I’m still on summer vacation, but figured I’d post an analysis I did earlier this month on how to value the stock market relative to bond rates.  While some of the prices may have changed a bit, the point is for this to be a long term analytical framework.  I welcome comments challenging or adding to the theory, as I’m always searching for the right answers…

HISTORICAL RETURNS

From 1926 to 2001, stocks, bonds and t-bills produced the following returns:

Source: Ibbotson Associates

It is from Ibbotson’s older studies that market participants have settled in on an equity risk premium of 5-6%. This analysis would imply an equity risk premium of as high as 7%. Since the market has basically moved sideways since 2001, with relatively low dividends and a rally in bonds, I would suspect that a more recent run of Ibbotson’s analysis would have the spread come down to around the historical average of 5-6%.

The purpose of this paper is not to determine whether 5-6% is the right number. Instead I am seeking to provide a method of calculating what the priced-in return of the market is today, and then to use a "disequilibrium analysis" to determine how the market may have it wrong.

COMPONENTS OF EQUITY RETURNS

On a basic level, equity returns are driven by two things: the beginning dividend yield and the long term growth rate of dividends.

Using the Gordon growth model

P=D/(r-g)

Where P= stock price, D=dividend, r= expected rate of return and g=dividend growth rate

Rearranged to

D/P + g = r

So that the dividend yield plus the long term dividend growth rate equals the expected rate of return.

Dividend yield and payout ratio. Ok, easy enough. The problem with the dividend yield is that the payout ratio has fluctuated over time, due both to changes in management optimism and to changes in the tax code and options compensation that encourage stock buybacks. Stock buybacks are a form of dividend in that they are not reinvested in the business.

Dividend growth. We will focus on the market as a whole to determine the general valuation level of the market. Over the long term corporate profits will grow in line with Nominal GDP. There are some periods when profits’ share of GDP goes up, like the late 1990s and 2000s, and period when it goes down, like the 1970s and early 1980s, but over the long term they will grow in line with GDP. S&P 500 profits, however, grow at a rate that is about 1% slower than GDP, as that index consists of larger, more mature companies.

GDP Growth. Nominal GDP growth consists of three components: growth in the workforce, growth in worker productivity and inflation. Long term real GDP growth has traditionally been 2.5% to 3%, with workforce growth at about 1% and productivity at 1.5% to 2%. Workforce growth has slowed recently and will likely move toward 0% for a while as the baby boomers retire, and then pick back up to its historical pace in the latter part of next decade. Productivity growth, on the other hand, has been running above trend recently.

Real earnings growth. If I strip out inflation, real S&P earnings have grown at a rate of 1.74% a year since 1960, which makes sense relative to real GDP growth of 2.5-3.0%.

Inflation. Inflation has been volatile since the 1920s. It was negative in the 1930s, regulated and then high in the 1940s, moderate in the 1950s, rising in the 1960s, very high in the 1970s, falling then rising in the 1980s, stable in the 1990s, and rising in the 2000s. As of August 7, 2008, the 30-year treasury bond was yielding 4.55% and the 30-year TIPS (Treasury Inflation Protected Security) was yielding 2.05%, meaning the market expects long term inflation of 2.5%.

Below I plot out today’s yield curve relative to my "equilibrium" yield curve. As interest rates, earnings and inflation are volatile, yet mean-reverting, I need to anchor the values in reasonable, long term assumptions.

Source: PIMCO, author’s analysis

Trend real earnings. To determine whether today’s market is over- or under-valued, I calculated long term real trend earnings for the S&P. I use inflation-adjusted trend earnings to smooth out the effect of business and inflation cycles. A graph of annual S&P real earnings is shown below.

Source: Damodoran, S&P, author’s calculations

Trend earnings for 2008 are estimated to be $58.65. The S&P is currently trading at 1,266.07, which results in a PE to trend earnings of 21.6. The long term average payout ratio of S&P companies is 50%, so the implied dividend yield to trend is about 2.3%, which is about what the actual dividend yield is today, if we include stock buybacks. Focusing on dividend yield is a better way to value the market than focusing on current year PEs, because dividends are far less volatile than earnings. Corporate managers tend to only pay dividends relative to their long term earnings power, because they don’t like to have to cut dividends at a later date.

Expected S&P Return. We now have all of the pieces to calculate what return is priced into today’s S&P.

Fixed Income Alternatives. No compare this to current fixed income alternatives.

The equity risk premium is currently only 3.56% relative to the equilibrium risk-free rate. The best deal looks like investing in long term investment grade bonds, particularly if you own them in a tax deferred account. On an after-tax basis, the spread is 3.72%.

Disequilibrium Analysis. Looking at the above numbers, one could make the argument that the assumed inflation rate is below the long term trend of 3.0%. If inflation was 0.5% higher, that would accrue to stock returns (to 7%) and eat in to real bond returns. Either way, it appears the spread between stock returns and investment grade bond returns is too low. Treasury rates are either in line with, or slightly below equilibrium. Real earnings growth has more risk of surprising to the down side after the big rise over the past two decades. Taxes are likely to rise near term, with the difference between taxes on equities and bonds narrowing.

Tax-free alternatives. The above after tax rates should be compared to municipal bonds when investing in taxable accounts. The equilibrium rates are compared to treasuries on an after-tax basis. You would probably want to add a few basis points to compensate for the fact that muni bonds carry a little more risk than treasuries. And to make sure that the equilibrium rate is at least above inflation.

Here I’m assuming you are not investing in triple tax-free bonds and are paying state tax of 5%. It would appear that municipal bonds offer terrific value on an after-tax basis and are well above their equilibrium yields and are even above investment grade corporates on an after-tax basis. In addition, with tax rates more likely to rise than fall, the attractiveness of muni bonds only increases.

Sadly, it’s tough to beat inflation on an after tax basis by investing in bonds. The key is to hold bonds in your tax deferred accounts and stocks and muni bonds in your taxable accounts. I know it sounds counter-intuitive to put fixed income in your long term retirement accounts, but if you run the math, you’ll save a lot on taxes versus holding taxable bonds in a taxable account and stocks in a tax deferred account.

S&P Values at different Expected Returns. I personally believe that the current earnings yield is too low and that the stock market is overvalued. The reason the long term return of the market is 8-10% is that in starting point year 1926 the dividend yield was higher than 5%, which together with 3% inflation and 2% real earnings growth gives you a 10% return. The great returns in the market since that time have come from multiple expansion, aka yield compression. With the implied dividend yield of only 2.5% today, the potential for continued multiple expansion is diminished, and the potential for multiple contraction (a process that has been playing out since 2000, by the way) is increased.

Here is how the S&P would need to be valued to provide a range of expected returns.

                                    Source: author’s calculations

In other words, to target a long term 8% return that provides a 5% equity risk premium to the average risk-free rate, the market would need to fall 38% from today’s levels. If long term inflation ends up being 3% instead of the 2.5% that the treasury market predicts, then the market only needs to fall 29%.

Buy bonds.