人口結構變化對股票市場報酬影響 - 政大學術集成

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(1)國立政治大學財務管理研究所碩士論文. 政治大. 學. ‧ 國. 立demographic changes to stock The impact of market. ‧. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. 指導教授：周冠男研究生：張丁互. v. 博士撰. 中華民國一百零四年六月.

(2) Abstract: This study examine the reactions in different portfolios under demographic changes for a deeper scope of the equity market. By six features: 1) beta 2) volatility 3) nonsystematic risk 4) size 5) B/M 6) D/P, we distribute stocks into high or low level groups and test the reactions in each of these 12 portfolio. Empirical results in this study do. 政治大. suggest an increasing required risk premium for a growing population in retired-age. 立. (65+) group and a decreasing required risk premium for a growing population in. ‧ 國. 學. middle-aged (44-64) group. Both effects in middle- and retired-age groups are stronger. ‧. in a long time-horizon. Changes in demographic structure significantly add explanatory. sit. y. Nat. power to equity premium regressions involving Fama-French three factors. Moreover,. er. io. we found retired-age population significantly demand more premium for high volatility. al. n. v i n C h stocks. However,Uthere is no preference for any stocks, growth stocks and large-cap engchi types of stock in middle-age population.. Keywords: demographic change, life-cycle hypothesis, equity return. i.

(3) Table of contents 1.. Introduction ...................................................................................................... 1. 2.. Literature review and Hypothesis ................................................................... 6. 4.. Literature review ........................................................................................ 6. 2.2. Hypothesis development .......................................................................... 12. Data and Methodology ................................................................................... 14 3.1. Data Description ...................................................................................... 14. 3.2. Methodology............................................................................................ 16. 4.1. Portfolio returns ....................................................................................... 20. 4.2. Multi-Year regression .............................................................................. 25. 政治大 Empirical result .............................................................................................. 20 立. 學. ‧ 國. 3.. 2.1. Conclusion ...................................................................................................... 37. 6.. Reference ........................................................................................................ 38. ‧. 5.. y. Nat. n. al. er. io. sit. Appendix................................................................................................................ 40. Ch. engchi. ii. i n U. v.

(4) 1. Introduction There are many impacts of demographic change to a country’s economic health. An aging population’s potential effects on labor supply, employment, social security, levels of aggregate consumption and saving are of interest not only to academics but to policy analysts. Despite actuaries have long recognized the need for factoring demographic characteristics into payment schedules, less is widely accepted about the. 政治大. effect of demographics on asset markets.. 立. ‧ 國. 學. The intuition behind the link between changing demographics and financial asset. ‧. prices is the life cycle hypothesis of demand, pioneered by Franco Modigliani, which. y. Nat. er. io. sit. suggests in the early stage of life (25~44), people are likely to be net borrowers. Therefore financial asset prices would decline or be unaffected as the age group. n. al. Ch. engchi. i n U. v. increases. The middle-aged (45~64) are involved heavily in accumulation of net assets because they are at the peak of their earnings potential, and likely to be saving for retirement. An increase in the size of this group would lead to a higher demand for financial assets, stocks and bonds, resulting to an increase in financial asset prices. Finally, as the age group enters retirement (65+), they start to decumulate their wealth. As a result, financial asset prices could come under downward pressure. Special interest is drawn toward claims that the aging of the "baby boom" cohort is a key factor in 1.

(5) explaining the rise in asset values such as the sharp rise in US stock prices in the 1990s. This has been supported by many authors such as Dent (1993), Shiller (2000), and Sterling and Waite (1998) who suggest that this pattern is due to the baby-boom cohort which had entered their prime earning years and begun saving for retirement. And by predictions that asset prices will decline when this group reaches retirement age and begins to reduce its asset holdings (see Davis and Li (2003)).. Population aging. 立. 政治大. ‧ 國. 學. The trend of population aging and the possible consequences had long been cried. ‧. out by many researches. World Population Ageing (2013) 1 declare that population. sit. y. Nat. ageing is concurrently taking place in nearly all the countries of the world and has. n. al. er. io. major social and economic consequences. The old-age support ratios2 were already low. i n U. v. in the more developed regions and are expected to continue to fall in the coming. Ch. engchi. decades with ensuing fiscal pressures on support systems for older persons. Most of developed countries, including US, witnessed an acceleration of population growth in the 1950s (see Chart 1), followed by a decline during the late 1960s. Such slowing pace of population growth could be a pressure to the health of demographic structure.. 1. United Nations, Department of Economic and Social Affairs, Population Division, World Population. Ageing committee 2013 2. number of working-age adults per older person in the population 2.

(6) 2.50% 2.00% 1.50% 1.00% 0.50% 0.00%. 1929. 1939. 1949. 1959. 1969. 1979. 1989. 1999. Chart 1. The U.S. Population growth rate after great recession Source: US Census Bureau. 政治大. 立. Separately, life expectancy had increased gradually since 1950 by the. ‧ 國. 學. improvement of medical techniques. Chart 3 shows, life expectancy has increased by. ‧. 15 years in the last 50 years. By the end of 2014, the life expectancy at birth have reach. n. al. er. io. sit. y. Nat. the nearly 80 years old, resulting the ever-urged necessity to save for retirement.. 85.0 80.0. Ch. engchi 74.5. 75.0 69.2. 70.0. 70.9. i n U. 76.1. 77.4. v. 78.7. 71.7. 65.1 65.0. 60.9 57.4. 60.0 55.0. 51.9. 50.0 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010. Chart 3. Life expectancy at birth in US Source: U.S. Dept. of Commerce, Bureau of the Census, Historical Statistics of the United States.. 3.

(7) Baby-boom cohort Given the importance to population structure of the high levels of births from late1940s to mid-60s, and the subsequent decline in fertility, the baby boom generationthose born in roughly the two decades following World War II-has had and will continue to have important effects on the U.S. economy. At its youth stage, this group placed high demands on infrastructure for education and other types of training. The entry of this large cohort into the labor market may have been associated with an increase in the aggregate unemployment rate.. 政治大 During the 1990’s, the 立baby boom generation entered its peak savings years.. ‧ 國. 學. Individuals aged between 40 and 60 years old are the prime savers of the economy in the US. Several theoretical models have argued that the baby boom generation was a. ‧. contributing factor to the high stock returns and the large increase in stock prices. sit. y. Nat. observed from 1990 to 1999 (see graph 1).However, after years of prosperity, this. n. al. er. io. cohort is going to retire (first wave come in 2011, as the people born in 1946 have. i n U. v. reached retirement age, see graph 2). Concerns have been raise about how this ever-. Ch. engchi. large retired cohort would impact the financial market.. Graph 1. Population pyramid 1990. Graph 2. Population pyramid 2010. Source: United Nations, Department of Economic and Social Affairs, Population Division. World Population Prospects: The 2012 Revision.. 4.

(8) In this context, this paper seeks to investigate empirically the impact of demographic changes on stock market returns. More specifically, we examine the potential links of changes in three age groups, young (25~44), middle (45~64) and retired (65+) to stock returns among portfolios formed by six equity features: (1) beta (2) size (3) B/M (4) D/P (5) volatility (6) non-systematic risk.. 立. 政治大. The structure of this paper is as follows: Latter in this Section, we present the. ‧ 國. 學. historical evolution of the population structure in the US. Section 2 does a review of. ‧. the theoretical and empirical literature on demographics and financial asset demands,. sit. y. Nat. including aspects of the life cycle hypothesis and the potential linkage of demographic. er. io. changes and equity returns. Section 3 presents the sources of data we use and explain. al. n. v i n C Section the methodology of this study. the relation between U h e n g4 ctests h iempirically demographics and equity returns in US. With the construction of portfolio by different characteristics, we try to reveal hidden information within reaction of equity return.. 5.

(9) 2. Literature review and Hypothesis. 2.1 Literature review. There have been an ongoing debate among researchers concerning the link between stock market and demographic changes. In the US, in particular, much has been said about the relationship between the baby boom generation retirement savings. 政治大 from 1990 to 1999. As Dent立 (1993), Shiller (2000), and Sterling and Waite (1998) have and the phenomenal increase in financial asset prices which characterized the period. ‧ 國. 學. suggested, the rise in the US stock market during the 1990’s was at least partly due to the post-war baby boom cohort who had entered into their prime earning years and. ‧. begun saving for their retirement (see graph 1). Abel (2003) also finds empirically that. sit. y. Nat. a baby boom will increase the price of capital. Specifically, when baby boomers are in. n. al. er. io. the labor force earning wage income, national saving and investment are high.. Ch. engchi. i n U. v. Many academics had developed theoretical hypothesis trying to support and explain such linkage. There are four well recognized hypothesis among this subject: life cycle hypothesis of saving, behavioral lifecycle hypothesis, life-cycle investment hypothesis and life-cycle risk aversion hypothesis. We summarize each of their main concept in the following context.. Life-cycle hypothesis of saving. The intuition behind the link between changing demographics and financial asset. 6.

