Sunday, April 8, 2012

Markets Disappointed by Signs of Recovery?

This week's equity market losses have been attributed, to a large degree, on fed meeting minutes indicating further economic stimulus is not warranted. An article from Bloomberg, here, provides the basic message.  According to the media, the market logically sold off upon hearing this news, as further stimulus was unlikely.

First, I have to point out that I am skeptical of singular causes for market activity described by the media.   Due to the complexity of the market and the interaction between multiple sources of information and expectations, media commentary on market movements is highly specious.

Even if the Fed's comments about stimulus did spark the market decline, I question why such news should rationally cause a sell-off.  Fed stimulus is used to help rehabilitate a struggling economy.  Stimulus is not a standard part of our economy, as evident from opposite actions occasionally adopted by the Fed (e.g. early 1980s), designed to slow our economy.  Given the Fed believes stimulus is not necessary, this should be a positive sign of our economic recovery, and the need for additional stimulus should be worrisome.  All else equal, I would view the Fed's announcement as bullish for our market.

A good analogy here is a hospitalized patient.  When the patient shows signs of of sickness, medication may be warranted.  Similarly, monetary stimulus may be helpful when economy is sluggish.  If I had a friend or family member on medication in the hospital, and were told that he or she would be well enough to come off medication soon, I would view that as promising news for his or her long term health.  I see no reason why the Fed's comments that further stimulus is not necessary would be any different as it applies to our economic well being.

Thursday, April 5, 2012

"Expected" is Not the Same as "Most Likely" -- the Case of Bond Valuation

A common valuation approach is the discounted cash flow method.  Future cash flows are discounted to present value using a risk adjusted rate. The mechanics behind this valuation approach are important in establishing an appropriate valuation mindset.  In the case of standard bond valuation, I believe the widely accepted discounted cash flow valuation mechanics are incorrect, and fail to incorporate an important valuation consideration.

The standard bond valuation equation is:

V = SUM{C/ [(1+d)^(t)]} + Px / [(1+d)^(x)], where 

V = bond value
C = bond coupon
t = time period, beginning at t=1 and ending at t=x
d = risk adjusted discount rate
P = bond principal
x = remaining life of bond, expressed in number of periods

Here and here are two websites that provide bond valuation equations like the one shown above.

The problem with such a valuation lies in the cash flows used.  The appropriate cash flows to use are expected cash flows, a standard valuation concept.  Coupon and principal payments represent the maximum cash flow possible, not the expected cash flow.   Therefore, the cash flows used to value bonds should be lower than the coupon and principal amount if there is any risk of default.  Even if the bond will probably pay off in full, expected cash flows should incorporate probabilities of possible scenarios.  Thus, I draw an important distinction between "expected" and "most likely."  Coupon and principal payments can only represent expected cash flow if the investor (naively) believes default probability is zero.

For highly rated, low risk bonds, I concede the difference between the standard approach and the probability adjusted approach is likely negligible.  Nevertheless, the importance of illuminating the theoretical shortfall in the standard valuation approach remains.  Thinking in probabilistic terms is challenging. Substituting a shortcut approach for a theoretically sound approach encourages intellectual laziness.  I think students and practitioners would benefit from reinforcing the need to assess alternative scenarios and the probability of occurrence for each.

 An approach incorporating scenario probabilities is useful for more than determining the expected cash flows of an investment.  It also is highly relevant in evaluating the appropriate risk adjusted discount rate.*  After all, in the standard bond equation noted above, the expected cash flows are the promised, or maximum, cash flows.  Implicitly, using them as expected cash flows implies no chance of default.  Conversely, the discount rate used in the equation is a risk adjusted discount rate, with credit risk a component of the risk premium.  This creates a schizophrenic proposition--that bond's cash flows have no risk, yet are discounted using a risk adjusted rate.

Even if it does not always result in a meaningful valuation difference, better to use probability adjusted cash flows with a risk adjusted discount rate.  When done properly, the cash flow scenarios will be consistent with the expected cash flows (numerator) and the risk adjusted discount rate (denominator).used in the valuation equation.*

* The risk adjusted discount rate depends on more than simply the variability of the cash flows.  The correlation of the cash flows  with those of other assets is another factor in determining the appropriate risk adjusted discount rate.  

