Dynamic asset allocation for pension funds

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10001626 | Jack Kroon

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1. INTRODUCTION ... 2

2. LITERATURE ... 3

2.1. BUSINESS CYCLE ... 3

2.2. BASIC ASSET ALLOCATION THEORY ... 4

2.3. ASSET ALLOCATION STRATEGIES ... 6

3. DATA & METHODOLOGY ... 7

3.1. BUSINESS CYCLE INDICATOR ... 7

3.2. RETURNS OF ASSETS ... 10

3.3. ASSET ALLOCATION ... 11

4. RESULTS & DISCUSSIONS ... 12

4.1. BUSINESS CYCLE INDICATOR ... 12

4.2. RETURNS OF ASSETS ... 14

4.3. ASSET ALLOCATION ... 17

5. CONCLUSION ... 20

REFERENCES... 21

1. I

NTRODUCTION

Since the 2007-2008 financial crisis, many countries worldwide find themselves in a bad economic condition. The unemployment rate is rising and the confidence of the consumer and producer is decreasing. Different countries have had to deal with a valuation markdown of their risk-bearing bonds and stock markets fluctuations. These developments ensured that risk-bearing assets have become even more riskier in bad economic situations. For pension funds it is important to take the time-varying risk profile into account.

In practice, many pension funds are using static strategic asset allocation for their portfolios. These asset portfolios are suffering from a pro-cyclical risk profile, which means that the portfolio risk increases in declining markets. Blitz and Van Vliet (2011) proposed a dynamic strategic asset allocation approach to stabilize risk across the economic business cycles. To identify where the economy is standing in the business cycle, they used economic data of the United States from the period 1948 to 2007 to construct a business cycle

indicator. This indicator is based on the unemployment rate, purchase manager index, credit spread and earnings yield. For each phase in business cycle they allocated an optimal portfolio based on historical risk-return performances of different kinds of assets. The business cycle phases depend on economic data but not on statistical properties of asset classes, so a broad opportunity set can be considered instead of focusing on a limited set of assets. The framework of Blitz and Van Vliet (2011) is intended to help long-term investors design a transparent and feasible dynamic strategic asset allocation strategy over the business cycle.

The study by Blitz and Van Vliet (2011) focused on a period before the start of the current financial crisis in 2008. This thesis will replicate the study by Blitz and Van Vliet and will extend it with the period from 2008 to 2013. More importantly, this thesis analyzes the risk-return profiles cross business cycle of a broader asset menu. And this thesis also discusses the possible improvement in constructing business cycle indicator.

The theory behind this study will be explained in the next chapter. In chapter 3 information is specified about the data and methodology. Next, the results of the calculations are given and discussed. At last, conclusions are given.

2. L

ITERATURE

The main objective of this paper is to create an asset mix for pension funds with stabilized risk across the business cycle. In this chapter, the theory behind this topic will be explained in three steps. First, information will be given about the business cycle. Then, the basic theory behind asset allocation will be described. At last, the ideas about asset allocation strategies will be explained.

2.1. B

USINESS CYCLE

Blitz and Van Vliet (2011) have split the business cycle into four phases: expansion,

slowdown, recession and recovery. This can be seen in figure 1. Each phase is defined using the following method: For each month, the indicator can be compared with previous year. If the indicator is positive and increasing, the business cycle is in the expansion phase. In the slowdown stage, the level of the indicator is positive, but the economy goes downward. If both indicator and yearly change are negative, the economy can find itself in a recession. During the recovery phase, the level of the indicator is still negative, but it is improving.

FIGURE 1:FOUR PHASES OF THE BUSINESS CYCLE

Good times

Bad times

Slowdown Recession Recovery

Level : +

Change : + Level : +Change :

Level : Change : Level : -Change : + Expansion 3

By combining a selected number of economic variables and using a simple method of model construction, a good match can be made with official business cycle publications by the NBER. This idea was set by Blitz and Van Vliet (2011) and they used in their paper the unemployment rate, earnings yield, credit spread and purchase manager index as indicators for the economy. In this paper, their method will be replicated to create an economic

indicator.

Gorton and Rouwenhorst (2006) used a comparable method. They segregated the stages between early and late expansion and early and late recession using data of the National Bureau of Economic Research about expansion and contraction periods.