(10) market is the life cycle hypothesis of saving (see Modigliani and Brumberg (1954) and Ando and Modigliani (1963)) which suggests that early in one’s life, consumption may well exceed income as individuals may be making major purchases like buying a new house or starting a family, and beginning a career. At this stage in life, individuals may borrow based on their expected labor income in the future (human wealth). When comes to mid-point in life, labor income increases while these expenditures begin to level off. Individuals at this stage repay debts and start to save for retirement in stocks, bonds, pension schemes which makes middle-aged households the most prominent. 政治大 withdraw savings. This involves selling off some of their financial assets. The empirical 立 investors. At retirement, income normally decreases, and individuals may start to. evidence (Modigliani (1986)) supports the essential idea that consumers want to smooth. ‧ 國. 學. consumption over time in order to maximize their lifetime utility and, thus, have a. ‧. hump-shaped saving pattern.. er. io. sit. y. Nat. Behavioral Lifecycle Hypothesis. al. n. v i n Follows on from LifecycleCtheory of saving byU h e n g c h i Modigliani and Brumberg, the. Behavioral Lifecycle Hypothesis (Shefrin & Thaler 1988) holds that households treat components of their wealth as non-fungible. Specifically, wealth is assumed to be split. into three mental accounts: current assets, current income, and future income. The propensity to spend money is assumed to be greatest from current income and least from future income. They further suggest that the marginal propensity to consume dividend income is greater than the marginal propensity to consume capital gains of stock holdings. Assuming the BLC theory holds true, it’s more likely that investors substitute more defensive, income yielding assets for out of risk assets as they retired. Moreover, as long as the assets can generate sufficient income for investors to live off, 7.

(11) there would be no necessary for them to sell them. As a result, one would expect stocks with lower level of risk and stocks with higher steady cash flows to be less affected by demographic changes.. Life-cycle investment hypothesis. The life-cycle investment hypothesis suggests that the investment needs in terms of types of assets to hold are different at different stages of an investor's life cycle. At. 政治大 will allocate a higher proportion of wealth to these consumption at the family-building 立. the 20s and 30s, housing and other durables are desirable investment. Therefore, one. stage. However, the demand for housing will eventually stabilize or even decrease and. ‧ 國. 學. the demand for financial assets will rise. This is clear to understand. As one grows. ‧. older, the number of remaining paychecks declines and the need to invest for retirement. sit. y. Nat. increases. Over the past decades, this need was made even stronger by the ever -. io. er. increasing life expectancy. The implication of life-cycle investment hypothesis is very simple, as the population ages, the aggregate demand for housing decreases which. al. n. v i n depresses housing prices, whileCthat for financial investment increases, which boost hengchi U financial prices.. Life-cycle risk aversion hypothesis Bakshi and Chen (1994) proposed the life-cycle risk aversion hypothesis, which suggests that risk aversion will increase over the lifecycle – the older a person gets, the more risk averse they become. Explanation among this theory lies in the relative importance of labor income and asset income over the lifecycle. It have been said that the further a person is from retirement the more risk they are willing to accept in their 8.

(12) investments since the number of paychecks they expect to receive is large and labor income can offset any unexpected adverse investment outcomes. Otherwise, the closer to retirement a person reaches, the fewer paychecks they have to cover any such adverse investment outcomes. In the empirical tests, they used Euler equations and a two-factor model based on consumption growth and percentage change in average age, and found a positive and statistically significant relationship which strongly supported their lifecycle risk aversion hypothesis. The implication for this is clear. To get an aging population to participate in the equity market, expected premiums must increase. Davis. 政治大 but then as the 65+ cohort becomes predominant, it will rather benefit bond markets 立. (2007) found that ageing tends initially to benefit equities (as the 40-64 cohort grows). relative to equity markets, which is consistent with risk aversion effects.. ‧ 國. 學 ‧. Overall, the life cycle hypothesis of saving and the life-cycle investment. sit. y. Nat. hypothesis both suggested a tendency that young adults and retired people keep. io. er. financial market away and middle-aged adults are the most promising investor. The behavioral lifecycle hypothesis further suggested that the marginal propensity to. al. n. v i n C hthan consume capital consume dividend income is greater gains of stock holdings engchi U. which implies income yielding stocks would be resilient to impact of demographic changes. On the other side, the life-cycle risk aversion hypothesis proposed that risk aversion will increase over the lifecycle.. Empirical studies. Followed by these hypothesis, many empirical studies were implemented to find statistical back up and tried to put them to a greater extent.. 9.

(13) Yoo (1994) estimated multivariate time-series regressions of annual U.S. stock, corporate bond, and government bond returns on fractions of total population for the 25–34, 35–44, 45–54, 55–64, and 65+ age groups by using an overlapping generations model. He found a strong result the negative relationship between the size of the middle aged group (45-54) and the low frequency returns on financial assets including common and small corporate stocks, long corporate bonds, and long government bonds. He further estimated the regressions with three- and five year centered moving averages and found a significant increase in terms of both statistical significance and fit. Which. 政治大. motivate us to impose the long horizons estimation in our test.. 立. Erb, Harvey, and Viskanta(1997) found the relationship between demographic. ‧ 國. 學. change and real stock returns on cross-national data for the period 1970-1995 at 18. ‧. developed and 45 developing countries. The authors presented evidence suggesting. sit. y. Nat. that there is a positive correlation between the fraction of the population between the. io. er. ages of 25 and 45 and real stock returns in the United States, and this also holds for the fraction 65+ and real stock returns. They found a negative relationship between the. al. n. v i n C h returns in the data population share 45-65 and stock sample. Finally, a positive engchi U. relationship in both developed and developing countries between stock returns and the change in the average age of a country's inhabitants is also suggested.. Using both a short panel (1970–2000; 15 countries) and a long panel (1900–2001; 5 countries), Ang and Maddaloni (2003) examined the relationship between excess stock returns (with one-, two-, and five-year horizons) and log changes in three demographic variables: average age of the population over 20, fraction of adults over 65, and fraction of people in the 20–64 age group. Their results found a negative effect for the fract ion of retirees in the populat ion (65+) in poo led regressions. 10.

(14) Interestingly, they captured an opposite and positive result in isolated regressions for the United States and the United Kingdom. By an additional test for this difference in results, they found that the effect for the 65+ age group is stronger in countries with well-developed social security systems and less developed financial markets.. Brooks (1998) focused on the determination of the level of equity prices in 14 OECD countries using the share of the 40-65 age group in the population as an independent variable, and found it to be significant for 11 countries. Brooks (1998). 政治大 as the ‘life-cycle hypothesis of saving’. 立. calls the positive correlated relationship between asset prices and the size of the cohorts. ‧ 國. 學. Goyal (2004) modeled the investments in the stock market in an OLG model with. ‧. wealth effects in which each generation has more than two periods to live. He found. sit. y. Nat. outflows from the Stock Market are positively correlated with changes in the fraction. io. er. of old people and negatively correlated with changes in the fraction of middle-aged population. In addition to a decrease in outflows from the stock market with an increase. al. n. v i n in the middle-aged population, C the stock prices are postulated to rise. Furthermore, in hengchi U absence of fundamental changes, the long horizon returns are predicted to fall.. The empirical tests confirm these suggests. Stock returns increase following an increase in the middle-aged population and decrease following an increase in the oldage population. However long horizon returns are also negatively correlated with an increase in the middle-aged population, and positively correlated with a decrease in the middle-aged population.. 11.

(15) 2.2 Hypothesis development. Life-cycle hypothesis of saving proposes that labor income approach to its peak in the middle-aged stage of life and which, as a consequence, makes mid-aged population the most prominent investors along with their necessity to save for retirement. Therefore, following an increase of mid-aged population was the increased aggregate demand for equity securities. The increased demand would then boosts the equity price but the expected return would fall otherwise. Our first hypothesis is. 政治大. developed in a clear way under this basis:. 立. ‧ 國. 學. Hypothesis 1:. The increase of the fraction of middle-aged population would. ‧. decrease equity returns. n. er. io. sit. y. Nat. al. i n U. v. In terms of retired people, on the other hand, income normally decreases and. Ch. engchi. individuals may start to withdraw savings from financial market. This involves selling off some of their financial assets, which puts the equity price under pressure and rise the expected return. As Life-cycle hypothesis of saving suggests, in the early stage of life, consumption may well exceed income as individuals may be making major purchases and have less intention to invest. Thus, we expected younger population would impact equity market in the similar way of retired population and made the hypothesis 2 as following:. 12.

