4. Empirical result
4.2 Multi-Year regression
國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
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 five year centered moving averages increase in terms of both statistical significance and fit. Hence, we impose long-horizon tests, trying to capture the impact of changing demographics on multi-year returns in this subsection. The structure of the regressions are:
𝐸𝑥𝑅𝑘𝑡 = 𝛼0+ 𝛼1𝑀𝑀𝐹𝑡 + 𝛼2𝑆𝑀𝐵𝑡 + 𝛼3𝐻𝑀𝐿𝑡 + 𝛼4𝑃𝑘𝑡,25−44 (2) 𝐸𝑥𝑅𝑘𝑡 = 𝛽0+ 𝛽1𝑀𝑀𝐹𝑡 + 𝛽2𝑆𝑀𝐵𝑡 + 𝛽3𝐻𝑀𝐿𝑡 + 𝛽4𝑃𝑘𝑡,45−64 (3) 𝐸𝑥𝑅𝑘𝑡 = 𝛼0+ 𝛾1𝑀𝑀𝐹𝑡 + 𝛾2𝑆𝑀𝐵𝑡+ 𝛾3𝐻𝑀𝐿𝑡 + 𝛾4𝑃𝑘𝑡,65+ (4)
Where 𝐸𝑥𝑅𝑘𝑡 = [∏𝑘𝑢=1(1 + 𝐸𝑥𝑅𝑡+𝑢)]1/𝑘 − 1 is the K year average excess return, and 𝑃𝑘𝑡,25−44 = (𝑃𝑡,25−44 /𝑃𝑡−𝑘+1,25−44)1/𝑘 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.
‧
Results of Multi-year Regressions – Beta portfolio
Panel A. High Beta portfolioMMF SMB HML P25-44 P45-64 P65+ a. 𝑅2
Panel B. Low Beta portfolio
MMF SMB HML P25-44 P45-64 P65+ a. 𝑹𝟐
‧
Results of Multi-year Regressions –Volatility portfolio
Panel A. High Volatility portfolioMMF SMB HML P25-44 P45-64 P65+ a. 𝑅2
Panel B. Low Volatility portfolio
MMF SMB HML P25-44 P45-64 P65+ a. 𝑹𝟐
‧
Results of Multi-year Regressions –Non-sys risk portfolio
Panel A. High Non-systematic risk portfolioMMF SMB HML P25-44 P45-64 P65+ a. 𝑹𝟐
Panel B. Low Non-systematic risk portfolio
MMF SMB HML P25-44 P45-64 P65+ a. 𝑹𝟐
‧
Results of Multi-year Regressions – Size portfolio
Panel A. Big size portfolioMMF SMB HML P25-44 P45-64 P65+ a. 𝑹𝟐
Panel B. Small size portfolio
MMF SMB HML P25-44 P45-64 P65+ a. 𝑹𝟐
‧
Results of Multi-year Regressions –B/M portfolio
Panel A. High B/M portfolioMMF SMB HML P25-44 P45-64 P65+ a. 𝑹𝟐
Panel B. Low B/M portfolio
MMF SMB HML P25-44 P45-64 P65+ a. 𝑹𝟐
‧
Results of Multi-year Regressions –D/P portfolio
Panel A. High D/P portfolioMMF SMB HML P25-44 P45-64 P65+ a. 𝑹𝟐
Panel B. Low D/P portfolio
MMF SMB HML P25-44 P45-64 P65+ a. 𝑹𝟐
‧
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 explain portfolio returns significantly.In the long-horizon regression, Adjusted R2s of regressions with both 3 factors 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 confirm out hypothesis that the increase of both young-aged population and retired- 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 coefficient of variable P65+ have highest positive value of 6.69 in 5-year horizon high 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.
‧
國立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
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 demand in small cap stocks across all age groups.
In general, the absolute value of coefficients in high risk level portfolios are larger than in low risk level portfo lios. This implies that, in terms of positive coefficients, the rise of expected returns in high risk portfolios for compensating those who are less willing to buy stocks are larger than the necessary amount in low risk 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 stabilized at this life stage, which means that middle-aged has the most risk tolerance 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).
‧
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:
t-stat = (β1− β2)/√SE.β12+ SE.β22 . The P25-44 factoris the fraction of population aged from 25 to 44 and other variables are defined in a similar way.
Panel A.
Beta portfolio Volatility portfolio Non-systematic portfolio
P25-44 P45-64 P65+ P25-44 P45-64 P65+ P25-44 P45-64 P65+
Size portfolio B/M portfolio D/P portfolio
P25-44 P45-64 P65+ P25-44 P45-64 P65+ P25-44 P45-64 P65+
‧
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.β12+ SE.β22 . The P25-44 factoris the fraction of population aged from 25 to 44 and other variables are defined in a similar way.
Panel A.
Beta portfolio Volatility portfolio Non-systematic portfolio
P25-44 P45-64 P65+ P25-44 P45-64 P65+ P25-44 P45-64 P65+
Size portfolio B/M portfolio D/P portfolio
P25-44 P45-64 P65+ P25-44 P45-64 P65+ P25-44 P45-64 P65+
‧
國立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
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
portfolio suggest a propensity for retired people to choose small stocks. Surprisingly, there is no significant difference between high risk portfolio and low risk portfolio for middle-aged population implying no preference for high or low risk stocks.
‧
國立 政 治 大 學