The performance of American pension funds

The performance of American pension funds

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Abstract

On average pension funds are not able to beat the market index according to the literature. This paper uses a simple empirical model to test the performance of American pension funds against the S&P 500 index. Jensen’s Alpha, Alpha according to the Fama-French Three-factor model and the Sharpe ratio are used as performance measures. Pension funds are not able to exceed their benchmarks significantly with both measures. Pension funds do perform better than the S&P 500 during the recent crisis. 1. Introduction

Pension funds are institutions with a huge amount of assets in their portfolios. At the end of 2012 the American pension funds all together, had an asset amount of 16851 billion Dollar. This amount is 108% of the gross domestic product of the United States (Towers Watson, 2013). Because of the large amount of assets that these funds hold, the investment costs of pension funds should be relatively low (Andonov et al. , 2012). This low investment costs should apparently lead to higher net returns. This thesis tries to give an answer to the question whether this American pension funds do perform so well that they outperform the market?

According to the literature pension funds are on average not able to outperform their benchmarks.

Jensen (1968) and Sharpe (1966) both invented a performance measurement for funds to compare with their benchmark. Funds were not able to outperform the market with both Jensen’s Alpha and the Sharpe ratio. The expenses of active management led to underperformance.

Pawel Wieprzowski did a research on the performance of Chilean pension funds. He concluded that the pension funds that followed an active investment strategy were not able

to outperform their benchmark. Whereas funds which choose to invest less in stocks and more in bonds (passive strategy) were able to outperform the market index (Wieprzowski, 2012).

The literature concludes that active management on average does not outperform a passive investment strategy. Following the literature, one should buy the portfolio of a certain market index and hold this portfolio. In practice, it is not that easy as it seems. There are some difficulties that arise when replicating an index. People consider an index as a paper portfolio, where transactions can occur at any time and without any costs (Frino, Gallagher, 2001). In reality, tracking an index will not give identical returns as the benchmark index itself. This is due to the fact that, an index presents a mathematical calculation which is derived from a portfolio without market frictions (Frino, Gallagher, 2001). Whenever the index changes, it assumes that the new weights of the portfolio can be achieved automatically. Managers cannot make this assumption, because physical trading needs to be done (Frino, Gallagher, 2001).

In this thesis the performance of the American pension funds is tested against the S&P 500 index. Jensen’s Alpha, Alpha according to the Fama-French Three-factor model and the Sharpe ratio are the measurements that are used to test the performance of the pension funds against the S&P 500. Jensen’s Alpha and the Fama-French Alpha are used to test for absolute performance and the Sharpe ratio looks at the relative performance of the funds. The return on the plan assets of the pension funds is used to do the research. In the literature the data only contains observations till 2008. This thesis uses another dataset which extends the data until 2012. This is useful to look at the effect of the crisis on the performance of pension funds in the United States. This thesis also uses an extra model: Fama-French Three-factor model and reviews the Beta of the several pension funds and whether a higher beta leads to higher Alphas and Sharpe ratios. The main question in this thesis is whether American pension funds are able to exceed the returns of the S&P 500 index significantly?

Conclusions of this thesis confirm the results with the hypothesis based on the literature. The pension funds do not outperform the S&P 500 index significantly on average. All three performance measures, Jensen’s Alpha, Alpha according to the Fama-French Three-factor model and the Sharpe ratio, do not conclude a significant outperformance by the 47 American pension funds. During the crisis, pension funds held less negative returns

than the S&P 500 index.

In the second section of this thesis the relevant literature is reviewed. In section three, important theories are discussed. In the fourth section of this thesis the hypothesis are given. Section 5 provides the research design and the data. In the sixth section the results are given and analysed. The last section of the paper is the conclusion of this research.

2. Literature review

There is a lot of research done about active and passive management. Most of the papers conclude that on average active management is not better than a passive investment strategy. There are two papers that were very important in the history of finance.

Sharpe came up with the Sharpe ratio in the paper Mutual fund performance in 1966. The Sharpe ratio was used to compare the performance of mutual funds with a certain market index. The higher the Sharpe ratio the better the performance of a certain mutual fund was. Sharpe collected the returns of 34 mutual funds and compared their performance against the Dow Jones index. It appears that on average managers construct a portfolio that was as good as the Dow Jones index, but after operational cost have been deducted, they underperformed the benchmark index (Sharpe, 1966).