(16) Hypothesis 2: The increase of the fraction of retire-aged population (or young adult population) would increase equity returns.. In addition to the difference of propensity to hold financial assets, Life-cycle risk aversion hypothesis also proposes that risk aversion will increase over the lifecycle –. 政治大 population to participate 立 in the equity market, expected premiums must increase.. old-aged people would be more risk averse then young-aged. Thus, to get an aging. ‧ 國. 學. Moreover, if risk aversion hypothesis holds, it’s more likely that investors substitute more defensive, income yielding assets for out of risk assets as they retire. We build. ‧. hypothesis 3 by this concept :. er. io. sit. y. Nat. Hypothesis 3:. The impacts of demographic changes on high risk level. al. n. v i n portfolios are larger thanC onhlow risk level U portfolios. engchi. The third hypothesis is the most prominent aspect in this study, since other studies among demographic changes and asset returns usually treat equity securities as a whole market (by using indexes as independent variables). Although they did find the impact of demographic changes to equity market, but still not sure about the effect to specific stocks. Here in the study, we test this effect by portfolios with different risk profiles trying to capture the information among different reactions of these portfolios.. 13.

(17) 3. Data and Methodology. 3.1 Data Description. In this study, we use all listed firms in the intersection of the NYSE, AMEX, and NASDAQ return files from the Center for Research in Security Prices (CRSP) and the COMPUSTAT monthly securities files of income statement and balance sheet data.. 政治大 available prior to 1962. Along with the matter, COMPUSTAT data for earlier years 立. The 1962 start date reflects the fact that book value of common equity, is not generally. (pre-1962 data) are tilted toward big historically successful firms, which leads to a. ‧ 國. 學. serious selection bias.. ‧. sit. y. Nat. To ensure that the accounting variables are well recognized before the returns they. io. er. are used to explain, we match accounting data for all fiscal year-ends in calendar year t - 1 (1962-2014) with the returns for January of year t to December of t leaving a one-. n. al. i C and year delay between fiscal yearend the return tests.U n hengchi. v. Thus, to be included in the return tests for December of year t, a security file must obtain a CRSP stock price for December of year t - 1 and must also have monthly returns for at least 24 of the 60 months preceding December of year t (for pre-rankings of beta, volatility and nonsystematic risk). And the firm must have COMPUSTAT data on book equity (BE), and Dividends per Share (D), for its fiscal year ending in calendar year t - 1.. 14.

(18) Demographic data could be retrieved back to 1920s but were more accurate at the post-war period. We obtain all the demographic data since 1946 among all age groups from the United States Census Bureau. But in particular, only data from 1958 (for one or multi-time horizon tests) are effective to match security data which have a shorter period available since 1962. More important, by reason of the difficulties and costs, population census is launched for the United States, states, counties, cities, and towns at a five-year basis, which means that the data between censuses rely on professional estimates3. However, with an ongoing effort to improve the accuracy, the Intercensal. 政治大 average absolute difference between the final total resident population estimates and 立. estimates were very accurate, even accounting for ten years of population change. The. next decade’s Census counts was only about 3.1 percent across all counties (and only. ‧ 國. 學. 1.02 in a state level).. ‧ y. Nat. io. sit. As the fact that Fama-French three factors have been widely accepted as the most. n. al. er. effective capturer of expected asset returns. We implement these factors to test the. i n U. v. solidity of significance of demographic variables in the study. Data of Fama-French. Ch. engchi. three factors are from Kenneth R. French - Data Library in both monthly and annually horizon.. 3. see appendix A for more description. 15.

(19) 3.2 Methodology The major contribution in this study is the implementation of portfolio sorting in analyzing equity market. This method allows us a possibility to extract hidden information inside the reaction of equity market. In the light of reaching the goal, after retrieving all equity data from the database, by six different characteristics: (1) beta (2) volatility (3) non-systematic risk (4) size (5) B/M (6) D/P, we distribute those securities. 治政 into high or low level groups. The features of (1), 大(2), and (3) are traditional 立 ‧ 國. 學. measurement of financial risk, which we expect to test the risk aversion hypothesis. (hypothesis 3). Term (4) and (5) are as suggested by Fama and French (1992), that. ‧. these two features may imply some sort of risk factors. The final (6) is for the effort to. y. Nat. al. er. io. sit. test whether income yielding securities more reluctant to be impacted. In practice, we. n. implement this by four steps.. Ch. engchi. i n U. v. First, we sort these portfolios with the ending value in the last month of each year. For example, in a specific year, securities with higher beta in the last month (which is also year-end value) would be include in the high-beta group and this method also similar when treating other risk features. In terms of D/P, we use the yearly ending value by adding up all the dividend yield from beginning to the end of year.. 16.

(20) Secondly, once the ending value of each stocks are all collected, we distribute the upper 70 percentile into high-group and the lower 30 percentile into low-group.. By now, in each high/low portfolio, we could specified what the components are. Third step here is to compute the portfolio returns4. Due to our hypothesis that equity return would be affected by demographic changes are based on the variation of aggregate demand, stocks with large market size are resilient to be affected. Therefore,. 治政 we value weighted those stocks in computing portfolio 大 returns to reflect this 立 ‧ 國. 學. particularity (table 1 shows the descriptive statistics of these portfolio returns).. ‧. In the final step, we subtract risk-free rates from the returns and regress this yearly. sit. y. Nat. portfolio excess returns on demographic variables and the Fama-French factors. The. n. al. er. io. basic model are as following:. Ch. engchi. i n U. v. 𝐸𝑥𝑅𝑡 = 𝛼0 + 𝛼1(𝑅𝑚 − 𝑅𝑓 ) + 𝛼2𝑆𝑀𝐵𝑡 + 𝛼3𝐻𝑀𝐿𝑡 + 𝛼4𝐷𝑒𝑚𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑠𝑡−1 𝑡. 4. Before computing portfolio returns, we exclude outliers by omit stocks with return larger than 99. percentile or smaller than 1 percentile.. 17. (1).

(21) The demographics operated in this study are three population variables: 𝑃25−44 , 𝑃45−64 and 𝑃65+ each of them represent the fraction of population in group age from 25-44 (young adult), 45-64 (middle aged) and 65+ (retired). These variables are suggested by Goyal (2004) that could capture the dynamic of demographic changes. In the regression model, demographic variables are lagged by one year to ensure that they are well recognized before the returns they are used to explain.. 立. 政治大. The Fama-French factors are constructed using the 6 value-weight portfolios. ‧ 國. 學. formed on size and book-to-market5. SMB (Small Minus Big) is the average return on. ‧. the small portfolios minus the average return on the big portfolios, HML (High Minus. sit. y. Nat. Low) is the average return on the portfolios minus the average return on the growth. er. io. portfolios, Rm-Rf, the excess return on the market, value-weight return of all CRSP. al. n. v i n C h bill rate (from Ibbotson firms minus the one-month Treasury e n g c h i U Associates).. 5 See. Fama and French, 1993, "Common Risk Factors in the Returns on Stocks and Bonds," Journal of. Financial Economics, for detailed description of the factor returns.. 18.

(22) Table 1. Summary statistics for portfolio returns This table presents descriptive statistic for each of the 12 portfolios. Every year we sort stocks into percentiles based on their year-end betas, volatility, non-systematic risks, sizes, B/Ms or D/Ps and compute value-weighted portfolio returns for top 30 percentiles and bottom 30 percentiles. Therefore, with each of the six portfolio features, we show High (high than 70 percentile) and Low (lower than 30 percentile) portfolio returns. Betas and volatility are estimated over the 60 months or at least 24 months preceding December of year t. Non-systematic risks are computed by squaring residual terms in market model with estimated betas and intercepts. Size, B/M are calculated by the end ing va lue o f year t . D/ P is t he su m o f d ivide nd yie lds in ye ar t . The sample extends from 1962 to 2013 with all stock files in CRSP and Compustat.. 學. Portfolio sorted by. ‧ 國. 政治大 The terms Vol and Non in the table refer to volatility and non-systematic risk 立 respectively. High (Big) level. Low(Small) level. Std.. Kurt.. Skew.. Beta. 0.33. 0.39. 0.53. 0.60. 0.17 0.13. Vol. 0.64. Nat. Mean. Std.. 1.32. 1.15. 0.16 0.14. Non. 0.33. 0.25. Size. 0.22. 0.18. B/M. 0.10. D/P. 0.17. ‧. Mean. Kurt. Skew.. -0.13. -0.38. 0.25. 0.44. 0.23. y. -0.28. sit. er. 0.66. io. -0.33. n. a l1.64 0.62 0.15 v i n Ch engchi U -0.34. -0.35. 0.12 0.31. 0.35. 0.50. 0.22. 0.66. -0.05. 0.29 0.23. -0.18. 0.13. 0.16. -0.15. -0.32. 0.34 0.34. -0.51. 0.31. 19.

