Monday, January 2, 2012

Stock Market Attractiveness - A Theoretical Framework

With the choppy stock market of 2011, I thought it would be interesting to evaluate a step-by-step approach to assessing the attractiveness of the stock market.  DISCLAIMER:  I do not want to offer investment advice and this is not a recommendation to buy or sell stocks or any other investments.  Instead, I'd like to share a fairly common approach based on some ideas from CAPM and general macroeconomic evaluation, with some personal tweaks built in.

Because we are looking at the attractiveness of a diversified portfolio of equity securities, we can measure that attractiveness by the risk premium earned relative to other risky assets.  For this post, I'll simply evaluate the risk premium on S&P 500, and not other asset classes. A full analysis would be to evaluate the risk premium's across all investable asset classes (bonds, real estate, private equity, art, coins, etc.), and see which premium-to-risk ratio appears most appealing.  Opinions certainly can differ, even if two investors share the same investment analysis data.

First, lets look at what common stock investments represent.  Each share is entitled to receive 1/X of the firm's dividends, where X is total shares outstanding at the time of the dividend.  Although dividends are paid in cash ("earnings"  can not be distributed), I am going to assume that earnings = free cash flow to equity.  And although dividends are traditionally less than 50% of corporate earnings, to simplify our analysis I'm going to assume that all earnings are distributed.

We can evaluate the attractiveness of the market by first evaluating the price of earnings implied by the market, and then evaluating the expected trends for those earnings.  Thats it.

The price of earnings

Our first step evaluates the cost of "purchasing" the right to annual earnings.  This is simply the P/E ratio. The S&P 500 closed at 1,277.81 at the time of this analysis.  Earnings for 2011 are expected (actuals through 6/30 and estimates for Q3 and Q4) at 97, and expected earnings for 2012 are 106.  In a perfect world, forward earnings should be used.  I prefer current P/E unless its an exceptional year--our world certainly isn't a perfect one.  For this analysis, I'll use an earnings number of 100, resulting in a P/E of 12.8.

What does this number tell us?  On a first approximation,  it tells us that, assuming earnings remain constant into eternity, we'll earn a return on investment of 7.8% (7.8% = 1/12.8).  Again, we're assuming all earnings are paid out in dividends.

Is this a good return for an index of stocks?  I depends on our alternative investments available.  A good benchmark for a safe investment is  US treasury bills, notes, and bonds.  As stocks have no maturity date, its generally considered appropriate to compare yields on stocks to yields on long term notes and bonds.  Currently, the 10 year note is yielding 2.0% and 30 year bonds are yielding 3.1%.  Therefore, our stock yield is between 4.7% and 5.8% more than "safe" government investments.  Is that enough of an additional expected return?  It depends on the investor.  For the past 100+ years, stocks have returned over 7% more than US treasury bonds.  In more recent times, though, many experts believe any excess returns of stocks over treasuries greater than 3% is quite attractive.  Ultimately, attractiveness ex ante is the eye of the beholder.

Adjustments and additional considerations

Our analysis above has been more "back of the envelope" than comprehensive.  Therefore, a number of additional factors may considerably alter the preliminary calculation.  These factors are all considered in the context of the following widely known valuation formula:

V = D / (k - g)

Where,V = Value, in this case the value of the S&P 500 index
D = Dividend, in this case equal to current earnings of the S&P 500 of 100
k = Discount rate.  Discount rate represents the required return for the investment.
g = Annual growth rate in dividends, or equivalently in our case, earnings

The variables V and D in the above equation are known already.  All of our adjustments  are going to affect the value of the index by affecting the future growth rate for earnings.  Once we know g, we'll impute k, which is the market's required return at the moment.   If the market's required return is attractive to us, we invest.  If its insufficient, we invest in other assets, or hold cash.  Note if g = 0, then market's required return is 7.8%, the inverse of the P/E ratio.

Below are factors that should be considered when determining the appropriate value of g in the above valuation formula.