In 1968 Jensen came up with another measure for portfolio performance. Jensen’s Alpha is the absolute performance up or under the predicted return of the CAPM model. Jensen did a research about the performance of 115 mutual funds between 1945 and 1964, with Jensen’s Alpha. On average these mutual funds were not able to predict future prices well enough to outperform a passive investment strategy. This conclusion even holds without taking into account the management expenses these funds made (Jensen, 1968). The paper also concluded that mutual funds did not significantly made better performance than a random chosen portfolio (Jensen, 1968).

The papers of Jensen and Sharpe give a good view on the performance of financial funds as a whole. They are useful in the theory about active and passive management. The papers of Wieprzowski and Antolin are from a more “pension fund” nature.

In the paper , The Investment Results of the Chilean Pension Funds, Paweł

the pension funds in four different categories. Type A, B, C and D. Type A funds have an aggressive investment strategy with a share weight (Risky) up to 80% and 20% invested in bonds (low risk) and type D funds have a more conservative strategy with a share weight of only 20%. The data consist of 8 years of Chilean pension fund performance, in the period 2003-2010. The outcome of the research shows that type A and B funds were not able to exceed the performance of the benchmark index, as where type C and D funds were able to beat the benchmark index. Both the Sharpe Alpha and the Jensen’s Alpha are negative for the A and B funds. For most of the C and D funds these measures are positive. There can be concluded that pension funds with a higher degree of conservatism in their investment field (More passive management)are able to outperform their benchmark index, following the research of Wieprzowski (Wieprzowski, 2012).

Another research is done on pension fund performance by Pablo Antolin. Antolin uses data from pension funds of 23 countries all over the world. The Sharpe Ratio and Jensen’s Alpha are used to compare the returns of the pension funds against their

benchmark. For every pension fund a country-specific benchmark is used. This is important because, in several countries, pension funds have investment restrictions. Antolin concluded that almost all the pension funds around the world underperformed their benchmark. Interestingly is that in several countries with investment restrictions, these restrictions had a negative impact on pension fund performance (Antolin, 2008).

During the financial crisis of 2008 large negative returns were held by pension funds all over the world. Especially OECD pension funds were hit critically by the financial crisis. On average OECD pension funds experienced a negative nominal return of 21.4 percent (Pino, Yermo, 2010). In the United States the average negative return was almost 24 percent. During the first half year 2009, most of the pension funds recovered a fraction from the negative strike on returns in 2008. Compared to December 2007, returns were on average 14 percent lower (Pino, Yermo, 2010). Pension funds that held a large amount of equities in their portfolio were hit heavily. Most of the pension funds in the United States held a lot of equities in their portfolios. On average, pension funds in the United States invested 46 percent of their portfolios in equities (Pino, Yermo, 2010).

In this paper the returns held by American non-public pension funds are compared to the S&P 500. In 2008 the S&P 500 experienced a negative return of 38.49 percent. Compared to the data of Pino and Yermo, the pension funds had less negative returns on

average (21.4 percent and almost 24 percent for US pension funds).

In contradiction to the other papers discussed in this section, Petraki and Zalewska found evidence that UK pension funds are able to outperform their Primary Prospectus Benchmark, but the question is, whether these benchmarks are challenging enough for the pension funds. It is interesting to see that these funds do outperform their benchmark but are not able to perform better than T-bills, while the amount of risk taken is about 10 till 20 times lower compared to the portfolios of the pension funds (Petraki & Zalewska, 2013).

Another important factor that pension funds have to deal with is transaction costs and management fees. The hedge funds, real estate funds and private equity funds that invest the money of the pension funds, generally take 20 % of the profit they make with the plan assets of the pension funds (NY times, 2010).

Theory

In the management of equity there are two trends: Active equity management and Passive equity management. The people that believe in active management, do not follow the efficient market theory. The efficient market theory states that prices reflect all the public information. Active managers constant look for mispriced stocks to outperform the market index. People that believe in active equity management, invest in funds that create portfolios different from the market index. Mutual and hedge funds are examples of such funds.

A passive strategy aims only at establishing a well-diversified portfolio without trying to find under- or overvalued stocks (Bodie et al., 2011, p.378). Passive managers often use a “buy-and-hold strategy”, where stocks are bought and hold for a long period of time. The efficient market theory states that given all available information, stock prices are fairly priced. So it makes no sense to buy and sell stock frequently, because this costs large brokerage fees, without increasing returns (Bodie et al., 2011, p.379).

