) -0.009 -0.016 0.108 0.066 -0.014 -0.009 0.013 0.006
Sharpe ratio (1 year) -0.032 -0.058 0.401 0.241 -0.050 -0.034 0.044 0.019
Information ratio (1 month) -0.114 -0.107 0.056 0.000 -0.072 -0.046 -0.007 -0.018
Information ratio (1 year) -0.414 -0.386 0.216 0.002 -0.263 -0.166 -0.024 -0.062
This table presents the performance of the bottom quintile portfolios. For the construction of the strategy portfolio the exposure to the factors value, momentum and low-volatility for each stock are calculated given the phase of the business cycle using a rolling regression described in equation (6). After this procedure the expected returns of each month t+1 can be calculated for all stock by multiplying the factor exposures with the factor values of month t, this is described in equation (7). The strategy portfolio is constructed by giving the stocks in the bottom-quintile of these expected returns a linear decreasing weight according to their rank in the quintile, described by equation (8). For the construction of the strategy without business cycle portfolio the exposure to the factors value, momentum and low-volatility for each stock are calculated using a rolling regression, described in equation (11). After this procedure the expected returns of each month t+1 can be calculated for all stock by multiplying the factor exposures with the factor values of month t, as is described in equation (12). The strategy portfolio is constructed by giving the stocks in the bottom-quintile of these expected returns a linear decreasing weight according to their rank in the quintile. This is described in equation (8). Both portfolios are rebalanced at the end of each month.
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Table 8. Evaluation of the bottom quintile portfolio returns using the Carhart four-factor model
Strategy
Strategy without
business cycle Strategy
Strategy without
business cycle Strategy
Strategy without
business cycle Strategy
Strategy without business cycle Alpha -0.004 0.100 0.774** 0.446 0.024 0.078 0.133 0.023 RMRF 0.674** 0.731** 0.910** 0.932** 1.300** 1.367** 1.144** 1.158** SMB 0,526** 0.624** 1.050** 1.092** 1.589** 1.745** 1.125** 1.162** HML 0.076 -0.160* -0.348** -0.302** -0.301** -0.125 0 0.133* WML -0.301** -0.354** -0.443** -0.440** -0.274** -0.281* -0.255* -0.267** R² 0.804 0.702 0.709 0.704 0.683 0.417 0.871 0.892 P-value F-statistic 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
*statistically significant at a 5% level, **statistically significant at a 1% level
Eurozone US UK Japan
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value and momentum, whereas in this paper the strategy portfolio is constructed using expected return based on a combinations of the risk premiums value, momentum, volatility and the business cycle.
Hypothesis H1b states that the strategy portfolio outperforms a portfolio that is constructed using only risk premiums. I find that the four-factor alphas generated by the strategy in all economic zones are lower than those of the portfolio using only risk premiums. Furthermore, the Sharpe ratio of the strategy does not differ significantly from that of the portfolio using only risk premiums in the Eurozone, the UK and Japan, and does even significantly underperform that of the US, therefore leading to the rejection of H1b.
This is not in line with Cooper and Priestly (2009), who find evidence that the output gap is a good predictor for stock returns, since this paper finds that in the US the business cycle combined with three factor premiums is an inferior predictor of stock returns compared to using only the three factor premiums. This difference might be caused by the fact that the output gap is only one of the two components of the business cycle which is also dependent on inflation.
The last hypothesis states that the strategy portfolio outperforms an equally weighted portfolio. The four-factor alphas of the strategy portfolios are higher than those of the equally weighted portfolio in the Eurozone, US and Japan. Furthermore, the Sharpe ratio of the strategy in the Eurozone is significantly higher than the equally weighted portfolio. This means that the hypothesis can be rejected for the US, UK and Japan but not for the Eurozone.
Another important conclusion apart from the hypotheses is the strong performance of the strategy without business cycle portfolio. In all economic zones it has the highest CAGR and in all economic zones, except for the Eurozone, it has the highest Sharpe ratio. Although the Sharpe ratio of the strategy without business cycle is only significantly higher than that of the market portfolio in the Eurozone and the US. Furthermore, the strategy portfolio without business cycle generates the highest significant positive four-factor alpha in each economic zone.
8 Limitations and recommendations
Lastly, I will discuss the limitations of this research and provide some
out-29
of-sample period. This means that stocks that would have been bought if the strategy was really implemented are not included in the portfolios described in this paper.
Another limitation is the business cycle model developed in this paper, which does not fit the phases of the business cycle perfectly. This is caused by the fact that only backward looking data can be input of the model, making a perfectly fitting model an impossibility. However, a more sophisticated model, for instance one developed by an institutional investor, might improve the fit of the model and therefore also the performance of the strategy
portfolio.
Furthermore, as the momentum and low-volatility factor premiums are used as an input of the model, only stocks that are listed for at least two years can be included in the strategy portfolios. This might lead to bias in the results as IPO underpricing effects (Ibbotson et al, 1994) and the major part of the three year underperformance of IPO firms (Ritter, 1991) are not included in the strategy portfolios.
Finally, the Fama and French factors that are used for the Carhart four-factor model evaluation of the portfolios in the UK are European factors as there are no UK factors available. Using the UK factors might lead to other results of this evaluation.
As the results between the economic zones differed significantly and this research only focused on developed markets, further research focusing on other countries or economic zones might provide new insights in this field. In addition, this research could be replicated using other methods to estimate the business cycle or different factor premiums to find if the conclusions still hold.
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Appendix A. Inflation cycles
Figure A.1 Direction signals of inflation cycle Eurozone
Vertical solid lines are decelerating signals, vertical dashed lines are accelerating signals
Figure A.2 Direction signals of inflation cycle US
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Figure A.3 Direction signals of inflation cycle UK
Vertical solid lines are decelerating signals, vertical dashed lines are accelerating signals
Figure A.4 Direction signals of inflation cycle Japan
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Appendix B. Output gap cycles
Figure B.1 Direction signals of output gap cycle Eurozone
Vertical solid lines are decelerating signals, vertical dashed lines are accelerating signals
Figure B.2 Direction signals of output gap cycle US
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Figure B.3 Direction signals of output gap cycle UK
Vertical solid lines are decelerating signals, vertical dashed lines are accelerating signals
Figure B.4 Direction signals of output gap cycle Japan
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Appendix C. Business cycle phases
Figure C.1 Phases of the business cycle Eurozone
Figure C.2 Phases of the business cycle US
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Appendix D. Portfolio graphs
Figure D.1 Performance of the portfolios Eurozone
Figure D.2a Performance of the portfolios US 0 2 4 6 8 10 12 14 16 18 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 M illi o ns
Market Strategy Strategy without business cycle Equally weighted
0 20 40 60 80 100 120 140 160 180 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 M illi o ns
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Figure D.2b Performance of the portfolios US (logarithmic scale)
Figure D.3 Performance of the portfolios UK 100.000 1.000.000 10.000.000 100.000.000 1.000.000.000 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014
Market Strategy Strategy without business cycle Equally weighted
0 2 4 6 8 10 12 14 16 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 M illi o ns
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Figure D.4 Performance of the portfolios Japan
0 1 2 3 4 5 6 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 M illi o ns
