Optimal Portfolio Strategy in Defined Contribution Pension Plans with Company Stock

Optimal Portfolio Strategy in Defined Contribution Pension Plans with Company Stock Hui-Ju Tsai and Yangru Wu * July 3, 2013 ABSTRACT We study employees optimal portfolio choices in defined contribution plans with company stock in various industries. We find that there is significant variation in the optimal portfolio across industries. Permanent labor income risk, however, has a limited effect on employees optimal portfolio as well as welfare in most industries. Welfare analysis also shows that 1/n rule is better than all stock, followed by all bond portfolios when employees degree of risk aversion is low. But the reverse is true when employees become more risk averse. Finally, unless employees degree of risk aversion is low, their significant investment in company stock cannot be justified with economic reasons alone, including higher expected company stock return, familiarity, and employers matching policy. JEL classification: G11, G12 Keywords: portfolio choice, consumption, predictability, labor income * The authors are from Rutgers Business School-Newark and New Brunswick, Rutgers University, 111 Washington Street, Newark, NJ 07102, huitsai@pegasus.rutgers.edu, yangruwu@andromeda.rutgers.edu. Financial support from Rutgers Business School and the Whitcomb Financial Services Center is greatly acknowledged. 1

Over the past two decades, defined contribution plans have become the most important pension plans that Americans use to save for retirement. For instance, in 2010 there are 654,469 defined contribution pension plans in U.S. that covers more than 88 million workers and manages assets of more than $4.2 trillion. 1 In defined contribution plans, asset allocation autonomy is rendered to the employees. The popularity of defined contribution plans thus makes employees optimal portfolio choice in their pension plans an important research topic. Recent studies have found that employees are not portfolio optimizers: they tend to adopt some heuristic strategies. For instance, Benartzi and Thaler (2001) and Huberman and Jiang (2006) find that employees tend to adopt the 1/n strategy that allocates contribution evenly across either all available or some chosen investment objects in pension plans. The most interesting example comes from Nobel Economics laureate Harry Markowitz - a founding father of classic portfolio theory, who admitted that he split his contribution evenly between bond and stock fund in his TIAA-CREF account during the period when TIAA-CREF had only two options (Benartzi and Thaler, 2007). Empirical studies also find that employees have inertia in their pension management. Beshears, Choi, Laibson, and Madrian (2007) point out that the default option has a wide influence on employed investors participation rate as well as asset allocation decision. In addition, Waggle and Englis (2000) reports that the average number of trades in pension plans during a year is zero for more than 87 1 Source: U.S. Department of Labor. 2

percent of the participants and only 7 percent of plan participants trade more than once a year. 2 Another sub-optimizing evidence about employees pension investment regards their tendency to allocate a significant amount of pension wealth to company stock. Table I shows the percentage of defined contribution plan assets invested in company stock in some well-established companies. Coca-Cola (KO), for instance, has more than 50 percent of its defined contribution plan assets invested in company stock. This is puzzling because according to portfolio theory, employees should not invest in company stock for more than what a diversified market portfolio suggests. In addition, individual stock can crash and employees may lose their pension wealth if they invest too much in company stock. For instance, Enron s employees lost 60 percent of their wealth in their 401(k) plan when Enron s stock collapsed. Finally, when the correlation between labor income and company stock return is considered, employees' high allocation to company stock becomes even more puzzling. This paper studies employees' optimal portfolio choice in pension plans when company stock is available for investment. Specifically, we consider labor income risk and its correlation with asset returns faced by employees working in different industries and in the five companies listed in Table I. Although there are several papers studying the optimal investment strategy in defined contribution plans, most of them do not address the issue of company stock (see, e.g., Vigna and Haberman, 2001, 2002; Boulier, Huang, and Taillard, 2001; Deelstra, Grasselli, and Koehl, 2003; 2 This is contrary to Odean (1999) who uses data from the trading record in a brokerage firm and finds that investors are quite active traders. This difference may be due to sample selection bias. People who open brokerage accounts are more likely to be active traders. Another reason for this difference may be that while investment targets in a brokerage account could be individual stocks, most assets in pension plans are mutual funds that may reduce investors incentives to trade actively. 3