Friday, March 30, 2012

Deleveraging and Financial Intermediation

One consequence of the financial crisis was that our economy had to experience a period of deleveraging.  This period, according to conventional wisdom, constrains the ability of an economy to grow.  I thought it would be interesting to examine the economics of  deleveraging and how the process harms the economy.

In this discussion of deleveraging, I focus on deleveraging that occurs in financial services industry, as that was the primary focus of the deleveraging concerns following the financial crisis.  Nevertheless, the same principles apply to any industry whose participants utilize nonequity capital (e.g. debt, deposits, etc.) to fund its operations.

Financial services companies help savings equal investment in the economy.  Individuals can make direct investments in stocks, bonds, or real estate.  Many, though, don't have the expertise or familiarity with risky investment opportunities to make informed decisions. Financial services companies, also known as financial intermediaries, allow investors to contribute to valuable, yet risky investments, without having to select the investments and, in many cases, accept the risk of the investment.  For example, a bank depositor may earn a small return on his or her deposit, which is guaranteed by the bank and the FDIC.  Meanwhile, the deposit can be used to make a mortgage or small business loan, investments with considerably more risk.  The financial intermediary has expertise in selecting quality investments from among those available, channeling individuals' savings into the most productive investments.  For this service, the intermediary keeps the difference in return between its investment (mortgage or small business loan) and the individual's investment (savings deposit).

The critical contribution that financial intermediaries make to our economy is they allow uninformed, risk adverse individuals to provide capital for risky investments.  Although their investments are risky, financial intermediaries (generally) possess the expertise to select only those investments where the expected return compensates for the risk borne.  When financial intermediaries take lower risk capital and use it in higher risk investments, they are creating financial leverage.  The use of financial leverage requires that the providers of low risk capital have confidence in the financial intermediary to select the appropriate investments and perform appropriate investment monitoring.  

When intermediaries have lost the confidence of those seeking lower risk investments, they can no longer rely on financial leverage.  Deleveraging is the process by which financial intermediaries have to decrease their use of low risk capital sources to make their investments, likely because of a loss of confidence from these low risk investors. Companies can lose investor confidence through a variety of means, including making poor investment selections, experiencing accounting irregularities, or through bad publicity.  During the financial crises, all of these examples were present in some capacity.

When financial leverage is unavailable, the intermediary may be able to raise equity capital to fund its investment opportunities.  As described above, however, many investors don't have the expertise or familiarity to make risky investments in equity.  These investors seek lower risk investments, and when traditional low risk investment alternatives become unacceptable, no investment occurs.  In essence, the individuals with capital to invest don't have the expertise to determine which investments are profitable; during the process of deleveraging they are also unwilling to provide the capital to institutions that do have such expertise.  Profitable investment opportunities are lost as a result, and economic growth suffers.

Thursday, March 15, 2012

Money's Impact on Economic Output and Growth - Part 2

In Part 1 of  Money's Impact on Economic Output and Growth, the implication of money's role as a a medium of exchange and a store of value was discussed.  The third role of money in our economy--a unit of account--follows here.

Unit of account

Because money trades against all goods and services, it is easy to compare value across goods and services in a monetary economy.  Austrian economists discuss how prices send signals to market participants, and these signals result in resource allocation and innovations.  Prices (and interest rates) are the unit of account that occurs in monetary economy.  Barter economies don't have a common unit of account until one of the goods trades against all other goods. If a good started trading against all other goods (think of gold for example), the common good being traded has essentially evolved into a form of money.

The benefits from the information content in prices and interest rates is vast.  Business managers and entrepreneurs make decisions based on current and expected prices for the goods and services.  Allowing the value of goods and services to easily be measured against one another makes decision making more effective.  As prices change in our economy, businesses are able to respond and new companies form to seize profitable opportunities.

