ABSTRACT. CHIANG, TSUN-FENG. Three Essays on Financial Economics. (Under the direction of Dr. Douglas Pearce).

Transcription

1 ABSTRACT CHIANG, TSUN-FENG. Three Essays on Financial Economics. (Under the direction of Dr. Douglas Pearce). This dissertation is composed of three research-based essays. The first two take Korea, an economy with high income risk, as an example to calibrate optimal portfolio choices. The first essay confirms that Korean households are subject to higher idiosyncratic income risk (compared with US households) and that the risk increases with age. Using the estimated income risk, the study finds that even though Korea has impressive income growth and average returns on stocks, a Korean household should be conservative in its investment in risky assets since high income and return uncertainty could have negative effects on consumption smoothing. The second essay discusses a similar issue but extends the context of international financial markets. It asks how Korean workers in different industries should allocate their wealth in the equities of selected countries to hedge against their wage risks. Without considering the foreign exchange risk, this study finds that workers in most industries have large hedging demands for French and Canadian stocks. These results may be due to the competitiveness or the complementarity between Korean industries and the two studied countries industries. The topic of the third essay is also portfolio choice. However, it aims to improve upon previous empirical studies to avoid the ambiguity of the definition of risky assets by introducing ordered financial risk. This study concentrates on the effects of household characteristics on that household financial risk-related choices, using US household data. It finds some characteristics, such as marriage status and education, are more influential than economic variables, such as income and net worth. The predicted probabilities show that a household is unlikely to choose high financial risk unless it possesses more than one characteristic that has positive effects on the taking of high risk. Additionally, the effects of households expectations could change because of the global financial crisis. The results are robust in terms of model selection and the criteria established for ordering financial risk.

2 Copyright 2013 by Tsun-Feng Chiang All Rights Reserved

3 Three Essays on Financial Economics by Tsun-Feng Chiang A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Economics Raleigh, North Carolina 2013 APPROVED BY: Douglas Pearce Committee Chair Robert Clark Mark Walker Xiaoyong Zheng

4 DEDICATION To my parents and brother ii

5 BIOGRAPHY Tsun-Feng Chiang was born in a harbor city, Kaohsiung, in Taiwan. He went to the US for graduate education in He received his Master s degree in economics in 2009 at North Carolina State University. He then continued his pursuit of the Ph.D. in economics. iii

6 ACKNOWLEDGMENTS I thank my advisor Dr. Pearce for teaching me the importance of the economic implications behind models and empirical results. His patience is quite impressive. Thanks also to my other committee members, Dr. Clark, Dr. Walker and Dr. Zheng, for their suggestions about my dissertation and job seeking. I thank Dr. Leblebicioglu for her advice on the first chapter. I also would like to thank my parents and brother. Without their support, I would not have made it so far. iv

7 TABLE OF CONTENTS LIST OF TABLES... vii LIST OF FIGURES... viii CHAPTER 1 INCOME RISK, RETURN RISK AND PORTFOLIO CHOICE: AN EXAMPLE OF KOREA Introduction Evidence on the Effect of Income Risk on Consumer s Choice Income Process and Income Risk... 4 The measurement of Income Risk... 4 Data and Estimation Results The Life-Cycle Model The Calibration Results for Optimal Portfolio Choices Other Parameters Optimal Choices Optimal Choices under Borrowing Constraints Conclusion References CHAPTER 2 INTERNATIONAL PORTFOLIO DIVERSIFIACTION IN KOREA Introduction Mean-Variance Analysis Literature Review: International Portfolio Diversification Models of Hedging Demands for Income and Inflation Risks Methodology and Data Hedging demands and Optimal International Portfolio Home Bias Issue Conclusion References CHAPTER 3 FINANCIAL RISK AND CONSUMER CHARACTERSITICS Introduction Literature Review Household Portfolios and Financial Risk The Effects of Household Characteristics and on Financial Risk The SCF Data and Variables Household Financial Assets and Financial Risk Explanatory Variables Methodology Empirical Results Partial Proportional Odds by Logit Predicted Probabilities Conclusion References v

8 CHAPTER 4 FINANCIAL RISK AND CONSUMER CHARACTERSITICS References APPENDICES Appendix A Detailed Outlines of Estimated Income Risk A1. Pairs of Income Differences and d A2. Income Risks by Different Categories Appendix B Life-Cycle Model References Appendix C International Asset Pricing with Hedging Demands References Appendix D Estimated Results for Optimal International Diversification without Hedging Foreign Exchange Risk Appendix E Estimated Results of Ordered Logit Models References Appendix F Estimated Results of Multinomial Logit Models vi

9 LIST OF TABLES Table 1.1 Income Risks by Age Group... 8 Table 1.2 Household and Economy-Wide Parameters Table 1.3 Optimal Proportion of Investment in the Risky Asset Table 1.4 Shares of Risky Assets in Table 1.5 Optimal Proportion of Investment in the Risky Asset for Unconstrained and Constrained Table 2.1 Hedging Demands for Inflation and Industrial Wage Risk Table 2.2 Covariance Matrix of Wage Growth and Stock Returns Table 2.3 Optimal National and Industrial Portfolios Table 2.4 Distance between National and Industry Portfolios Table 2.5 Portfolio Holdings of Selected Countries (Unit: Million USD) Table 3.1 The Risk Orderings of Financial Assets Table 3.2 The Criteria for Ordinal Risk Exposure Table 3.3 Descriptive Statistics Table 3.4 Estimated Results of Partial Proportional Odds by Logit (2007) Table 3.5 Estimated Results of Partial Proportional Odds by Logit (2009) Table 3.6 Discrete Change in the Predicted Probability (Partial Proportional Odds by Logit) Table A1 Income Risks by Education and Industry Group Table A2 Income Risks by Age Group with and without Borrowing Constraints Table D1 Hedging Demands for Inflation and Industrial Wage Risk (Exchange Risk Unhedged) Table D2 Optimal National and Industrial Portfolios (Exchange Risk Unhedged) Table E1 Estimated Results of Ordered Logit for 2007 and Table F1 Estimated Results of Multinomial Logit (2007) Table F2 Estimated Results of Multinomial Logit (2009) Table F3 Discrete Change in the Predicted Probability (Multinomial Logit) vii

10 LIST OF FIGURES Figure 2.1 Efficient Frontier Figure 2.2 Wald Test for Industry-Pair Coefficients viii

11 INCOME RISK, RETURN RISK AND PORTFOLIO CHOICE: AN EXAMPLE OF KOREA 1.1 Introduction In a world without uncertainty, there is only one asset and one interest rate. A consumer allocates his wealth to either consumption or saving. But what will be the consumer s choice if the world is uncertain and there is more than one riskless asset? And the consumer has at least one more potential argument, the proportion of investment in the risky asset, in his resource constraint. When the returns of the risky asset are much larger than the riskless interest rate and income is certain, consumers would choose to invest more in the risky asset because of larger expected future returns. In the real world, however, both returns and income are changing and uninsurable. The existence of income uncertainty implies that consumers will want to secure future consumption by adopting a conservative portfolio choice, given the volatility of risky returns. This study considers how both types of risk affect a consumer s portfolio choices. Does he allocate more wealth in the risky asset because of higher returns? Or do income and return risks neutralize the effects of expected high returns and discourage his risky investment? Income risk reflects the unpredictability of a consumer s income growth that depends on not only the performance of the whole economy but also on his background characteristics. Hence, income risks vary from one consumer to another. By pooling consumers into groups with similar characteristics, one can estimate the average income risk for groups. In addition, the empirical literature indicates that income risks have permanent and transitory components. These will also be incorporated into this study. This study will analyze Korean data for two reasons. First, Korea is an economy with high and volatile income growth and asset returns. From 1997 to 2010, its annual real GDP per capita growth rate was about 3.6%, and the real return on stocks was about 11%. However, its instability is as noticeable as its growth and returns. The standard deviation of annual real GDP per capita and stock returns were 0.04 and 0.31, respectively, compared to 1

12 0.02 and 0.2 in the US, respectively. 1 Although GDP per capita is a different concept from labor income, the fluctuation suggests that labor income could also be volatile. Second, quality household panel data are available for Korea. The data requirement for estimating income risk is demanding. Besides income information, the estimation needs household and personal background data over a successive period of time. The Korean Labor & Income Panel Study (KLIPS) provides all household information needed for income risk estimation. Furthermore, the similarity of KLIPS to the US Panel Study of Income Dynamics (PSID) allows comparisons between the results of this study and empirical results for the US. The rest of this study is structured as follows. The next section briefly reviews the relationship between income risk and a consumer s choice. Section 3 summarizes the labor income process and presents the estimates for Korea. Section 4 summarizes the finite horizon model this study uses to calibrate the optimal choice. Section 5 explains the parameters other than income risk, especially the returns of riskless and risky assets, and presents the numerical solutions of portfolio allocations. The last section concludes. 1.2 Evidence on the Effect of Income Risk on Consumer s Choice This section reviews how important income uncertainty is and discusses its effect on a consumer s choices. Earlier literature focuses on income uncertainty s relationship with consumption and wealth accumulation. Hall and Mishkin (1982) divide income into permanent and transitory components and examine how they affect food consumption. They find that permanent income movement has stronger effects on consumption than transitory income movement. Income risk generates precautionary savings. While a consumer faces future income shocks, his savings or wealth accumulation will be larger than the optima under no uncertainty. Empirical studies by Carroll and Samwick (1997, 1998) estimate income shocks for different groups and confirm that wealth is increasing in the scale of income risk. 1 This study calculates these values based on databases from the Korea Exchange and World Bank and OECD 2