People that believe in efficient market theory, often make use of the Capital Asset Pricing Model. The CAPM is a measure to determine the rate of return that should be achieved given the systematic risk of the portfolio with the market ( , the expected return of the market ( ( ) and the risk-free rate ( ( . The general idea behind the CAPM model is that investors need to be compensated for risk and for the time value of money. The risk-free rate represents the time value of money in the formula. It

compensates the investor for putting money in an investment for a period of time. The other part of the formula represents risk. It calculates the compensation the investor needs for additional risk. The CAPM presumes some additional assumptions(Berk & DeMarzo, 2007, p.363-364):

1. All investors are able to buy and sell their securities at the market price and everyone can lend and borrow at the risk-free rate

2. Investors only construct portfolios that are efficient

3. All investors have the same view on returns, correlations and the risk of securities

The CAPM model: ( [ ( ]

= Systematic risk of portfolio i with the market

( = the expected return of the market portfolio = the risk-free rate.

( = expected return of portfolio i according to the CAPM

Fama and French introduced a model that extends the CAPM model. Fama and French implemented two extra factors in the CAPM model, Firm size and Book-to-market ratio. These two factors are implemented in the model because Fama and French found empirical evidence that stocks of small firms and stocks with a high book-to-market ratio give higher returns than predicted by the CAPM (Bodie et al., 2011). The Fama-French three-factor asset pricing model is stated as follow:

( [ ( ] ( ( = Beta of the Small minus Big factor

= Beta of the High minus Low factor

The differential return on small firms verus large firms

HML = The return on firms with high book-to-market ratios minus firms with low ratios (Bodie et al., 2011)

The small minus big factor (SMB) in the Fama-French Three-factor model is implemented because of the additional returns investors have made by investing in stocks

of companies that have a small market capitalization (Womack et al., 2003). The return of the 30% smallest stocks minus the 30% biggest stocks is computed every month to calculate the SMB factor (Womack et al., 2003).

The high minus low factor (HML) is implemented in the model because investors make additional returns by investing in stocks with high Book-to-market ratios. The HML factor is calculated by taking the 50% of stocks with the highest Book-to-market ratio minus the 50% of stocks with the lowest Book-to-market ratio (Womack et al., 2003).

Passive managers do believe in the efficient market theory. Passive managers think that the best strategy is to invest in index funds. Index funds replicate the performance of a market index such as the S&P 500 (Bodie et al., 2011). The advantage of investing in an index fund is the broad diversification and low management fees. These fees are kept low because, the transaction costs are very low, because of the low portfolio turnover (Bodie et al., 2011).

3. Research design

5.1 Performance measurement

The return of the pension funds is measured with three measurement methods. Jensen’s Alpha using the CAPM model, Alpha using the Fama-french three-factor model and the Sharpe ratio. Jensen’s Alpha is used for absolute performance. It looks at the

performance of the fund in absolute numbers. Whereas the Sharpe ratio looks at relative performance. It adjusts the performance for risk.

Jensen’s Alpha compares the prediction of the CAPM model and the actual

performance of the fund. The difference between these two values is called the Alpha. The Alpha is calculated from the equation of the CAPM:

 rp – rf +  rm – rf

rf = Risk-free interest rate, in this case the T-bill rate (data from FRED) =The return on the portfolio of the pension fund (data from Compustat) = The return on the market, in this case the S&P 500 (data from FRED)

 = Beta of the portfolio of the pension fund (Calculated with Stata)

Using the method of Ordinary least Squares, the Alpha’s and Beta’s will be calculated with Stata. The equation of the CAPM model can be written in another way:

(rp-rf) =  + (rm-rf)

Now the CAPM model can be used in Stata. With the equation Y= x, ordinary least squares can be applied. In this equation Y is the return on the portfolio of the pension fund, minus the return of the risk free asset (T-bill rate). X is the return of the S&P 500, minus the return of the risk free asset (T-bill rate). With the data of 47 pension funds, 47 regressions will be done to calculate Alpha’s and Beta’s. The t-values of the Alpha’s will be used to look whether these values are significantly different from zero. The t-values of Beta will be tested to find out whether these values are significantly different from 1.

The Alpha using Fama-French three-factor model is calculated in the same way as the Jensen’s Alpha with the CAPM. The only difference between the two models is two extra variables that Fama and French implemented. The OLS-regression that will be done with Stata is stated as follow: Y= x + SMB + HML

( [ ( ] ( ( = Beta of the Small minus Big factor (Calculated with Stata) = Beta of the High minus Low factor (Calculated with Stata)

The differential return on small firms verus large firms (Data from Fama French liquidity factors in WRDS)

HML = The return on firms with high book-to-market ratios minus firms with low ratios (Data from

Fama French liquidity factors in WRDS)

Rf = Risk-free interest rate, in this case the 3-month T-bill rate (data from FRED)

( = Expected return on the market, in this case the S&P500 (data from FRED)

The Sharpe ratio is used to look at relative performance. The Sharpe Ratio is the excess return of the portfolio divided by the standard deviation of the portfolio:

(rp-rf)/SDrp

rp = The return on the portfolio

rf = Risk free interest rate, in this case the T-bill rate SDrp = Standard deviation of the portfolio

A higher Sharpe ratio implies better performance of the fund. The Sharpe ratio’s of the S&P 500 and the pension funds will be compared using t-tests.

