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International Portfolio Allocation over the

Business Cycle

Bachelor Thesis University of Amsterdam July 2020

Abstract

This thesis examines if investors can benefit from incorporating cyclical information on asset returns during international portfolio allocation. This is tested through comparing the ability

of portfolios to achieve the highest Sharpe Ratio. First, we find evidence for international diversification benefits through the comparison of the Sharpe Ratios of domestic portfolios

with an international portfolio. Second, we observe that asset classes perform differently during different phases of the business cycle. This observation suggests that portfolio allocation should be based on the upcoming business phase. The idea behind this is that we want to use the best performing periods of an asset class to maximize the Sharpe Ratio. We provide a methodology to find the optimal allocation using the Composite Leading Indicator provided by the Organization for Economic Co-operation and Development. A test for equal

Sharpe Ratios gives evidence for the substantial gain in achieving a higher Sharpe Ratio using the business cycle approach. These results are consistent with the expectations as

discussed in the research thesis.

Name: Maarten In de Braekt Student Number: 11904674 Program: Business Administration Specialization: Finance

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Statement of Originality

This document is written by student Maarten In de Braekt who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no

sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Table of Contents

Abstract ... 1 1 Introduction ... 4 2 Literature review ... 6 2.1 Portfolio Diversification ... 6

2.2 Home Country Bias... 7

2.3 Correlation ... 7

2.4 Asset Allocation ... 8

2. 5 Business Cycles ... 9

3 Data ... 11

3.1 Jorda-Schularick-Taylor Microhistory database ... 11

3.2 Composite Leading Indicator ... 12

4 Methodology ... 13

4.1 Hypotheses ... 13

4.2 Portfolio Allocation ... 14

5 Results ... 18

5.1 Results International Diversification ... 18

5.2 Asset performance over the business cycle ... 19

5.3 Results Business Cycle Allocation ... 20

6 Discussion ... 23

7 Conclusion ... 24

References ... 25

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1 Introduction

It is a well-known phenomenon for economies to go through periods of expansion and recession. However, the most popular asset allocation approaches do not incorporate the fluctuations of the business cycle in the portfolio allocation process. Business cycles are fluctuations around a long-term growth rate that differ in strength and duration. Asset classes have shown to experience dissimilar return characteristics during the different phases of the business cycle. Therefore, using information on dissimilar return characteristics during the different cycle phases could potentially result in better portfolio performance.

The objective of this research thesis is to evaluate the potential benefits of

incorporating cyclical information during the portfolio allocation process with regards to an international diversification strategy. More specifically, the benefits of the construction of a stage-switching internationally diversified portfolio that allocates recourses among

international asset classes on the basis of the business cycle phase is evaluated.

This research thesis will add to the existing literature on international diversification benefits and asset allocation over the business cycle. Existing literature contains research on the effect of using cyclical data during asset allocation and international diversification benefits, separately. This thesis analyses the effect of combining both theories. The research question of this paper that combines both these theories is “Can cyclical information be used to improve the asset allocation process for an internationally diversified portfolio over the long run?”.

To find an answer to the research question, first, the potential benefits of international diversification over domestic diversification is tested on the dataset used in this paper. To do this, portfolios that are created to maximize the Sharpe Ratio over the period 1975-2015 are compared. The domestic portfolios are made for 8 developed economies and include stock, housing and bond markets. The domestic portfolios and the international portfolio are tested for equal Sharpe Ratios. Next, cyclical data and its uses in the asset allocation process are explored. The Composite Leading Indicator by the Organization of Economic Co-operation and Development (OECD, 2020) is used to display the business cycle phases of the countries included in the paper. The main goal of the analysis is to evaluate a potential positive effect of using cyclical information on the business cycle in the asset allocation process. This is tested by comparing the internationally diversified portfolio with portfolios that incorporate

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5 this cyclical information. This test is again based on the performance of the portfolio to

acquire the highest Sharpe Ratio, which is the ratio between excess return and risk of the portfolio. The test for equal Sharpe Ratios is done through the corrected version of the Jobson-Korkie (1981) test by Memmel (2003).

