# Vanguard research August 2015

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7 Measuring wealth: Stochastic versus static returns In our projection of retirement wealth, we used deterministic or static returns for ease of presentation and communication. But returns are volatile, so our method may overstate the positive benefit of increased returns or the negative impact of lower returns. To illustrate the difference between static and stochastic returns, we computed the change in net retirement wealth using a stochastic simulation of expected returns for the average participant in decile 7 (see Figure 6). The average decile 7 participant moved from approximately a 60% stock portfolio to an 80% stock portfolio. Therefore, we generated ten-year expected returns for portfolios with 60% stock/40% bonds and 80% stock/20% bonds using the Vanguard Capital Markets Model (VCMM), a proprietary financial simulation tool. We used these values to compute the change in projected tenyear retirement wealth 10,000 times. Figure 7. Stochastic model of projected retirement wealth Distribution of net value for the average decile 7 participant Net value using static expected return 12% Net value using stochastic model of expected returns 11% 40% 30% 20% 10% 31% 11% 18% 10% Based upon the distribution on the right (Figure 7), a participant would experience a net increase of 11% in retirement wealth on average. This is only slightly lower than the estimate of 12% generated using a static return calculation. Fifty percent of participants (within the box) would fall within a range of 3% to 18%. A quarter of participants may experience even higher wealth gains, while a small percentage of participants may experience a loss in wealth. 0% 6% 10% 3% Another way to address the debate over stochastic versus static modeling is to use a measure known as expected growth rate (see Appendix B). The expected growth rate method yields similar results. Impact on company stock A total of 12% of the study s managed account participants held concentrated positions in company stock. One benefit of a managed account service is the reduction in single-stock risk. Before adopting managed account advice, nearly one-third of participants in this sample held more than 50% of their accounts in company stock (Figure 8, see next page). One in 7 participants held more than 80% of their assets in company stock. After adopting the advice service, allocations to company stock were reduced to only 4% on average. The majority of participants held less than 10% of their retirement account assets in company stock. On average, this group of participants increased their projected retirement wealth by 4% using managed account advice (Figure 9, see next page). Unlike participants with less or no company stock, the overall magnitude of the change was lower across all deciles. More participants experienced modest changes. Most of the benefit of the advice for this group was in the reduction in diversifiable single-stock risk. IMPORTANT: The projections and other information generated by the VCMM regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results, and are not guarantees of future results. Distribution of return outcomes from VCMM, derived from 10,000 simulations for U.S. equity returns and fixed income returns. Results from the model may vary with each use and over time. For more information, please see the last page of this research paper. 7

8 Figure 8. Change in company stock exposure Managed account participants with 20% or more in company stock before service adoption 100% 87% Average company stock holding: Before managed accounts: 46% After managed accounts: 4% 32% 0% 22% 15% 10% 8% 6% 4% 5% 6% 2% <0.5% <0.5% <0.5% 3% <0.5% 0% to 10% 11% to 20% 21% to 30% 31% to 40% 41% to 50% 51% to 60% 61% to 70% 71% to 80% 81% to 90% 91% to 99% 100% Post service adoption Pre service adoption Figure 9. Advice, retirement wealth, and company stock Managed account participants with 20% or more in company stock before service adoption Decile Annual contributions Increase wealth Decrease wealth Expected real return Expense ratio Advice fee Change in projected 10-year retirement wealth 10 45% 25% 0.53% 3.45% 66% Average 4% The values in this table represent the relative difference before and after service adoption. 8

10 Appendix A: The analytical approach Projected ten-year retirement wealth was calculated using a participant s elected deferral rates and portfolio and investment parameters six months before and after managed account enrollment. Assumptions: A participant s base pay was averaged over the fiveyear study period. In some cases, base pay wasn t available in all years, so the average was based upon the available data. Base pay was assumed to grow 1% annually over the ten-year period. Annual dollar contributions were calculated by multiplying an adopter s elected deferral rate by his average base pay. The deferral rate was assumed to remain constant over ten years and annual dollar contributions were capped at \$20,000 per year. This cap value represented a reasonable single estimate of 402g and catchup limits from 2009 to 2013 and impacted less than 5% of the sample. Expense ratios were extracted from Vanguard s internal financial reporting system and reflected the year of service adoption in most cases. In other cases, the most current expense ratios were used. Missing expense ratios were populated with the average of all values within a specific fund classification. Expected ten-year real returns were estimated using the Vanguard Capital Markets Model (VCMM). The value for U.S. equities returns was used for all single-stock funds. Projected returns were calculated using estimated real returns for four major asset classes: U.S. equities, international equities, bonds, and cash. 8 Appendix B: Expected growth Achieving higher expected returns generally requires an investor to take more risks. Describing higher expected returns as more desirable without acknowledging that more risk-taking is required to achieve these higher returns overstates their actual value. Even if expected returns remained constant, the increased risk would decrease the long-term growth of the portfolio. More volatile returns mean that the cumulative effect of compounding is reduced. An alternate method to estimate portfolio returns and account for the risk-return trade-off is to calculate expected growth. The formula for expected growth is: Expected growth = Expected return ½ (portfolio variance) The term ½ (portfolio variance) can be viewed as a risk penalty. Expected return is penalized for any increase in the risk profile of the portfolio. As a result, an increase in any expected return because of managed account adoption needs to account for any increased risk in the portfolio. The expected growth rates for the bifurcated sample are shown on the next page (Figure 11). The results are consistent with the broader findings in the paper. On average, the expected growth rate for participants with less than 20% in company stock increased by 15%. The rate for participants with concentrated company stock holdings was smaller at only 2%. Equation: The change in projected retirement wealth reflects the percent increase or decrease in the ending projected account balance, using managed accounts relative to the projected ending account balance had enrollment not occurred. Expressed as an equation: Change in projected 10yr retirement wealth = ((Projected 10yr ending balance) Post Projected 10yr ending balance Pre ) Projected 10yr account balance Pre IMPORTANT: The projections and other information generated by the VCMM regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results, and are not guarantees of future results. Distribution of return outcomes from VCMM, derived from 10,000 simulations for U.S. equity returns and fixed income returns. Results from the model may vary with each use and over time. For more information, please see the last page of this research paper. 8 Estimated ten-year real returns obtained from Vanguard Capital Markets Model. (U.S. equity 7.3%, international equity 8.1%, bonds 2.4%, cash 1.3%.) 10

11 Figure 11. Expected growth rates before and after service adoption A. Managed account participants with less than 20% in company stock before service adoption Expected growth Decile Before After Absolute difference Relative difference % 5.8% 1.8% 47% Average B. Managed account participants with 20% or more in company stock before service adoption Expected growth Decile Before After Absolute difference Relative difference % 5.8% 0.7% 13% Average References: Aon Hewitt and Financial Engines, Help in Defined Contributions: 2006 through Blanchett, David, 2014 The impact of Expert Guidance on participant savings and investment behaviors. GAO (United States Government Accountability Office), (k) plans: Improvements can be made to better protect participants in managed accounts. Hewitt Associates and Financial Engines, Help in Defined Contributions: 2006 through Madamba, Anna and Stephen P. Utkus, Managed accounts and participant portfolios. Vanguard Center for Retirement Research, Malvern, PA. institutional.vanguard.com Vanguard, How America Saves 2014: A report on Vanguard 2013 defined contribution plan data. Vanguard Center for Retirement Research. institutional.vanguard.com 11

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