13 However, income risk affects not only the saving rate, but also the allocation of savings. Letendre and Smith (2001) randomly generate income and interest revenue based on income risk and return volatility to examine the effects of both types of risk on consumption and portfolio choice in an infinite horizon model. Their simulation results show that both risks affect the allocation in the risky asset negatively. Viceira (2001) uses a life cycle model in which a consumer is subject to income risk and the probabilities of retirement and death. The calibration results suggest a linear investment pattern. Young consumers should invest larger shares of savings in the risky asset and the shares should decrease with age. Different from previous studies which calculate the optimal portfolio choice by assigning estimated income and return risks, Angerer and Lam (2009) use the National Longitudinal Survey of Youth with detailed household financial asset holdings to examine the effect of income risks on the portfolio shares in risky assets. They find that permanent income risk negatively affects the shares in risky assets, but the effect of transitory risk is trivial. Maurer et al. (2010) discuss social security policy and income. Their finite horizon model allows holding multiple types of assets, riskless and risky. Their estimation results show that high labor income risk discourages the holdings of risky equities, older consumers tend to purchase annuities, and the holding of equities slightly decreases with low social security replacement rates, given the same level of income risk. The recent literature emphasizes the role the time horizon plays in portfolio choice. Given the level of income and return risks, calibrations based on finite horizon models with impatience always predict decreasing holdings of risky assets with age. The earlier literature, however, also indicated that income risk changes with age (or education, occupation, industry, etc.). The level of risk should be dependent on an economy s specific performance. Therefore, the pattern of portfolio choice could be economy specific. This study concentrates on the Korean economy and is a complement to literature studying this topic in the US. 3

14 1.3 Income Process and Income Risk The measurement of Income Risk The standard deviation of GDP per capita suggests that the Korean economy is volatile. To estimate the true level of income uncertainty and then its effect on portfolio choice, formal measures are needed. There are several income uncertainty measures, ranging from the complicated equivalent precautionary premium introduced by Kimball (1990) to simple estimates such as the variance of the log of income. This study adopts one of the most common measures in the literature. Assume the income process has the following form: lny i,t = g + lny i,t!1 +! t (1.1) where Y t is the current income for household i at time t; g is the predictable income growth and! t ~ N(0," 2 ). (To simplify the notation, the subscript i representing a household is suppressed hereafter.) The variance of the innovation,, captures the unpredictable income shocks. An alternative income process that distinguishes permanent and transitory shocks is proposed by Hall and Mishkin (1982) and generalized by Carroll and Samwick (1997). The household labor income follows a geometric process:! 2 lny t = lny p,t + lny n,t, (1.2) where Y p and Y n are permanent and transitory components, respectively. Assume that the evolution of permanent income has a form similar to (1.1): Y p,t lny p,t = g + lny p,t!1 +! p,t,! p,t ~ N(0," 2 p ) (1.3) 4

15 Following the setting in Letendre and Smith (2001), the transitory component has the following form: lny n,t =!! 2 n, (1.4) 2 +" n,t! n,t ~ N(0," 2 n ) To estimate the actual income volatility, the predictable part should be removed from the actual income data. Permanent income without the predictable component is denoted as. Therefore, (1.3) follows a random walk:!y p,t ln! Y p,t = ln! Y p,t!1 +! p,t (1.5) Assume! p,t and! n,t are white noise and uncorrelated over time. The variance of and 2 2! n,t in (1.3) and (1.4),! p and! n, measure the permanent and transitory income risks, respectively. In practice neither permanent income!y p,t nor! p,t are clearly observable. To get rid of!y p,t and keep! p,t and! n,t, define the d-year current income difference as:! p,t r d = ln Y! t+d! ln Y! t, (1.6) where ln Y! t = ln Y! p,t + lny n,t. Substitute (1.4) and (1.5) into (1.6) recursively to obtain an equation with only error terms: r d = (! p,t+1 +! p,t ! p,t+d )+! n,t+d!! n,t, (1.7) Take the variance on both sides and impose the uncorrelated assumption to obtain: 5

16 var(r d ) =! 2 p! d +! 2 n! 2, (1.8) where d is a vector with each element d as the time difference between two periods of adjusted income, t+s+d and t+s; 2 is a vector of 2s. 2 Since the true var(r d ) is unknown, we take the actual estimate represented by the following empirical model for each household: r 2 d =! 2 p! d +! 2 n! 2 +" d, (1.9) r d 2 where is var(r d ) plus a mean-zero disturbance. By estimating (1.9) with OLS, one can obtain the estimated income risks,! p,t and! n,t. It is possible for two transitory error terms in (1.7) to be serially correlated, i.e. var(! n,t+d!! n,t ) = 2 "" 2 n! cov(! n,t+d,! n,t ) and cov(" " ) # 0 n,t +d. Taking a longer lag period can, n,t alleviate this problem. 3! d Data and Estimation Results The database used to estimate Korean income risks is the Korean Labor & Income Panel Study (KLIPS). It contains data for 5000 households and members above age 15 belonging to these households in This study considers the sample of households with complete income and demographic information over the period 1998 to The household income measure consists of earned labor wage, social security income, social insurance, and transfer income. 4 Financial income is excluded, since it does not follow the assumed income processes like labor income. 2 Appendix A1 describes details about pairs of income differences and the formation of d. 3 MaCurdy (1982), however, shows if the lag period is larger than 3, the transitory income risk could not be detected. This study takes two cases d 1 and d 2 to prevent this problem. 4 Earned income is net of taxes. Income taxes are a cushion to the income volatility over time so the income shocks measured with after-tax income are closer to true risks for a household. 6

17 To remove the drift g in (1.3), Carroll and Samwick (1997) suggest regressing the logarithm of current income on age, occupation, education, industry, time trend, demographic variables (gender, household size etc.) and age-interaction terms of household heads. Actual income is then divided by its predicted value and adjusted for economy-wide income growth to obtain adjusted income,!y t. This study sets two criteria to drop observations that could distort the estimation of income risk. First, households with household heads over age 60 are dropped. Elder household heads are usually retired and rely heavily on social security payments, transfers and other members earned income. Therefore, their income is not often closely related to demographic characteristics. Second, samples with unusually large income risks, found with preliminary estimates of total income risks are considered as outliers and dropped. After filtering the household data by the criteria, the full sample size for this study is 1,868. Table 1.1 presents the resulting income risk for the full sample and each age group in Korea. 5 The first column shows the total income risks ( ); the other four columns show the permanent and transitory income risks for d 1 and d 2 cases. The values of income risks themselves do not reveal clear economic information. They would be more meaningful while being compared with income risks estimated in different economies and within groups in the same category. The first row comprises estimates for the whole economy. What sets this study apart from the previous literature is that the scales of income shocks are significantly larger. The average total shock is , which is larger than for the US households estimated by Carroll and Samwick (1997) using PSID data. Comparing age groups, the pattern is similar to what the previous literature finds in the US: the total income risk is increasing with age of investors. The risk is lower than the average level for younger consumers until they are in the age group and older. The uncertainty increases by a significant amount for the two oldest groups. This result might be because of the combination of easier job! 2 5 The income risks for education and industry groups are reported in Appendix A2. 7

18 Table 1.1 Income Risks by Age Group d 1 d 2 Age Group Sample Size Total Shock Permanent Shock Transitory Shock Permanent Shock Transitory Shock Full Sample and below [0.0355] [0.0305] [0.0305] [0.0331] [0.0326] [0.0433] [0.0511] [---] (0.0111) (0.0099) (0.0083) (0.0106) (0.0117) (0.0121) (0.0131) (0.0117) (0.0265) (0.0236) (0.0198) (0.0253) (0.0278) (0.0289) (0.0312) (0.0278) [0.0217] [0.0205] [0.0170] [0.0219] [0.0030] [0.0248] [0.0389] [---] [0.0440] [0.0418] [0.0441] [0.0422] [0.0168] [0.0404] [0.0320] [---] Notes: 1. The groups categorized by age are designated by the household heads ages in Values in parentheses are standard errors; values in brackets are the income shocks of the US households estimated by Carroll and Samwick (1997). Their estimations do not include the group of age substitutability for elders and developing social security. 6 The logic is that unemployed elders find it difficult to come back to the job market, and their lost income cannot be fully compensated by the social security system. Thus elders suffer higher income uncertainty. If we assume that the income process follows the geometric form, income risk would have permanent and transitory components whose estimates are reported in the second and third columns. For either the full sample or for each age group, transitory shocks contribute more to income uncertainty than permanent shocks do. The variance of permanent shocks is significantly larger for the age groups and The transitory uncertainty presents a different pattern from the total risks. People in the young groups experience large transitory 6 Older households generally have lower education levels. Table A1 in Appendix A.2 shows lower educated groups have larger income risks. Therefore, we predict the entrance barriers for the jobs that older households can do are also lower. 8