Battocchio and Menoncin, 2004; and Cairns, Blake, and Dowd, 2006). This is contrast to the empirical evidence that company stock can greatly affect employees portfolio choices. Douglass, Wu, and Ziemba (2004) consider the optimal company stock investment in pension plans, but they do not discuss how the variation of labor income risk as well as company stock return faced by employees working in different industries can affect their optimal decisions. Since labor income has a higher correlation with company stock, and the risk of labor income as well as company stock varies across industries, we believe that it is important to consider industry factor when discussing the optimal portfolio decision in pension plans, especially the optimal investment in company stock. Our paper fills the research gap. The second part of this study examines if employees high allocation to company stock can be justified with the following economic reasons (see Douglass, Wu, and Ziemba, 2004; Meulbroek, 2005; Mitchell and Utkus, 2005; and Cohen, 2009). 3 Firstly, due to borrowing and short sale constraints, aggressive employees may want to earn a higher expected return by investing in company stock because a leveraged position in market portfolio is not allowed in pension plans. Secondly, employees may have a higher expected company stock return than the market does since they may be able to buy company stock at a discounted price or they are more optimistic about their own company s future. The third argument relates to employees familiarity with their own company. Finally, it can also be attributed to employers' match to employees' contribution exclusively with company stock. Employees may view this as an endorsement of company stock investment from the management. 3 Behavioral arguments such as loyalty or peer pressure can also possibly explain investors' high allocation to company stock (see Cohen, 2009). For simplicity, we do not consider these factors in this paper and we leave it for future research. 4

There are several interesting findings in our study. First of all, there is great variation in employees optimal portfolio decision in their pension plans across industries and the five companies listed in Table I, especially when their degree of risk aversion is low. Employees working in public administration or finance industry should optimally not invest in their company stock while the portfolio weights in company stock can be higher for employees in manufacturing, transportation or business industry. Secondly, the effect of permanent labor income risk on the optimal portfolio decision is usually limited in most industries but has a relatively higher effect in agriculture, construction and professional services industries, which have higher variance of permanent labor income risk and show a higher correlation between labor income and stock or bond market returns. Then, our welfare analysis shows that, for most industries, when employees degree of risk aversion is low, 1/n rule is better than all stock portfolio, followed by all bond portfolio. But the reverse is true when employees degree of risk aversion is high. These strategies are all inferior to the optimal strategy. Finally, we examine several possible economic reasons but find none of them alone may justify employees high allocation to company stock unless employees degree of risk aversion is low. These economic motives only have small effects on the portfolio decisions of employees with high degree of risk aversion. Section I specifies the model and describes the methodology used to solve the optimal portfolio choice problem. Section II shows the simulation results and compares the performance of the optimal strategy with some benchmark strategies. Section III examines if employees' high investment in company stock can be justified with economic reasons. Concluding remarks are given in Section IV. 5

I. Optimal Portfolio Strategy in Pension Plans A. Model Specification We assume that employees have a power utility over terminal pension wealth maturing at time T: 1 W T W, Y, MaxE Vt t t Z t t, x 1 subject to the budget constraint W W HY R s 1 s s s 1 x, s t, where is the coefficient of relative risk aversion, W s denotes pension wealth, Y s is labor income, H is the contribution rate, x is the vector of portfolio weights in securities, and R s 1 ~ N( μ, ) is the vector of asset returns. Each period before retirement, employed investors contribute a proportion H of their labor income to their pension accounts, and receive their pension wealth at maturity date T. For simplicity, we do not consider non-pension wealth and the corresponding consumption and asset allocation decision. We assume that labor income process follows Y Y exp( g 1), where g is labor income growth rate t 1 t t 2 and t 1 ~ N(0, ) denotes labor income risk. The covariance between labor income and asset returns is denoted by v. B. Model Simulation 6

We assume that there are three assets in pension plans available for investment: stock portfolio, company stock, and long-term bond. We use monthly CRSP value-weighted market portfolio and 20 year corporate bond returns for the period 1972.1-2011.8 to estimate stock market portfolio and bond returns, respectively. The estimated annualized mean (variance) of stock and bond returns are 10.74% (2.59%) and 8.85% (1.15%), respectively. The estimated correlation coefficient between stock and bond returns is 13.51%. To estimate company stock returns, we use two methods. First of all, we consider all companies that are listed in NYSE during the sample period and estimate their mean, variance, and correlation with stock and bond returns. Then, for each industry, we choose the median of these statistics and use them as our estimates of mean, variance, and correlations of a typical company in that industry. Table II Panel A reports the summary statistics. 2 The second method we use to estimate company stock return is to consider each of the companies listed in Table I and compute their mean, variance, and correlation with stock and bond returns during the sample period and use them as our parameters. The results are reported in Table II Panel B. To estimate the correlation between labor income and asset returns, we use the data provided in Campbell, Cocco, Gomes, and Maenhout (2001). Campbell et al. (2001) use the family questionnaire of the PSID for years 1972-1994 to estimate the variance of permanent labor income risk and the correlations between permanent labor income risk and excess stock as well as excess long-term government bond returns for household working in different industries. Table III summaries their findings of permanent labor income risk across industries. We assume the correlation 2 The industries are selected to be consistent with the data reported in Campbell, Cocco, Gomes, and Maenhout (2001). 7