(23) 4. Empirical result. 4.1 Portfolio returns6 In the first subsection, one-year horizon in the regression was implemented. That is, we regress yearly portfolio excess returns (which are computed from the beginning of t to its end) on dependent variables as model (1) shows in last section. Summary of the regression results in each portfolio is shown in Table 2. Adjusted R2s range from. 政治大 However, with the existence 立of Fama-French three factors, demographic variables still. 53% to 90% and this are mainly due to the presence of Fama-French three factors.. ‧. ‧ 國. 學. obtain the explanatory power.. Overall, the results are as expected that both young adult and retired group have a. sit. y. Nat. positive coefficient. The results confirm our hypothesis that as one reaches retirement,. n. al. er. io. income decreases and individuals start to withdraw savings from equity market.. i n U. v. Therefore, the increase of the fraction of retire-aged population put pressure to stock. Ch. engchi. prices but increase expected returns. This results are similar to Erb, Harvey, and Viskanta(1997) which suggests that there is a positive correlation between the fraction of the population who ages over 65 and real stock returns in the United States. In addition, the results also confirm the life-cycle hypothesis of saving which proposes that young adults may be making major purchases like buying a new house or starting a family, even beginning a career and, as a consequence, expected returns of equity increase to attract this group of people to participate in the stock market.. 20.

(24) On the other hand, the coefficient of middle aged group shows a negative sign and proves our hypothesis that as individual comes to mid-point in life, labor income approach to its peak while expenditures begin to level off and then start to save for retirement in financial assets (see Arnott (2012)). As a result, following an increase of mid-aged population, the increased aggregate demand for equity securities would boosts the equity price and the expected return would fall otherwise. What’s more, we could find that the results in this age group are more stable then young adults and retired-aged since some results of the two age groups are in opposite position of our. 政治大 and further examination is necessary. 立. hypothesis or expected. But in general, these surprising estimations are not significant. ‧ 國. 學. In some cases, the significance of young adult group are larger than the retired. ‧. aged group. This result could be explained by that even though retired people are. sit. y. Nat. subject to possibility of selling assets from stock market, the aggregate demand of. io. er. stocks contributed by retired group still larger than that of young adult group. Most incomes of young adult population are mainly for the purpose of making major life. al. n. v i n durable purchases and few for C investing. However, while h e n g c h i U retired population do have the intention of selling holdings to cover consumption, there is no clear distinction. between hold and sell. That is to say, as individuals reach retired-age (set at 65 in this study), they won’t sell holdings immediately but defer the action to a later time or smooth it throughout the remaining life.. 6. Before conducting regression, we test the correlations between independent variables to avoid potential. problems of multi-collinearity and details of the results are not reported. The results suggest a good reason to run demographic variables separately (the absolute value of correlations range from 0.25 to 0.70).. 21.

(25) Table 2. Results of One-year Regressions This table shows the results of one-year regressions with both Fama-French factors and demographic variables. The model of the regression are: 𝐸𝑥𝑅𝑡 = 𝛼0 + 𝛼1 (𝑅𝑚 − 𝑅𝑓 )𝑡 + 𝛼2 𝑆𝑀𝐵𝑡 + 𝛼3 𝐻𝑀𝐿𝑡 + 𝛼4 𝐷𝑒𝑚𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑠𝑡−1 , where demographics are three population variables: 𝑃25−44 , 𝑃45−64 and 𝑃65+ each of them represent the fraction of population in group age from 25-44 (young adult), 45-64 (middle aged) and 65+ (retired). Demographic variables are lagged by one year to ensure its information was fully recognized by the market. Rm-Rf, the excess return on the market, SMB (Small Minus Big), HML (High Minus Low) are Fama-French three factors. High beta portfolios refer to stocks with year-end beta value higher than 70 percentile and low beta portfolios refer to stocks with year-end beta value lower than 30 percentile. Portfolios sorted by other. 政治大. 立. features (volatility, non-systematic, size, B/M, D/P) have the meaning in a similar way. The sample period of this regression is from 1962 to 2013.. (9.94). ***. (4.05). ***. 0.76 (4.02). ***. -0.61 (-3.18). ***. 0.67 (0.78). -0.62. -0.76. (-3.22). (-0.76). ***. -0.61. (9.71)***. (3.87)***. (-3.13)***. 0.79. (-0.16). Panel B. Volatility portfolio High volatility portfolio Rm-Rf. SMB. 1.82 (5.56). ***. 1.95 (5.94). ***. 1.92 (5.67). ***. HML. 1.82 (4.43). ***. 1.64 (3.99). ***. 1.66 (3.95). ***. P25-44. -1.34 (-3.30). ***. -1.35 (-3.22). ***. -1.29 (-3.07). ***. 0.79. -0.32. 0.79. al. P45-64. P65+. 3.61 (1.98). SMB. 0.89. 0.67. (-0.04). (0.16). (2.57)***. 0.92. -0.04. 0.01. -0.55. (15.62)***. (-0.58). (0.08). (-1.41)*. -0.04. 0.02. 0.80. (-0.47). (0.31). (1.02). v ni. (15.62) -2.10. 0.65. (17.00) 2.47. SMB ***. 0.78. (-0.98) 0.65. ***. 0.79. (0.57). (15.48) 22. a. 𝑹𝟐 0.86 0.85 0.84. Low volatility portfolio. 0.76. **. P65+. (15.39)***. Rm-Rf. a. 𝑹. P45-64. 0.83. engchi U. 𝟐. P25-44. 0.01. (14.92)***. Ch. HML. 0.00. 0.91. n. 0.75. Rm-Rf. a. 𝑹𝟐. io. 1.52. P65+. Nat. 1.51. 0.79. P45-64. y. (9.54). ***. P25-44. ‧. 1.49. HML. sit. SMB. Low beta portfolio. er. Rm-Rf. ‧ 國. High beta portfolio. 學. Panel A. Beta portfolio. ***. HML. -0.14 (-2.36). ***. -0.16 (-2.88). ***. -0.18 (-2.81). ***. P25-44. 0.21 (3.46). ***. 0.19 (3.32). ***. 0.21 (3.39). ***. P45-64. P65+. 0.55 (2.01). a. 𝑹𝟐 0.85. ***. -0.84 (-2.81). 0.86. ***. -0.09 (-0.14). 0.83.

(26) Table 2. - continued Results of One-year Regressions Panel C. Non-systematic risk portfolio High non-systematic risk portfolio -0.20. 1.27. (1.57). *. (-1.08). (1.56). *. 0.23. -0.21. -1.08. ***. (1.27). (-1.14). (-1.14). 0.93. 0.22. -0.18. (1.21). (-0.98). (6.47). P25-44. P45-64. SMB. 1.14 (11.57). ***. 0.54. 1.16 (11.96). 0.41. 0.53. P65+. 0.89. 0.00. 0.01. 0.83. (15.39)***. (-0.04). (0.16). (2.57)***. 0.92. -0.04. 0.01. -0.55. (15.62)***. (-0.58). (0.08). (-1.41)*. 0.91. -0.04. 0.02. 0.80. (14.92)***. (-0.47). (0.31). (1.02). 0.40. ***. a la. 𝑹 0.86 C h. Rm-Rf. 𝟐. iv. n 0.97 i U e n g c h (10.80) ***. 0.85. 0.06. 0.30. (0.48). (0.54). 0.39. P65+. a. 𝑹𝟐 0.80. 0.06. -0.11. ***. (0.47). (-0.18). 0.39. 0.06. 0.37. (3.21). (0.51). (0.29). ***. SMB. HML. 1.37 (12.12). ***. P25-44. 0.29 (2.62). ***. P45-64. (-2.28). -0.56. ***. (-0.94). 0.99. 1.38. 0.26. ***. ***. ***. (2.45). a. 𝑹𝟐 0.89. 0.27. (12.84). 0.80. ***. ***. (2.30). P65+. -1.15. 1.44 (12.58). 0.80. Small size portfolio. ***. (11.34). 23. P45-64. 0.92 (10.06). 0.84. P25-44. ***. (3.21). 1.15 (11.62). HML. (3.24). ***. n. HML. 0.55. io. Big size portfolio SMB. Rm-Rf. (0.21). Panel D. size portfolio Rm-Rf. 𝟐. Nat. (6.22). ***. 立a. 𝑹. y. 0.29. P65+. ‧. 0.93. P45-64. sit. (6.06). ***. P25-44. 學. 0.89. HML. Low non-systematic risk portfolio. er. SMB. ‧ 國. Rm-Rf. 政治大. 0.88 -3.37 (-3.02). ***. 0.90.