19 risk. The risk decreases with age until they are in the age group Then the transitory risk increases rapidly for the age group and older. The estimation of the d 2 case in the fourth and fifth columns is a robust test that examines whether the serial correlations between transitory error terms distort the results. The two pairs of values are not statistically different. Transitory shock dominates income uncertainty for every household group. Again we can compare both permanent and transitory risks with what they are in the US. The only similarity is that the transitory shock is larger than the permanent shock. In an economy with high growth, like Korea, the increasing income will contribute to larger income risk. But since the time trend was removed from the income process, the idiosyncratic income risk should not be affected by expected economic growth. This study attributes the high transitory risk to a transition toward an innovation-intensive economy during the time covered by the study. There would be an inevitable labor mismatch during the process of transition for older age workers with outdated skills. They could take more time to find replacement jobs in their skill set. 1.4 The Life-Cycle Model In financial economic models, consumers possess both risk-free and risky assets. Risky assets have higher expected returns, which are volatile. Consumers choose not just consumption and savings, but consumption and portfolio allocations. An earlier model that incorporates the risky asset into a consumer s choice is that of Samuelson (1969) and Merton (1969). In their infinite horizon model, a consumer s optimal proportion of riskless (or risky) assets is a constant, not affected by age. In the real world, consumers have finite lifetimes and want to consume large parts or all of their wealth before they die. Dynamic life-cycle models developed by Viceira (2001), Cocco et al. (2005), Maurer et al. (2010) and others incorporate the fact of aging into models designed to find aging s impact on consumers economic behaviors. Different from other models, whose numerical solutions depend heavily on simulations, Viceira s model provides more concrete results and the possibility of international comparisons. Furthermore, in addition to 9

20 considering probabilities of employment and death after retirement for the finite horizon setting, the model allows the income process and interest rates to be stochastic. The following section summarizes Viceira s work and explains the iteration method for approaching numerical optima. 7 A representative consumer is either in the employment or retirement state. The transfer from the employment to the retirement state is irreversible. The consumer has the probability of being in the employment state π e or the probability of being in retirement, π r. After retirement, he has no income and faces the probability of death π d. At time t, he allocates α t percent of his savings to risky assets and (1- α t ) percent to riskless assets. The gross interest rate R p,t+1 at time t+1 is a weighted average of the riskless return R f and risky return R t+1 : s R p,t+1 =! t s (R t+1! R f )+ R f, (1.10) where s=e, r denotes the employment and the retirement state, respectively. R f is a constant; the ratio of R t+1 to R f follows the lognormal distribution with mean excess return and volatility of the risky asset of µ and! u 2, respectively: R t+1 / R f ~ LN(µ,! 2 u ), µ > 0. (1.11) A representative consumer in the employment state at time t distributes his total income from earned income Y t+1 and interest revenue of financial wealth W t accumulated at time t-1 to consumption C t and W t+1. We can log-linearize the intertemporal budget constraint and then take the first-order Taylor expansion around E[log(W e t /Y t )] and E[log(C e t /Y t )] to obtain the linear form: e w t+1! y t+1 " k e +! e w (w e t! y t )!! e c (c e e t! y t )! #y t+1 + r p,t+1, (1.12) 7 Appendix B will show the detailed outline of the model derivation. 10

21 ! w e! c e where and are log-linearization constants dependent on exponentiated E[log(W t e /Y t )] and E[log(C e t /Y t )] only; k e e e is also a constant dependent on! w and! c ; other lowercase letters, w t, y t, and r p,t, represent the corresponding logarithmic variables. Assuming CRRA utility with time discount rate β and relative risk aversion parameter, γ, the combination of (1.12) and log-linearized Euler equations leads to the solutions of optimal consumption and portfolio choice in the retirement state: c r t = b r 0 + b r r 1 w t, (1.13)! r = µ +" 2 u / 2 2 #b 1r " u, (1.14) where b 1 r =1 and ". 0( " b r 1 0 = log 1! exp!! b % r $ /* $ 1 # 10 )# & r 'E[r p,t+1 ]+ 1! log"r + 1 2! (1! b r + 2 1!) 2 r 0% Var(r p,t+1 )-3, ' 40 & (1.15) The discount factor! r = (1! " d )! captures the idea that the consumer becomes more impatient while facing the probability of death after retirement. Since the consumer does not have earned income, the optima are not affected by the randomness of the income process. Optimal consumption c t r in (1.13) is a linear function of wealth. The excess return of the risky asset µ and the interest rate risk shift optimal consumption through. The optimal portfolio choice α r in (1.14) is increasing in µ and decreasing in.! u 2 In the employment state, the consumer s optimal consumption to income ratio and portfolio choice are:! u 2 b o r 11

22 c e t! y t = b e 0 + b e 1 (w e t! y t ), (1.16)! e = µ +" 2 u / 2! $ e (1! b 1 2 #b 1 " u b 1 e ) " " %"u " u 2, (1.17) where b 1 =! e b 1 e + (1!! e )b 1 r (1.18) and b e 1 )" 1 0 =! (1!! e )+ " e c b 1 #! b % + $ 1 *# & e 'E[r p,t+1 ]+ 1 (! s log$ s +! # s=e,r! 1 2! V e!! e (1! b e 1 )g! (1!! e )b r 0! k e" # $, (1.19) b 0 r b 0 e inside the equation of above shows that the optima in the employment state cannot be solved without solving the optima in the retirement state. The second term on the right-hand in (1.17) is the hedging demand for the risky asset. Its sign depends on the covariance between innovations in the log income, u t+1, where,! t+1 and unexpected log returns on the risky asset, Cov t (u t+1,! t+1 ) = " #!u, (1.20) If the change in labor income is positively correlated with the returns on the risky asset, the consumer will invest less in the risky asset to avoid possible consumption fluctuations, i.e. 12

23 the hedging demand for the risky asset is negative. 8 in of (1.16) is a term consisting of! u 2 return risk,, income risk, and covariance between innovations of the income process and unexpected returns,.! "!u! 2 It might not be obvious how income risk affects portfolio choice in the employment state. V e b 0 r Given the budget constraint, (1.12) and b 0 r, (1.16) and (1.17) are an equation system. The income risk in choice. V e that appears directly in (1.16) will affect (1.17) and then the portfolio With all parameters needed,! r r and b 0 can be seem as constants and calculated immediately. To solve the optimal choice for employment, one has to apply an iteration e e method. We can give initial values for! w and! c (or E[w e t! y t )] and E[c e t! y t )], equivalently) and substitute into (1.16). One can then solve (1.16) and (1.17) for and! e e (or b 0 which is a function of and! e ) simultaneously. This reveals the clear linear relation between w e t! y t and c e t! y t in (1.16). We then update w e t! y t and c e t! y t through (1.12) and (1.16), which determines a new set of and. Repeat the process until and! c e b 0 e converge to steady state for and. b 1 e b 1 e! e! w e! c e b 1 e! w e 1.5 The Calibration Results for Optimal Portfolio Choices Other Parameters To find the optimal portfolio choice with the life cycle model, one needs more information about parameters. This section discusses the parameters other than income risks used to calculate numerical solutions. Assume the financial market is complete, i.e. all households have full information for market returns. Without considering capital taxes and 8 Although the hedging demand can be negative, the share of the risky asset is always positive in this model. The representative consumer cannot short the risky asset. 13

24 any costs associated with asset trading, every household faces the same real asset returns. 9 This study uses the average annual interest rates on certificates of deposit provided by the OECD database as the return on the riskless asset; the return of the risky asset is the annualized monthly Korea Stock Price Index (KOSPI) which is adjusted for splits and dividends. During the period of 1998 to 2010, the average excess return on the risky asset was around 7.2%; the standard deviation of the unexpected excess return was These two values were 6% and 0.18 for the US, respectively. 10 The age-specific parameter is the predictable income growth rate g, which can be derived from the income process given the estimated income risk and the expected income growth rate. From the same set of household data used to estimate income risk, this study obtains the average income growth rate for each age group. The results show that young households enjoy higher average income growth rates; after age 50, the growth rates decline significantly. The signs and scales of hedging demands are dependent on the correlations between income shocks and returns on the risky asset. Again, using household income data, excluding outliers, and the KOSPI index, we obtain the coefficients of correlation during the period 1998 to The values might be imprecise due to the short period of time, but the signs shed some light on how income and returns co-move. Overall, the co-movement is , a weakly positive correlation. It implies that people in Korea should hold less risky assets to hedge their income risk. What is unusual is that the correlations for the youngest age group and for are negative. We believe this is because of sample selection in which some unobservable household characteristics affect income such that it moves inversely with capital returns Real asset returns are various to each household. Given the financial markets, households with easier access have higher real returns than others. Bertaut (1998) finds education levels, for example, determines information cost and households participation in financial markets. 10 The values based on the long historical data are from Mehra and Prescott (1985). 11 Davis and Willen (2000) find there is a stronger relationship between the income risk of an industry group and returns on its associated industry portfolio. Their finding hints that correlations between stocks returns and income growth of industry groups might be more meaningful than the correlations between stocks returns and income growth of age groups. Since this study concentrates on the income risk and its level in different age group, we do not extend our discussion to industry groups and their income risk. 14