between permanent labor income and company stock returns is equal to 1.1*Max (Corr(labor income, stock returns), Corr(labor income, bond returns)). Yt 1 The labor income growth rate g is set such that E t 1. 03 Yt and t 1 ~ N(0, 0.01). The annual contribution rate H is assumed to be 6 percent. We consider the case where the employees have 20 years to retirement and the initial wealth and labor income equal to 0 and 1 respectively. Under these assumptions, we simulate 5000 times and use a grid search over portfolio weights [0,1] [0,1] [0,1] in step 0.01 0.01 0.01 to find the optimal portfolio decision for investors with degrees of relative risk aversion γ ={2, 6, 10}. II. Simulation Results A. Optimal Portfolio Weights Table IV shows the optimal portfolio decisions for employees in different industries or in the five companies listed in Table I. For comparison purposes, we also display the optimal strategy when labor income risk is ignored; that is, when labor income is assumed to grow at a constant rate for sure and labor income have no correlation with asset returns. As shown in Table IV, there is great variation in the optimal decision across industries especially when employees level of risk aversion is low. Employees working in public administration or finance industry, for instance, should not invest in their company stock while the optimal portfolio weight in company stock for employees with r=2 working in manufacturing, transportation or business industry is between 28~29%. The change in company stock investment across industries can be attributed to the variation in their company stock return-to- 8

risk ratio. 3 According to Table II, among the industries considered, manufacturing, transportation or business industry has the highest return/risk ratio while finance and public administration industry shows the lowest. Agriculture industry also has a high company stock return-to-risk ratio but the optimal investment in company stock is not as high as the other industries because its permanent labor income risk is higher and has a higher correlation with company stock returns. As to the five companies, again there is great variation in the optimal pension choice. For instance, employees with r = 6 working in Coca-Cola (KO), Caterpillar (CATE), or Occidental Petroleum (OXY) should allocate more than ten percent of their contribution to company stock while employees working in Target (TGT) should put nothing in their company stock. Among these five companies, Target (TGT) has a much lower company stock return-to risk ratio than the other four firms. General Electric (GE) has a high return-to-risk ratio, but its optimal company stock investment is not comparable to the other companies. This is mainly due to GE s high correlation between company stock and stock returns. In addition, companies including Occidental Petroleum (OXY), Caterpillar (CATE), and Target (TGT) have a lower correlation between their company stock and bond returns, employees in these companies have a higher portfolio weights in bonds when compared to those working in Coca-Cola (KO) and General Electric (GE). When permanent labor income risk is ignored, as expected, employees optimally increase their investment in company stock since labor income has a higher correlation with company stock returns than with the other financial asset returns. However, as shown in Table IV, for most industries permanent labor income risk does 3 The return-to-risk ratio is computed by dividing the annualized mean return by the standard deviation of returns. 9

not have a large effect on investors portfolio decision in pension plans. The inclusion of permanent labor income risk will decrease the investment in company stock but only up to three percentage points in most industries except agriculture, construction and professional services. The limited effect of permanent labor income risk on pension investment can be attributed to the fact that permanent labor income risk is much lower than investment risk. For instance, from Table III, the highest variance of permanent labor income risk is from the agriculture industry of 2.49 percent, which is much lower than the lowest variance of company stock returns in the finance industry of 7.85 percent. Industries in which labor income risk has a larger effect on portfolio decision are usually those with higher variance of permanent labor income risk and a higher correlation between labor income risk and stock or bond market returns. For the five companies considered here, the ignorance of permanent labor income risk has a larger effect on pension investment than when industries are considered. This may due to that the variance of these five company stock returns are much lower than that of the industries and thus labor income risk plays a relatively important role in employees optimal decision in pension plans. B. Performance Test To evaluate the economic significance of adopting the optimal strategy, we compare the performance of the optimal strategy with four benchmark strategies: (1) the 1/n rule that allocates the contribution evenly across all available investment objects; (2) all stock strategy that allocates all contribution to stock portfolio; (3) all bond strategy that allocates all contribution to bond; and (4) the optimal strategy that ignores labor income risk. 1/n strategy is found to be popular among employees in their pension plan investment (see, e.g., Benartzi and Thaler, 2001; and Huberman 10