The nominal value of money can also cause our economy problems, most notably when there are unexpected changes in the overall price level (inflation or deflation).  Contracts are generally written in nominal terms, unadjusted for price changes.  For example, the standard bond (a very common business contract) promises to pay the holder a set amount of money over time, regardless of what happens to prices in the future.  A large price increase makes the bond issuer better off, but the bond holder worse off,  because the payments under the bond contract now purchase fewer goods.  Possibly even more destructive to our economy is a deflation, where prices drop across the board.  Because nominal contracts do not fall with prices, companies are faced with larger debt balances relative to their operating profits.  Widespread bankruptcies can occur during deflations, leading to large levels of unemployment.  This is one of the common observations of what occurred during the great depression.

Both parties of any contracts based on nominal dollars are subject to risks from changing price levels.  This is a main reason why central banks, including the Federal Reserve, generally have a mandate to keep overall price levels stable.*  Because governments control the money supply and inflation rates to a large extent, the credibility of the government to enforcing price stability is paramount to participants willingness to contract.  As contracts, including debt contracts, play such a large role in our economy, a loss of government credibility in fighting both inflation and deflation can lead to a loss of total output and employment.

* A mandate to keep the overall price level stable does not mean central banks prevent relative price changes. Price changes occur as preferences change between goods, leaving some goods more expensive and others less expensive.  Overall the price level in such a scenario remains the same.

Thursday, March 1, 2012

Money's Impact on Economic Output and Growth - Part 1

We take our use of money in society as a given.  It seems ridiculous to think of an economy as sophisticated as ours trying to operate on a barter system.  The benefits of using money are large.  However, the use of money creates obstacles as well.  Here I'd like to explore the effects of a monetary economy on the total output (GDP), and also fluctuation in that output.

There are many definitions of money.  The Federal Reserve has tracked money in the form of M1, M2, and M3; each of these terms, respectively, is a broader definition of the concept of money.  For example, M1 includes currency in circulation, plus demand deposits ((i.e. checkable deposits).  M2 includes all of M1, plus savings deposits, time deposits less than $100,000, and money market deposits.  Other measurements of money, such as the monetary base and money of zero maturity (MZM) are also referred to and discussed in the media.

The role that money plays in an economy are generally categorized into the following three groups.
  1. Medium of exchange
  2. Store of  value
  3. Unit of account
I'd like to examine these roles for money, and how each impacts the economy output and growth.  In my opinion:
  • the medium of exchange role results in large benefits at no costs for an economy.  
  • the store of value role results in harmful effects for an economy.  
  • the unit of account aspect of money results in benefits as well as costs for an economy, although the benefits exceed the costs.  
Overall, money increases total output in an economy, and facilitate economic growth as well.  It is no certainly no panacea, however, and a study of its harmful effects is important to understanding how our economy functions.  In Part 1, I'll discuss the medium of exchange and store of value aspects of money.  In Part 2, I'll address benefits and costs that result from the unit of account role of money.

Medium of exchange

By having an asset that is readily accepted to settle all transactions, costs associated with exchange are significantly reduced.  The costs of a barter economy include search costs, negotiation costs, divisibility costs (how could you buy a truck from someone who wanted payment in cars, when the truck was worth between 1 and 2 cars?)  As a result, in monetary economies individuals and institutions can specialize in producing a narrow range of goods or services, assured that they can trade for other goods and services they need.  The alternative to a specialization and exchange society is one in which individuals produce all goods and services they consume. Such a proposition is tremendously costly, and reduces the total output available.

I believe the medium of exchange characteristic of money is the easiest of the three to understand and observe in daily life.  Its impact on economic output is exclusively positive, unlike the other two characteristics of money.

Store of value

Individuals can store wealth in money or in other assets.  In our fiat monetary system (fiat simply refers to money has value because the government says it does, and not because it can be redeemed for real assets), money demonstrates two unusual characteristics:
  1. Money, unlike other assets, is not affected by certain market forces.
  2. The marginal value of money to the real economy is zero.
Lets look at these characteristics separately.

When demand for all other assets increases, the price of that asset increases.  Not so with money, which always keeps its nominal value.*  In addition, fiat money is controlled by the government and the banking institutions.  With fractional reserve banking, banks can alter the supply of money to a point.  However, banks are subject to governmental regulation, so ultimately money supply is a function of the government control.  Whereas for most real assets (e.g. oil, trucks, housing), market forces cause supply to increase when demand increases, this does not necessarily hold true under a fiat monetary system.