25 Other values of parameters left undetermined are probabilities of being employed until retirement,! e and the death rate after retirement! d, the coefficient of relative risk aversion γ, and the time discount rate β. Unlike most parameters that are estimated from data, this study assigns these values based on reasonable assumptions. Assume on average consumers retire at age 65, and die at age 75. A consumer in the age group of 30 or below, for example, is expected to work for 35 years until retirement. We represent this in the equation (1!! e )!1 = 35 or! e = 34 / 35. A consumer in the group between 31 and 35 is expected to have the probability 29/30 to be in the employment state, so on and so forth. In the same manner, the death rate after retirement,! d, is set to 1/10 for each age group. For comparison with calibrations in the US, γ and β are set as 5 and 1/ (1+ 0.1), respectively. 12 By giving the same values for these two subjective parameters, this study can focus on how income and return risks affect asset allocation. Table 1.2 summarizes the values of parameters. Optimal Choices Employing parameters estimated in this section and income risk estimated in Section 3 to establish the finite horizon model, the convergence of wealth to income and consumption to income ratios would lead to the numerical solutions of the optimal portfolio choice. Table 1.3 reports the calibration results under different settings. The first part assumes that the income process is idiosyncratic, i.e. the correlation between income growth and returns of the risky asset is zero. The first column is a replication of Viceira (2001) s calibration, applying the average total shock to each age group. As the model implies, allocation to the risky asset decreases as consumer age increases; however, allocation to the risky asset in Korea is less than one-half that for the US for each age group. The high excess risky returns and income growth rates should promote an increase in the risky asset share, but the numerical solutions show that the negative effects of income risk and interest rate volatility dominate. When 12 This study estimates γ and β with quarterly aggregate consumption data and three sets of instrumental variables. The set of instrument that give estimates satisfy theory are the constant, stock returns and lag consumption growth. The GMM estimates are γ= and β= However, the estimation is based on infinite horizon model so this study chooses arbitrary values used in Viceira (2001) closer to our estimates. 15

26 Table 1.2 Household and Economy-Wide Parameters Parameter E t (Y t+1 /Y t ) Full Sample 30 and Below Household (Age Group) Corr(r t+1,!y t+1 )! e /35 29/30 24/25 19/20 14/15 9/10 4/5 E t (R t+1 / R f ) 2! µ! d Economy-Wide [1.06] [0.0324] 1/10 γ 5 β 1/(1+0.1) Note: Specific values of economy-wide parameters for the US are in square brackets. facing larger risk that leads to unpredictable future income and returns, a risk-averse consumer s investment must be more conservative. The empirical literature shows that different groups are subject to different income risks, and that the differences could be large enough to give different results for portfolio choices. The second column reports the numerical solutions for each age group with specific total income risk. Although the values are not monotonically decreasing as age increases, they follow a pattern similar to the present study s values when the average risk is used. A consumer at a younger age should invest more in the risky asset than when he is older. The proportions increase by around 10 percentage points for age groups 35 and below; they do not change much for other age groups. Overall, the allocation of savings in the risky asset is still conservative. If the income process is geometric, then income risks have permanent and transitory components. Values in the third column are optimal proportions for age groups subject to both risks reported in Table 1.1. In this case, the optimal choices form an inverse U curve. The younger groups do not possess the largest proportions of the risky asset. The proportion increases slightly with age and then decreases after age 45. The effects of transitory risk on 16

27 Table 1.3 Optimal Proportion of Investment in the Risky Asset Age Group (I) (II) (III) (IV) (V) (VI) and Below [76.29] (-22.11) (3.88) (9.54) Retired [71.23] [66.02] [60.63] [54.97] [48.92] [42.25] [35.97] corr(r t +1,"y t +1 ) = 0 corr(r t +1,"y t +1 ) # (-22.64) (-12.71) (-9.38) (-6.94) (-3.01) (-0.36) (-31.58) (-3.64) (21.49) (-9.13) (-1.02) (-0.49) 3.92 (-22.58) (-3.42) (19.58) (-7.90) (-0.90) (-1.05) Note: 1. Values are given in percentages. Values in square brackets are the calibration for the US data extracted from Viceira (2001); Values in parentheses are hedging demands. Positive (Negative) correlations lead to negative (positive) hedging demands of the risky asset. 2. (I) the average total income shock; (II) group-specific total income shock; (III) group-specific permanent/transitory shocks; (IV) the average correlation coefficient and group-specific total income shocks; (V) group-specific correlation coefficients and total income shocks; (VI) group-specific correlation coefficients and permanent/transitory shocks. the allocation in the risky asset are larger than for permanent risk. The negative effect of transitory risk on the predictable income growth and the investment in the risky asset is larger than for permanent risk. 13 Age groups and 41-45, who only suffer from permanent risk, have larger proportions of the risky asset than the younger groups suffering the transitory risk. The second part of the model allows returns of the risky asset and income to be correlated. From the fourth to the last column are the optimal portfolios under different 13 From the geometric income process, equations (1.2) and (1.3), by the lognormal properties the relationship between income risks and the growth can be written as the following equation, E t [Y t+1 /Y t ] = exp[g + 0.5(! 2 p + 2! 2 n )] It implies one unit of transitory risk contributes to the unexpected income growth twice as much as one unit of permanent risk. 17

28 assumptions. In the fourth column we assume that the correlation between income growth and risky returns for each age group is equal. The optimal holdings of the risky asset and hedging demands decline with age. Now the two youngest groups should hold 22 to 23 percent of the risky asset of their wealth in the risky asset; other age groups should hold less than one fifth in the risky asset. The last two columns allow the correlations to change as age group changes. The magnitude of the effect of correlations depends on the assumptions of the income processes. When considering only total income risks, the fifth column shows that age groups and are the two that should have aggressive hedging demands. The former group hedges against the positive correlation by holding only 16 percent in risky assets, but the latter one should hold 50 percent in the risky asset because for the coefficient is negative and large. Similar to optimal portfolios without hedging components for the two oldest groups, their portfolios do not change much. The effect of correlations on hedging demands and portfolios are negligible. For other groups, the hedging demands are relatively moderate. The last column shows the optimal portfolios and hedging demands subject to permanent and transitory income risk. Comparing it with the fifth column, it seems that the change from the standard to the geometric income process does not matter. Values for each age group are close except for the youngest two groups. Age group 30 and below now should hold 35 percent in risky assets, 8 percent larger than it holds in the fifth column. And people in age group should hold less than 4 percent in risky assets. The calibration results reveal that both income and return risks dominate high income growth and capital return in determining the optimal portfolio choice in Korea. Under different assumptions of income processes and correlations between income growth and returns, some age groups should invest more than 40 percent in the risky asset. Other than that, on average the investment strategy should be conservative. It might be productive to compare the optimal choices and real portfolios. Table 1.4 reports the households shares of risky assets to financial assets for each group in The data of risky assets include stocks, bonds and trusts undividable. The data show that only a few households buy risky assets. The participation rates for age groups 31 to 45 are between 18

29 Table 1.4 Shares of Risky Assets in 2007 Sample Size Financial Market Participation (%) Share of Risky Assets to Financial Assets (%) Age Group (I) (II) 30 and Below Data Resource: KLIPS wave10. Note: 1. Financial assets include (i) savings in banks, (ii) stocks, bonds, and trusts, (iii) saving-type insurance, (iv) savings in private mutual saving club, and (v) personally made loans. 2. (I) are shares of risky assets to total financial assets without excluding outliers whose shares of risky assets are 100 percent; (II) are shares without outliers. 13 percent and 16 percent, and lower than 10 percent for other age groups. The shares of risky assets for market participants are 54 percent for the age group 46-50, and from 40 percent to 45 percent for other groups. When outliers are excluded, the shares decline by 5 to 10 percent for each age group. The shares are quite stable, unlike the optimal portfolios where the youngest and oldest groups have relatively lower shares but the middle-age groups have relatively larger shares. Instead, in the data, older groups have larger shares invested in risky assets than younger groups. Only the shares for the two youngest groups are close to the optimal shares under the assumption of total income risks. Although we find no evidence that the real portfolios follow what the model predicts for optimal portfolios, the small sample size of market participants and the crude survey of financial assets are insufficient to make a decisive conclusion. Optimal Choices under Borrowing Constraints The last section shows that representative consumers in different age groups have different portfolio strategies. In practice, a household s wealth distribution could depend on how wealthy it is. Dynan et al. (2004) confirm that rich and poor people have distinct saving 19

