Understanding the Leveraged Life Cycle Investment Strategy for Defined-Contribution Plan Investors
, oraz | 19 mar 2024
O artykule
Data publikacji: 19 mar 2024
Zakres stron: 12 - 30
Otrzymano: 25 sty 2017
Przyjęty: 15 cze 2017
DOI: https://doi.org/10.2478/fprj-2017-0006
© 2017 Luo Wang et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
Correlation Matrix
| US | Stocks | Bonds |
|---|---|---|
| Stocks | 1 | 0.067 |
| Bonds | 0.067 | 1 |
Descriptive Statistics for the US Nominal Returns Data (1900-2011)
| Stocks | Bonds | Bills | |
|---|---|---|---|
| Geometric Mean (%) | 9.30 | 5.00 | 3.90 |
| Arithmetic Mean (%) | 11.27 | 5.38 | 3.95 |
| Median (%) | 13.78 | 3.67 | 4.07 |
| Maximum (%) | 57.09 | 40.36 | 14.71 |
| Minimum (%) | -43.54 | -14.90 | -0.02 |
| Standard Deviation (%) | 19.97 | 8.87 | 2.82 |
| Skewness | -0.37 | 1.22 | 0.73 |
| Kurtosis | 2.84 | 5.40 | 4.02 |
| Jarque-Bera Statistic | 2.62 | 54.55 |
14.72 |
Investment Strategies
| Investment Strategy Symbol | Description | |
|---|---|---|
100 stocks 100 bonds Balanced |
100% stocks allocation 100% bonds allocation 60% stocks and 40% bonds allocation |
|
| LC90 | Modelled after Vanguard Target Retirement Funds. Start with 90% stocks, 10% bonds allocation for the first 20 years, and then decrease the stock weights 2% annually in a linear pattern to reach an allocation of 50% stocks and 50% bonds at retirement. | |
| LC95 | Modelled after Principle Funds. Start with 95% stocks, 5% bonds allocation, and experience a gradual decline 1% annually away from stocks to reach an allocation of 56% stocks and 49% bonds at retirement. | |
| DLC2020 | Start with 100% stocks for the first 20 years. At the end of 20 years, if the target is achieved, the assets are switched to a portfolio comprising of 80% stocks and 20% fixed income; otherwise, remain invested in 100% stocks. This process is also carried out for the next 10 years. In the last 10 years, the assets are switched to a portfolio of 60% stocks and 40% fixed income if the target is achieved. Otherwise, remain invested in 100% stocks. | |
| DLC3010 | Similar to above, except that it starts with 100% stocks for the first 30 years. This process is carried out for the next 5 years. In the last 5 years, the assets are switched to a portfolio of 60% stocks and 40% fixed income if the target is achieved. Otherwise, remain invested in 100% stocks. | |
| LLC100 | Start with leverage at 2:1 and fully invested in stocks. When the current savings exceed 20% of discount lifetime savings; investors start to deleverage as savings continue to rise, until the current savings hit the 50% stock allocation. After that, investors maintain the market exposure. Risk-free rate plus 100 basis points is used as the margin rate. | |
| LLC200 | Similar to above, except that, instead of using risk-free rate plus 100 basis points as the margin rate, it uses a risk-free rate plus 200 basis points as the margin rate. |
Value at Risk (VaR) and Expected Shortfall (ES) Estimates for Different Investment Strategies
| Investment strategy | VaR at different confidence levels | ES at 95% confidence level | ||
|---|---|---|---|---|
| 99% | 95% | 90% | ||
| LLC100 | 3.03 | 4.28 | 5.16 | 3.52 |
| LLC200 | 2.98 | 4.28 | 5.19 | 3.50 |
| 100 Stocks | 2.02 | 3.36 | 4.50 | 2.53 |
| 100 Bonds | 2.44 | 2.87 | 3.16 | 2.60 |
| Balanced | 2.94 | 4.01 | 4.85 | 3.35 |
| LLC100 | 3.03 | 4.28 | 5.16 | 3.52 |
| LLC200 | 2.98 | 4.28 | 5.19 | 3.50 |
| LC90 | 2.82 | 4.02 | 4.92 | 3.29 |
| LC95 | 2.89 | 4.06 | 5.00 | 3.35 |
| LLC100 | 3.03 | 4.28 | 5.16 | 3.52 |
| LLC200 | 2.98 | 4.28 | 5.19 | 3.50 |
| DLC3010 | 2.01 | 3.38 | 4.54 | 2.54 |
| DLC2020 | 2.04 | 3.45 | 4.64 | 2.58 |
Distribution Parameters of Retirement Wealth Ratio (RWR)
| Investment strategy | Mean | Median | 75th Percentile | 25th Percentile |
|---|---|---|---|---|
| LLC100 | 12.41 | 10.50 | 15.38 | 7.16 |
| LLC200 | 12.22 | 10.31 | 15.11 | 7.09 |
| 100 Stocks | 19.70 | 13.02 | 23.52 | 7.35 |
| 100 Bonds | 4.86 | 4.53 | 5.62 | 3.74 |
| Balanced | 10.81 | 9.29 | 13.28 | 6.65 |
| LLC100 | 12.41 | 10.50 | 15.38 | 7.16 |
| LLC200 | 12.22 | 10.31 | 15.11 | 7.09 |
| LC90 | 13.61 | 10.69 | 16.68 | 7.03 |
| LC95 | 12.71 | 10.28 | 15.62 | 6.96 |
| LLC100 | 12.41 | 10.50 | 15.38 | 7.16 |
| LLC200 | 12.22 | 10.31 | 15.11 | 7.09 |
| DLC3010 | 18.31 | 13.23 | 22.69 | 7.54 |
| DLC2020 | 15.91 | 13.20 | 20.18 | 7.73 |
Key Assumptions
| Variable | Assumption |
|---|---|
| Starting Balance | $0 |
| Starting Salary | $25,000 |
| Salary Growth Rate | 4% p.a. |
| Contribution Rate | 9% p.a. |
| Starting Age | 25 |
| Retirement Age | 65 |