TIP$TER projects the sustainable retirement budget that a tax-deferred portfolio fully invested in inflation-protected bonds would support.  Then, it ranks and compares the retirement budgets supported by a simulated part-equity portfolio.
What is a Reasonable Equity Risk Premium?

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The equity risk premium is a very simple concept: it is simply the difference between risky equity returns and riskless asset returns.  What isn't so easy is predicting what the equity risk premium will be in the future. 

Just because the exercise isn’t easy doesn’t mean you should ignore it.  Too much depends on it.  The dominant factor that should drive the basic stock/bond split asset allocation decision is the additional return that you expect from stocks over approximately risk-free assets.

To estimate forward-looking equity risk premiums, you must first estimate forward-looking equity returns.  That is, what annualized return do you expect the total stock market to deliver over the long term?

Here, it is critical that you not simply fall back on historical returns, and hope that the past will repeat itself.  To estimate future equity returns, you must break them down into their constituent components. 

Principal #1: In the very long term, total market equity returns = current dividend yields + dividend growth rate

Future equity returns, over the very long term, will be made up of two very simple components: current dividend yields plus the expected very-long-term dividend growth rate.  See William Bernstein, "The Expected Return One-Step" (2001) ("[L]ong-term equity returns are closely approximated by the sum of dividend/earnings growth and the dividend rate"); see also Credit Suisse Global Investment Returns Yearbook 2009* ("For the seriously long-term investor, the value of a portfolio corresponds closely to the present value of dividends."). 

Principal #2: In the very long term, dividends cannot grow faster than the economy

You can be sure that the very-long-term dividend growth rate cannot exceed the very-long-term economic growth rate.  As William Bernstein* wrote in “The Returns Fairy…Explained”:

“It is impossible for long-term corporate growth to be higher than GDP growth
for this would entail corporate profits eventually growing larger than the economy itself.” 

Principal #3: The Lag – in the long run, dividend growth lags economic growth

In fact, the very-long-term dividend growth rate is likely to lag the very-long-term economic growth rate.  That is what has happened historically.

            In Credit Suisse Global Investment Returns Yearbook 2009*, Elroy Dimson, Paul Marsh, and Mike Staunton of the London Business School report their findings on a database of stock and bond returns for 17 countries over the 109-year span from 1900 to 2008.  They found that real dividends rose by only 0.65%/year in a “world index” they constructed for the 17 countries.  See page 8.  This was more than 1% below global real economic growth over the same period (which was approximately 2%/year).  See page 22.  They report that in the United States, real dividends grew at an annualized rate of 1.2%/year between 1900 and 2008.  See page 8. This is 2% below the 3.23% in annualized growth in real GDP that the U.S. experienced.   Others, including Robert Arnott* and William Bernstein*, have also written about this “dilution” of earnings as it passes through to dividend growth.

Principal #4: Low payout ratios and larger stock repurchase programs portend (but don't guarantee) less of a subsequent lag between economic and dividend growth

However, today the payout ratio (dividends/earnings) of the S&P 500 is well below historical norms.

            Today's lower-than-historical payout ratio may explain as much as 0.4% of that historic 2% lag between U.S. economic growth and U.S. dividend growth.  That is, if the companies in the S&P 500 had issued about 50% of their earnings over the past 5 years as dividends, then the lag between economic growth and dividend growth between 1900 and 2008 would have only been about 1.6%.

            Fortunately, today's smaller payout ratio should portend even less of a future lag between economic growth and dividend growth.  After all, companies that reinvest most of their earnings ought to grow faster than they would if they had distributed those earnings as dividends instead. 

            Today, companies are also using a larger share of their earnings to buy back stocks than they did in the past.  Companies that use some of their earnings to buy back their stock may be able to afford to distribute more dividends/share in the future than they otherwise would.  After all, stock buy-back programs result in fewer shares amongst which to distribute future dividends.  So stock buy-back programs should also result in a higher dividend growth rate. 

            Lower payout ratios also give dividend yields more room to grow, so dividend yields may grow a little bit faster than they otherwise would.

            In summary, there is a reasonable basis to expect less of a lag, in the U.S. and its stock market, between future economic and dividend growth.

The Formula (Part I):

So here’s one plausible formula for the future equity returns for the total stock market:

ER = DY + G - Lag - Fees

Where ER = equity returns, DY = dividend yield, G = long term expected real economic growth, Lag = the amount dividend growth in market indices is expected to lag overall economic growth, and Fees = expense ratio fees, loads (if any), transaction costs, and (if you entrust your investments to an advisor) assets-under-management fees.

            (You can also incorporate estimated small & value premiums into the formula.  For more information, see here).

Dividend Yield Information:

So what are broad stock market dividend yields today?  Surprisingly, it takes a lot more digging than it ought, to find that out.  Do a search for "index dividend yields," and you get a bunch of links to ETFs and mutual funds that screen stocks in favor of high dividend yields. 