30 patterns. Guo (2001) finds stocks and other risky assets are concentrated in a few rich households in the US. He attributes this to initial wealth inequality. In his overlapping generation model, poor people with lower bequests are subject to higher borrowing interest rates (or lower returns in the risky asset) and fixed entry costs so they choose not to hold any stock. Households with borrowing constraints face borrowing interest rates higher than returns of the riskless asset. The incentive for a poor household to purchase equities by borrowing is that the expected net returns are large enough. From Korean data, the real net gains between stock returns and borrowing interest rates from 1998 to 2001 are close to the riskless interest rate. Due to the high volatility of stock returns, the potential gains of borrowing to buy stocks can be large. It then seems useful to compare the optimal portfolio choices for unconstrained and constrained households. We now consider two additional datasets: borrowing interest rates and the standard of borrowing constraints. The former data are from the World Bank. To determine which households are borrowing constrained, this study uses the values of net financial assets as a criterion. Households with zero or negative financial assets are considered borrowing constrained because they have to borrow to invest. 14 Under this criterion, around one half of households are borrowing constrained. Again, this study allows income risk (shown in Table A2 of Appendix A) and growth to vary across unconstrained and constrained age groups. The criteria used in Section 3.2 for dropping outliers are kept here. Table 1.5 reports the calibration results for both unconstrained and constrained households. The optimal choices under borrowing constraints are very different from those in Table 1.3. First, for most unconstrained groups the proportions of the risky investment increase. Especially for those who are 35 and younger, the proportions are over one half in the case with permanent and transitory shocks. The increase is not so large for older groups, however. Second, for constrained groups, the optimal proportions are much smaller than they are for unconstrained households. None of the proportions for each age group is larger than 14 Real estate is not considered a financial asset due to its low liquidity. A household owning several housing units could be borrowing constrained if it does not have net liquid assets. Therefore, a household with borrowing constraints is not necessarily poor. 20

31 Table 1.5 Optimal Proportion of Investment in the Risky Asset for Unconstrained and Constrained Unconstrained Constrained Age Group (I) (II) (I) (II) 30 and Below Note: 1. Values are given in percentage. 2. In both (I) and (II) income shocks are group-specific. (I) considers total shocks only; (II) considers both permanent and transitory shocks. 10 percent. This reconfirms the assertion of previous studies; i.e., the resource constraints do substantially affect households investment choices. The calibration results suggesting that constrained households hold almost no risky assets are not surprising. All factors considered in this life-cycle model are adverse to constrained households. Although the expected net return is larger than the riskless return, constrained households are still exposed to the same return risk as unconstrained households are. Furthermore, higher income risk for most age groups deters risky investment further. On the other hand, income risk is relatively moderate for unconstrained households and hence the younger households invest more in risky assets. 1.6 Conclusion Allowing income risk to vary across different age groups, this study finds that income risk is larger for older groups and moderate for younger groups in Korea. But overall, household income is more volatile in Korea compared with the US. The decompositions of 21

32 income risk show that people are subject to transitory income shocks rather than permanent income shocks, except for those belonging to age groups and Accompanied with the high risk of stock returns, high income risk dominates the effect of highly risky returns on the portfolio choices. The numerical calibrations reveal that consumers should invest less than half of savings in the risky asset. In addition, the pattern of optimal allocation is not linear. Consumers slightly increase their shares of the risky asset until age 40, and decrease the shares to less than 20 percent after age 51. When hedging demands are taken into consideration, the shares of the risky asset decrease for most age groups due to moderate positive correlations between the growth of income and risky returns. For consumers in age groups and 41-45, the effects of correlations are significantly larger. The former should aggressively decrease their risky asset holdings; the latter, however, are suggested to hold many more risky assets. The findings of positive effects of hedging demands for the risky asset are not definite and need to be confirmed by further studies. With its high growth rate and returns, Korea is an example of a highly volatile economy that makes people conservative. While the discussion of the development of Asian financial markets often centers on openness and regulation alleviation, income and return risks are fundamental determinants of financial participation, at least domestically. Their effects on the introduction of diverse financial assets will be a topic worth further study. Also, the calibrations for the effect of borrowing constraints indicates that a substantial proportion of households can only partially participate in the financial market because of high risks and low expected net returns. These findings confirm a universal phenomenon in the world: most financial assets and the potential to make those assets grow are in the hands of richer households. References Angerer, X., Lam, P.-S., Income risk and portfolio choice: an empirical study. Journal of Finance 64,

33 Bertaut, C., Stockholding behavior of US householders: evidence from the Survey of Consumer Finances. The Review of Economics and Statistics 80, Carroll, C., Samwick A., The nature of precautionary wealth. Journal of Monetary Economics 40, Carroll, C., Samwick A., How important is precautionary saving? Review of Economics and Statistics 80, Cocco, J., Gomes, F., Maenhout, P., Consumption and portfolio choice over the life cycle. Review of Financial Studies 18, Davis, S., Willen, P., Occupation-level income shocks and asset returns: their covariance and implications for portfolio choice. CRSP Working Paper No Dynan, K., Skinner, J., Zeldes, S., Do the rich save more? Journal of Political Economy 112, Guo, H., A simple model of limited stock market participation. The Federal Reserve Bank of St. Louis Review 83, Hall, R., Mishkin, F., The sensitivity of consumption to transitory income: estimates from panel data on households. Econometrica 50, Kimball, M., Precautionary saving in the small and in the large. Econometrica 58, Letendre, M.-A., Smith, G., Precautionary saving and portfolio allocation: DP by GMM. Journal of Monetary Economics 48, MaCurdy, T., The use of time series processes to model the error structure of earnings in longitudinal data analysis. Journal of Econometrics 18, Maurer, R., Mitchell, O., Rogalla, R., The effect of uncertain labor income and social security on life-cycle portfolios. NBER working paper Mehra, R., Prescott, E., The equity premium: a puzzle. Journal of Monetary Economics 15, Merton, R., Lifetime portfolio selection under uncertainty: the continuous time case. Review of Economics and Statistics 51,

34 Samuelson, P., Lifetime portfolio selection by dynamic stochastic programming. Review of Economics and Statistics 51, Viceira, L., Optimal portfolio choice for long-horizon investors with nontradable labor income. Journal of Finance 56,

35 CHAPTER 2 INTERNATIONAL PORTFOLIO DIVERSIFIACTION IN KOREA 2.1 Introduction In the last chapter, calibration results indicate that high labor income and return risks dominate high household income growth and excessive returns between domestic stocks and riskless savings in determining the optimal portfolio in Korea. A representative consumer should have a larger proportion of riskless assets and a smaller proportion of stocks. 15 For households with liquidity constraints, the optimal share of the risky asset is negligible. When the correlation between income and capital returns is taken into account, consumers will have hedging demands. Due to very different values of the correlation between income growth rates and returns on equities, hedging demands fluctuate across age groups, and so do the holdings of the risky asset. Merton (1971) pointed out that optimal portfolios should hedge income risk. This study continues to probe the hedging demands in Korea for its higher income risk, but from the international perspective. Viceira (2001) s model that our last study applies assumes that investment opportunity is confined to the domestic financial market. A representative investor either purchases domestic equities or domestic riskless assets. It assumes that the shift between domestic stocks and riskless assets is enough to fulfill the hedging demands due to income risk. For some economies with restrictive financial access, the assumption of a closed financial market is not inappropriate. However, international financial markets are becoming integrated and accessible such that investment options are increasing. If purchasing foreign equities can hedge country-specific and individual-specific risks, why should an investor stay only in the domestic market? One might be curious to know what the optimal international portfolio would look like. 15 Comparing optimal and real portfolios, for a few households who directly hold stocks have shares larger than the optimal shares. Overall, the real shares of the risky asset are smaller than the optimal shares. 25

36 Additionally, the household level and aggregated data have different properties. One example is the correlation of income and asset returns. The 10-year-long household annual data employed in the last study are rich enough for estimating individual income risk, but may not be enough to obtain precise estimates of the correlations between risky returns and household income growth. For some age groups, the correlation is negative, and people belonging to these groups should increase shares of risky assets. It is possible that the counterintuitive sign is the result of the study s data choice. 16 It is also possible, as Baxter and Jermann (1997) find, that there is no clear evidence that income growth and domestic risky returns are related. Furthermore, they claim that domestic marketable assets alone cannot be used to perfectly hedge labor income risk. To have more convincing estimations of hedging demands, more observations are needed. Based on these questions, this study will estimate the hedging demands and optimal portfolio choices in the international context. When the equity choices extend to international financial markets, the optimal portfolio depends not only on domestic risk, but also returns specific to destination countries. The previous chapter allows the household level income risk to vary with age; this study, however, discusses income risk based on the aggregate industrial wage and examines the following question: how does a country like Korea, with high-income risk, achieve risk hedging through international financial markets? A new risk, domestic inflation rates, will be added for the representative investor s consideration for hedging. Among OECD developed countries, Korea had comparatively higher inflation rates in the years under study. 17 Incorporating inflation rates that eroded returns on domestic equities in estimating optimal hedging portfolios is more meaningful for Korea. The well-diversified portfolios hedging both income and inflation risks might not be reasonable for individual investors. However, its application in the management of pension funds or retirement 16 For some cases, using micro- and macro-data could lead to very different results. One of the most noticeable examples is the estimation of risk aversion. Under the CRRA utility function, coefficients of risk aversion are small (e.g. Dynan (1993)) or even negative for household data, but positive and large for aggregate data (e.g. Engsted and Møller (2010)). Similarly, the aggregated shares of capital and labor are always positively correlated. 17 The reference data are from OECD Statistics Database. Let 2005 be the base year and CPI be 100, in 2011 the CPI in Korea is ; the average CPI in OECD countries is given that some countries, like Iceland and Turkey, encountered unusual financial crises and high inflation. 26