2.2. B

ASIC ASSET ALLOCATION THEORY

Pension funds are trying to balance the risk and returns of investments by regulating the allocation of capital into different kind of assets. The theory of asset allocation is based on the principle that several types of investments perform differently in various economic

situations. According to Ibbotson (2011), asset allocation is a very important strategy to get an effective investment portfolio. An earlier study by Ibbotson and Kaplan (2000) showed that 40% of the variation of returns in investment funds is explained by asset allocation. Also, it explained practically 100% of the level of fund returns. They used five asset classes in their study: large-cap US stock, small-cap US stock, non-US stock, US bonds, and cash. The study of Ibbotson and Kaplan (2000) replicated a study by Stevens, Surz and Wimer (1999), who made a similar analysis on quarterly returns of 58 pension funds over the period 1993-1997. Ibbotson and Kaplan (2000) used the actual weights and asset-class benchmarks of the pension funds.

Samuelson (1967) argued that diversification is an important feature of asset allocation. Hence diversification reduces the overall risk for an assumed expected return. However, as we will high light later in this thesis that, the return correlations may vary across business cycles. The diversification capacity among risky assets becomes weaker especially in difficult economic regimes.

Markowitz (1952) introduced the Modern Portfolio Theory, which assumes returns of assets as normal distributions and risk as the standard deviation of the returns. The expected

returns and standard deviations are based on historical returns. The portfolio has to be a weighted mix of assets. By combining different assets whose returns are not perfectly positively correlated, the Modern Portfolio Theory tries to reduce the risk of the portfolio return. Samuelson (1967) argued that diversification reduces the overall risk for an assumed expected return, since different assets have returns that are not perfectly correlated. Though variation of returns is reduced as long as correlations are not perfect, it is based over a historical period. When the method of looking on historical returns is used to forecast future returns or risks, there is no guarantee that previous relationships will hold in the future.

An asset portfolio can consist of many types of assets, for example: bonds, equities, commodities and real estate. Bonds are obligations with a duration usually between three and ten years. They can be split between corporate bonds and treasury bonds. The yields of corporate bonds are generally higher than the yields of treasury bonds, although the yields depend on the bond rating, which can vary from the less riskiest AAA to D for debt already overdue. Bonds with a higher risk of default have a higher yield. Another part of the main asset class are equities (or stocks). Equities can be divided between value stocks and growth stocks. Value stocks are defined as those in which the market price is relatively low in relation to the book value per share. Contrary, growth stocks have relatively high market prices in relation to the book value per share. Fama and French (1992) have found that value stocks have higher returns than growth stocks in the U.S. stock market. They suggested that value stocks may be riskier and thus require a return premium. Equities can also be divided between small-cap, mid-cap and large-cap, which are categories for the size of the firms. Small-cap stocks have on average higher returns, however the variation of the returns is higher. Another asset class in which to invest are commodities. According to Kang (2012), commodities have low or negative correlation with the main asset classes over the long-term, and can perform as a portfolio diversifier. Alternatively, investments in real estate can also act as portfolio diversifier. Real estate has a low correlation with stocks and bonds and has a positive correlation with both anticipated and unanticipated inflation. Therefore it provides an inflation hedge. Although the value of real estate grows over the long-run, the prices of house declined during the recession of recent years.

2.3. A

SSET ALLOCATION STRATEGIES

Usually pension funds use a suitable strategic asset allocation policy for the long-term on the basis of an asset liability management study. Within certain years, the asset portfolio will turn into an asset portfolio with fixed allocation. As risk and returns vary over the business cycle (Gorton & Rouwenhorst, 2006), this static asset portfolio is inefficient. The use of tactical asset allocation may be a way to solve this problem. This is also stated by Dahlquist and Harvey (2001). However, the tactical portfolio is used to maximize returns and therefore the risks still vary over the different economic phases. Blitz and Van Vliet (2011) proposed a dynamic strategic asset allocation framework, which purposes to maximize portfolio return while at the same time the portfolio risk is stabilized across the business cycle.

3. D

ATA

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M

ETHODOLOGY

Information about the data and how it is retrieved will be given in this section. Thereafter, the methodology of the construction of the business cycle indicator will be explained. Also, the methodology of the portfolio construction and how the data are retrieved will be explained in this chapter.