(27) Table 2. - continued Results of One-year Regressions. High B/M portfolio. 1.05. (4.30). ***. 0.38 (4.14). ***. (6.38). ***. -0.29 (-0.70). 0.58 (6.26). 0.87 (16.89). ***. 0.87 (16.05). ***. (-1.43). *. -0.12 (-1.84). **. -0.12 (-1.79). **. 0.37 (5.66). ***. 0.36 (5.46). ***. 0.37 (5.57). ***. P45-64. P65+. 0.53 (1.83). al. n. (16.24). ***. -0.09. P25-44 **. -0.53 (-1.58). ***. 1.01. 0.85. (-0.64). io. 0.85. HML. f. (11.03). -0.61. ***. High D/P portfolio SMB. 0.85. (-0.15). Panel F. D/P portfolio MMF. m. (10.64). -0.07. ***. 0.57 (6.30). 𝟐. Low B/M portfolio SMB. HML. 0.04 (0.34) -0.03. ***. (-0.29). 1.00. -0.03. (10.25). Nat. (14.33). ***. 0.39. 0.58. P65+. ***. ‧. (14.47). ***. (4.01). ***. P45-64. (-0.23). -0.47 (-4.22). ***. P25-44. P45-64. (3.05). 0.81. ***. -1.27 (-2.12). ***. 0.79. ***. -0.45 (-3.72). a. 𝑹𝟐. 1.53. -0.49 (-4.14). P65+. 1.22. 0.77. (0.97). ***. y. 1.04. 0.37. P25-44. 學. (14.34). ***. HML. sit. 1.06. SMB. ‧ 國. Rm-Rf. 政治大 R -R 立a. 𝑹0.85 0.96. a. 𝑹. MMF. 𝟐. 0.86. Ch 0.85. SMB. i v 1.07 n U (6.36) e n g c h i(8.59) 1.14 ***. ***. 1.18. 1.04. (9.83). *. 0.28. er. Panel E. B/M portfolio. 0.85. ***. 1.19. (0.40). (9.07). 24. ***. (6.93). ***. 1.02 (6.25). ***. Low D/P portfolio HML -0.51 (-2.78). ***. -0.59 (-3.47). ***. -0.55 (-3.04). ***. P25-44. P45-64. P65+. a. 𝑹𝟐. 0.24. 0.85. (0.29) -1.89 (-2.62). 0.88. ***. -2.16 (-1.38). *. 0.86.

(28) 4.2 Multi-Year regression Changing population structure affects not only the next year’s stock returns but also has a longer term effect on stock prices. Moreover, given the low-frequency variation in population age structure, annual returns may introduce substantial noise to any relationship with demographic structure. Testing for low-frequency changes in expected returns should be done with long time-series. This was confirmed as Yoo (1994) suggested, while estimating demographic impact, regressions with three- and. 政治大 and fit. Hence, we impose long-horizon tests, trying to capture the impact of changing 立 five year centered moving averages increase in terms of both statistical significance. demographics on multi-year returns in this subsection. The structure of the regressions. ‧. ‧ 國. 學. are:. (2). sit. y. Nat. 𝐸𝑥𝑅 𝑘 𝑡 = 𝛼0 + 𝛼1𝑀𝑀𝐹𝑡 + 𝛼2 𝑆𝑀𝐵𝑡 + 𝛼3 𝐻𝑀𝐿𝑡 + 𝛼4𝑃𝑘 𝑡,25−44. (3). er. io. 𝐸𝑥𝑅 𝑘 𝑡 = 𝛽0 + 𝛽1 𝑀𝑀𝐹𝑡 + 𝛽2 𝑆𝑀𝐵𝑡 + 𝛽3 𝐻𝑀𝐿𝑡 + 𝛽4 𝑃𝑘 𝑡,45−64. n. a l 𝑡 + 𝛾2 𝑆𝑀𝐵𝑡 + 𝛾3 𝐻𝑀𝐿𝑡 + 𝐸𝑥𝑅 𝑘 𝑡 = 𝛼0 + 𝛾1 𝑀𝑀𝐹 i v 𝛾4 𝑃𝑘 𝑡,65+ Ch. engchi 1/𝑘. Where 𝐸𝑥𝑅 𝑘 𝑡 = [∏𝑘 𝑢=1(1 + 𝐸𝑥𝑅𝑡+𝑢 )]. Un. (4). − 1 is the K year average excess 1/𝑘. return, and 𝑃𝑘 𝑡,25−44 = (𝑃𝑡,25−44 /𝑃𝑡−𝑘+1,25−44 ). is the K year average. level of the fraction of population aged from 25 to 44 and the other demographic variables are defined likewise. Particularly, I forecast the next K-period returns based on the last K-period levels in the population structure. Panel A of Table 3 - 8 shows regressions of three-year excess stock returns on three-year level while panel B performs the same exercise for five-year horizon.. 25.

(29) Table 3. Results of Multi-year Regressions – Beta portfolio Panel A. High Beta portfolio. 3 year horizon. MMF 0.26 (1.73)** 0.31 (2.10)*** 0.30 (2.03)***. SMB 0.20 (1.11) 0.12 (0.70) 0.14 (0.76). HML -0.29 (-1.61)* -0.30 (-1.66)** -0.26 (-1.41)*. P25-44 1.64 (2.04)***. P45-64. P65+. -1.38 (-1.41)**. 0.17 2.02 (1.03). 1.76 (2.14)***. 立. HML 0.03 (0.22) 0.01 (0.11) 0.05 (0.39). P25-44 1.47 (2.49)***. 2.77 (1.36)** P65+. P45-64. 0.25 0.12. 學. 0.04 0.05. n. Ch. P45-64. P65+. sit. P25-44 0.76 (2.46)***. -0.81 (-2.17)***. i e n g c h0.81. i n U. v. a. 𝑹𝟐 0.14 0.12. er. io. HML 0.07 (1.06) 0.06 (0.86) 0.09 (1.20). y. ‧. 3.02 (1.84)**. Nat. 3 year Horizon. 2.38 (1.59)*. -1.55 (-1.72)**. al. a. 𝑹𝟐 0.31. **. 1.69 (2.69)***. SMB 0.05 (0.70) 0.02 (0.22) 0.02 (0.31). 0.02. 0.25. -1.35. Panel B. Low Beta portfolio MMF 0.09 (1.58)* 0.11 (2.00)*** 0.11 ** (1.91). 0.01. (-1.67) 政治大. ‧ 國. 5 year horizon. SMB 0.15 (1.10) 0.09 (0.65) 0.09 (0.67). 0.15 0.07. -1.30 (-1.24). MMF 0.34 (3.13)*** 0.38 (3.50)*** 0.38 (3.45)***. a. 𝑅2 0.20. 1.06 * (1.40). 0.07 0.11. (2.70)*** -0.89 (-2.36)***. 5 year horizon. MMF 0.07 (1.34)* 0.08 (1.71)** 0.09 (1.71)**. SMB 0.13 (2.13)*** 0.11 (1.81)** 0.10 (1.64)*. HML 0.09 (1.50)* 0.08 (1.27) 0.10 (1.62)**. P25-44 0.73 (2.71)***. P45-64. 0.08 1.16 * (1.54) P65+. -0.98 (-2.76)***. a. 𝑹𝟐 0.22 0.22. 1.19 (1.74)** 0.67 (2.44)***. 0.15 0.09. -1.01 (-2.70)***. 0.12 1.14 (1.60)*. 26. 0.03. 0.03.