Once an economy has a well accepted monetary exchange system in place, additional money does not increase the wealth in the economy.  This is because, as widely accepted among economists, prices adjust to  reflect changes in the money supply.  The relationship between money and prices is referred to as the quantity theory of money.  Paradoxically, we can conclude that, for the economy as a whole, money is the only asset where an increase in quantity does not result in an increase in wealth.  Consider any other asset in an economy (e.g. oil, trucks, housing)--as more of these assets are held, the economy becomes richer.  For money, such a fundamental, logical relationship does not hold, as an increase in money only makes prices of real assets move higher.

Why does all this matter?  Well, when demand for money increases in our society, i.e. when people seek to hold more money for its store of value attributes, we face economic problems. Any supply response (whether from banks or from the government) does not add any value to our economy.  Any additional money supplied in an economy can be considered artificial assets, as it ultimately results in higher prices, not any value creation.  In essence, when demand for money increases in our society, we switch our demand from wealth creating assets (i.e. real assets) to wealth neutral assets (i.e. artificial assets).  Total real output suffers as a result.  

Macroeconomists that follow the concepts first articulated by John Maynard Keynes, generally termed Keynesian macroeconomists, refer to an increase in demand for money as "a fall in aggregate demand."  I believe a more precise term such an effect should be "a fall in demand for real goods and services."  After all, money is generally considered an asset, and demand for goods (including assets) and services has not actually changed in aggregate.  Instead, demand has been shifted, in part, from real goods and services to artificial assets. Our GDP and employment levels depend on the amount of  real goods and services produced.  When demand reallocates from real to artificial assets, we face declining real output and employment.

* Unlike other assets, whose price is generally expressed as an amount, the price of holding money can be expressed as the prevailing interest rate.

Wednesday, February 29, 2012

Good Overview of Austrian Economics

I came across this issue of Journal of Economics and Finance Education in perusing my favorite blogs:  (hat tip to Peter Boettke at Coordination Problem).

This issue is focused on Austrian economics.  I've read the first two papers and am quite impressed.  Although not the easiest of reads, they do convey:

1) Principal economists in the history of the Austrian School
2) Key features of the Austrian perspective to economics
3) How Austrian economics differs from traditional economics


Sunday, February 5, 2012

Free Riding and the Financial Crisis

We've heard many people describe contributors to the financial crisis:
  • Alan Greenspan kept interest rates too low in the mid 2000s
  • Freddie Mac and Fannie Mae's quasi government status provided too much easy credit into housing
  • A speculative bubble fueled by greed and "animal spirits"       
I agree that each of these points were important enablers.  I'd like to address one additional contributor, that  worked in conjunction with those points above, that was important in creating the financial crises.

An important economic concept is the notion of "free riding."  Free riding occurs when one person's activities provide as a group benefit. It is difficult to make those parties receiving a benefit from the activity from bearing a proportional cost of the activity.  An often used example of a free riding problem is police or personal safety.  If policing was privatized,  those who purchased protection would likely provide some unintended protection to their neighbors. The security guard that would be on watch would prevent crime for the client, and also the client's nearest neighbors as well.  Many economists think that the total personal safety expenditures would be smaller than we would actually prefer, because many people would hope that others would purchase protection, allowing them to "free ride."  Of course, if too many people feel this way, total expenditures on a valuable service will be quite small.

Free riding can also occur when ambiguity exists.  When two or more parties are involved in completing a complex activity, and there is imperfect information between them, often times each of them will attempt to free ride on the others actions. It is inefficient and costly to duplicate work; it is natural to seek to avoid such duplication.  The risk becomes when all parties, in the name of efficiency, assume another party is addressing a critical activity in the process. Therefore, unless there is clearly defined responsibility, accountability, and transparency, the potential that all parties are trying to "free ride" exists, so that the activity in question does not get performed appropriately.  As the process becomes more complex and involves more parties, the risk of such a free riding problem becomes greater.  