3.1. B

USINESS CYCLE INDICATOR

Blitz and Van Vliet (2011) collected monthly data of the United States from the beginning of 1948 till the end of 2007. A limited set of potential business cycle indicators is available, because the data should be at least 60 years old. The four indicators which are used by Blitz and Van Vliet (2011) are available from 1948 and can be divided into two categories: financial market indicators and macro-economic indicators.

The first category consists of the credit spread and the earnings yield. The credit spread is defined as the difference between BAA and AAA corporate bond yields from Moody’s. A high credit spread suggests a contraction of the economy, contrarily a low credit spread indicates an economic expansion. If the economy is slowing down, the market is factoring an higher risk of default on lower grade bonds and investors can receive a higher yield on those bonds. So the difference between high rated and low rated bonds is higher. The earnings yield is the earnings/price ratio of the S&P500. A high earnings yield indicates an economic contraction, while a low earnings yield indicates economic expansion

(Campbell & Shiller , 1987).

The Purchase Manager’s Index (PMI) and unemployment rate are macro-economic variables. The PMI is the result of a monthly survey of 400 purchasing managers in the manufacturing sector and those managers report if conditions are better, same or worse than previous months. The index is seasonally adjusted and a value above 0.50 suggests

expansion, while below 0.50 indicates a contraction. The unemployment rate is the seasonally adjusted US unemployment rate from the Bureau of Labor Statistics. Low unemployment indicates economic expansion and high unemployment indicates a contraction.

The data of the earnings yield are retrieved from the database of Robert Shiller and the data of the other economic indicators (CS, PMI, Unemp) are from the Federal Reserve Economic Data (FRED). In figure 2 are the time series given of the variables from 1948 to 2013.

FIGURE 2:TIME SERIES OF THE FOUR ECONOMIC VARIABLES

Time series of the four economic variables. The observations of the economy of the United States and data are from 1948 to 2013.

Each has a different cycle length. The credit spread level has five main phases: the spread is mostly between 0.50 and 1.25 during 1950 and 1970, then rises to 0.75 and 3.0 per cent during 1970 and 1990. From 1990, the spread falls back between 0.5 and 1.25 per cent until 2008. From the autumn of 2008 till the summer of 2009 the spreads rises to a level of 3.38 per cent. This can also be seen in table 1, where basic statistics of the economic variables are given. The credit spread falls back between 0.75 and 1.25 per cent from the end of 2009.

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 1-19 48 1-19 53 1-19 58 1-19 63 1-19 68 1-19 73 1-19 78 1-19 83 1-19 88 1-19 93 1-19 98 1-20 03 1-20 08 1-20 13

C

REDITSPREAD 0,0% 2,0% 4,0% 6,0% 8,0% 10,0% 12,0% 14,0% 16,0% 1-19 48 1-19 53 1-19 58 1-19 63 1-19 68 1-19 73 1-19 78 1-19 83 1-19 88 1-19 93 1-19 98 1-20 03 1-20 08 1-20 13

E

ARNINGSYIELD 0,0 20,0 40,0 60,0 80,0 100,0 1-19 48 1-19 53 1-19 58 1-19 63 1-19 68 1-19 73 1-19 78 1-19 83 1-19 88 1-19 93 1-19 98 1-20 03 1-20 08 1-20 13

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0,0 2,0 4,0 6,0 8,0 10,0 12,0 1-19 48 1-19 53 1-19 58 1-19 63 1-19 68 1-19 73 1-19 78 1-19 83 1-19 88 1-19 93 1-19 98 1-20 03 1-20 08 1-20 13

U

NEMPLOYMENTRATE 8

The earnings yield can be divided into three stages. It falls from 10 to 5 per cent from 1948 to 1973. The yield goes up to 15 per cent during the period from 1973 to 1985 and then varying between 3 and 7 per cent during the period from 1985 to 2013, with a significant rise in 2009. The PMI varies more frequently, it passes the neutral level of 0.50 about 30 times over the full-sample period. Next, the unemployment rate passes the median value of 5.6 per cent about 15 times. Hence, the cycles of the indicators last between 2 and 25 years.