and Jiang, 2006). The last benchmark strategy allows us to evaluate the welfare loss of ignoring labor income risk when making pension investment decision. We assume that the investment opportunity set and the correlation coefficients between labor income and asset returns are the same as described in Section I.B. Employees have 20 years to retirement and we consider the cases where they have degrees of risk aversion equal to 2, 6, and 10, respectively. For each trading strategy, we estimate the certainty equivalent terminal wealth that provides the same expected utility as each strategy. Table V shows the loss in certainty equivalent wealth if the benchmark strategies are adopted instead of the optimal strategy. The simulation results show that the optimal strategy is better than the benchmark strategies since employees incur a welfare loss if they adopt the benchmark strategies instead of the optimal strategy. However, the utility loss of ignoring labor income risk when making portfolio decision is small in most industries except agriculture industry. Employees with r=6 working in agriculture industry can lose about 4.66 percent in their certainty equivalent wealth if they ignore labor income risk when making pension investment decisions. This is followed by professional service industry with a welfare loss of 1.89 percent and then by the construction industry with a loss 1.46 percent. When employees have a high degree of risk aversion, 1/n is the worst among all trading strategies in all industries considered. The reason is that 1/n strategy allocates one third of all pension wealth to the company stock and it can be costly to employees with high degrees of risk aversion who may want to adopt a more conservative trading strategy. This observation does not apply to the five companies considered here. For Coca-Cola (KO), for instance, employees with r=10 are better off if they adopt 1/n instead of either all stock or all bond strategy. 11

In the cases where employees have a low level of risk aversion, 1/n strategy is a better strategy than the strategy of all stock or bond in most industries, except public administration. For public administration industry, employees with r=2 incur a 26.92 percent loss in certainty equivalent wealth if they adopt 1/n strategy, compared to a 3.11 and 10.93 percent welfare loss if all stock and bond strategies are adopted, respectively. As to the five companies considered, for all of them except Target (TGT), 1/n is a better strategy than all bond and all stock strategies when investors degree of risk aversion is low. When comparing all stock and all bond strategy, we find for conservative employees, all bond strategy is better than all stock strategy in most industries and all of the companies considered. By contrast, all stock strategy is usually better than all bond strategy when investors degree of risk aversion is low. This is consistent with the fact that stock is more risky than bond. The only exception is the agriculture industry. For employees working in the agriculture industries, all stock strategy is always better than all bond strategy, regardless of their degree of risk aversion. This may be attributed to the fact that employees in the agriculture industry face higher permanent labor income risk which also has a higher correlation with bond returns (correlation coefficient = 0.51) than with stock returns (correlation coefficient = 0.22). III. Why Do Employees Hold Company Stock? Empirical studies show that employees tend to allocate a significant amount of their pension wealth to company stock when company stock is available for investment in their pension plans. For instance, Meulbroek (2005) finds that company 12

stock accounts for about 27 percent of total assets in those plans that have company stock in their investment menu (see also Mitchell and Utkus, 2005). According to our simulations, allocating a significant amount of pension wealth to company stock can only be explained when investors degree of risk aversion is low. For investors with moderate degree of risk aversion, they should only have a small investment, if not zero, in company stock. Furthermore, for employees working in industries such as finance and public administration, our simulation suggests that they should not invest in company stock at all. Employees significant investment in company stock is puzzling because according to portfolio diversification theory, employees should not invest in company stock for more than what the market portfolio suggests. Besides, individual stock can crash and employees may lose their pension wealth if they invest too much in company stock. For instance, Enron s employees lost 60 percent of their wealth in their 401(k) plan when Enron s stock collapsed. Also, investing in a single stock can be very costly since investors may not be compensated for the incurred idiosyncratic risk. And the positive correlation between company stock returns and labor income makes the investment in company stock become even less attractive. The literature has proposed several economic reasons that may explain employees high allocation to company stock. Firstly, since the investment in pension accounts generally has borrowing and short sale constraints, employees may invest in company stock to earn a higher expected return because they cannot hold a leveraged position in the market portfolio. Secondly, employees may expect a higher return from company stock investment than the market does. Plausible reasons are that employees can buy company stock at a discounted price or that they are more 13