37 accounts for financial agents is informative. Additionally, since 2003 the controls on overseas investment were largely relaxed so that hedging domestic risk through international financial markets became more feasible. 18 This study will follow the previous asset pricing literature to examine how an investor in Korea exposed to changing industrial income and inflation might hedge his risk by diversifying investments across major financial markets in the world. It will also compare the difference between actual portfolios and the optimal portfolio choices. This study is organized as follows: Section 2 applies the traditional mean-variance analysis to an international context; Section 3 reviews the literature; Section 4 and 5 describe the models and data; Section 6 shows the estimation results for optimal international portfolios; Section 7 discusses home bias and the application of the optimal hedging portfolios; Section 8 concludes. 2.2 Mean-Variance Analysis Within a financial market, an investor can choose from among a bunch of financial assets: stocks, bonds, certificates of deposit, etc. Mean-variance analysis is a traditional method in finance to describe the tradeoff between returns and risk for different asset combinations. This section applies the same approach to international portfolio choices. 19 Given the rates of return and the covariance of returns between stock markets, one can calculate the expected return and risk (or the variance of the return) associated with each portfolio choice. 20 Given a total return rate as a constraint, the efficient portfolio is the one that minimizes the risk. Figure 2.1 shows efficient portfolios and efficient frontier for eight 18 Refer to Chapter 2, OECD (2007) for Korea s liberalization of overseas portfolio investments. There are two important policies expected to have large positive effects on international portfolio investment: first, in 2006 the restrictions on the range of foreign securities have been removed. Second, investments in foreign equities through domestic companies are exempted from the tax on capital gains. 19 In the earlier literature, Grubel (1968) and Levy and Sarnat (1970) for example, also use this method to analyze the potential gains from international diversification. 20 All stock returns and risk are calculated from selected countries stock price indices that have been adjusted by exchange rates to the won, the unit of Korean currency to reflect the viewpoint of a Korean investor. Levy and Sarnat (1970) also adopt the same approach. 27

38 Figure 2.1 Efficient Frontier Data Source: Datastream Equity Index. Note: The efficient frontier is the curve created by spline interpolation that connects all efficient portfolios. selected stock markets from January 2002 to December 2007 (see Section 4: Methodology and Data for details). An investor holding any portfolio with return and risk not on the frontier can gain potential welfare by changing his portfolio to move to an efficient point on the frontier. The optimal point depends on his risk aversion. The efficient portfolio in an upper-right point of the frontier is exactly Korean stock only. It implies that holding only Korean stocks would efficient if the investor is just the type with low risk aversion since Korean stocks are relatively risky during this period of time. This traditional approach does not show how an investor subject to any risk other than return risk should manage their investments. For example, if an investor can predict the covariance of his income and stock markets returns, he will have a better strategy by which to allocate his wealth than the efficient portfolios. Optimal portfolio theory can fill this gap. It says an investor can still benefit from risk hedging or sharing by diversifying his portfolios no matter what level his risk aversion is. The hedging equities in the portfolios would be either within 28

39 the country or across countries. To serve the research purpose of this study discussing international diversification, the next section reviews influential international asset pricing and cross-country models. 2.3 Literature Review: International Portfolio Diversification Either for consumer markets or less expensive productive factors, a firm invests in foreign countries to maximize its expected profit; an individual purchases foreign equities for utility maximization. The major difference between both kinds of agents is their risk-taking behaviors. A firm can withstand high risk or negative profits over a short period of time if it expects that future profits are promising, but an individual consumer always needs positive consumption. Shocks that reduce and increase consumption radically over the individual s lifetime generally reduce utility. Living over a long horizon implies that an individual cares more about smoothed consumption than asset returns. The presence of international financial markets weakens the relationship of domestic shocks and consumption and so provides an opportunity for smoothing consumption and gaining higher expected utility. The most basic model to support the logic of international equity investment is standard Arrow-Debreu securities, or claims contingent to any future state in complete international financial markets. By diversifying portfolios internationally, a consumer s future consumption is subject to the smaller systematic global uncertainty, instead of both country-specific and global uncertainties. Lucas (1982) provides good intuition about this concept. His one-good endowment and two-countries model says the optimal portfolio for both countries is half domestic and half foreign securities. Open economy models do not guarantee a consumer s lifetime utility will be larger than it is in autarky (that the consumer in an open economy has higher utility is generally true in a deterministic finite horizon model), but consumption distributed evenly across each period is insured. The gains from international diversification 29

40 are general even if the trading assets are equities that claim a proportion of a country s future output. 21 Since consumers derive potential gains by diversifying their portfolios, what is their optimal combination of world equities (given all output is capitalized and can be traded in the form of equities)? One of the most familiar optimal portfolios is derived from the international capital asset pricing model (ICAPM). The model indicates that in a frictionless world a consumer in every country should hold a portfolio in which the share of country i s equities is its share of capitalization; e.g. if the shares of capitalization in the US and UK are about 40 and 10 percent respectively, then a consumer should hold 40 and 10 percent of his wealth in the US and UK equities respectively, so on. Since the ICAPM, many studies relax the assumption of a frictionless world and introduce different types of risk to explain a consumer s diversification motives. In the same stock market, Adler and Dumas (1983) add the inflation rate in the ICAPM and derive the portfolio choice in the presence of inflation risk. They conclude that when an investor has some risk tolerance (the value is between 1 and 0), his optimal portfolio is a combination of two funds: a universal fund independent of inflation risk, and a personalized fund for hedging inflation risk. The weights of the two funds depend on his risk tolerance or risk aversion. (Before Adler and Dumas, ICAPM derived by Solnik (1974) and Sercu (1980), who consider the effects of real exchange rates, indicates that every investor should hold a portfolio consisting of a universal internationallydiversified fund and his home riskless bond, assuming home inflation is zero. The weights of two funds are also determined by the investor s risk tolerance). Furthermore, Coën (2001) adds the wage risk when deriving the consumer s decision rule to explain how income change could affect the diversification. Fuggaza et al. (2011) found consumers in Italy with smaller volatility of wages across industries and time have lower hedging demands for foreign equities; consumers in the US and Canada with the larger volatility of wages, instead, need to diversify portfolios more aggressively. Previous works have asserted that risk- 21 Not only for the utility gains, international trading of securities and equities are equivalent in terms of equilibrium asset prices and interest rates. Some restrictions such as identical preferences and risk aversion apply, however. See Obsfeld and Rogoff (1996, Ch.5) for details. 30

41 hedging motives matter, so this study will follow their viewpoint to examine the impact of inflation and wages risk on consumers optimal portfolios. Because international portfolio diversification is much closer to the individuals problem, Henry (2007) indicates that using household instead of aggregate data in empirical studies is more convincing. Despite his useful suggestion, data availability is always a barrier for empirical studies so that the literature focuses on theoretical frameworks and employing aggregate data to estimate optimal international allocations. 22 Almost all theoretical frameworks support the benefits of international diversification in hedging future uncertainty and smoothing consumption. However, actual data show that few investors diversify their investments internationally across markets. The investors bias toward their domestic equities is an important issue unavoidable in the studies of international portfolio diversification. 23 This study leaves the issue of home bias to Section 6, after the estimation of optimal portfolios. 2.4 Models of Hedging Demands for Income and Inflation Risks Research has extensively discussed models of international diversification. Even so, models that can be used for estimation and calibration with cross-country panel data are still uncommon. To overcome the data problems and satisfy the research purpose, this study will apply international asset pricing models developed by Adler and Dumas (1983), Coën (2001) and Fugazza et al. (2011), which have minimum data requirements, to estimate the optimal portfolio diversification. 24 In the model to be used here, there are N markets (countries), each market issues one stock, and there is one nominally riskless asset with constant return r. For any market i, Adler and Dumas (1983) assume that the change of its consumption price (the inflation rates) and 22 Becker and Hoffmann (2010) can be considered an exception. Their samples are still within the border of one country, but they divide it into regions and treat them as different countries. They use the holdings of mutual funds as a proxy of diversification scale and confirm the benefit from regional diversification. 23 Domestic equities could include equities issued by foreign firms. This study neglects the share of the foreign part due to its small share compared with the domestic part. 24 This part shows derivation results only. See Appendix C for details. 31