5.2 Data

The data consists of annual returns on pension plan returns of the 47 biggest non-public pension funds of the United States, according to the P&I/Towers Watson global 300 pension funds ranking. The data comes from the Compustat database in WRDS. The returns of public pension funds were not available in the database. That is why only non-public pension funds are used in this paper. Some of the pension funds were not available in the Compustat database or had incomplete data. These funds* were left out of the data. The annual returns of the S&P 500 and T-bill rate were gathered from the Federal Reserve database in St. Louis (FRED). The pension plan returns are only available in Millions of dollars. That is why the total Pension Plan assets are also gathered from Compustat. Pension plan returns are divided by Pension plan assets to get the annual percentage return of the pension funds. The positive returns of the funds are multiplied by 0,8, because of the 20 % fee that is charged by the investment funds. The data of the Fama-French three-factor model are gathered from the Fama-French liquidity factors database in WRDS.

*Pension funds that are left out of the data: Kaiser, J.P. Morgan Chase, Chrysler group, DuPont, Shell Oil, Wal-Mart, BP America, Kraft Foods, Eastman Kodak, Siemens.

4. Results

6.1 Summary statistics

Table 1 shows the summary statistics on the data of the 47 pension funds and the S&P 500. This table does not contain any test on significance.

The first thing that is interesting to see is the average return of all the pension funds, compared to the average return of the S&P 500. The S&P earned a higher average return in the period 2000 till 2012, 3,40% vs. 2,84%. This is in alignment with the results presented in the literature. In the period 2000 till 2002, the S&P 500 had negative returns, whereas the pension funds only had negative returns on average in 2001 and 2002. During the crisis in

2008 both the pension funds and the S&P 500 held extremely negative returns, 26,71% vs. -36,55%. The lower return of the S&P 500 index compared to the returns of the pension funds is in alignment with the results of the literature. This difference is probably due to different risk profiles. The portfolios of the pension funds held higher returns than the market index according to Pino and Yermo (Pino, Yermo, 2010). What strikes out is that the pension funds had a more stable return over the whole period compared to the index. The S&P had higher positive and negative outliers. It seems that the pension funds hedged their portfolio better than the index.

Table 1: This table contains the summary statistics of the 47 pension funds and the yearly returns of the S&P 500. N is the number of pension funds, Size is the average amount of total pension plan assets in millions of dollars.

Pension funds

S&P 500

Year N Size Avg.

Return (yearly)

Median Standard deviation

Minimum Maximum Return (yearly) 2000 47 14593.19 4,35% 1,98% 6,29% -6,27% 19,44% -9,03% 2001 47 12917.78 -8,82% -6,49% 6,69% -27,93% 1,04% -11,85% 2002 47 11684.28 -8,69% -8,96% 4,32% -21,29% 0,95% -21,97% 2003 47 14144.41 11,68% 12,22% 5,11% -11,38% 19,30% 28,36% 2004 47 15672.91 8,94% 8,75% 2,07% 5,49% 18,00% 10,74% 2005 47 17155.40 9,78% 7,87% 13,86% 3,25% 101,82% 4,83% 2006 47 20175.40 8,71% 4,40% 1,82% 0,76% 11,19% 15,61% 2007 47 21410.47 7,17% 7,16% 1,88% 4,26% 12,10% 5,48% 2008 47 16312.40 -26,76% -29,74% 13,47% -48,93% 5,91% -36,55% 2009 47 18349.76 9,43% 10,77% 6,41% -21,33% 17,48% 25,94% 2010 47 20065.66 8,97% 9,14% 1,32% 3,61% 12,00% 14,82% 2011 47 20693.74 3,70% 3,95% 3,36% -2,75% 12,25% 2,07% 2012 47 21728.60 8,48% 8,79% 1,46% 4,60% 11,30% 15,83% 2000-2012 611 17300.31 2,84% 7,43% 12,52% -48,93% 101,82% 3,40% 6.2 Jensen’s Alpha

Comment [CS1]: Laat ook andere

To test for absolute performance Jensen’s Alpha is used. 47 regressions are done to see if the individual pension funds outperform the S&P 500 significantly. Also one regression is done to test the 47 funds jointly against their benchmark. Table 2 and 6 show the results of these regressions. A positive Alpha tells us that the fund(s) outperformed the index and that the prediction of the CAPM is not correct. Which implies that the market portfolio is not efficient. A negative Alpha says that the fund(s) did not outperform the S&P 500 and that the CAPM predicted correctly. Which implies efficient markets.