TABLE 1:BASIC STATISTICS OF THE ECONOMIC VARIABLES

Credit spread (in %)

Earnings Yield PMI (in %) Unemployment rate (in %) Mean 0,95 6,37% 52,73 5,81 Median 0,82 5,61% 53,20 5,60 Standard deviation 0,44 2,61% 7,56 1,31 Minimum 0,32 2,26% 29,40 2,50 Maximum 3,38 15,06% 77,50 10,80

Basic statistics of the economic variables from 1948-2013.

Now the four different variables should be added to one composite business cycle score (Blitz & Van Vliet, 2011). The four economic factors are standardized by deducting the full-sample medians and then divide each by their full-sample standard deviations. The medians are used to limit the impact of outliers. Also, the standardized variables are

limited between -3 and +3. The z-scores are summed and divided by the square root of the number of variables, which is two in this case. This results in the economic indicator.

For each monthly period, the indicator can be compared with the previous year. If the indicator is positive and increasing, the business cycle is in the expansion phase. In the slowdown stage, the level of the indicator is positive, but the economy goes downward. If both indicator and yearly change are negative, the economy can find itself in a recession. During the recovery phase, the level of the indicator is still negative, but it is improving. This arrangement of phases is consistent with Gorton and Rouwenhorst (2006), who segregate the stages between early and late expansion and early and late recession using data of the National Bureau of Economic Research about expansion and contraction periods.

3.2. R

ETURNS OF ASSETS

Six different asset classes will be considered: real estate, equities, treasury bonds,

commodities, AAA corporate bonds and BAA corporate bonds. Data about equities, AAA bonds and BAA bonds are available from 1949 to 2013 and are retrieved with DataStream. For the equities, the S&P500 index is used. AAA bonds and BAA bonds are collected from the FRED. Yield rates of treasury bonds are also gathered from the FRED and are available from 1953 till 2013. The sample periods of commodities and real estate are respectively from 1970 and 1972. For the commodities, a composite index of S&P for commodities is used. Real estate is represented with the FTSE NAREIT US Real Estate Index Series, which are also gathered with DataStream. All data are retrieved with a monthly frequency and the bonds have a maturity of five years.

First, the monthly returns of each kind of asset will be calculated per month. To compute the return on a constant maturity bond, two components are combined: the promised coupon at the start of the year and the price change due to interest rate changes. The formula used for the returns on bonds is stated as follows (Damodaran, 2012):

yt−1+ �yt−1∗

1−_(1+yt)n1 yt +

1

(1+yt)n− 1� with ytas yield at time t and n as years of maturity. To

calculate the returns of the equities, commodities and real estate, the following formula is used: log( xt

x_t-1) with xt as index at time t. These are log monthly returns. The risk of the

returns is defined as the standard deviation of the returns.

3.3. A

SSET ALLOCATION

Now, a static strategic asset allocation portfolio (SAA) will be considered. This portfolio consists of: 20 per cent treasury bonds, 10 per cent commodities, 10 per cent real estate, 25 per cent equities, 25 per cent AAA bonds and 10 per cent BAA bonds. The static portfolio will be optimized for the full-sample with maximum return. The different business cycles are not taken into account. This optimized static asset portfolio (SAA-O) has the same complete risk as the static portfolio, however the returns are higher. Hereafter, two dynamic asset allocation methods that are based on the business cycle indicator will be considered. For each method, the asset allocation will be optimized for each business cycle phase. The two

strategies have different sets of restrictions. First, a tactical asset allocation portfolio (TAA) will be constructed. For each business cycle, the returns are maximized. The risk of the full-sample is restricted to be equal at the risk of the base portfolio. Second, a dynamic strategic asset allocation portfolio (DSAA) will be created and for every economic phase, the asset returns are maximized. Now, for each business cycle and the total period, the risk has to be equal or lower than the risk of the base portfolio. A summary of the asset allocation

strategies is given in table 2.

TABLE 2: SUMMARY OF ASSET ALLOCATION STRATEGIES

SAA-O TAA DSAA

Optimization approach

Full-sample or phase-based full-sample phase-based phase-based

Risk constraints

Volatility limit full-sample 𝜎𝜎𝑆𝑆𝑆𝑆𝑆𝑆 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑠𝑠 𝜎𝜎𝑆𝑆𝑆𝑆𝑆𝑆 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑠𝑠 𝜎𝜎𝑆𝑆𝑆𝑆𝑆𝑆 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑠𝑠

Volatility limit for each phase - - 𝜎𝜎𝑆𝑆𝑆𝑆𝑆𝑆 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓𝑠𝑠

4. R

ESULTS

&

D

ISCUSSIONS

In this chapter, the results of the calculations are given and discussed. First, the constructed the business cycle indicator will be shown. Thereafter, results of the constructed asset allocation portfolios for different strategies will be displayed.