optimistic about their own company s future. Thirdly, employees may think that they know better about their own company and want to invest in what they are more familiar with. Fourthly, some companies have a restricted match policy that matches employees contribution exclusively with company stock and employees may view this as an endorsement from the management that company stock is a good investment target. In this section, we examine if any of these reasons can justify employees high allocation to company stock. A. Higher Expected Return Employees may invest in company stock because they expect a higher return from their company stock investment than the market does. The reason can be that employees are more optimistic about their own company or that they can buy company stock at a discounted price. To see how higher expected company stock return affects employees portfolio strategy, we consider the cases where employees expect a mean company stock return that is higher than that described in the original model in Section I.B. by 2 and 4 percents while holding the same expected stock and bond returns. The other baseline assumptions are the same as described in Section I.B. The result is provided in Table VI. Not surprisingly, when company stock has a higher expected return, employees optimally increase their allocation to company stock and reduce their investment in other risky assets. For most industries and companies considered here, consistent with Douglass, et al. (2003), higher expected company stock return can explain employees high allocation to company stock when employees' degree of risk 14

aversion is low or when employees have extremely high expectation of company stock return. 7 For instance, for employees in General Electric (GE) with r=4, increasing expected company stock return by 4 percent can increase their optimal company stock investment from 4 to 33 percent. However, when employees have a moderate degree of risk aversion, increasing company stock return by 4 percent still cannot justify the significant investment in company stock for all of the industries considered here. Furthermore, for finance and public administration industries, employees still should not invest their pension wealth in company stock even its return is 4% higher than the market expect. In sum, our simulation suggests that in most cases, employees higher expectation about company stock return cannot justify their significant investment in company stock unless their degree of risk aversion is low. B. Parameter Uncertainty It has been argued that employees invest much of their pension wealth in company stock because they think that they know better about their companies and want to invest in what they are more familiar with. To examine if familiarity can justify employees high allocation to company stock, we now incorporate parameter uncertainty to the investment opportunity set described in Section I.A. For simplicity, we assume that there is parameter uncertainty in the mean asset returns μ, but the 7 Assuming a mean-variance utility function, Douglass, et al. (2003) show that the risk aversion parameter needs to be below 0.5 or the employees believe that the expected company stock return to be as high as 50 percent such that it is optimal for the investors to hold company stock above 50 percent. When considering other retirement savings outside pension plans, they show that investors with relative risk aversion equal to 8 need to have 50 percent of their savings outside pension plans for them to optimally hold 50 percent of their pension wealth in company stock. 15

variance of asset returns Σ is known to the investors. According to Zellner (1971) and Barberis (2000), the posterior distribution of μ can be described as T ri i 1 μ ~ N,, T T where ri denotes the vector of asset returns in period i and T is the number of observations. We then simulate 5000 sample paths in asset returns from the posterior distribution to compute the optimal portfolio decision with parameter uncertainty. 4 To examine how familiarity in company stock can change employees portfolio decision, we compare two scenarios: (1) employees have parameter uncertainty in the return generating processes of all asset returns, and (2) employees have parameter uncertainty in the return generating process of all assets except company stock. We use the same historical data as in Section I.B. to estimate mean and variance of asset returns, but allowing parameter uncertainty in μ here. The other parameter values are borrowed from the baseline model in Section I. Table VII shows the results. Compared to employees who have uncertainty in the return generating processes of all financial assets, employees without parameter uncertainty in company stock will allocate more wealth to company stock while reducing their investment in stock and bond. For instance, employees with γ = 6 in the transportation industry will 4 Here we use T=40 since we have forty years of sample period from January 1972 to August 2011. 16

allocate 36 (4) percent to stock market (company stock) when they have parameter uncertainty in all assets, but their investment in stock market (company stock) will decrease (increase) to 31 (10) percent when they have uncertainty in all financial assets except company stock. Employees familiarity in company stock, however, has only a marginal effect on their investment in company stock, and the effect decreases with their level of risk aversion. For extremely risk-averse employees, their optimal allocation to company stock is small even when they have no uncertainty in the return generating process of company stock. For example, among all industries considered, employees with γ = 12 should at most invest 5 percent of their contribution to company stock. As to those employees with a low level of risk aversion, the effect of parameter uncertainty is also limited. Take the transportation industry as an example: employees with γ = 2 should increase their portfolio weight in company stock from 24 to 30 percent when they have no uncertainty in company stock's return generating process. Thus, the possibility that employees are more familiar with their own company cannot fully justify the observed high allocation to company stock. C. Employer s Match Another possible reason for employees' high allocation to company stock is related to employers exclusive match in company stock. Employees may view this match as an endorsement from management that company stock is a good investment target. In addition, employees are usually prohibited from re-allocating employers' 17