The mean Alpha, which is the constant in the jointly regression, is 0,00002239. Looking at the t-value of 0,07 there can be concluded that the funds jointly did not outperform the S&P 500 at a 1% level. This result is consistent with the results of the literature. The paper of Jensen concluded that the funds were not able to outperform the market index on average (Jensen, 1968). 20 of the 47 pension funds outperformed the S&P 500 in absolute numbers. Whereas only 6 of them outperformed the index significantly at a 5% level. Which means that only 12,77% of the funds outperformed the index significantly. 27 funds held a lower return than the S&P 500 in the period 2000 till 2012, but this

underperformance is not significant at a 5% level. Only 2 of the funds held a significant lower return than the market index at a 5% level.

According to the measurement of Jensen’s Alpha, there can be concluded that Pension funds do not outperform the market on average, but individually there are some funds that perform better than the S&P 500.

Table 2: Jensen's Alpha

This table contains the relevant information on Jensen’s Alpha. Positive is the number of funds with a positive Alpha, negative is the number of funds with a negative Alpha. Significant stands for the number of funds that significantly outperformed the S&P 500 at a 5%

level. T-values are calculated as follow:

Period N Mean Std. Dev.

T-value

Positive Negative Significantly greater than zero Significantly lower than zero 2000-2012 47 0,0002239 0 ,003142 0,07 20 27 6 2 6.3 Beta

Beta is the measure of the systematic risk of the portfolios of the pension funds (Bodie et al., 2011, p. 1023).The reason why beta is discussed in this paper is because it can be useful to explain the returns of the pension funds. The beta of the market index is one. Is it better to have an beta close to one? So the portfolio of the fund moves in the same direction of the market. Or is a portfolio with beta that is closer to zero or maybe negative more useful? Leads a higher beta to a higher return or vice versa? The market risk of a portfolio can be reduced with a beta smaller than one.

Table 3 shows the relevant information on the Beta’s of the 47 pension funds. From the 47 pension funds only four did not significantly differ from one at a 5% level. This means that almost all of the funds have reduced the market risk of their portfolio. The four funds that did not significantly differ from 1, tend to follow market fluctuations. None of the 47 pension funds has a negative beta. So there is not a fund that fluctuates in the opposite direction of the S&P 500 index. None of the corresponding funds has a beta higher than one.

The mean beta of all 47 funds is 0,5414. The corresponding t-value is 32,31, which is significantly different from zero at a 1% level. Looking at the mean beta of the 47 pension funds, there can be concluded that on average pension funds tend to decrease market risk.

Table 3: Beta

This table contains all the relevant information on Beta. <1 and >1 stand for Beta smaller than one and Beta larger than one. “T-value”shows if the value of Beta is significantly different from 0. “Significantly different from 1” shows the number of funds with a Beta

significantly lower than one. T-values are calculated one sided, with the following formula:

Period N Mean Std. Dev. T-value <1 >1 Significantly

lower than 1

2000-2012 47 0,5414 0,0168 32,31 47 0 43

Table 4 shows relevant parameters of the 47 funds, categorized in groups of their corresponding beta-value. What stands out is the negative value of Alpha and the low value of the Sharpe ratio for the beta values between 0,5 and 0,75. The parameter values from the category zero to 0,25 are much higher. From the information provided by table 4, there can be concluded that a high beta leads to a lower return. Although the low number of observations has to be considered.

Graph 1 and 2 give a better view of the information in table 4. Both graph 1 and graph 2 support the conclusion made in this paragraph.

Table 4: Categorized Beta

This table shows the average Alpha and Sharpe ratio for the several Beta categories. N is the number of funds and αis the value of Alpha. β<0 means a beta lower than 0, 0<β<0,25 means a beta between 0 and 0,25, 0,25<β<0,5 means a beta between 0,25 and 0,5,

0,5<β<0,75 means a beta between 0,5 and 0,75 and 0,75<β<1 means a beta between 0,75 and 1.