42 the change of its stock price index (the returns) follow stationary Ito processes (Brownian motions). Define ω i as the vector of covariances between market i s inflation rate and the returns on N stocks, in market i the representative consumer s optimal portfolio x i is: x i = 1!!"1 (µ " r1)+ 1 1"!!"1 " i (2.1) where α is the coefficient of relative risk aversion; µ is a vector of instantaneous expected returns on stocks across all markets; 1 is the vector of ones and Ω is the covariance matrix of stock returns across all markets. This equation says the optimal portfolio is a weighted average of two components on the right-hand side. First, the component general to all markets is the expected excess returns (µ r 1) between stocks and the riskless asset; second, the component specific to the market i is the hedging demands of inflation risk. Coën (2001) incorporates income risk into the model. He neglects idiosyncratic risk by assuming that income risk is country-specific. Fugazza et al. (2011) extend Coën s work and assume income risk to be country- and industry-specific. Assume there are J industries in country i, and the labor wage growth in an industry also follows a stationary Ito process. The share of labor income to total income is a constant η in the long run. On the other hand, the share of capital is (1-η). Therefore, the optimal portfolio x ij for a representative consumer employed in industry j is: x ij =! "1 { 1/! (1"1/!) (µ " r1)+ 1"" (1"") # i " " 1"" $ ij } (2.2) where κ ij is the vector of covariances between growth of labor income in industry j and country i and stock returns across markets. The first two components on the right-hand side are similar to (2.1), with each part weighted by the product share η. The third component is the hedging demands of the income risk. It says if wage growth and risky returns for some markets are positively (negatively) correlated, then the proportion of stock holdings on these 32

43 markets stocks will be lower (higher), all else equal. After imposing the market clearing condition, (2.2) can be written as: x ij = MS + (1!1/!) (1!") "!1 (# i!# $ i # i )! " 1!" "!1 (% ij!# $ ij % ij ) i ij (2.3) where MS is a vector of the market shares of N markets capitalization; ψ i and ψ ij are the shares of country i s wealth and industry j s wealth in the world, respectively. In a world without inflation and income risk (but still subject to return risk), investors in every country would have the same portfolio diversification equal to the market shares, as the original international capital asset pricing model had indicated. The second and third terms are hedging demands for inflation risk in country i and income risk in industry j, respectively. Some features in this model make it distinct from others and are worth emphasizing further. In a riskless world, ICAPM models and this model suggest that an investor in country i should diversify his portfolio according to destination countries market shares, i.e. MS in (2.3). The inclusion of inflation and income risks asks the investor to hedge these risks by adding or reducing the shares. In this model the relative magnitude of the correlation between inflation rates (wage growth) and returns determine the addition and the reduction. The negative correlation between country i s inflation rate (wage growth) and country l s return does not necessarily lead to negative (positive) hedging demands for country l s stocks. The signs of hedging demands on country l s stocks depend on whether the correlations between country i s inflation rate (wage growth) and country l s return are larger or lower than the correlations between world average inflation rate (wage growth) and country l s return. If the former case holds, the investor country i has positive demands and negative hedging demands for inflation and income risk, respectively. For the latter case, the directions are exactly reverse. 33

44 2.5 Methodology and Data Equation (2.3) provides a framework for calculating the hedging demands and optimal portfolios. Before the calculation, we need to confirm that covariances between inflation rates (wage growth) and stock returns exist. The following is a convenient approach. Let p l be the inflation rate for market l and R t be the vector of market returns for all N markets, Adler and Dumas (1983) propose for investors in market l of interest the part of inflation hedging demands in (2.3) can be approximated by the vector of coefficients b l : $ & & &! "1 (! l "#" i! i ) = & i & & % b 1 l! b i l! b N l ' ) ) ) ) ) ) ( (2.4) where b l is from the regression of the term (p l!"! i p i ) i t on R t. The dependent variable, (p l!"! i p i ) i t, measures the difference of inflation rates between county l and the world average. The estimation examines whether the relative inflation rates are correlated to the returns. Let X ls be the wage growth rate for investors belonging to industry s and market l of interest. Similarly, the contribution of wage hedging in (2.3) can be approximated by the coefficients q ij : $ & & &! "1 (! ls "##" ij! ij ) = & i j & & % q 1 ls! q i ls! q N ls ' ) ) ) ) ) ) ( (2.5) 34

45 where q ij is from the regression of the term (X ls!"! ij X ij ) t " i j on R t. Finding industrial wage data across countries is quite challenging. To alleviate the difficulty, one can consider just the average wage growth x i for any country i to construct the dependent variable by the approximation (X ls!"! ij X ij ) t # (X ls!"! i X i ). In summary, with data for market shares and industrial wages, this study runs the regression of (p l!"! i p i ) t on R t for market l (Korea in this case) and (x ls!"! i x i ) on R t for each specific industry s to obtain coefficients, and then inserts significant coefficients with assigned values of two parameters, α and η into (2.3) to calculate the hedging demands and optimal international portfolios. 25 Past work, such as Boudoukh and Richardson (1993) and Palacious-Huerta (2001), has confirmed the correlations between inflation and stock returns and between wage and returns. The concern about possible endogeneity requires applying GMM as the estimation method. This study takes the vector of ones and lagged stock returns as instrumental variables. The lagged lengths do not substantially affect the estimation results, so the results reported in the following section are based on the instrument choice where the one period lag of return and the vector of ones are used. i " i j The expected values of risk aversion, α, are between 2 to 5. This study follows Fugazza et al. (2011) and assigns α as 5. The arbitrary assignment, however, does not affect portfolio diversification much because it affects only hedging demands for the inflation risk, which has smaller correlation with returns compared to the industrial income risk. Furthermore, the estimated results will show hedging demands for inflation risk are small compared with hedging demands for wage risk. For the parameter of labor s share, η, this study follows Campbell (1996) and takes it as 0.66 since labor contributes about two-thirds of GDP. To estimate the international diversification for hedging demands, cross-country data during a period of time are needed. The time length is determined by the availability of 25 Cooper and Kaplanis (1994) and Coën (2001) estimate how much the hedging demands can explain home bias and the coefficient of relative risk aversion simultaneously. Their estimations give unusual and insignificant values of risk aversion. Therefore, this study assigns arbitrary risk aversion to avoid the same problem. i i 35

46 industrial labor wages in Korea. Since the industrial classification was revised a few times, the length is quite short for each revision. To have enough consistent observations this study adopts monthly nominal wage data from January 2002 to December Korea Ministry of Employment and Labor provides both very crude and very detailed industrial categories. To keep the differentiation between industries and avoid meaningless details, this study uses the moderate classification, where there are 15 industries. 26 Given the time length, another question is: in which equity markets should investors participate? Fugazza et al. (2011) choose nine markets; Cooper and Kaplanis (1994) choose eight markets. The set of equity markets is arbitrary, but it should be able to represent major international financial markets where investors can participate. In addition to the Korean stock market and KOSPI 200, this study chooses another 7 destination markets and stock indices unadjusted for dividends. 27 They are the United States (S&P 500), the United Kingdom (FTSE 100), Japan (NIKKEI 225), Germany (DAX), France (CAC 40), Italy (FTSEMIB), and Canada (S&P/TSX 60). During the period of interest, the fractions of trading volumes and capitalization of these 8 markets account for around 70 to 80 percent of the world. The monthly inflation rates for all markets are derived from CPI indices provided by International Monetary Fund s International Financial Statistics; the monthly market returns are derived from the stock market indices from Datastream. 28 The use of market returns from stock indices evaluated in local currencies in the estimation implies that the exchange rate risk is hedged. In reality an investor can have gains or losses from exchange rates while trading foreign assets. The market returns measured by home currency could differ from those measured by local currencies. The estimation in the next section will focus on the case of wage and inflation risk and neglect exchange rate risk. Similar to the mean-variance analysis in Section 2, the estimation for the hedging demands, 26 The labor wage survey excludes the agriculture, fisheries and forestry sectors. The omission will not influence on the analysis substantially considering their relatively small production and employment. 27 The stock indices are not adjusted by dividend because the adjusted indices are not available for all stock markets of interest. 28 Merton (1980) points out realized returns are not good proxies for expected returns. The estimated portfolio weights do not match actual portfolio weights since the latter ones are highly sensitive to expected returns. The problem is still common empirically. 36

47 considering the influence of exchange rates on stocks returns, will be presented in Appendix D. In this case, all stocks indices are converted to the indices measured by the Korean currency. The monthly exchange rates are from OECD Statistics. Data on wealth shares for country i, ψ i, are not available. Cooper and Kaplanis (1994) use the share of market capitalization at the last month as a proxy for the wealth share. The constant values of market capitalization are reasonable proxies in earlier periods; they could not be applied nowadays, when international financial markets are changing. Therefore, this study allows market shares to vary to reveal the changing environment. 29 We assume that investors can access only these eight destination markets; the market shares are normalized so that their sum is 1. Monthly data are available from the World Federation of Exchanges. 30 Data for monthly wage growth are from IMF International Financial Statistics. 2.6 Hedging demands and Optimal International Portfolio Table 2.1 reports the hedging demands for inflation and wage risks (see Appendix D for hedging demands in the case considering the influence of the exchange rate risk). The values in the table indicate how a representative worker adjusts components of wealth invested in destination stock markets to avoid of inflation and income risk. The first row shows that half of the destination markets can provide a hedge for nation-wide inflation risk. The correlation between inflation rates in Korea and stock returns in the US and France is significantly larger than it is between the average inflation rates and stock returns in the US and France. In other words, all else equal, a Korean investor should hold 1.8 and 3.6 percent of wealth in US and French stocks respectively. On the other hand, the correlation between domestic inflation and returns on Korean and Italian stocks is significantly smaller than the correlation between the 29 The most noticeable change is the decrease of the US s market share. For other selected countries, the shares stay stable, but increase slightly after normalizing the market shares. 30 The World Federation of Exchanges is an association of publicly regulated stock exchanges (see the webpage for more information: The market values of France are from market values of Euronext including several European markets: France, Netherland, Belgium and Portugal. The incapability of extracting pure market value for France is expected not to affect the market shares and then the calibration results since the French stock market is substantially larger than other markets in Euronext. 37