4.1. B

USINESS CYCLE INDICATOR

The historical values of the economic indicator and the coloured business cycle indicator are presented in figure 3. The time series are showing the full-sample period from 1948 to 2013. A positive value of the economic indicator suggests a good economic period, while a negative score is indicating a bad period. The business cycle indicator indicates in which phase the economy is. This indicator is based on the economic indicator. For example, a negative, but increasing score of the economic indicator suggests a recovery period.

Time series of the economic indicator combined with the coloured business cycle indicator. Monthly observations for the economy of the United States over the period from 1948 to 2013.

Expansion Slowdown Recession Recovery -6 -4 -2 0 2 4 6

FIGURE 3: TIMES SERIES OF INDICATORS

For comparison, the NBER recession time series is plotted in the figure above, together with the time series of 10-year treasury yields and Year-on-10-year percentage changes of S&P index.

TABLE 3: DISTRIBUTION AND TRANSITION MATRIX OF ECONOMIC PHASES

Distribution of phases Transition matrix Total number of

monthly periods From\To Expansion Slowdown Recession Recovery

226 Expansion 88,9% 10,2% - 0,9%

130 Slowdown 12,3% 77,7% 10,0% -

236 Recession 1,3% 2,5% 88,6% 7,6%

178 Recovery 3,4% - 7,3% 89,3%

Distribution of the economic phases and a transition matrix with monthly transitions between the economic business cycles in the United States during the period from 1948 to 2013.

Table 3 displays the distribution of the four business cycles and the additional transition matrix. The expansion and recession phases occur more often than slowdown and recovery phases. Gradual increases in economic situations have a tendency to be followed by

relatively quick drops. The transition matrix illustrates that the probability of staying in the similar state from month to month is between 77.7 per cent and 89.3 per cent, so the

probability of moving to another phase is between 10.7 per cent and 22.3 per cent.

TABLE 4: COMPARISON WITH NBER PUBLICATIONS

BCI - recession BCI - no recession

NBER - contraction 105 16

NBER - no contraction 131 519 Distribution of NBER contraction periods and recession periods of the business cycle indicator. Monthly periods from 1948 to 2013.

As table 4 shows, when the business cycle indicator indicates a state of recession, there is a 44.5 per cent chance that NBER will set this month as a part of a contraction period. 86.7 per cent of the NBER contraction periods are within the model recession phase, where 13.3 per cent falls in either slowdown or recovery. NBER contraction periods overlap many times with the business cycle indicator. Mostly all contraction centre-points are foreseen appropriately, although the exact start and end points are not always good predicted.

4.2. R

ETURNS OF ASSETS

The empirical analysis starts with the risks and returns of the different kind of assets. In table 5, the averages and volatilities of the annualized returns are given.

TABLE 5: RETURNS AND RISK OF ASSET CLASSES

Average of returns

Business Cycle Treasury bonds Commodities Real Estate Equities AAA bonds BAA bonds Expansion 2.17% 16.53% 13.76% 15.17% 4.33% 5.60% Slowdown 4.79% 8.18% 9.33% 4.57% 5.24% 5.52% Recession 8.74% 6.59% 1.47% -3.47% 7.25% 6.96% Recovery 8.63% 7.14% 20.77% 12.60% 10.01% 12.60% Full-sample 6.19% 9.03% 11.45% 7.02% 6.70% 7.63%

Standard deviations of returns

Business Cycle Treasury bonds Commodities Real Estate Equities AAA bonds BAA bonds

Expansion 3.57% 19.96% 13.89% 9.70% 2.72% 2.81%

Slowdown 4.71% 30.04% 15.84% 13.25% 3.40% 3.51%

Recession 5.96% 28.73% 22.86% 16.97% 5.01% 5.48%

Recovery 7.71% 14.82% 13.13% 12.32% 5.58% 5.86%

Full-sample 6.40% 23.58% 19.13% 15.58% 4.86% 5.42% Annualized returns and standard deviations of returns for different kind of assets per economic

regime, based on monthly periods between 1948 and 2013.