The thesis is structured as follows: In section 2 the literature review will go over research relating the research question. This consists of research on portfolio diversification, home country bias, asset correlation, asset allocation and business cycles. In section 3 the data that is used during the thesis for the analysis is shown. Section 4 contains the

methodology on how the data is used and how the hypotheses are tested, as well as the portfolio allocation processes. In section 5 the results of the hypotheses testing are presented. In section 6 the results are interpreted and discussed. At last, section 7 will give an answer to the research question and summarizes the findings.

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2 Literature review

In this section, the literature review of this thesis is presented. First, the origin of diversification and the theories on portfolio diversification research are provided.

Furthermore, the transition to international diversification and evidence on the benefits are introduced. Home country bias and its effect on performance are discussed. Furthermore, research on correlation between international markets and asset classes are discussed. The literature about asset allocation and asset classes is also considered. Lastly, the findings on business cycles and their effect on the asset allocation process are mentioned.

2.1 Portfolio Diversification

Markowitz (1952), often seen as the founder of the modern portfolio theory, constructed the idea that diversifying a portfolio with stocks that are not perfectly correlated can lower the risk of that portfolio without sacrificing the return. He noticed that the risk of assets should not be considered independent. Economic influences make it so that, to a certain level, the risk of assets is correlated. The risk that is correlated between assets which cannot be diversified away is systematic risk. The risk that is specific to an asset which can be diversified away is called idiosyncratic (unsystematic) risk. Diversifying wealth among multiple assets can decrease the risk of a portfolio by diversifying away the unsystematic risk. This theory was tested by Solnik (1974) in an international setting to examine potential international diversification benefits. He found that substantial gains from diversifying internationally throughout 8 countries could be realized over diversifying domestically in the United States. The main advantage from international diversification comes forth from the non-perfect correlations between markets. Grubel (1968) found that stock prices in different countries had little correlation. This non-perfect correlation makes it possible to diversify among markets to reduce risk exposure to a certain market because of the dissimilar behavior. Solnik (1974) found that in domestic markets, increasing the number of stocks held to more than 20 would have a relatively small reduction in risk. However, for international portfolios the reduction of risk would still be substantial if the number of international stocks would increase past 40. This makes international diversification more interesting for institutional investors compared to individual investors because of the requirement for more capital to diversify among more assets (Solnik, 1974). Research over the years has extended to include international diversification benefits on multiple asset classes. Evidence has been found for

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7 non-perfect correlation and diversification benefits within international stock markets

(Lessard, 1976; Driessen & Laeven, 2007), international bond markets (Levy & Lerman, 1988; Fletcher, Paudyal & Santoso, 2019) and international real estate markets (Eichholtz, 1996; Giliberto, 1990; Gordon, 1992). These papers show that international diversification strategies through international portfolio allocation can be more profitable than through domestic portfolio allocation.

2.2 Home Country Bias

Vanguard, one of the biggest investment management companies in the world, did a study on global equity investing (Scott, Balsamo, McShane & Tasopoulos, 2017). In that study it found that investors hold a larger amount of equity in their domestic market than their market capitalization share in the world would indicate. Furthermore, they found that U.S. investors hold around 1.5 times the amount of U.S. stocks the market capitalization would suggest. According to the study, most investors have a home country bias and therefore hold a higher share of domestic stocks. Stulz (2005) and van Nieuwerberg and Veldkamp (2005), also found the same home country bias among investors. Moreover, investors that do hold internationally diversified portfolios, often invest in foreign countries that have a higher correlation to their domestic market (Chan, Covrig & Ng, 2005). This shows that investors still forgo to take (full) advantage of the benefits of holding an internationally diversified portfolio.