Category β<0 0<β<0,25 0,25<β<0,5 0,5<β<0,75 0,75<β<1 N 1 4 10 32 0 α 0,0113 0,0162 0,0138 -0,0064 Sharpe ratio 0,0997 0,3029 0,2113 0,0134 ` Graph 1 Graph 2

6.4 Relative performance: Sharpe ratio

-0.01 -0.005 0 0.005 0.01 0.015 0.02 β<0 0<β<0,25 0,25<β<0,5 0,5<β<0,75 0,75<β<1

α

Sharpe ratio

Relative performance is measured by the Sharpe ratio. The T-bill rate is subtracted from the portfolio returns of the pension funds, this value is divided by the standard deviation of the portfolio. Standard deviations are calculated from the yearly returns of the pension funds .

Sharpe ratio:

Table 5 shows the relevant information on the Sharpe ratios of the 47 funds and the S&P 500 index. The mean Sharpe ratio of the funds is 0,0572, which is lower than the Sharpe ratio of the S&P 500 index. This is in consistence with the results of the literature. Following the research of Sharpe, none of the funds should be able to significantly outperform the market index (Sharpe, 1966). Only 19 of the 47 pension funds had a higher Sharpe ratio than the index. 17 of the funds had a negative Sharpe ratio. Only 6 funds significantly

outperformed the S&P 500 at a 5% level. Which means that only 12,77% of the funds outperformed the index. This outcome is in complete alignment with the results on Jensen’s Alpha earlier discussed. The results on the Sharpe ratio are in alignment with the earlier results found on Jensen’s Alpha. Pension funds in the United States do not seem to outperform the S&P 500 index significantly.

Table 5: Sharpe ratio This

table contains all the relevant information about the Sharpe ratios of the 47 pension funds and the S&P 500. T-value is calculated using

following formula: . “Higher” means the amount of funds that have a higher Sharpe ratio than

the S&P 500 index and “Negative” is the amount of funds that have a negative Sharpe ratio.

Category Sample period

N Mean Std.

Dev.

T-value Higher Negative Significantly higher than the S&P 500 Significantly lower than the S&P 500 Pension funds 2000-2012 47 0,0572 0,1435 -0,6497 19 17 6 0 S&P 500 index 2000-2012 0,0708

According to the paper of Jensen and the results on Jensen’s Alpha earlier discussed, American pension funds do not perform better than the market index. The results on Jensen’s Alpha are based on the CAPM model, but what if the predictions made by the CAPM model are not correct? That is why the Fama and French Three-factor model is also used to calculate the Alphas of the pension funds.

Table 6 shows the relevant parameters on the Alphas of 47 funds according to the Fama-French Three-factor model. The mean Alpha of the jointly regression is 0,00587. This value is not significantly different from zero at a 5% level. The mean Alpha is higher than the value calculated with the CAPM model 0,00587 vs. 0,0002239. From the 47 pension funds, 26 funds have a positive Alpha, which is 55,32% of all the funds. From these 26 funds only 8 of them significantly outperformed the S&P 500 index at a 5% level. None of the funds had a Alpha significantly lower than zero.

According to the Fama-French Three-factor model, American pension funds do not earn significantly higher returns than the market index in absolute numbers. Although funds do perform better using the Fama-French Three-factor model instead of the CAPM model.

Table 6: Fama and French Three-factor model Alpha

This table contains the relevant information on Fama and French Three-factor model Alpha. Positive is the number of funds with a positive Alpha, negative is the number of funds with a negative Alpha. Significant stands for the number of funds that significantly

outperformed the S&P 500 at a 5% level. T-values are calculated as follow:

Period N Mean Std. Dev. T-value Positive Negative Significantly greater than zero Significantly lower than zero 2000-2012 47 0.00587 0.00369 1,59 26 21 8 0 Conclusion

Pension funds try to outperform market indices by looking for mispriced stocks constantly. According to the literature and theory, pension funds are on average not able to outperform these indices significantly. Still managers of funds believe in active management. According to this thesis managers of pension funds do not have a point with their believe in active management.

According to the results of Jensen’s Alpha, the 47 pension funds do not outperform the market significantly on average. According to the Fama-French Three-factor model, the funds do perform a bit better but there is still no significant outperformance of the S&P 500 market index. So these results support the conclusions made in the literature. According to the CAPM model, only 12,77% of the funds individually outperform the S&P 500 significantly. The model of Fama and French gives an outperformance of the market index by 17,02% of the funds.

The results on Beta give a view on the degree of market risk pension funds tend to take. The mean Beta of the 47 pension funds is 0,5414, which is significantly lower than one. This means that these funds diversify risk, by lowering the market risk. From the results on Beta also can be concluded that the lower the positive Beta, the higher the return of the pension fund.