Real estate had an average return of 1.47 per cent during recession times, yet during the recovery periods returns were on average 20.77 per cent. Contrarily, bonds performed better

during recession periods with higher returns and lower risk. Equities had on average negative returns and a standard deviation of 16.97 per cent during the recession phase. On the other hand, during the expansion states, equities had 15.17 per cent return and with a standard deviation of 9.70 per cent. In the paper by Blitz and Van Vliet (2011), equities performed during recession periods better than other periods. This is due to the sample period until 2007, which they used. Equities performed badly during the recession between 2008 and 2009. A striking finding is that treasury bonds have a higher risk than corporate bonds. This can be explained by the part of the price change for the returns of bonds. The yields on treasury bonds are relatively low, so the part of the price change is relatively higher.

The correlations of the returns for different assets per business cycle are given in table 6. As expected, bonds are highly correlated with each other. During the most of the periods, commodities are negatively correlated with other asset classes, except with real estate. Although, during recessions equities and commodities have a correlation of +45.3 per cent. Another finding is that equities and treasury bonds are almost uncorrelated, as the

coefficient is -0.7 per cent for the full-sample.

TABLE 6: CORRELATIONS OF RETURNS

Correlation of returns during expansion periods

TB C RE E AAA BAA TB 100,0% -20,8% 37,1% 5,9% 80,7% 70,6% C -20,8% 100,0% -8,0% -17,4% -14,1% -3,1% RE 37,1% -8,0% 100,0% 46,5% 49,6% 53,5% E 5,9% -17,4% 46,5% 100,0% 5,8% 11,3% AAA 80,7% -14,1% 49,6% 5,8% 100,0% 96,7% BAA 70,6% -3,1% 53,5% 11,3% 96,7% 100,0%

Correlation of returns during recession periods

TB C RE E AAA BAA TB 100,0% -1,5% 5,0% 12,5% 85,8% 78,3% C -1,5% 100,0% 42,1% 45,3% -8,6% 0,0% RE 5,0% 42,1% 100,0% 73,5% 22,9% 33,2% E 12,5% 45,3% 73,5% 100,0% 18,1% 28,4% AAA 85,8% -8,6% 22,9% 18,1% 100,0% 95,4% BAA 78,3% 0,0% 33,2% 28,4% 95,4% 100,0%

Correlation of returns during full-sample period

TB C RE E AAA BAA TB 100,0% -19,2% 4,9% -0,7% 88,8% 76,1% C -19,2% 100,0% 20,5% 14,9% -18,7% -11,9% RE 4,9% 20,5% 100,0% 63,8% 23,2% 39,7% E -0,7% 14,9% 63,8% 100,0% 12,8% 27,1% AAA 88,8% -18,7% 23,2% 12,8% 100,0% 94,0% BAA 76,1% -11,9% 39,7% 27,1% 94,0% 100,0%

Correlations of annualized returns for different assets per business cycle phase and the full-sample period from 1948 to 2013. The assets are: treasury bonds, commodities, real estate, equities, AAA bonds and BAA bonds.

Correlation of returns during slowdown periods

TB C RE E AAA BAA TB 100,0% -27,3% -11,0% 8,1% 82,7% 78,0% C -27,3% 100,0% 12,8% -52,9% -26,5% -16,1% RE -11,0% 12,8% 100,0% -2,9% 15,5% 20,0% E 8,1% -52,9% -2,9% 100,0% 16,9% 17,0% AAA 82,7% -26,5% 15,5% 16,9% 100,0% 98,0% BAA 78,0% -16,1% 20,0% 17,0% 98,0% 100,0%

Correlation of returns during recovery periods

TB C RE E AAA BAA TB 100,0% -29,7% 17,1% 33,1% 95,3% 83,9% C -29,7% 100,0% -12,7% -4,3% -28,4% -31,5% RE 17,1% -12,7% 100,0% 53,5% 19,7% 34,1% E 33,1% -4,3% 53,5% 100,0% 37,0% 47,5% AAA 95,3% -28,4% 19,7% 37,0% 100,0% 92,3% BAA 83,9% -31,5% 34,1% 47,5% 92,3% 100,0% 16