2.3 Correlation

Research has found that over the years a trend has been seen which shows markets getting more correlated and international diversification benefits diminishing (Solnik, Boucrelle & Le Fur, 1996). The research was done on multiple developed bond and stock markets between 1958 and 1995 and found a general increase in correlation within both bond and stock markets over time. They also observed that in times of high market volatility, the domestic markets tend to move in unison, a phenomenon that is called volatility contagion. In these high volatility periods, the correlation within international stock and international bond markets also increases. High correlation tends to diminish diversification benefits (Bergin & Pyun, 2006). This indicates that during these periods of high market volatility the

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8 diversification benefits are diminished. Developed markets tend to have a higher correlation with other developed markets than with emerging markets (Korajczyk, 1996). This makes including emerging economies in the portfolio allocation a profitable endeavor. However, a trend has been seen of emerging markets becoming more correlated with developed markets (Bekaert & Harvey, 2002). The main reason for the increase in international correlation is globalization according to Inci, Li and McCarthy, (2011). They mention the increase in international trade and more integrated financial markets as main contributors to this increase in correlation over the years. This trend of increased correlation will endure as long as

international markets are getting more integrated.

2.4 Asset Allocation

According to Sharpe (1992), asset allocation is the practice of allocating an investor’s

portfolio according to a number of asset classes. Assets can take on many forms. Examples of well-known asset classes are stocks, bonds and real estate. The main issue facing investors is how to distribute resources among a group of assets (Elton & Gruber, 1997). Modern

Portfolio Theory tries to give answers to questions surrounding asset allocation. Markowitz (1959) developed the mean variance efficiency theorem with regards to the asset allocation issue. This theorem gives an approach to construct an optimal risky portfolio by determining the share of wealth that will be allocated to each asset in the chosen group of assets. In this process the Efficient Frontier is constructed. The Efficient Frontier consist of all optimal portfolios that have the highest expected return for the amount of risk taken. The level of risk an investor is willing to take on will determine where on the Efficient Frontier the portfolio will end up. This approach is done by using the estimates of the expected return, standard deviation and the correlation between the assets in the group. This allocation of resources creates the optimal risky portfolio which maximizes the expected return for a given level of risk or minimizes the risk for the level of return. The main theoretical contribution of the model was that not only the asset specific characteristics were seen as important but also the relationship between certain assets, which is expressed as the correlation. Assets that are not perfectly correlated can create diversification benefits. Other models have built upon the ideas of Markowitz and created new asset allocation models. Even though some models give a more realistic representation of return characteristics the mean variance theory of

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9 reason for the persistence of the theorem is not necessarily because the model is the best at

predicting results. The reasons for the persistence come from the intuitive nature of the theory and the lack of evidence for additional explanatory power of the other models. The lack of computing power before the 1960s made it so that there had not been any breakthrough research done on stock returns and risk (Elton, Gruber & Padberg, 1976). Fisher and Lorie (1964) did a study on the return of stocks on the New York Stock Exchange for different holding periods since 1926. In 1968 Fisher and Lorie published another research in which they included standard deviations of stock market returns (Fisher & Lorie, 1968). The first factor model to determine the expected return an investment should have according to the amount of risk it has was the Capital Asset Pricing Model developed by William Sharpe (1964) and extended by Litner (1965) and Mossin (1966). The CAPM uses asset classes in the allocation process to determine the return that is acceptable for the level of risk. The CAPM has been an important contribution the Modern Portfolio Theory.

2. 5 Business Cycles

According to Burns and Mitchell (1946), business cycles are fluctuations of economic variables around its long-term growth trend. The business cycle generally consists of

fluctuating periods of expansions and contractions. The sources of business fluctuations have been widely theorized (Shapiro & Watson, 1988). The theory of Keynes thinks of the short-term demand as the driving factor behind business cycle trend. If the current output level is not fully obtained by consumers the output level will decrease to adjust for the difference in demand. Blanchard and Quah (1989) stated that the long-term output level is determined by supply shocks. Supply shocks entail events that change the supply level in a short amount of time. There has been done a lot of research on macroeconomic cycle trends and their effect on economic variables. According to Canova (1998), it has become popular over the years to characterize the movements of macroeconomic variables over the business cycle with a collection of statistics. The Composite Leading Indicator provided by the OECD (2020) tries to predict business cycles through the use of macroeconomic components. Figure 2.5 shows that the CLI and the economic activity of countries tracked by the OECD move in a similar way. However, the movements of the CLI precede the movements in the economic activity. This gives the CLI the ability to predict changes in the business cycle before they happen.

