The authors conducted 10,000 Monte Carlo simulations with three different sets of assumptions about stock and bond returns, equity risk premia as well as inflation rates, 121 lifetime asset allocation glide paths, annual withdrawal rates of 4% and 5%, and time horizons of 20, 30 and 40 years. The conclusions were:

Accordingly, for those households looking to maximize their level of sustainable retirement income, and/or to reduce the potential magnitude of any shortfalls in adverse scenarios, portfolios that start off in the vicinity of

20 percent to 40 percentin equities and rise to the level of60 percent to 80 percentin equities generally perform better thanstaticrebalanced portfolios ordecliningequity glide paths. The results hold even in situations where the final equity exposure is no higher than what the client’s static portfolio allocation may have been in the first place.The results also reveal that in particular scenarios where the equity risk premium is depressed, the optimal glide path includes less equity overall. In scenarios where the goal is to withdraw at a level that

stressesthe portfolio [5%] and its expected growth rate,higheroverall levels of equity are necessary (with such high-risk goals, having a relatively high-risk portfolio, even with the danger this approach entails, is still the optimal solution).

The key reason for starting with the initial lower allocation to stocks is that

…in the case of a 30-year time horizon, the outcome of a withdrawal scenario is dictated almost entirely by the real returns of the portfolio for

the first 15 years. If the returns are good, the retiree is so far ahead relative to the original goal that a subsequent bear market in the second half of retirement has little impact. Although it is true that final wealth may be highly volatile in the end, the initial spending goal will not be threatened. By contrast, if the returns are bad in the first half of retirement, the portfolio is so stressed that the good returns that follow are absolutely crucial to carry the portfolio through to the end.

This is supported by Vanguard portfolio allocation models that range from 100% bond to 100% stock allocations and are analyzed in the 87 years from 1926 through 2012. As can be expected, the average annual return of a portfolio increases with allocation to equities, but generally so does the number of down years as well as the maximum annual loss. So, is there an optimal allocation that would maximize the average annual return while minimizing the probability of a loss year? To determine that, Alpholio™ compiled the following chart:

The ratio peaks for a portfolio with 20% stocks and 80% bonds, which is consistent with the findings of the study.

The main problem with this and similar studies is that they assume a mechanical annual adjustment of withdrawals based on the prior year’s inflation rate. This is done to maintain the purchasing power of withdrawals. However, in reality expenses fall with age during retirement, as an article in The Wall Street Journal indicates:

“Pretty much every paper you read about retirement assumes that spending increases every year by [the rate of] inflation,” Mr. Blanchett says. But when he analyzed government retiree-spending data, he found otherwise: Between the ages of 65 and 90, spending

decreasedin inflation-adjusted terms.

Most models would assume that someone spending $50,000 the first year of retirement would need $51,500 the second year (if the inflation rate were3%). But Mr. Blanchett found that the increase is closer to1%, which has big implications over decades, “because these changes become cumulative over time,” he says.

In the above example, the terminal annual withdrawal after 25 years would be $104,689 with a 3% annual increase vs. only $64,122 with a 1% increase. This significant difference would certainly change the outcome of simulations with the rising equity glide paths. Most likely, either a flatter (less risky) path would suffice for a given success rate, or a success rate would increase for a given glide path.

To determine the optimal asset allocation in retirement, it is also useful to see the spending distribution among major expense categories:

Not surprisingly, in a typical retirement period healthcare and charity expenditures grow, while insurance/pensions, transportation and clothing expenditures shrink as a percentage of the overall budget. A recent slowdown in medical-price inflation, which historically outpaced the overall inflation, is likely a result of passing on more costs to consumers (as well as a temporary effect of the Great Recession). Therefore, it seems reasonable to keep a sizable exposure to equities even late into retirement, while minimizing the risk in early years. This is what a U-shaped glide path strives to accomplish.

For most of current retirees, Social Security is a major source of income:

However, with the ongoing shift from the defined-benefit to defined-contribution plans, careful (and *individualized*) planning of retirement asset allocation in employer-sponsored plans and IRAs as well as other personal investments is evermore important.

To arrive at this conclusion, the authors of the post analyzed 29 different ERP models and weighted them so that the cross-section R-squared was maximized. The authors further concluded that the high level of the ERP is currently driven no so much by dividends (roughly, at the historical average) or dividend growth (anticipated to be slightly above average), but rather by the exceptionally low Treasury yields that result from the Fed’s actions. In other words, while in the traditional CAPM

R

_{e}= R_{f}+ β * ERP

where R_{e}= expected return on equity

R_{f}= risk-free rate

β = beta coefficient, by definition equal to 1 for the equity market

also

ERP = f(R

_{f})

i.e. the equity risk premium is a function of the risk-free rate, so R_{e}is doubly so.

By various accounts, a long-term average return of the equity market is just over 10%. Subtracting the average ERP of 3%, this would imply a risk-free rate of about 7%. In today’s low-rate environment, the risk-free rate is in the 0.03% to 2.8% range, depending on which Treasury instrument with a maturity from one month to 30 years is used (while many models use three-month T-bills, others may use T-notes or T-bonds depending on the duration of the analysis period).

The following chart shows that the currently expected ERP falls only slightly from the one-month ahead value of 5.4% when the forecast period is extended:

Let’s assume that the ERP in the next two years is expected to be about 5% and use a corresponding two-year Treasury note yield of 0.2% as a proxy for the risk-free rate. Adding the two, the expected annualized return of the equity market in that period is about 5.2%, which is significantly below the aforementioned historical average.

So, while the ERP rose to a historically high level, it is still insufficient to compensate for the decline in the risk-free rate. In addition, at 14.3-times estimated next-twelve-month earnings, the price-to-earnings ratio of the S&P 500® is only slightly below the historical average. Therefore, based on the ERP measure alone, one cannot conclude that stocks are cheap now.

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