4.3. A

SSET ALLOCATION

With the calculated returns, standard deviation and correlations, it is possible to construct optimal portfolios for given restrictions related to an asset allocation strategy. In table 7, the results of the calculations for several asset allocation strategies are shown. The static asset allocation portfolio (SAA) embraces higher risk during bad economic times. The static portfolio is optimized with the highest returns for the same full-sample risk. The constraints are mentioned in table 2. Also, a constraint is added that the asset allocations should be between 0 per cent and 100 per cent. This method, which is also used by Blitz and Van Vliet, is not in line with the Mean-Variance Optimization (MVO) method. The MVO method minimizes the risk for a given return. However, the outcomes of both methods should be part of the efficient frontiers in figure 4. The volatilities of the optimized portfolio (SAA-O) are more stable across the business cycles. The SAA-O consists for the most part, 71.3 per cent, of BAA bonds. Then, two phase-based approaches are considered. The tactical asset allocation portfolio has a restriction that the absolute risk has to be equal at the full-sample risk of the base portfolio. The returns are maximized and are significant higher than those of the static asset portfolio, 11.68 per cent against 7.48 per cent. During the expansion and recovery periods, the average returns are much higher than during slowdown and recession periods. However, this applies also for the risk across the different phases. To have an asset portfolio with stabilized risk, a dynamic strategic asset allocation portfolio should be

considered. The standard deviations of the returns for each business cycle are restricted to be equal or lower than the full-sample risk of the static asset portfolio. The average returns are 10.78 per cent on average and the risk is soothed over the business cycles. Only for the recession stage the risk is 5.56 per cent instead of 5.86 per cent. This is due to the recession portfolio, which is fully invested in treasury bonds. These results are dependent on the fictitious constructed static asset allocation portfolio. For all strategies, the risk levels of the portfolios are restricted to those of the base asset allocation. Nevertheless, the solutions for each period should be a part of the efficient frontier. This is a set of optimal portfolios that offers maximized expected return for a defined level of risk. The efficient frontiers for each cycle are shown in figure 4.

TABLE 7: CONSTRUCTED ASSET ALLOCATION PORTFOLIOS

TB C RE E AAA BAA Return Risk

SAA Full-sample 20.0% 10.0% 10.0% 25.0% 25.0% 10.0% 7.48% 5.86% Expansion 20.0% 10.0% 10.0% 25.0% 25.0% 10.0% 8.92% 4.11% Slowdown 20.0% 10.0% 10.0% 25.0% 25.0% 10.0% 5.59% 4.01% Recession 20.0% 10.0% 10.0% 25.0% 25.0% 10.0% 4.08% 8.68% Recovery 20.0% 10.0% 10.0% 25.0% 25.0% 10.0% 11.55% 5.69% SAA-O Full-sample - 10.0% 18.7% - - 71.3% 8.44% 5.86% Expansion - 10.0% 18.7% - - 71.3% 8.27% 4.39% Slowdown - 10.0% 18.7% - - 71.3% 6.33% 5.21% Recession - 10.0% 18.7% - - 71.3% 5.76% 7.81% Recovery - 10.0% 18.7% - - 71.3% 13.75% 5.62% TAA Full-sample 18.4% 11.2% 16.6% 20.5% 25.3% 8.1% 11.68% 5.86% Expansion - 22.9% 8.3% 65.1% - 3.7% 15.04% 7.63% Slowdown - 5.9% 3.2% 8.1% 82.8% - 5.35% 3.11% Recession 60.0% 3.0% - - 37.0% - 8.04% 4.93% Recovery - 10.9% 58.8% - - 30.3% 16.85% 6.86% DSAA Full-sample 32.1% 8.9% 20.7% 12.4% 0.2% 25.7% 10.78% 5.77% Expansion - 12.0% 19.7% 36.0% 0.3% 32.0% 12.01% 5.86% Slowdown 0.7% 8.3% 28.2% 4.8% - 57.9% 6.59% 5.86% Recession 100.0% - - - 8.66% 5.56% Recovery 5.7% 17.0% 43.9% 4.5% 0.5% 28.4% 15.09% 5.86% Returns are annualized and risks are in terms of standard deviations of returns. Used asset classes are: treasury bonds, commodities, real estate, equities, AAA bonds and BAA bonds.

FIGURE 4: EFFICIENT FRONTIERS

Efficient frontiers and asset classes for each business cycle.