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10 According to Fama and French (1989), the returns on stock can be predicted through the use

of cyclical information because of the dissimilar behavior of stocks over the business cycle. Furthermore, research dedicated to equity valuation shows that the relationship between stock prices and the state of the economy is statistically significant and positive (Moore, 1983). Moore found that growth cycles and inflation rate are closely connected. Significant declines in the inflation rate were linked with a slowdown in growth. He also found that economic indicators like spending and stock prices were more effective in predicting growth cycles than in predicting business cycles. Chen, Roll and Ross (1986) also found economic state indicators to have a good predicting power over expected stock returns and risk premia. The different behavior of bond and stock return characteristics during business cycles phases makes asset allocation using cyclical information interesting for investors. Total stock returns generally increase during periods of expansion while bonds perform better during periods of downturn (Brocato & Steed, 1998). Empirical research done between 1946 and 1970 by Moore (1983) shows this inverse relationship. The research uses economic data on equity returns, corporate bond yields and bond prices. Moore found that because of the fixed income characteristics of bonds, the relationship between bond prices and bond yields are inversely related.

Figure 2.5

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3 Data

The goal of this section is to show what data is used for this thesis. This research focuses on international diversification benefits using cyclical information during the asset allocation process. The countries on which the analysis is done are Australia, Italy, United States, United Kingdom, The Netherlands, Norway, Sweden and Japan. These 8 developed economies were choses due to the availability of the data of interest. The data obtained for every country consists of annual returns on equity, housing, bonds and the bill rates. The exchange rate between the U.S. dollar and the other currencies is included to account for changes in the exchange rates over the years. As for the risk-free rate, in the domestic

portfolios the domestic bill rates are used and for the international portfolios the treasury bill of the United States is used. All beforementioned data is obtained from the Jorda-Schularick-Taylor Microhistory database (Jordà, Knoll, Kuvshinov, Schularick & Jorda-Schularick-Taylor, 2019). This research uses the Composite Leading Indicator provided by the OECD (2020) as an indicator for the business cycle phase of the 8 countries. In the next two subsections the origin and the use of the data is explained.

3.1 Jorda-Schularick-Taylor Microhistory database

This section will give a brief explanation of the methodology used by Jordà, Knoll,

Kuvshinov, Schularick and Taylor (2019) for the data obtainment process for the variables of interest from the Jorda-Schularick-Taylor Microhistory database. The return on equity is obtained through a wide range of sources. These sources include domestic market indices, academic articles and statistical offices. The total equity return is made up of capital gains and dividends in a year and is expressed in the local currency of the country. Information on bond returns is obtained through local bond markets and are expressed in local currencies. Long-term government bonds with an aim of 10-year maturity are used. Return on housing is in presented in local currency and contains capital gains and rental income collected through domestic statistical offices. The bill rates amount to the yield on governmental short-term, fixed income securities in the countries of interest in the local currency. The Exchange rate between local currencies and the U.S. dollars is obtained through a financial statistics library (Jordà, Schularick & Taylor, 2017).

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12 3.2 Composite Leading Indicator

The business cycle measurement used in this thesis is the Composite Leading Indicator. This measure is provided by The Organization for Economic Co-operation and Development (OECD, 2020). The purpose of this index is signaling turning points in the business cycle of nations through peaks (expansion) and troughs (contraction). The CLI uses economic components to try and predict the state of the economy (OECD, 2009). These components differ per country and generally consist of production levels, consumer confidence and stock market index prices. The components are picked according to two requirements, economic relevance and practicality. The CLI is not developed for determining the agility and duration of a recovery or downturn but rather for discovering deviations from a long-term growth rate. The CLI is amplitude-adjusted which means that the indicator is adjusted to the long-term growth level and the average is adjusted to be 100 (OECD, 2007). The business cycle can be divided in 4 different phases according to the CLI value. These phases are determined as follows:

• Expansion: value is above 100 and increasing; • Downturn: value is above 100 and decreasing • Slowdown: value is below 100 and decreasing • Recovery: value is below 100 and increasing

The data is yearly and is therefore adjusted to the annual return data. This is done by picking one business cycle phase for a year by picking the phase that occurred the most. If there are ties the phase that is observed the latest in the year is chosen.