1) Inflation

Common stocks represent ownership of companies.  Companies provide real goods and services.   As prices change from inflation, revenues, expenses, and profits should also adjust.  This makes stocks quite different than bonds, which generally provide only nominal returns.  All else equal, earnings should grow with the rate of inflation.  An a good estimate of inflation is 2% annually going forward.

 Therefore, we should adjust variable g by +2% for inflation.

2) Growth in GDP

As the economy grows, so should corporate earnings.  A reasonable estimate for annual real GDP growth is approximately 2.5% per year.  Note that we should use real GDP growth as opposed to nominal GDP growth. Our adjustment for inflation has already been factored in as part of 1), above.

Therefore, we should adjust variable g by +2.5% for growth in GDP.

3) Earnings % of GDP 

GDP measures of the total value of goods and services produced in a given year.  The cash received for all of these goods and ultimately gets distributed to a variety of "factors of production," or resources used in the creation of those goods. Equity capital is only one factor of production.

If we believe that returns on equity capital (i.e. earnings) is going to increase or decrease as its percentage of GDP, our g variable must be adjusted for this change.  In making this evaluation, its helpful to make separate considerations on macro and micro levels.

a) Macro considerations

GDP reflects public goods and services (i.e. produced by the government) and private goods and services (produced by sole proprietorships, partnerships, and corporations).  If we believe there to be a shift in the sources from which goods and services are produced going forward, that should be considered in our evaluation.*  For our purposes, we will assume that government produced goods and services will remain constant, although I recognize this may be a highly debatable point.

b) Micro considerations

In the private sector, earnings share the value of goods produced with the following other factors of production:

Rents (land and property)
Debt capital (interest)
Government claims (taxes)

As these "claims" on value shift as a proportion of total value (i.e. total revenue), other sources must reflect the offsetting changes.  For our purposes, we will assume that our relative mix of claims is likely to remain consistent.

As a result of our macro and micro considerations, variable g is unaffected.

4) Creative destruction

Creative destruction is a hallmark of a capitalist society.  It was a phrased most recently offered by Austrian economists to describe the process of competition, innovation and improvement that occur from the entrepreneurial spirit in our economy.  Creative destruction results in the demise of some firms as new firms emerge.  Our creative destruction evaluation will be performed in two stages.

a) Corporate vs. noncorporate earnings

Not all economic activity occurs in publicly traded companies. Sole proprietorships, partnerships, and nonpublic corporations also are responsible for a large percentage of economic activity. Sarbanes Oxley made the costs of being a public company more expensive.  Access to the capital markets is quite value still, however.  We'll project in our analysis that the economic production from publicly traded companies remains the same percentage as currently exists.

b) New corporations vs. existing corporations in the S&P 500

In 10 years, the composition of the S&P 500 will be different than it is today.  Some companies will have  gone bankrupt, others been replaced in the index by new and growing companies, and others still acquired.  One thing that is predictable, however, is that the existing S&P constituents will be a smaller percentage of total public corporate earnings in 10 years than they are today.

This article here identifies that the average lifespan of a corporation is 40 years.  That equates to an average decay rate of 2.5% per year.  We'll use this rate as our adjustment to g to factor in creative destruction.

We'll assume this effect combines to erode existing corporate share of future profits by -2.5%, so we'll adjust variable g by -2.5%.


In total, we have a combined adjustment to our earnings growth of 2% (+2% inflation, +2.5% real GDP growth, -2.5% creative destruction).  We know from our equation above that D / V = 7.8% and  D / V = (k-g).  With g established at 2%, we can solve for our adjusted expected return on equity, which equals 9.8%.  Is 9.8% a good expected return?  As stated above, it depends.  Given the low level of interest rates, receiving an almost 10% expected return on stocks looks even more attractive.  We're still in turbulent times, however.  European debt crisis and American political dysfunction are only two of many concerns affecting economic progress.  It appears to me that our current environment remains one of above average reward requiring above average risk tolerance.  Thats my $0.02.

 *Government production of goods and services is not the same thing as government spending.  Government spending includes transfer payments, such as medicare/medicaid, welfare, and social security.  These payments do not produce goods or services, but transfer money from between sources.

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