48 world average inflation and returns on these two countries stocks. The Korean investor should rearrange his portfolio by decreasing the holdings of Korean and Italian stocks. The magnitude or the correlation between domestic inflation and returns, however, is weak. The hedging demands do not alter the optimal portfolio much. The following rows show the influence of wage risk on portfolio diversification. The third row considers the nation-wide case, i.e. assuming the effect does not depend on the industrial wage difference. In this case, the correlation between Korean wage growth and returns on French (Canadian) stocks is significantly smaller (larger) than the correlation between the world average wage growth and returns on these French (Canadian) stocks. A Korean investor should hold 37 percent more of his wealth in Canadian stocks and 24 percent less of wealth in French stocks. The calibration is based on a framework where investors have diversified their portfolios across markets. The nation-wide results indicate that a Korean investor does not need to extensively diversify their hedging demands. Instead, he can hedge his wage risk by re-distributing his wealth in two foreign stock markets (France and Canada), but the demands are stronger than they are for inflation risk. The hedging demands for different industrial wage risks are given in the fourth to the twentieth row. Industrial level demands are more diversified than nation-wide demands. For investors in most industries, hedging demands for the US, UK, German and Korean stocks are insignificant; demands for French and Canadian stocks are negative and positive, respectively. The demands for the UK and Korean stocks averaged out to 0 in the national level are, significantly, not 0 for industries like Mining and Utility Supply. In some industries, such as Post/Telecommunication, Utility Supply, and Manufacturing, hedging demands to some markets are relatively large since the correlation between their wage growth and returns are substantially larger than the correlation between the world average growth and returns. Post/Telecommunication is the industry that needs the widest range of hedging demands. This study s estimation shows that an investor in this industry should decrease his wealth invested in French stocks by 70 percent and increase wealth invested in Italian stocks by 75 percent. Investors in the Business, Education and Recreation industries 38

49 do not require diversified hedging demands since their relative wage growth is uncorrelated with the stock returns of most markets. Table 2.1 Hedging Demands for Inflation and Industrial Wage Risk US UK Japan Germany France Italy Korea Canada Inflation Hedging Wage Hedging National Mining and Quarrying Manufacturing Utility Supply Construction Whole Sale and Retail Trade Hotel and Restaurant Transport Post and Telecommunication Financial Institution and Insurance Real Estate Renting and Leasing Business Activities Education Health and Social Work Recreational, Cultural and Sporting Other Community Service Weighted Hedging Demand Note: 1. The table reports the hedging demands significant at 5% confidence level, or use the symbol ---, otherwise. 2. The values represent the change of wealth invested in selected stock markets for hedging demands. 39

50 Table 2.2 presents the covariance between industrial wage growth and destination countries stock returns. It gives us a clue as to why workers in some industries have large hedging demands of some countries stocks although the phenomenon has no clear pattern. As expected, the covariance is always positive and relatively larger in Korea. This implies that a Korean investor should have negative demands of domestic stocks. On the other hand, the covariance between wage growth and Canadian stock returns is relatively small compared with correlations between the wage growth and other countries stock returns. This study explains the negative relationship using the bilateral trade pattern. The correlation coefficient of imported and exported values between Korea and Canada is lower than that for Korea and other selected countries. 31 It can be inferred that the industries between Korea and Canada have a more competitive relationship. The higher export and the resulting higher industrial income in Korea imply higher imports and lower stock performance in Canada. On the other hand, the correlation coefficient between Korea and France is the second highest, which implies that industries in these two countries might be more complementary. Hence the Korean national income and French stock returns are positively correlated. These estimations prove that negative correlation is significant and Korean investors have positive hedging demands for Canadian stocks against the wage risk. Another approach to interpreting the correlations between industrial income growth and returns across foreign stock markets is through the co-movement of economic performances. According to this method, the correlation between any two economies performances determines the directions and amount of hedging demands. The long-run correlation coefficients of GDP between Korea and all selected countries in this study are all positively larger than 0.9. The pro-cyclical GDP movement might not tell much about the relations between Korean national income and returns on foreign stocks, but from the industrial perspectives, wage growth rates in some industries, like Mining/Quarrying and Utility Supply, are not sensitive to the national wage growth or GDP growth. This might explain why workers in these industries have different hedging demands for their portfolios. 31 The data of bilateral trade are from NBER s project. From 1990 to 2000, the correlation coefficient of imported and exported values between Korea and Canada is the lowest, which is The largest correlation coefficient is between Korea and Japan, which is around

51 The values in the last row in Table 2.1 are the weighted sum of hedging demands for wage risk. 32 This is another measurement of national hedging demands, also shown in the third row. The negative and positive demands for French and Canadian stocks are substantial. The weighted hedging demands for other stocks are insignificant in the estimations and are relatively small. Table 2.2 Covariance Matrix of Wage Growth and Stock Returns US UK Japan Germany France Italy Korea Canada Mining and Quarrying Manufacturing Utility Supply Construction Whole Sale and Retail Trade Hotel and Restaurant Transport Post and Telecommunication Financial Institution and Insurance Real Estate Renting and Leasing Business Activities Education Health and Social Work Recreational, Cultural and Sporting Other Community Service The weight for each industry is the ratio of the total wage earned by workers in this industry to the total wage earned by all workers. The data are from Korea Ministry of Employment and Labor. 41

52 Given the hedging demands for inflation and wage growth estimated and taking the average market shares as MS, optimal portfolio diversification can be obtained by applying equation (2.4). Table 2.3 reports the nation-wide and industry-specific results, in which the exchange rate is ignored (see Appendix D for a case considering the influence of exchange rate). From the national perspective, a Korean investor should allocate most of his wealth in the US, the UK, Japanese, and Canadian stock markets and short French and riskless assets. The aggressive long and short of Canadian and French stocks are due to higher hedging demands for the wage risk. But the long for stocks in the US, the UK and Germany is more from their share of capitalization, not hedging demands. This calibration also suggests that the investor should invest only a small amount of wealth in the domestic (Korean) market, given its small share of capitalization in the world. For investors in five industries (Mining, Utility Supply, Whole Sale/Retail, Financial/Insurance and Real Estate), taking a short position in the domestic stock is suggested. These seemingly unusual results are common in international portfolio diversification (Baxter and Jermann, 1997; Julliard, 2002; Fugazza et al., 2011). The later section on home bias will further discuss this issue. Again, the last row shows the weighted sum of the industry portfolios, an alternative measurement of optimal national portfolio. The estimations so far are under the assumption that workers in different industries have different optimal portfolios. The assumption can be test by employing the Wald test with the null hypothesis: H 0 : q i lj = q i ls If the coefficient distances between industry j and industry s are close enough, one can claim that workers in both industries have similar optimal portfolios for stock in market i. The tests can tell us whether estimating optimal portfolios industry by industry is necessary. For each industry-pair and each destination market, this study tests one null hypothesis. There are 105 industry-pairs and 8 markets, so the tests are repeated 840 times. 42

53 Table 2.3 Optimal National and Industrial Portfolios US UK Japan Germany France Italy Korea Canada Riskless National Mining and Quarrying Manufacturin g Utility Supply Construction Whole Sale and Retail Trade Hotel and Restaurant Transport Post and Telecommunicatio n Financial Institution and Insurance Real Estate Renting and Leasing Business Activities Education Health and Social Work Recreational, Cultural and Sporting Other Community Service Weighted National Figure 2.2 shows the graphical presentation of the Wald test. Out of 840 pairs, 49% are statistically different. There are 57 industry-pairs whose portfolios differ in 4 or more markets, and 48 industry-pairs whose portfolios differ in less than 4 markets. The obvious differences in industry portfolios indicate that the wage risk does have distinct effects on workers portfolio choices in different industries. 43

54 numbers of industry- pairs numbers of different coef3icients Figure 2.2 Wald Test for Industry-Pair Coefficients Note: The hypothesis test is performed at 5% confident interval. Next, this study measures the distance between the national and industry portfolios to find which industry portfolios deviated from the national portfolio. Similarly to the comparison of industry-pair coefficients, the Wald test is employed to test the null hypothesis: H 0 : q i lj = q i l The portfolio distances calculated are based on the test results represented in Table 2.4. There are workers in three industries, Mining/Quarrying, Utility and Post/Telecommunication, whose portfolios are very different from the national portfolio. Workers in these industries have significantly larger hedging (either positive or negative) demands for wage risk in three stock markets: UK, France and Italy. On the other hand, the workers in Construction are close to a representative worker. Their specific hedging demands for the wage risk in every market follow the national ones. If the distances between national portfolios and each industry s portfolios are too small, the dispersion measured by the standard deviation can give an overview of how greatly the industry portfolios differ from the national portfolio. 33 The overall dispersion is 0.17 (for 33 The formula for the dispersion level σ is 44