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4 Methodology

This section aims to provide the tools needed to replicate the analysis done in this thesis. In section 4.1 the hypotheses of the research are presented. Section 4.2 gives the methodology of the portfolio allocation process and the tests used to determine results.

4.1 Hypotheses

According to the information in the literature review, we expect the results of creating an international diversified portfolio to outperform domestically diversified portfolios. This is tested again on this dataset to establish if this is the case for the time period and countries of interest. The first hypothesis tests the international diversification benefit in the dataset over a 41-year period. All 8 domestic portfolios are compared to the same international portfolio.

(1) H0: Domestically diversified portfolios perform equally well in maximizing the Sharpe Ratio as an internationally diversified portfolio.

H0: SRi – SRd = 0

(2) H1: An internationally diversified portfolio performs better in maximizing the Sharpe Ratio than all domestically diversified portfolios.

H1: SRi – SRd > 0

Where SRi is the Sharpe Ratio of the international portfolio using Markowitz and SRd the Sharp Ratio of a domestic portfolio using Markowitz

In order to examine the potential gain of using business cycles throughout the asset allocation process, three portfolios that use the CLI in the allocation process are compared to an

internationally diversified portfolio. The internationally diversified portfolio is allocated using the theory of Markowitz (1959) to maximize the Sharpe Ratio. The other portfolios use the four different cycle phases of the CLI in the allocation process and switch its asset

allocation when the business cycle enters a different phase. We expect the portfolios that incorporate the business cycle phases in the asset allocation decisions to be able to achieve a higher Sharpe Ratio than the fixed international portfolio.

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(3) H0: An internationally diversified optimal portfolio allocating resources among stocks, housing and bonds in eight developed economies, performs equally well in maximizing the Sharpe Ratio as an internationally diversified portfolio that uses the CLI in the asset allocation process.

H0: SRc – SRi = 0

(4) H1: An internationally diversified portfolio that uses the CLI in the asset allocation process performs better in maximizing the Sharpe Ratio than an internationally diversified optimal portfolio allocating resources among stocks, housing and bonds in eight developed economies.

H1: SRc – SRi > 0

Where SRi is the Sharpe Ratio of the optimal international Markowitz portfolio and SRc the Sharp Ratio of the portfolio using cyclical information

Both hypotheses are tested with a 10% significance level. 4.2 Portfolio Allocation

In this section the portfolio allocation processes, and the analysis method are explained. To compute the portfolios, first, the annual returns are adjusted for the change in U.S. dollar exchange rates to account for changes in the exchange rate over time. This is done by

dividing the annual return by the change in exchange rate where the change in exchange rate is the exchange rate in a year by the exchange rate the year before.

(1) 𝑟̅𝑖(𝑡) = 𝐴𝑛𝑛𝑢𝑎𝑙 𝑅𝑒𝑡𝑢𝑟𝑛𝑖(𝑡)

𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝐸𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑅𝑎𝑡𝑒𝑖(𝑡)

(2) 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 𝑈𝑆𝐷𝑖(𝑡) = 𝐸𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 𝑈𝑆𝐷𝑖(𝑡)

𝐸𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 𝑈𝑆𝐷𝑖(𝑡−1)

The average return is calculated by taking the average of the yearly returns over the whole period. This is done for stocks, housing and real estate for every country.