(30) Table 4. Results of Multi-year Regressions –Volatility portfolio Panel A. High Volatility portfolio. 3 year horizon. MMF 0.32 (1.22) 0.45 (1.69) ** 0.44 (1.61) *. SMB 0.33 (1.04) 0.15 (0.45) 0.18 (0.54). HML -0.64 (-2.04) *** -0.67 (-2.04) *** -0.58 (-1.73) ***. P25-44 3.88 (2.74) ***. P45-64. P65+. -2.93 (-1.66) **. 0.16 4.31 (1.22). 4.01 (2.78) ***. 立. HML -0.02 (-0.10) -0.05 (-0.18) 0.03 (0.11). P25-44 3.28 (3.11) ***. P45-64. -2.53. 0.05. P65+. y. P45-64. sit. P25-44 1.09 (3.43) ***. -0.98 (-2.48) ***. e n g c h1.29i. i n U. v. a. 𝑹𝟐 0.30 0.23. er. n. Ch. 0.08. ‧. io. al. HML 0.01 (0.09) -0.01 (-0.09) 0.03 (0.33). 0.22 0.20. 6.69 (2.31) ***. Nat. 3 year horizon. 5.20 (1.90) **. -3.02 (-1.87) **. SMB -0.05 (-0.72) -0.10 (-1.39) ** -0.09 (-1.19). a. 𝑹𝟐 0.31 0.21. 學. 3.88 (3.61) ***. 0.03. **. Panel B. Low Volatility portfolio MMF 0.15 (2.64) *** 0.19 (3.14) *** 0.18 (2.97) ***. 0.02 5.66 (1.55) * P65+. (-1.69) 政治大. ‧ 國. 5 year horizon. SMB 0.01 (0.01) -0.14 (-0.58) -0.13 (-0.51). 0.13 0.12. -2.70 (-1.44) *. MMF 0.55 (2.87) *** 0.66 (3.27) *** 0.65 (3.22) ***. a. 𝑅2 0.23. 1.45 (1.79) **. 0.18 0.24. (4.10) *** -1.08 (-2.55) ***. 5 year horizon. MMF 0.11 (2.45) *** 0.14 (2.96) *** 0.14 (2.86) ***. SMB 0.07 (1.20) 0.03 (0.43) 0.02 (0.40). HML 0.05 (0.97) 0.04 (0.65) 0.07 (1.14). P25-44 1.13 (4.50) ***. P45-64. 0.10 1.93 (2.31) *** P65+. -1.20 (-3.32) ***. a. 𝑹𝟐 0.40 0.30. 1.81 (2.63) *** 1.18 (4.60) ***. 0.24 0.30. -1.29 (-3.38) ***. 0.18 2.01 (2.79) ***. 27. 0.08. 0.12.

(31) Table 5. Results of Multi-year Regressions –Non-sys risk portfolio Panel A. High Non-systematic risk portfolio. 3 year horizon. MMF 0.26 (2.28) *** 0.31 (2.72) *** 0.31 (2.63) ***. SMB 0.00 (-0.01) -0.08 (-0.56) -0.07 (-0.47). HML -0.21 (-1.53) * -0.23 (-1.59) * -0.18 (-1.26). P25-44 1.68 (2.72) ***. P45-64. P65+. -1.39 (-1.81) **. 0.21 1.80 (1.16). 1.97 (3.11) ***. 立. HML 0.02 (0.15) 0.01 (0.01) 0.04 (0.35). P25-44 1.51 (3.26) ***. 2.76 (1.70) ** P65+. -1.45 2.21 (1.82) **. n. Ch. y. P65+. sit. P45-64. -0.38 (-0.54). e n g c h0.99i. i n U. v. a. 𝑹𝟐 0.13 0.07. er. io. al. P25-44 1.08 (1.91) **. 0.08. ‧. Nat. 3 year horizon. 0.09 3.08 (2.26) ***. HML -0.05 (-0.40) -0.05 (-0.38) -0.03 (-0.22). 0.30 0.22. -1.75 (-2.36) ***. SMB 0.26 (2.03) *** 0.20 (1.58) * 0.23 (1.85) **. a. 𝑹𝟐 0.39 0.32. 學. 1.90 (3.82) ***. 0.04. ***. Panel B. Low Non-systematic risk portfolio MMF 0.11 (1.07) 0.15 (1.47) * 0.13 (1.27). 0.04. P45-64. (-2.23) 政治大. ‧ 國. 5 year horizon. SMB -0.05 (-0.46) -0.11 (-1.01) -0.11 (-0.99). 0.18 0.15. -1.41 (-1.69) **. MMF 0.32 (3.81) *** 0.37 (4.20) *** 0.37 (4.13) ***. a. 𝑹𝟐 0.27. 2.26 (1.68) **. 0.12 0.04. (1.73) ** -0.36 (-0.50). 5 year horizon. MMF 0.09 (1.21) 0.13 (1.73) ** 0.11 (1.56) *. SMB 0.33 (3.76) *** 0.27 (2.94) *** 0.29 (3.35) ***. HML 0.08 (0.99) 0.08 (0.89) 0.11 (1.20). P25-44 1.16 (2.97) ***. P45-64. -0.02 2.24 (1.63) * P65+. -0.55 (-0.99). a. 𝑹𝟐 0.33 0.22. 2.43 (2.50) *** 0.94 (2.16) ***. 0.30 0.07. -0.52 (-0.83). -0.01 2.20 (2.00) ***. 28. 0.03. 0.06.

(32) Table 6. Results of Multi-year Regressions – Size portfolio Panel A. Big size portfolio. 3 year horizon. MMF 0.18 (2.75)*** 0.23 (3.24)*** 0.21 (3.07)***. SMB -0.02 (-0.3) -0.09 (-1.10) -0.07 (-0.78). HML -0.09 (-1.12) -0.10 (-1.13) -0.07 (-0.80). P25-44 1.43 (4.08)***. P45-64. P65+. -0.77 (-1.63)*. 0.22 2.39 (2.67)***. 1.64 (4.52)***. HML 0.03 (0.47) 0.02 (0.30) 0.05 (0.80). P25-44 1.44 (5.40)***. 2.80 (3.86)***. -1.06 (-2.20)***. 0.23. ‧. n. Ch. P45-64. P65+. y. P25-44 -0.43 (-0.60). sit. HML 0.06 (0.39) 0.04 (0.23) 0.05 (0.30). -0.87 (-1.02). i engch -1.07. i n U. v. a. 𝑹𝟐 0.28 0.29. er. io. al. 0.40. 0.07 3.15 (3.91)***. SMB 0.71 (4.40)*** 0.75 (4.80)*** 0.70 (4.48)***. a. 𝑹𝟐 0.52. 0.37. 學. 1.56 (5.37)***. 0.15. 0.27. 政治大. 立. Nat. 3 year horizon. 3.00 (3.17)*** P65+. P45-64. Panel B. Small size portfolio MMF -0.03 (-0.20) -0.06 (-0.47) -0.02 (-0.16). 0.03. -0.91 (-2.09)***. ‧ 國. 5 year horizon. SMB 0.07 (1.10) 0.01 (-0.02) 0.02 (0.27). 0.29 0.28. -0.84 (-1.60)*. MMF 0.17 (3.14)*** 0.22 (3.70)*** 0.20 (3.77)***. a. 𝑹𝟐 0.40. -1.85 (-1.1). 0.30 0.02. (-1.33)* -0.69 (-0.68). 5 year horizon. MMF 0.09 (0.79) 0.04 (0.36) 0.08 (0.77). SMB 0.38 (2.72)*** 0.44 (3.24)*** 0.39 (2.19)***. HML 0.16 (1.21) 0.14 (1.04) 0.15 (1.10). P25-44 -0.72 (-1.17). P45-64. -0.01 -2.49 (-1.53)* P65+. -0.79 (-0.96). a. 𝑹𝟐 0.18 0.17. -2.45 (-1.64)* -1.00 (-1.56)*. 0.20 0.03. -0.63 (-0.70). -0.01 -2.90 (-1.83)**. 29. 0.03. 0.05.

(33) Table 7. Results of Multi-year Regressions –B/M portfolio Panel A. High B/M portfolio. 3 year horizon. MMF 0.09 (0.96) 0.10 (1.17) 0.10 (1.15). SMB 0.24 (2.22) *** 0.21 (2.05) *** 0.22 (2.05) ***. HML 0.15 (1.42) * 0.14 (1.31) * 0.16 (1.50) *. P25-44 0.59 (1.23). P45-64. P65+. -0.67 (-1.17). 0.11 0.85 (0.74). 0.46 (0.94). HML 0.14 (1.88) ** 0.13 (1.72) ** 0.15 (1.94) **. P25-44 0.56 (1.64) *. 立. 0.56 (0.48) P65+. -0.88 0.76 (0.90). -0.01. ‧. n. Ch. P45-64. P65+. y. P25-44 1.98 (4.06) ***. sit. io. HML -0.25 (-2.35) *** -0.26 (-2.18) *** -0.22 (-1.83) **. -1.28 (-1.97) **. er. Nat. 3 year horizon. 0.04 0.54 (0.59). al. 0.19 0.01. -0.88 (-1.78) **. SMB -0.05 (-0.46) -0.15 (-1.24) -0.11 (-0.97). a. 𝑹𝟐 0.22 0.24. 學. 0.41 (1.14). -0.02. ***. Panel B. Low B/M portfolio MMF 0.25 (2.77) *** 0.32 (3.26) *** 0.30 (3.09) ***. 0.01. P45-64. (-1.98) 政治大. ‧ 國. 5 year horizon. SMB 0.22 (2.89) *** 0.21 (2.81) *** 0.20 (2.60) ***. 0.10 0.00. -0.74 (-1.24). MMF 0.07 (1.15) 0.08 (1.35) * 0.09 (1.42) *. a. 𝑹𝟐 0.12. e n g c h2.32i. i n U. v. 3.02 (2.39) ***. a. 𝑹𝟐 0.44 0.30 0.32 0.26. (4.34) *** -1.30 (-1.72) **. 5 year horizon. MMF 0.23 (3.33) *** 0.30 (3.67) *** 0.28 (3.66) ***. SMB 0.08 (0.94) -0.01 (-0.07) 0.01 (0.11). HML -0.03 (-0.39) -0.05 (-0.45) 0.00 (-0.01). P25-44 1.97 (5.14). P45-64. 0.04 4.06 (2.92) *** P65+. -1.45 (-2.40) ***. a. 𝑹𝟐 0.51 0.30. 3.54 (3.36) *** 2.15 (5.16). 0.37 0.35. -1.63 (-2.40) ***. 0.09 4.13 (3.54) ***. 30. 0.13. 0.19.