The Sharpe ratios of the pension funds are on average significantly lower than the Sharpe ratio of the S&P 500 index. This means that these 47 funds do not outperform the market index relatively on average. This is in line with expectations and the conclusions made in the literature. 12,77% of the funds outperformed the index individually, which is in complete alignment with the results found on the Jensen’s Alpha.

Do American pension funds outperform the S&P 500 index? From the results on the regression of the 47 pension funds this question can definitely be answered negative. Both on relative and absolute performance and with the CAPM and the Fama-French Three-factor model, the pension funds do not outperform the S&P 500 index significantly on average. Individually not all funds do underperform the index significantly. Most of the pension fund managers do believe in active management, but according to this thesis, this believe is unreasonable.

Table 7: All relevant parameters of the 47 pension funds.

“r2” is the R-squared, “Sharpe S&P 500” is the Sharpe ratio of the S&P 500 and “T-value B <1” is the value of the one-sided t-test whether the Beta is significantly different from 1. Size is the average size of the Plan assets during the period 2000-2012 in millions of Dollars. “F-F α” is the value of Alpha according to the Fama-French Three-factor model and “F-F T-value α” is the T-value of the Alpha according to the Fama-French Three-factor model.

Number Pension fund

Size β T-value β α T-value α r2 Sharpe ratio Sharpe S&P 500 T-value Sharpe Ratio T-value β <1 F-F: α F-F: T-value α 1 3m 12847.38 0,483 7,64 0,0070 0,59 0,8416 0,1344 0,0708 0,65 -6,81 0,0197 1,65 2 Abbott Laboratories 4738.492 0,727 10,47 -0,0252 -1,94 0,9088 -0,1100 0,0708 -1,25 -3,24 -0,0205 -1,28 3 Alcatel-Lucent 21457.69 0,051 1,00 0,0119 1,24 0,0836 0,4296 0,0708 12,25 -16,1 0,0197 1,54 4 Alcoa Inc 9250.385 0,466 6,92 0,0082 0,65 0,8134 0,1442 0,0708 0,75 -7,31 0,0049 0,31 5 American Airlines 7252.154 0,471 6,17 0,0297 2,08 0,7760 0,3509 0,0708 2.75 -5,95 0,0200 1,29 6 AT&T 44433.31 0,721 9,44 -0,0173 -1,21 0,8901 -0,0554 0,0708 -0,87 -3,00 -0,0146 -0,84 7 Bank of America 14493.15 0,652 8,19 -0,0119 -0,79 0,8591 -0,0263 0,0708 -0,73 -3,83 -0,0176 -0,91 8 Boeing 43130.77 0,506 4,72 0,0057 0,28 0,669 0,1033 0,0708 0,28 -3,86 0,0257 1,34 9 Caterpillar 11025.69 0,744 6,66 -0,0091 -0,44 0,8012 0,0025 0,0708 -0,43 -1,73 -0,0177 -0,75 10 Centurylink 2644.105 0,701 11,81 -0,0233 -2,07 0,9269 -0,1025 0,0708 -1,25 -4,09 -0,0111 -0,93 11 Chevron 9273.077 0,599 8,10 -0,0118 -0,85 0,8565 -0,0331 0,0708 -0,84 -4,84 -0,0153 -1,02 12 Citigroup 15240.54 0,323 6,36 0,0175 1,84 0,7862 0,3233 0,0708 3,77 -10,4 0,0235 1,81 13 ConocoPhillips 4124.308 0,584 9,45 -0,0081 -0,7 0,8904 -0,0053 0,0708 -0,66 -5,87 -0,0014 -0,11 14 Edison 7316.069 0,711 9,62 -0,0123 -0,89 0,8937 -0,0227 0,0708 -0,66 -3,24 -0,0165 -1,00 15 Deere & Co 8058.308 0,493 4,07 0,0035 0,15 0,6007 0,0795 0,0708 0,07 -3,51 0,0179 0,83 16 Delta Air Lines 7252.462 0,524 6,72 -0,0021 -0,15 0,8043 0,0424 0,0708 -0,26 -4,91 0,0123 0,71 17 Walt Disney 4307.462 0,176 1,59 0,0250 1,20 0,1868 0,3290 0,0708 3,12 -6,19 0,0355 1,55 18 Dow Chemical 13270.38 0,628 13,03 -0,0052 -0,58 0,9392 0,0230 0,0708 -0,39 -7,11 -0,0024 -0,23 19 Duke Energy 3883.462 0,730 7,22 -0,0199 -1,05 0,8256 -0,0698 0,0708 -0,92 -2,11 -0,0131 -0,65 20 Eastman Kodak 8479.462 0,479 5,43 0,0171 1,03 0,7285 0,2152 0,0708 1,34 -4,98 0,0212 1,11 21 Exelon 8345.385 0,668 8,84 -0,0059 -0,42 0,8767 0,0194 0,0708 -0,38 -3,8 -0,0082 -0,49 22 Exxon Mobil 21037.08 0,682 8,57 -0,0153 -1,03 0,8699 -0,0470 0,0708 -0,84 -3,34 -0,0142 -0,95 23 Fedex 10006.96 -0,048 -0,30 0,0113 0,37 0,0080 0,0997 0,0708 0,27 -5,67 0,0375 0,99 24 Ford Motor 57869.54 0,450 11,42 0,0134 1,82 0,9222 0,2229 0,0708 1,77 -11,44 0,0202 2,13 25 General Dynamics 6338.385 0,701 5,19 -0,0129 -0,50 0,7101 -0,0235 0,0708 -0,58 -1,76 -0,0335 -1,17 26 General Electric 51005 0,694 7,73 -0,0156 -0,93 0,8445 -0,0457 0,0708 -0,80 -2,8 -0,0166 -0,87 27 General Motors 95723.15 0,456 9,69 0,0174 1,98 0,8952 0,2645 0,0708 2,20 -9,38 0,0210 3,39 28 Hewlett-Packard 13377.31 0,524 4,22 -0,0042 -0,18 0,6178 0,0194 0,0708 -0,40 -3,2 0,0071 0,31 29 Honeywell International 14178.77 0,660 8,19 -0,0081 -0,54 0,8591 0,0021 0,0708 -0,51 -3,71 -0,0151 -0,84 30 Intl Business 78624.46 0,510 10,27 0,0014 0,15 0,9056 0,0784 0,0708 0,08 -8,43 0,0096 0,98