(3) 𝐸(𝑟𝑖) = 1

𝑛× ∑ 𝑟̅(𝑡)𝑖 𝑁

𝑡=1

The standard deviation of an asset within a country is calculated as follows:

(4) 𝜎𝑖 = √ ∑𝑁𝑖=1(𝑟̅𝑖 − 𝐸(𝑟𝑖))2

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15 A portfolio is created by choosing the weights of the assets in which will be invested. Once

the weights are known, the expected return and the standard deviation of the portfolio can be calculated in the following way:

(5) 𝐸(𝑟𝑃) = ∑𝑁𝑖=1𝑤𝑖𝐸(𝑟𝑖)

(6) 𝜎𝑝= √∑𝑖=1𝑁 ∑𝑁𝑗=1𝑤𝑖𝑤𝑗𝐶𝑜𝑣(𝑟𝑖, 𝑟𝑗)

The covariance between two assets can be calculated as follows: (7) 𝐶𝑜𝑣(𝑋, 𝑌) =∑𝑁𝑖=1(𝑋𝑖−𝐸(𝑋𝑖))∗(𝑌𝑖−𝐸(𝑌𝑖))

𝑁

A covariance matrix is created using excel for all used assets. For the domestic portfolios, this consists of equity, housing and bond returns. For the international portfolio, this contains equity, housing and bond returns for all countries. The Solver Extension of Excel is used to find the optimal allocation through maximization of the Sharpe Ratio. The Sharpe Ratio is calculated by dividing excess return by the standard deviation of the portfolio:

(8) 𝑆𝑅𝑝 =𝐸(𝑟𝑃)−𝑅𝑓

𝜎𝑝

The corrected version of the Jobson-Korkie test (1981) for equal Sharpe Ratios by Memmel (2003) is used to compare the Sharpe Ratios and show statistical (in)significance. This test consists of calculating a Z-value. First, the correlation between two portfolios is calculated. (9) 𝜌(𝑥, 𝑦) = 𝜎𝑥𝑦

𝜎𝑥𝜎𝑦

With the correlation and the Sharpe Ratios of the portfolios, the asymptotic variance can be determined. (10) 𝑉 = 1 𝑇(2 − 2𝜌𝑥𝑦+ 1 2(𝑆𝑅𝑥 2 + 𝑆𝑅 𝑦2− 2𝑆𝑅𝑥𝑆𝑅𝑦𝜌𝑥𝑦)

Lastly, the Z-value is calculated by dividing the difference of the Sharpe Ratios by the square root of the Asymptotic Variance.

(11) 𝑍 =𝑆𝑅𝑥−𝑆𝑅𝑦

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16 The Composite Leading Indicator is used as measurement for the phase an economy is in.

Three portfolios are made that use the CLI during the asset allocation process. One uses the cycle data that corresponds with the business phase of that year. The other two use the business phase of a year prior. This matches the returns of a year with the business cycle in the same year or the year before. The portfolios using cyclical data hold an equal weight in a country during the whole period but change the asset allocation within a country on the basis of the phase the economy is in. The business cycles are Recovery, Expansion, Downturn and Slowdown. The return for a given country for a given year (t) equals the sum of the weight allocated to equity (e) in a business cycle phase (p) times the return of equity of that country in that year, the weight allocated to housing (h) in a business cycle phase (p) times the return of housing of that country in that year and the weight allocated to bonds (b) in a business cycle phase (p) times the return of bonds of that country in that year.

This is shown as a mathematic equation as follows:

(12) 𝑅𝑒𝑡𝑢𝑟𝑛 𝐶𝑜𝑢𝑛𝑡𝑟𝑦(𝑡)𝑝 = 𝑤𝑒𝑝∗ 𝑟𝑒(𝑡) + 𝑤ℎ𝑝∗ 𝑟(𝑡) + 𝑤𝑏𝑝∗ 𝑟𝑏(𝑡) 𝑤ℎ𝑒𝑟𝑒 𝑤𝑒𝑝+ 𝑤ℎ𝑝+ 𝑤𝑏𝑝 = 1

The total return in a year is the sum of the Returns per country: (13) 𝑟(𝑡) = ∑𝑁𝑖=1𝑤𝑖 ∗ 𝑅𝑒𝑡𝑢𝑟𝑛 𝐶𝑜𝑢𝑛𝑡𝑟𝑦(𝑡)

𝑤ℎ𝑒𝑟𝑒 ∑𝑁𝑖=1𝑤𝑖 = 1

The expected return is calculated by dividing the sum of all yearly returns by the number of years (T) for the business phase (p) the country is in.