Russell Investments* provides one of the best resources Prospercuity has found for dividend yield information on different equity asset classes.  Russell Investments – which developed a series of U.S. and global indices that many investors are familiar with (e.g., the Russell 2000 Index) – provides dividend yield information on each of its indices.  For example, Russell reported the following dividend yields for the following indices as of June 30, 2009:

Index* Dividend Yield (as of June 30, 2009)
Russell Global 3.01%
Russell Global ex-U.S. 3.61%
Russell 3000 Index (U.S. broad market) 2.02%
Russell Developed 3.08%
Russell Europe 4.17%
Russell Asia Pacific 3.03%
Russell Asia Pacific ex-Japan 3.17%
Russell Emerging Market 2.60%
Russell BRIC 2.37%

WARNING: Beware of falling into the trap of considering only dividend yields when comparing different market styles (e.g., large-cap value) and different international indices.  After all, companies that distribute most of their earnings as dividends are not likely to grow as fast as companies that reinvest them.  Companies in different style and international indices may, on average, grow at different rates.  After all, the bigger the payout ratio, the bigger the likely lag between overall economic growth and dividend growth.  See Principal #4.

When using a dividend discount model to estimate the equity risk premium, it is best to just focus on the broadest market indices.  If you believe that certain market styles (like small value) will deliver additional risk premia in the future, you can add the additional risk premia you expect that style to deliver.

Forecast Economic Growth Information:

What are reasonable long term real economic growth rates?  A few years ago, William Bernstein wrote in “Of God, Mammon and Mars” that the world economy has, since about 1820, grown at a fairly steady pace of about 2% real per year.  The Credit Suisse Global Investment Returns Yearbook 2009* likewise remarks, on page 22, that "the very long-run growth rate of productivity ... has been around 2% per year."  The data provided by MeasuringWorth – a fascinating, bookmark-worthy website, by the way – reveals the following growth rates for the United States and the United Kingdom: 

Country United States United Kingdom
Real GDP growth rate, 1830-2008 3.65% 1.97%
Real GDP per capita growth rate, 1830-2008 1.83% 1.43%

Now you have a respectable method for estimating forward looking total stock market returns.  There’s still one step left.

The Formula (Part II):

To calculate the equity risk premium, you need to subtract the risk-free rate:

ERP = ER - RFR

Where RFR = the risk-free rate. 

Be Careful With Those Numbers!!

Make sure that if you are using a real value for the expected equity return, you use a real value (e.g., TIPS) for the risk-free rate.  On the other hand, if you are using a nominal value for the expected equity return, you must use a nominal return value (e.g., 30-year bonds) for the risk-free rate.

If you are using a source – like Credit Suisse Global Investment Returns Yearbook 2009* – to estimate the forward looking risk premium, be sure to understand what baseline that source is using for the premium.  In the Credit Suisse Global Investment Returns Yearbook 2009*, the authors use T-Bills as the proxy for the risk-free rate.  Historically, T-Bills have yielded about 1% above inflation.  Long-term TIPS, by contrast, were yielding between 2% and 2.5% above inflation as of late July 2009.  So Yearbook's forecast annualized 3-3.5% equity risk premium, compared to T-bills, translated – in late July 2009 – to about a 2% equity risk premium over long-term TIPS.

Example of an Informed Guess on the Forward-Looking Equity Risk Premium:

    Part I: Estimate Forward-Looking Equity Returns

        Assume an investment in a Total U.S. Stock Market (TSM-US) portfolio. 

        We are going to use the formula ER = DY + G - Lag - Fees, explained above.

        We need some dividend yield information.  As of late July 2009, the trailing 12-month dividend yield of Vanguard's VTSMX (Total Stock Market) index was about 2.4%.  So DY = 2.4%

        Now we need an estimate for long term expected real economic growth.  With the U.S. population stabilizing, a 2% estimate is fair and consistent with the U.S.'s 1.8% annualized per-capita GDP growth rate over the past 200 years.  G = 2% (est.)

        Now we need to estimate the "Lag" factor.  Historically, it has been about 2% in the U.S., but that covers a 200 year period of rapid population growth.  Credit Suisse reports that worldwide, the "Lag" factor has been closer to 1%.  So we can be optimistic: Lag = 1% (est.)

        Let's assume that very low expense ratio funds are used as vehicles for investing in equities.  So Fees = 0.1% (est.)

        Now we have an estimate for forward-looking equity returns:

ER = DY + G - Lag - Fees
ER = 2.4% + 2% - 1% - 0.1%
Expected Forward-Looking Equity Return = 3.3% (annualized)

    Part II: Compare with long-term TIPS yields to estimate

        Now, we calculate the expected equity risk premium: ERP = ER - RFR

        We are going to use the real yield on long-term TIPS as the "risk free rate."

        Bloomberg* reports that the real yield, as of late July 2009, on 20-year TIPS was about 2.3%.  But assume that an annualized 0.1%/year is lost in transaction fees.  So RFR = 2.2%

        Now we have an estimate for forward-looking equity risk premium on a TSM-US portfolio:

ERP = ER - RFR
ERP = 3.3% - 2.2%
Expected Forward-Looking Equity Risk Premium = 1.1% (annualized)

        Note that if we had used a more pessimistic "Lag" factor of 2%, our ERP estimate would drop to 0%.

Recommended reading on the equity risk premium:

*Credit Suisse is a trademark of Credit Suisse Group Société, with which Prospercuity claims no association, connection, affiliation, or sponsorship.
Russell Investments and the names for its indices are trademarks of the Russell Investment Group, with which Prospercuity claims no association, connection, affiliation, or sponsorship.
Bloomberg is a registered trademark of Bloomberg L.P., with which Prospercuity claims no association, connection, affiliation, or sponsorship.
Prospercuity also claims no association, connection, affiliation, or sponsorship with William Bernstein or Robert Arnott.