Machines 31 Johnson & Johnson 9115.538 0,697 11,09 -0,0183 -1,55 0,9179 -0,0677 0,0708 -1,00 -4,02 -0,0184 -1,28 32 Lockheed Martin 23417.77 0,687 8,18 -0,0139 -0,88 0,8587 -0,0363 0,0708 -0,76 -3,15 -0,0121 -0,60 33 Merck & Co 7432.677 0,704 11,10 -0,0132 -1,11 0,9181 -0,0301 0,0708 -0,73 -3,59 -0,0137 -0,85 34 Metlife 5734 0,410 7,82 0,0098 1,00 0,8475 0,1865 0,0708 1,44 -9,57 0,0223 1,97 35 Northrop Grumman 19084.23 0,500 16,28 0,0123 2,14 0,9602 0,1996 0,0708 1,38 -14,15 0,0186 2,59 36 Pepsico 6562.846 0,523 4,61 -0,0054 -0,26 0,6590 0,0103 0,0708 -0,48 -3,64 0,0025 0,14 37 Pfizer 12429.38 0,539 7,58 -0,0134 -1,00 0,8394 -0,0574 0,0708 -1,14 -5,61 -0,0090 -0,85 38 PG&E 8716.308 0,501 15,37 0,0134 2,20 0,9555 0,2137 0,0708 1,54 -12,53 0,0230 3,36 39 Procter & Gamble 4648.769 0,168 1,70 -0,0034 -0,18 0,2075 -0,0171 0,0708 -1,20 -7,27 0,0147 0,68 40 Prudential Financial 9983.538 0,212 2,09 0,0313 1,65 0,2851 0,4700 0,0708 5,52 -6,66 0,0508 2,11 41 Raytheon 12829.85 0,674 5,18 -0,0153 -0,63 0,7091 -0,0433 0,0708 -0,75 -2,01 -0,0033 -0,14 42 Southern 6097.846 0,697 4,78 -0,0069 -0,25 0,6750 0,0125 0,0708 -0,35 -1,68 0,0017 0,07 43 United Continental Holdings 3317.231 0,644 1,50 0,0591 0,73 0,1694 0,2206 0,0708 0,49 -0,55 0,0727 0,67 44 United Parcel Service 14188.15 0,603 3,85 0,0035 0,12 0,5742 0,0730 0,0708 0,01 -2,16 0,0125 0,43 45 United Technologies 18068 0,612 4,88 -0,0017 -0,07 0,6844 0,0437 0,0708 -0,19 -2,59 0,0117 0,55 46 Verizon Communications 36473.31 0,721 9,22 -0,0029 -0,20 0,8854 0,0434 0,0708 -0,19 -2,86 -0,0021 -0,13 47 Wells Fargo & Co 6030.308 0,487 5,53 0,0147 0,89 0,7353 0,1917 0,0708 1,11 -4,71 0,0162 1,13

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