(14) 𝐸(𝑟)𝑝= ∑𝑇𝑡=1𝑟(𝑡)

𝑇

The standard deviation is calculated in the same way as formula (4)

(4) 𝜎𝑖 = √ ∑𝑁𝑖=1(𝑟̅𝑖 − 𝐸(𝑟𝑖))2

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17 To find the optimal allocation during a business phase the Solver Extension of Excel will

maximize the Sharpe Ratio by changing both the asset allocation weights within each business phase as well as the weights invested in each country over the whole period. The weight allocation constraints of formulas 12 and 13 have to be held. This results in portfolios that have the optimal weights in each asset during the different business phases and a fixed country allocation.

The benefit of using business cycle data during portfolio allocation is tested. This is tested by comparing an internationally diversified portfolio using the optimal portfolio allocation process by Markowitz (1959) with portfolios using the Composite Leading

Indicator by OECD (2020) in the asset allocation process. The Markowitz portfolio finds the optimal allocation that achieves the highest Sharpe Ratio for a portfolio consisting of 24 risky assets over the investment period from 1975 to 2015.

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5 Results

In this section the results of the hypotheses testing are shown. In section 5.1, the results of diversifying internationally compared to domestically are presented. In section 5.2, the return characteristics during the different cycle phases are examined. And lastly, in section 5.3, the results concerning asset allocation using cyclical data are presented.

5.1 Results International Diversification

The asset allocations, arithmetic excess returns, standard deviations and the Sharpe Ratios of the international and all domestic portfolios over the period 1975-2015 are presented in Tables 1A and 1B in the Appendix. The asset allocation is done according to the theory of Markowitz (1959) where the Sharpe Ratio is maximized. The asset allocation shows that within every country the asset weight for equity is the lowest and the weight for housing is the highest except for Japan. Sweden, Norway and the United States achieved the highest Sharpe Ratios with 1.43, 1.31 and 1.20 respectively. The Sharpe Ratios of the domestically diversified portfolios are compared to the internationally diversified portfolio using the corrected Jobson-Korkie (1981) test by Memmel (2003) for equal Sharpe Ratios.

Table 5.1 shows that the effect of diversifying internationally can obtain a statistically significant higher Sharpe Ratio for all countries at a 1%, one-tailed significance level. All domestic portfolios can increase the Sharpe Ratio by diversifying among multiple countries over the 41-year during period.

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19 5.2 Asset performance over the business cycle

In table 5.2 the return characteristics of the asset classes during the different business cycle phases of our dataset between 1975 and 2015 are shown. It can be seen that during times of Recovery and Expansion, stocks outperform housing and bond investments in obtaining a higher average excess return. However, during times of Slowdown and Downturn, stocks seem to perform the worst and achieve the lowest average returns. Stock investments have a higher volatility than housing and bonds during all cycle phases. Housing investments

possess stable returns during the different phases with while during Downturn performing the best with an average excess return of 7,61%. Bonds show the highest average return during Slowdown periods and the lowest during Expansions. The volatilities of the asset classes seem to remain stable during changes in the cycle phase except for a large increase stock volatility during periods of Recovery. The standard deviations indicate that housing and bond investments possess of less risk than stock investments. Over the whole period housing obtained the highest Sharpe Ratio when disregarding business cycles.

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20 5.3 Results Business Cycle Allocation

The results of comparing the Sharpe Ratios, the portfolio characteristics and asset allocation of three portfolio with the international portfolio are shown in tables 5.3, 5,4 and 5,5. These results are based on the time period 1975-2015. The first portfolio, shown in table 5.3, matched the business cycle phases with the returns of that year and switched asset allocation yearly depending on the cycle phase. This portfolio is able to acquire a significant higher Sharpe Ratio than the fixed international portfolio at a 1% significance level.