match in company stock before reaching certain ages or service years. 10 This kind of restriction becomes even more popular among large companies. Here we are unable to test directly how the endorsement effect can affect employees optimal portfolio decision, but we can examine how employers restricted match in company stock can affect employees optimal allocation to company stock. We assume that each period the employers match employees' contribution dollar to dollar up to 6 percent of employees annual income, and for simplicity, employees are not allowed to reallocate employers match. Employees are assumed to have 20 years to retirement and face the baseline case as described in Section I. Table VIII shows the result of employees' optimal portfolio decision and total portfolio decision that includes employers' exclusive match in company stock. 11 Employees' optimal portfolio decision when there is no employers' match is also presented. As expected, when employers restrict their match in company stock and employees are not allowed to reallocate employers match, employees should optimally decrease their investment in company stock. For all industries except business, when companies match exclusively with company stock, employees should not invest in company stock even if their degree of risk aversion is low. For the business industry, the optimal portfolio weight in company stock is 1 percent when r=2. As to the five companies considered, only employees with low degree of risk aversion and working in Coca-Coola can still have a significant exposure to company 10 For many companies, it is usually until the age of 55 or 65 or after retirement that investors can freely allocate their employers match in company stock (see Meulbroek, 2005). 11 Since both employers and employees contribute 6 percent of annual labor income to the pension plans, we compute the total portfolio weights as the equally weighted average of employers and employees' portfolio choices. 18

stock. In addition, with company stock match, employees reduction in company stock investment is offset more by the increase in bond investment than by the increase in stock investment. For instance, for employees with r=2 in the agriculture industry, the reduction in company stock from 24 percent to 0 is offset more by the increase in bond investment from 34 to 49 percent than by the increase in stock investment from 42 to 51 percent. Since company stock is more risky than the other assets, employers exclusive match with company stock may induce employees to reduce their investment risk by allocating more to bond in order to achieve a target risk level in their overall portfolio. Employees' total portfolio weight shows how employers' exclusive match in company stock can affect employees' total portfolio when they are not allowed to reallocate. For instance, employees with γ = 6 in the agriculture industry optimally invest nothing in company stock, but due to employers' exclusive match, their total portfolio weight of company stock is 50 percent. It seems that employers' exclusive match in company stock may provide some explanations to company stock investment in pension plans. This result, however, is based on the assumption that employees are not allowed to reallocate employers' match. In reality, however, employees usually can do so after reaching certain ages or service years. It thus raises another puzzle that employees choose not to reallocate their employers' match when they can do so. Thus, we claim that employers exclusive match in company stock still cannot fully justify employees high allocation to company stock in their pension plans. 19

IV. Conclusion Due to the popularity of defined contribution plans and the empirical evidence that employees are not portfolio optimizers in their pension investment, how employees should make their portfolio decision for retirement thus becomes an important research topic. This paper studies employees optimal portfolio decision in defined contribution plans with company stock in different industries. We find that there is great variation in employees optimal portfolio choices in pension plans across industries and five companies, especially when their degree of risk aversion is low. Employees working in public administration or finance industry should not invest in company stock; by contrast, employees in manufacturing, transportation or business industry can have a higher portfolio weight in company stock when their degree of risk aversion is low. This can be explained by the variation in the mean as well as variance of company stock returns across industries. Another interesting finding in this study is that permanent labor income risk has a limited effect on the optimal portfolio decision in all but the agriculture, construction and professional services industries. The agriculture, construction and professional services industries have higher variance of permanent labor income risk and show a higher correlation between labor income and stock or bond returns. Then, our welfare analysis shows that, for most industries considered, when employees degree of risk aversion is low, 1/n rule is better than all stock strategy, followed by all bond strategy. But the reverse is true when employees degree of risk aversion is high. These strategies are all inferior to the optimal strategy. Finally, we find that in most cases, employees high 20

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Table I Percentage of DC Plan Assets in Company Stock Company Company Stock Percentage Coca-Cola (KO) 51.3 Caterpillar Inc. (CAT) 44.3 General Electric (GE) 42 Target Corp. (TGT) 42 Occidental Petroleum Corp. (OXY) 38 Source: Pension & Investments issue on July 12, 2010. http://www.pionline.com/article/20100712/printsub/307129967 23