(34) Table 8. Results of Multi-year Regressions –D/P portfolio Panel A. High D/P portfolio. 3 year horizon. MMF 0.15 (2.43) *** 0.19 (2.92) *** 0.18 (2.76) ***. SMB -0.06 (-0.73) -0.11 (-1.40) * -0.09 (-1.15). HML 0.05 (0.63) 0.04 (0.48) 0.07 (0.86). P25-44 1.15 (3.39) ***. P45-64. P65+. -0.78 (-1.78) **. 0.16 1.85 (2.18) ***. 1.35 (4.07) ***. HML 0.08 (1.39) * 0.07 (1.08) 0.10 (1.60) *. P25-44 1.18 (4.52) ***. 立. 2.27 (2.63) *** P65+. -0.93 2.28 (3.30) ***. 0.18. ‧. n. Ch. P45-64. P65+. y. P25-44 1.00 (0.98). sit. io. HML -0.13 (-0.55) -0.19 (-0.81) -0.12 (-0.52). -1.34 (-1.32) **. e n g c h0.47i. i n U. v. a. 𝑹𝟐 0.20 0.22. er. Nat. 3 year horizon. 0.11 2.47 (3.43) ***. al. 0.28 0.31. -1.07 (-2.59) ***. SMB 0.68 (3.23) *** 0.63 (3.10) *** 0.64 (3.04) ***. a. 𝑹𝟐 0.39 0.21. 學. 1.25 (4.78) ***. 0.11. ***. Panel B. Low D/P portfolio MMF -0.03 (-0.16) 0.01 (0.07) 0.00 (-0.01). 0.06. P45-64. (-2.35) 政治大. ‧ 國. 5 year horizon. SMB 0.04 (0.73) -0.01 (-0.14) 0.00 (0.04). 0.18 0.24. -0.91 (-1.99) ***. MMF 0.11 (2.40) *** 0.15 (2.87) *** 0.14 (2.82) ***. a. 𝑹𝟐 0.28. 0.43 (0.20). 0.18 -0.02. (0.42) -1.20 (-1.06). 5 year horizon. MMF 0.21 (1.38) * 0.22 (1.54) * 0.22 (1.51) *. SMB 0.31 (1.70) ** 0.30 (1.73) ** 0.29 (1.59) *. HML 0.17 (0.86) 0.12 (0.63) 0.17 (0.83). P25-44 0.49 (0.56). P45-64. 0.00 -0.05 (-0.02) P65+. -1.35 (-1.41) *. a. 𝑹𝟐 0.14 0.18. -0.10 (-0.05) 0.35 (0.38). 0.13 -0.03. -1.28 (-1.24). 0.02 -0.18 (-0.09). 31. -0.03. -0.03.

(35) Table 3 – 8 show the results of multi-year regression of each portfolio and perform three- and five- year horizon respectively. Clearly, estimations in multi-year forecasts are more stable than single year and we found a significant increase in terms of statistical significance. This increase of significance and stability is also confirmed by Yoo (1994) and Goyal (2004) which suggest that long horizons provide a better test for low-frequency population changes. Furthermore, under the existence of Fama and French three factors, these demographic variables (P25-44, P45-64, and P65+) still. 政治大. explain portfolio returns significantly.. 立. In the long-horizon regression, Adjusted R2s of regressions with both 3 factors. ‧ 國. 學. and demographic variables range from 7% to 52%. Adjusted R2s of regressions with. ‧. only demographic variables range from -3% to 37%. The sign of coefficients still. sit. y. Nat. confirm out hypothesis that the increase of both young-aged population and retired-. io. er. aged population have positive effect on stock returns and, on the other hand, the increase of middle-aged population (age from 44 to 64) decrease stock returns. The. al. n. v i n haveChighest positive value of 6.69 in 5-year horizon high hengchi U. coefficient of variable P65+. volatility portfolio, suggesting that retired people are most sensitive to high volatility.. Also, the significance of young adult groups are larger than retired-aged groups. However, in terms of value, the coefficient of retired-aged groups are larger than young adult groups. This shows that the necessary amount to increase for compensating the retired people’s propensity of re-allocating assets from riskier stock market into saver market (e.g. bond, cash) is larger than the amount for attract young adults to invest. Therefore, according to our results, the increase of the fraction of retired population could be a major drive of equity premium. 32.

(36) Unexpectedly, retired-aged groups shows a negative sign in low dividend ratio group. This result may overthrow our hypothesis that portfolios with more income yielding would be reluctant to be selling when people retired and suggest that instead of selling low-yielding holdings, they could even buy more. Other unusual results appear in size portfolio. We originally assume that as population getting more aged, the demand in high-risk small cap stocks would first decrease and is therefore resulting an increased value of equity premium. Conversely, the results suggest a sustain. 政治大. demand in small cap stocks across all age groups.. 立. In general, the absolute value of coefficients in high risk level portfolios are. ‧ 國. 學. larger than in low risk level portfolios. This implies that, in terms of positive. ‧. coefficients, the rise of expected returns in high risk portfolios for compensating those. sit. y. Nat. who are less willing to buy stocks are larger than the necessary amount in low risk. io. er. portfolios. With regard to negative coefficients, as mentioned in previous context, middle-aged group are at the peak of labor income level and the durable consumptions. al. n. v i n stabilized at this life stage, which middle-aged has the most risk tolerance C means h e nthat gchi U. and they even seek to take risks (see Brooks (1998), Erb, Harvey, Viskanta (1997) and Goyal (2004)) as we see in the results that declining returns are even lower in high risk portfolios. With the importance of this finding, we further conduct an empirical examination to test the significance of these differences (shown in table 9 and 10).. 33.

(37) Table 9. Difference test in regressions with Fama-French 3 factors This table reports the results of difference test in regressions with both Fama-French factors and demographic variables. Results of 3-year horizon and 5-year horizon are shown separately. The coefficients in panel A. are calculated by: coefficients of demographic variables in high risk portfolio – coefficients of demographic variables in low risk portfolio. The coefficients in panel B. are calculated by: coefficients of demographic variables in low (small) level portfolio – coefficients of demographic variables in high (big) level portfolio. T-stats are computed by the following model: tstat = (β1 − β2 )/√SE.β1 2 + SE.β2 2 . The P25-44 factor is the fraction of population aged from 25 to 44 and other variables are defined in a similar way.. Panel A.. 立. Beta portfolio. P25-44. Coeff. t-stat Coeff.. t-stat. Coeff.. P45-64. t-stat. Non-systematic portfolio P65+. Coeff. t-stat Coeff.. P25-44. t-stat. P45-64. P65+. Coeff. t-stat Coeff. t-stat Coeff. t-stat. 1.02 -0.57 -0.55. 0.96. 0.46. 2.79. 1.92** -1.95 -1.08. 2.87. 0.79. 0.59. 0.71 -1.01 -0.98 -0.46 -0.22. 0.74. 1.14 -0.37 -0.42. 1.19. 0.72. 2.15 1.98*** -1.33 -0.87. 3.38. 1.20. 0.36. 0.59 -0.90 -1.05 -0.23 -0.14. P25-44 Coeff.. t-stat. P45-64. P65+. Coeff. t-stat Coeff.. t-stat. y. sit. al. B/M portfolio. n. Size portfolio. er. io. Panel B.. ‧. 0.87. Nat. 3 year horizon 5 year horizon. t-stat. P65+. ‧ 國. Coeff.. P45-64. Volatility portfolio. 學. P25-44. 政治大. P C h Coeff.. i n U. P45-64. 25-44. et-stat hi n g cCoeff.. v. D/P portfolio P65+. t-stat Coeff.. P25-44. t-stat. P45-64. P65+. Coeff. t-stat Coeff. t-stat Coeff. t-stat. 3 year horizon. -1.86 -2.33*** -0.10 -0.10 -4.24 -2.23***. 1.39 2.03*** -0.61 -0.70. 2.17. 1.27. -0.15 -0.14 -0.57 -0.51 -1.42 -0.62. 5 year horizon. -2.16 -3.22***. 1.41 2.75*** -0.57 -0.76. 2.78 2.06***. -0.69 -0.75 -0.42 -0.41 -2.38 -1.12. 0.12. 0.12 -5.25 -3.16***. 34.