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21 The second portfolio, shown in table 5.4, matches the business cycle phase of a year with the

returns of a year later and switches asset allocation yearly. This portfolio therefore tries to predict the returns based on the business cycle phase of a year prior. This model shows a significant positive difference between the business cycle portfolio and the fixed international portfolio at a 10% significance level.

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22 The third portfolio, shown in table 5.5, matches the business cycle phase of a year with the

returns of a year later and switches the asset allocation every 5 years based on the phase of the previous year. The test for equal Sharpe Ratios cannot reject the null hypothesis and can therefore not achieve a significantly higher Sharpe Ratio than the fixed international

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23

6 Discussion

The results on international diversification benefits show that all domestically diversified portfolios in our dataset are able to obtain a higher Sharpe Ratio through international diversification. Furthermore, we found that stocks, real estate and bonds show dissimilar returns and volatilities during the different phases of the business cycle. These asset classes perform best in different business cycle phases. Stocks show the biggest change between excess returns during good and bad periods. Stocks also have the highest volatility in every business phase. This could be the reason for the big swings during changes in the business phase. This could be the reason for the big differences over different business phases.

We used the Composite Leading Indicator by OECD (2020) as an indicator of the business cycle phase an economy was in. Through the use of the CLI in the allocation process a portfolio could acquire a higher Sharpe Ratio than through asset allocation using Markowitz Optimal Portfolio Theory. A portfolio that uses the business phase a country was in a year ago to allocate recourses could acquire a higher Sharpe Ratio than the optimally diversified international portfolio. We did not find evidence for the ability of a portfolio using the CLI, that switches asset allocation every 5 years, to get a higher Sharpe Ratio than the optimally diversified international portfolio. The business cycle has a clear impact on the returns of asset classes and are therefore useful to include in the asset allocation process.

The results are based on the 8 developed countries mentioned in the analysis and during the time period 1975-2015. The results are therefore not directly generalizable to other time periods or other countries. The asset classes might perform differently in emerging economies. The analysis done in this thesis could be replicated for these emerging economies to find out if the findings are of similar nature. The returns consisted of annual data while the data on the business cycle was monthly. The business cycle data was manually converted to yearly data by choosing the business phase that occurred the most in a year. This is probably not the ideal way to interpret the Composite Leading Indicator. Future research could use monthly data on returns to analyze the relationship between returns and the business cycle with monthly lead times. Future research could also be done on other business cycle indicators and their ability to lead business cycles.

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7 Conclusion

This research thesis aimed to evaluate if incorporating cyclical information in the asset allocation process for internationally diversified portfolios could lead to potential benefits. The research question that we want to answer is “Can cyclical information be used to improve the asset allocation process for an internationally diversified portfolio over the long run?”. Based on the analysis of asset behavior and portfolio performance over the business cycle, it can be concluded that incorporating cyclical information in the asset allocation process can lead to substantial benefits.

The thesis found reconfirming evidence for international diversification benefits through the comparison of an international portfolio with domestic portfolios in achieving a higher Sharpe Ratio. These results on international diversification benefits are in accordance with previously found research (Grubel, 1968; Levy & Sarnat, 1970).

The approach evaluated in this thesis has shown that using cyclical information during asset allocation can achieve a higher Sharpe Ratio, which is expressed as the amount of return expected for the amount of risk taken. The reason for the better performance comes from the dissimilar performance of assets during the different business cycle phases. The use of the CLI (OECD, 2020) can create competitive advantages over fixed asset allocation approaches because it takes into account changes in asset performance.

This research adds to the existing literature on asset allocation. More specifically, the thesis integrates research on international diversification benefits and that of the usage of cyclical information during asset allocation. This thesis gives a way to approach the asset allocation process with a macroeconomic leading indicator and asset performance in mind. The relationships between cyclical information and returns has the ability to have valuable economic impact for investors and is therefore an interesting research topic to continue doing research on.

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