Table II Annualized mean return (%) Variance (%) Return/ standard deviation (%) Corr with stock returns (%) Corr with bond returns (%) Panel A Agriculture 18.19 20.03 40.64 37.46-2.81 Manufacture 16.96 16.77 41.42 45.12 3.07 Construction 16.04 21.38 34.69 42.17 1.89 Transportation 14.3 10.72 43.68 41.19 3.94 Trade 17.45 21.55 37.59 41.52 0.72 Finance 9.79 7.85 34.94 39.28 4.79 Business 18.83 22.03 40.12 43.81-2.33 Prof. Service 18.7 24.19 38.02 35.38-2.88 Public Administration 8.97 28.17 16.90 49.94-16.56 Panel B Coca-Cola 13.77 5.04 61.34 52.13 18.57 Caterpillar 14.89 8.87 50.00 59.7 2.52 GE 12.63 6.11 51.10 74.35 12.12 Target 8.02 8.34 27.77 48.75-6.58 Occidental Petroleum 16.31 9.16 53.89 44.87 4.92 Stock 10.74 2.59 67 Bond 8.85 1.15 83 13.51 24

Industry Table III Labor Income Risk Across Industries (Source: Campbell et. al. (2001)) Variance of permanent labor income risk (%) Correlation between permanent labor income risk and lagged excess stock returns (%) Correlation between permanent labor income risk and lagged excess bond returns (%) Construction 1.57 55.27 40.05 Business Service 2.13 19.49 16.00 Public Admin. 0.85 42.37 36.85 Manufacturing 0.70 35.24 36.37 Transportation 1.09 18.79 21.77 Prof. Service 1.14 26.44 45.40 Financial Service 1.33 12.81 37.79 Agriculture 2.49 22.18 50.83 Trade 1.42 2.83 19.80 All 1.23 45.62 54.57 25

Table IV With Labor Income Risk Ignore labor Income Risk r = 2 6 10 r = 2 6 10 Agriculture company stock 24 3 1 31 11 7 stock 42 45 50 31 29 29 Manufacturing company stock 28 7 3 31 10 5 stock 34 33 36 32 30 31 Construction company stock 15 1 0 20 6 2 stock 44 37 36 44 34 34 Transportation company stock 29 9 6 31 12 7 stock 41 34 35 40 31 31 Trade company stock 23 6 3 25 8 4 stock 42 38 41 37 32 32 Finance company stock 0 0 0 0 2 1 stock 71 47 47 69 40 36 Business company stock 28 8 7 30 10 5 stock 28 31 31 27 28 30 Prof Services company stock 23 5 2 27 10 5 stock 41 39 43 35 30 31 Public Administration company stock 0 0 0 0 0 0 stock 66 41 40 69 42 36 Coca-Cola company stock 65 18 9 69 24 16 stock 19 28 32 17 24 26 General Electric company stock 32 4 0 37 8 0 stock 32 37 40 28 33 37 Caterpillar company stock 45 12 6 48 16 8 stock 15 28 33 13 23 28 Occidental Petroleum company stock 49 10 4 56 20 14 stock 21 33 38 16 23 24 Target company stock 0 0 0 0 0 0 stock 71 46 46 69 42 35 26

Table V Please see the other attached file. 27

Table VI Original Case 2% Higher 4% Higher r=2 r=6 r=10 r=2 r=6 r=10 r=2 r=6 r=10 Agriculture company stock 24 3 1 31 5 2 39 7 3 stock 42 45 50 34 43 49 24 41 47 Manufacturing company stock 28 7 3 38 10 5 48 13 7 stock 34 33 36 22 30 34 10 26 31 Construction company stock 15 1 0 23 3 1 30 5 2 stock 44 37 36 34 34 35 25 32 33 Transportation company stock 29 9 6 44 14 9 58 18 12 stock 41 34 35 27 29 31 13 26 28 Trade company stock 23 6 3 30 8 5 38 11 6 stock 42 38 41 33 36 38 23 32 36 Finance company stock 0 0 0 13 3 1 34 9 4 stock 71 47 47 61 44 46 44 39 43 Business company stock 28 8 7 35 11 8 43 13 10 stock 28 31 31 19 26 29 8 24 25 Prof Services company stock 23 5 2 30 7 3 36 8 4 stock 41 39 43 32 37 42 25 35 40 Public Administration company stock 0 0 0 0 0 0 3 0 0 stock 66 41 40 66 41 40 60 41 40 Coca-Cola company stock 65 18 9 96 29 15 100 39 21 stock 19 28 32 0 21 29 0 15 26 General Electric company stock 32 4 0 69 19 8 88 33 17 stock 32 37 40 0 21 30 0 6 21 Caterpillar company stock 45 12 6 63 19 11 75 26 15 stock 15 28 33 0 20 27 0 12 22 Occidental Petroleum company stock 49 10 4 66 15 6 79 19 8 stock 21 33 38 4 29 37 0 26 35 Target company stock 0 0 0 0 0 1 15 6 5 stock 71 46 46 71 46 44 55 40 40 28

