Planning For The Future – What About Bond Yields?

for Current Bond Yields

important consideration is that current interest rates are lower than the
historical averages. The historical average return is not relevant for someone seeking
to estimate future market returns from today’s starting point. The general
problem with attempting to gain insights from the historical outcomes is that
future market returns are connected to the current values for the sources of
market returns, rather than to their historical performance.

Returns on bonds depend on the initial bond yield and on subsequent yield changes. Low bond yields will tend to translate into lower returns due to less income and the heightened interest rate risk associated with capital losses when interest rates rise. Decreasing interest rates provide the only mechanism for bond returns to outpace bond yields, but this can only go so far when bond yields already start low.

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Exhibit 1.1 demonstrates that, historically, the relationship between
interest rates and subsequent bond returns has been tight. The exhibit shows
the relationship between bond yields and the subsequent average annualized
returns on bonds over the next five years using the Morningstar and Ibbotson
Associates Intermediate-Term Government Bond (ITGB) index data since 1926 as a
proxy for bonds. Much of the variation in intermediate-term government bond
returns over the subsequent five years can be explained by their current yield.
The year 2019 began with five-year Treasury yields at 2.5 percent. This is 2.7
percent less than the historical average ITGB return of 5.2 percent. This type
of analysis suggests that the most reasonable return assumption for retirements
beginning at the start of 2019 is that these bonds will average 2.5 percent
returns rather than 5.2 percent returns.

Exhibit 1.1 The Relationship
Between Bond Yields and Subsequent Bond Returns

The Relationship Between Bond Yields and Subsequent Bond Returns

Source: Own
calculations from SBBI Yearbook data
provided by Morningstar and Ibbotson
Associates. Bonds are represented by intermediate term US government bonds.

In order
to maintain the same risk premium for stocks over bonds, it would be necessary
to reduce the return assumption for stocks by the same amount. Even if interest
rates were to increase later in retirement, sequence-of-returns risk describes
how it is the upcoming returns that matter most, making this adjustment for
returns necessary to obtain a more realistic picture about retirement

Adjustments for Market Valuations

A common
way to estimate stock returns is to add an equity premium to a bond yield. This technique for estimating returns is known as
the capital asset pricing model. This model was developed by William Sharpe in
the 1960s, and he was awarded a Nobel Prize in economics for his work in 1990
alongside Harry Markowitz.

The model posits that the expected return on a financial asset is equal
to a risk-free rate of return plus a risk premium multiplied by a factor
showing the relationship between the asset and the overall market portfolio.
For an overall market index like the S&P 500, this suggests that its return
should be equal to the return provided by low-risk assets like Treasury bonds
plus a risk premium to account for the volatility of stocks.

We have discussed how bond yields are the best predictors for subsequent
bond returns. Historically, the S&P 500 outperformed intermediate-term
government bonds by 6.7 percent in arithmetic terms. Lower bond
yields suggest one reason why stock returns could be less. Adding 6.7 percent
to the 2.5 percent bond yield at the start of 2019 would lead to an estimate
for stock returns of 9.2 percent, compared to the historical 11.9 percent arithmetic
average return. With low bond yields we
should also expect lower stock returns as well. Otherwise, stocks would end up
providing a higher return premium over bonds than they have historically, and
there is little reason to expect a higher risk premium today.

It is also
worth addressing estimates of the equity premium. Are the historical excess
returns really the best predictors for the future equity premium? An important
matter to address is the relationship
between the equity premium and the cyclically adjusted price-earnings ratio. When
price-earnings multiples are high, markets have historically tended to exhibit
mean reversion as relatively lower future returns were realized, and vice

In the
mid-1990s, Yale professor and Nobel laureate Robert Shiller popularized the
concept of the cyclically adjusted price-earnings ratio (commonly abbreviated
either as CAPE or PE10) as being a useful predictor of subsequent stock market
returns. The PE10 measure is the stock price divided by the average real
earnings on a monthly basis over the previous ten years. A research article
published by John Campbell and Robert Shiller in 1998 justifies this measure to
remove cyclical factors from earnings, though there is no particular reason to
pick precisely ten years other than as an approximation for the length of a
business cycle. Today, Robert Shiller provides updated data on the key
variables used to calculate PE10 at his website.

Robert Shiller focused on the relationship between the PE10 measure and
subsequent stock returns, the approach can just as easily be applied to the
relationship with the equity premium. The idea with both is that when the PE10
measure is higher, subsequent expected stock returns or their excess returns
over bonds should be less.

historical risk premium can vary based on the historical period under
consideration as well as on the choice of stock and bond indices. Robert
Shiller provides freely on his website data for US large-capitalization stock
returns, dividends, and earnings, as well as ten-year Treasury bond yields.
This data is available since 1871, making it the longest available data series
commonly used for retirement income research.

In this
dataset, large-capitalization stocks provided an average 5.8 percent higher
arithmetic return than ten-year bond yields. This is one way to estimate the
equity premium. Exhibit 3.9 parses this historical data in another way,
however. It plots the values of PE10 at each historical point against the
arithmetic average of the risk premium over the subsequent ten years. The line
fitting best through this data shows a negative historical relationship as
higher values of PE10 are associated with lower subsequent excess returns for stocks
over bonds. To the extent that we view this model as having credible predictive
power, it suggests that the best guess for the risk premium over the next ten
years from January 2019 is only 1.4 percent, rather than the historical average
5.8 percent. This lower risk premium results from the higher market valuations
facing retirees at the present, as PE10 was 28.64 in January 2019, compared to
its historical average of 17.0. This projection is well below the historical
average because PE10 is well above its historical average.

Exhibit 1.2 The Relationship
Between the Cyclically Adjusted Price-Earnings Ratio and the Risk Premium

The Relationship Between the Cyclically Adjusted Price-Earnings Ratio and Risk Premium

Source: Own
calculations with data from Robert Shiller’s website (

There is
more controversy about the predictive powers of PE10 for stock returns, or
their excess returns over bonds, than there is for bond yields to predict bond
returns. There are compelling behavioral explanations for why these
relationships could remain in the future, but there are also many arguments
specifically about the problems with using PE10. For instance, changing
accounting standards with regard to how earnings are calculated may be an
explanation for why today’s PE10 does not properly align with its historical

Bernstein has also written about the paradox of wealth, which is that returns
on capital tend to decrease as societies become wealthier. He tracks this trend
back to the middles ages. This could explain why we should expect PE10 to
center around a higher level than in the past as the returns on capital fall. A
related argument along these lines is that low interest rates could also
justify a higher value of PE10 than otherwise. Nevertheless, this issue of
market valuations exemplifies why it may not always be wise to use historical
averages for excess returns to create estimates for the future risk premium.

spending rates for retirees are intricately related to the returns provided by
the underlying investment portfolio. And with sequence-of-returns risk, the
returns experienced early on will weigh disproportionately on outcomes. In
other words, for those already spending, the assumption that returns will one
day normalize to their historical averages is much less relevant than it is for
accumulators who will rely on more distant market returns. Current market
conditions are much more relevant, making it a mistake to blindly apply a
historical average return without further thought.

This is an excerpt from Wade Pfau’s book, Safety-First Retirement Planning: An Integrated Approach for a Worry-Free Retirement. (The Retirement Researcher’s Guide Series), available now on Amazon.

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