(38) Table 10. Difference test in regressions with demographic variables only This table reports the results of difference test in regressions with only demographic variables. Results of 3-year horizon and 5-year horizon are shown separately. The coefficients in panel A. are calculated by: coefficients of demographic variables in high risk portfolio – coefficients of demographic variables in low risk portfolio. The coefficients in panel B. are calculated by: coefficients of demographic variables in low (small) level portfolio – coefficients of demographic variables in high (big) level portfolio. T-stats are computed by the following model: t-stat = (β1 − β2 )/√SE.β1 2 + SE.β2 2 . The P25-44 factor is the fraction of population aged from 25 to 44 and other variables are defined in a similar way.. Panel A.. 立. Beta portfolio. P25-44. Coeff. t-stat Coeff.. t-stat. Coeff.. P45-64. t-stat. Non-systematic portfolio P65+. Coeff. t-stat Coeff.. P25-44. t-stat. 1.09 -0.42 -0.37. 1.61. 0.74. 2.71. 1.84** -1.62 -0.84. 3.73. 1.00. 1.03. 1.49* -0.54 -0.56. 1.88. 1.05. 2.69 2.44*** -1.72 -1.04. 4.68. 1.57*. P25-44 Coeff.. t-stat. P45-64. P65+. Coeff. t-stat Coeff.. t-stat. y. P65+. 0.99. 1.16 -1.04 -0.94. 0.52. 0.24. 0.96 1.46* -1.23 -1.27. 0.88. 0.50. sit. al. n. Size portfolio. P45-64. Coeff. t-stat Coeff. t-stat Coeff. t-stat. er. io. Panel B.. ‧. 0.96. Nat. 3 year horizon 5 year horizon. t-stat. P65+. ‧ 國. Coeff.. P45-64. Volatility portfolio. 學. P25-44. 政治大. B/M portfolio. iv P P P n C U Coeff. Coeff. h t-stat e n g Coeff. c h i t-stat 25-44. 45-64. D/P portfolio. 65+. t-stat. P25-44. P45-64. P65+. Coeff. t-stat Coeff. t-stat Coeff. t-stat. 3 year horizon. -2.71 -3.07***. 0.15. 0.13 -5.49 -2.92***. 1.86 2.57*** -0.56 -0.58. 3.50 1.93***. -0.88 -0.75 -0.29 -0.24 -2.31 -0.95. 5 year horizon. -2.56 -3.64***. 0.43. 0.42 -6.05 -3.40***. 1.74 3.14*** -0.75 -0.90. 3.59 2.41***. -0.90 -0.94 -0.21 -0.19 -2.65 -1.23. 35.

(39) Under the presence of Fama-French three factors, panel A in table 9 shows insignificant results for both beta and non-systematic risk portfolios. Volatility, on the other hand, have significant and highest positive value. Retired people do be more sensitive to high volatility stocks and require more risk premium in this group of stocks. Panel B in table 9 and 10 present discrepant results. Positive results in B/M portfolio suggest a defensive tendency when retired people re-allocating their assets (results in panel B are computed by a contrast way to panel A: coefficients in low (small) level portfolio – coefficients in high (big) level portfolio). However, negative results in Size. 治政大 small stocks. Surprisingly, portfolio suggest a propensity for retired people to choose 立 there is no significant difference between high risk portfolio and low risk portfolio for ‧ 國. 學. middle-aged population implying no preference for high or low risk stocks.. ‧. n. er. io. sit. y. Nat. al. Ch. engchi. 36. i n U. v.

(40) 5. Conclusion There have been ongoing debates about the link between stock market and demographic changes. Life-cycle hypothesis provides a theoretical support to this subject. Empirical tests also suggest a positive relation between stock market returns and the fraction of retired population. These works focus on macroeconomics and treat stock market in a whole-market scale.. In this study, we examine the reactions of different portfolios under demographic. 政治大. changes for a deeper scope of the equity market. The increase of retired population do. 立. increase the future equity returns supporting hypothesis that the possible action of re-. ‧ 國. 學. allocating assets from risky stock market to saver market when people get retired would raise required risk premium. This effect is even stronger to high risk portfolios, which. ‧. further confirms that decreasing risk tolerance in retired population is one of the major. y. Nat. sit. drivers to the increased equity return. Middle-aged population, on the other hand, have. n. al. er. io. negative impact to future equity returns. Increasing fraction of middle-aged population. i n U. v. would decrease required risk premium with the urge to invest for retirement and the. Ch. engchi. consequent increased aggregate demand for profitable investment.. Overall, retired population is more sensitive to high volatility portfolio and request for more premium. However, there is no significant difference between high risk portfolio and low risk portfolio in measurements of beta and non-systematic risks. Finally, retired population do have propensity for value stocks and small-cap stocks and is therefore demanding higher premium in growth stocks and large-cap stocks.. 37.

(41) 6. Reference. 1.. Abel, A. B. (2003). The effects of a baby boom on stock prices and capital accumulation in the presence of social security. Econometrica, 71(2), 551-578.. 2.. Ando, A., & Modigliani, F. (1963). The" life cycle" hypothesis of saving: Aggregate implications and tests. The American economic review, 55-84.. 3.. Ang, A., & Maddaloni, A. (2003). Do demographic changes affect risk premiums?. 政治大. Evidence from international data (No. w9677). National Bureau of Economic Research.. 立. Arnott, R. D., & Chaves, D. B. (2012). Demographic changes, financial markets,. 學. ‧ 國. 4.. and the economy. Financial Analysts Journal, 68(1), 23-46.. Bakshi, G. S., & Chen, Z. (1994). Baby boom, population aging, and capital. ‧. 5.. markets. Journal of Business, 165-202.. y. Nat. io. sit. Brooks, R. (2000). Life cycle portfolio choice and asset market effects of the baby. er. 6.. boom. International Monetary Fund.. n. al. Ch. i n U. v. 7.. Davis, E. P. (2007). How will ageing affect the structure of financial markets.. 8.. Davis, E. P., & Li, C. (2003). Demographics and financial asset prices in the major. engchi. industrial economies. 9.. Dent Jr, H. (1993). The Great Boom Ahead-Your Comprehension Guide to Personal and Business Profit in the New Era of Prosperity.. 10. Erb, C. B., Harvey, C. R., & Viskanta, T. E. (1997). Demographics and international investments. Financial Analysts Journal, 53(4), 14-28. 11. Fama, E. F., & French, K. R. (1992). The cross‐section of expected stock returns. the Journal of Finance, 47(2), 427-465.. 38.

(42) 12. Goyal, A. (2004). Demographics, stock market flows, and stock returns. Journal of Financial and Quantitative Analysis, 39(01), 115-142. 13. Modigliani, F. (1986). Life cycle, individual thrift, and the wealth of nations. The American Economic Review, 297-313. 14. Modigliani, F., & Brumberg, R. (1954). Utility analysis and the consumption function: An interpretation of cross-section data. Franco Modigliani, 1. 15. Shefrin, H. M., & Thaler, R. H. (1988). The behavioral life-cycle hypothesis.Quasi Rational Economics, 91-126.. 政治大 Sterling, W., Waite, S., & O'Neill, B. (1999). Boomernomics: The future of your 立. 16. Shiller, R. J. (2000). Irrational exuberance. Princeton UP. 17.. ‧ 國. 學. money in the upcoming generational warfare.. 18. United Nations. Dept. of Economic. (2013). World population ageing, 1950-2050.. ‧. New York: United Nations.. sit. y. Nat. 19. Yoo, P. S. (1994). Age distributions and returns of financial assets. Federal. io. n. al. er. Reserve Bank of St. Louis Working Paper Series, (1994-002).. Ch. engchi. 39. i n U. v.

(43) Appendix. United States Census Bureau estimate the resident population for each year since the most recent decennial census by using measures of population change. The resident population includes all people currently residing in the United States. According to the publication of Federal Census Bureau. The population estimate at any given time point starts with a population base (the last decennial census or the previous point in the time. 治政 international migration. The individual methods we use大 account for additional factors 立 such as input data availability and the requirement that all estimates be consistent by series), adds births, subtracts deaths, and adds net domestic migration and net. ‧ 國. 學. geography and age, sex, race, and Hispanic origin.. ‧. n. er. io. sit. y. Nat. al. Ch. engchi. 40. i n U. v.

(44)