Table VII With parameter Original Case With parameter uncertainty in all assets uncertainty in all assets except company stock r=2 r=6 r=10 r=2 r=6 r=10 r=2 r=6 r=10 Agriculture company stock 24 3 1 19 0 0 25 3 0 stock 42 45 50 42 43 34 38 39 34 Manufacturing company stock 28 7 3 24 3 0 29 7 1 stock 34 33 36 34 35 32 31 32 31 Construction company stock 15 1 0 12 0 0 16 0 0 stock 44 37 36 43 37 30 41 37 30 Transportation company stock 29 9 6 24 4 0 30 10 5 stock 41 34 35 41 36 31 38 31 24 Trade company stock 23 6 3 19 2 0 24 6 1 stock 42 38 41 41 39 32 38 35 30 Finance company stock 0 0 0 0 0 0 0 0 0 stock 71 47 47 65 42 31 65 42 31 Business company stock 28 8 7 23 3 0 29 8 4 stock 28 31 31 30 34 30 27 29 22 Prof Services company stock 23 5 2 20 2 0 24 4 0 stock 41 39 43 39 38 33 38 37 33 Public Administration company stock 0 0 0 0 0 0 0 0 0 stock 66 41 40 61 40 37 61 40 37 Coca-Cola company stock 65 18 9 55 8 0 67 21 12 stock 19 28 32 22 33 29 17 27 22 General Electric company stock 32 4 0 26 0 0 37 9 4 stock 32 37 40 34 39 31 26 31 27 Caterpillar company stock 45 12 6 38 6 0 45 13 7 stock 15 28 33 18 32 33 15 27 25 Occidental Petroleum company stock 49 10 4 42 4 0 50 10 3 stock 21 33 38 23 35 32 20 32 29 Target company stock 0 0 0 0 0 0 0 0 0 stock 71 46 46 65 42 33 65 42 33 29

Table VIII With employers match Original case: without employers' match Portfolio weights Employees' Portfolio weights includes employers' match r=2 r=6 r=10 r=2 r=6 r=10 r=2 r=6 r=10 Agriculture company stock 0 0 0 50 50 50 24 3 1 stock 51 36 39 25.5 18 19.5 42 45 50 Manufacturing company stock 0 0 0 50 50 50 28 7 3 stock 40 22 24 20 11 12 34 33 36 Construction company stock 0 0 0 50 50 50 15 1 0 stock 39 23 23 19.5 11.5 11.5 44 37 36 Transportation company stock 0 0 0 50 50 50 29 9 6 stock 52 24 23 26 12 11.5 41 34 35 Trade company stock 0 0 0 50 50 50 23 6 3 stock 49 29 24 24.5 14.5 12 42 38 41 Finance company stock 0 0 0 50 50 50 0 0 0 stock 66 36 36 33 18 18 71 47 47 Business company stock 1 0 0 50.5 50 50 28 8 7 stock 36 20 15 18 10 7.5 28 31 31 Prof Services company stock 0 0 0 50 50 50 23 5 2 stock 49 31 30 24.5 15.5 15 41 39 43 Public Administration company stock 0 0 0 50 50 50 0 0 0 stock 44 25 23 22 12.5 11.5 66 41 40 Coca-Cola company stock 32 0 0 66 50 50 65 18 9 stock 36 24 33 18 12 16.5 19 28 32 General Electric company stock 0 0 0 50 50 50 32 4 0 stock 32 5 12 16 2.5 6 32 37 40 Caterpillar company stock 4 0 0 52 50 50 45 12 6 stock 25 9 13 12.5 4.5 6.5 15 28 33 Occidental Petroleum company stock 11 0 0 55.5 50 50 49 10 4 stock 35 25 38 17.5 12.5 19 21 33 38 Target company stock 0 0 0 50 50 50 0 0 0 stock 57 28 26 28.5 14 13 71 46 46 30