5. C

ONCLUSION

The main goal of this thesis is to present a basis for dynamic asset allocation, and the

empirical data are only meant to demonstrate the possibilities of such a strategy. The results do not aim to represent real-life investment strategies. A method is examined that can be used to convert economic variables into a business cycle indicator, which can indicate four different phases.

A data sample is used for the economy of the United States over the period from 1948 to 2013. Empirical analyses show that the risk and returns of asset classes are very dependent on the economic phases. Therefore, it is interesting to find different investing strategies to stabilizes risks across different economic states. A fictitious static asset allocation portfolio is used as a benchmark. It has static weights, although the risks are varying over the business cycle. The first alternative is the optimized static portfolio. The returns are higher for this portfolio, however it is not able to stabilize risk. The second alternative is the tactical asset strategy. For this asset allocation method, a different portfolio is constructed for each economic state. This portfolio yields the highest returns, although the risk is not stabilized across the business cycle. To solve is the problem, a dynamic strategic asset allocation portfolio is considered. The volatilities of the returns are equal for each economic state and the returns are significant higher than those of the static asset portfolio.

R

EFERENCES

Ang, A. and Bekaert, G. (2002). International asset allocation with regime shifts. Review of Financial Studies, 15(4): 1137–1187.

Ang, A. and Bekaert, G. (2004). How do regimes affect asset allocation? Financial Analyst Journal, 60(2): 86–99.

Blitz, D. and Van Vliet, P. (2011). Dynamic Strategic Asset Allocation: Risk and Return Across

Economic Regimes. Journal of Asset Management, 12: 360-375

Campbell, J.Y. and Shiller, R. (1987). Stock prices, earnings, and expected dividends. Journal of Finance, 43(3): 661–676.

Campbell, J. Y., Chan, Y.L. and Viceira, L.M. (2003). A Multivariate Model of Strategic Asset

Allocation. Journal of Financial Economics, 67: 41-80.

Cooper, I. and Priestley, R. (2011). Real investment and risk dynamics. Journal of Financial Economics, 101: 182-205.

Dahlquist, M. and Harvey, R.C. (2001). Global tactical asset allocation. Emerging Markets Quarterly, 51: 6–14.

Damodaran, A. (2012). Annual returns on Stock, T.Bonds and T.Bills: 1928 – Current. Retrieved from http://people.stern.nyu.edu/adamodar/New_Home_Page/datafile/histretSP.html. Fama, F.F. and French, K.R. (1992). The Cross-Section of Expected Stock Returns. Journal of Finance, 47(2): 427-465.

Gorton, G. and Rouwenhorst, K. (2006). Facts and fantasies about commodity futures. Financial Analyst Journal, 62(2): 47–68.

Guidolin, M. and Timmermann, A. (2007). Asset allocation under multi-variate regime

switching. Journal of Economic Dynamics and Control, 31(11): 3503–3544.

Hoevenaars, R., Molenaar, R. and Schotman, P. (2007). Strategic asset allocation for long-term

investors: Parameter uncertainty and prior information. Working paper, Maastricht University.

Ibbotson, R.G. and Kaplan, P. D. (2000). Does Asset Allocation Policy Explain 40, 90 or 100

Percent of Performance?. Association for Investment Management and Research.

Ibbotson, R.G.. (2010). The Importance of Asset Allocation. Financial Analysts Journal, 66(2). Ibbotson Associates. (2006). Strategic Asset Allocation and Commodities. Chicago, IL: Ibbotson Associates, 3.

Kang, X. (2012). Commidity Investments: The Missing Piece of the Portfolio Puzzle?. London: Standard & Poor’s.

Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1): 77-91.

Munk, C. and Sørensen C. (2010). Dynamic asset allocation with stochastic income and interest

rates. Journal of Financial Economics, 96: 433-462.

Owyang, M. T., Piger, J. and Wall, H.J. (2005). Business Cyle Phases in the U.S. States. The Review of Economics and Statistics, 87(4): 604-616.

Samuelson, P. (1967). General Proof that Diversification Pays. Journal of Financial and Quantitative Analysis, 2: 1-13.

Stevens, D.H., Surz, R. J. and Wimer, M. E. (1999). The Importance of Investment Policy. Journal of Investing, 8(4): 80-85.