I believe the financial crisis was largely subject to such a pervasive free riding problem.  Fueled by the issues listed in the bullets above, the mortgage finance industry expanded in complexity and the number of involved parties.  For example, the archaic model of mortgage financing is that a bank or savings and loan would make a mortgage loan to a home buyer and then hold the loan until it was paid.  On the financing side, there was one party - the bank or savings and loan.  In the modern mortgage finance model, the following parties may all be involved:

  • Mortgage broker
  • Mortgage underwriter and initial lender (bank, thrift, or mortgage finance company)
  • Wholesale lender
  • Mortgage security underwriter (investment bank, Fannie Mae, Freddie Mac)
  • Credit rating agency (S&P, Moody's, Fitch)
  • Institutional investors
So, we've moved from a process involving a single party to one that can involve up to six parties.  Whereas the underwriters were responsible for determining which loans to make, and suffered the consequences if they made poor decisions, such decisions and consequences could be spread among five parties in the new financing model (the credit rating agency bore no direct financial risks).  Importantly, all six of these parties shared some responsibility to investigate the quality of the loans:
  • The mortgage broker and underwriter were responsible for investigating the borrower.  
  • The wholesale lender was responsible for performing due diligence on the mortgage underwriter.
  • The security underwriter, credit rating agency, and institutional investor were responsible for performing due diligence on the portfolio of mortgages.
Without our hindsight knowledge, it would be easy to conclude that there were robust controls in this process, and therefore the mortgage investments that were distributed must be sound.  However, I'm convinced such complexity and lack of accountability and transparency created a massive free riding problem.  What actually happened was, in many cases, extensive cutting corners by each of these parties, under the assumption the other parties provided a safety net, or at least plausible deniability (as in "I was informed that [fill in other company's name] was responsible for addressing that risk").

My takeaway - when processes add layers of complexity and the number of parties involved increases, the risk of free riding increases.  If there is clear accountability and transparency in all aspects of the process, free riding is much less likely to occur.  Importantly, many times it is in the interest of parties involved to blur accountability and reduce transparency.  Doing so allows them increased flexibility and reduced costs, under the veil that another party shares their responsibilities and can be relied upon.  In the financial crisis, it took massive losses to illuminate what each of the parties involved in the process were actually doing.  Perhaps it's possible to identify environments subject to such free riding problems going forward and thereby avoid participating in the resulting losses.

Sunday, January 15, 2012

Opposing Cognitive Biases and Rational Behavior

A friend and I were discussing the logical fallacies that often occur when individuals are making decisions or constructing an argument (hat tip to Ryan Miller).  We identified a particular fallacy--the gambler's fallacy--that exists when an a sequence of identical outcomes is mistakenly construed as implying the probability of the opposite outcome increases for the next iteration.  For example, if the roulette wheel results in black outcomes for 5 spins in a row, there exists a common misperception that the next spin is more likely to land on a red outcome, because overall, red and black outcomes should be approximately equal.  According to the gambler's fallacy, red outcomes would need to "catch up" to make equal outcome possible, and therefore red outcomes become "due" when preceded by a series of black outcomes.

We then considered an alternative and opposite bias that can occurs in the exact same situation.  Many other gamblers believe that a series of black outcomes implies that black is more likely to occur going forward.  From this perspective, black is on a streak, or is the "hot" play.  Its common to hear in casinos that certain craps tables are hot, an implicit belief that a series of outcomes is likely to persist into the future.

I find it very interesting that, in certain circumstances like the one described above, we are prone to any erring on either side of the rational conclusion.  Its unclear whether a sample of 100 gamblers (each without a favorite roulette color) would be more likely to bet on black or red if they observed five black outcomes in a row.

Behavior finance teaches that humans have natural heuristics in evaluating issues and making decisions that make us prone to certain biases.  These biases are generally described as unidirectional.  For example, behavioral finance teaches that individuals generally sell winning investments too early, and hold on to losing investments too long.  This may certainly be true, in general.  However, as described above with the gambler's fallacy, the extent of biases can be more complex, with other possible biases working in the opposite direction.  When competing biases exist, the impact of such biases is not clear then. It depends on which bias, among those that exist, dominates in the circumstance.  Moreover, it seems odd to me that many finance and economics analyses assume investors act rationally, but for certain biases that can be accounted for.  Since we are subject to biases--biases that allow us to err on either side of the rational conclusion--it appears more likely to me to simply accept that humans don't always act rationally.  

Wednesday, January 11, 2012

Why Distressed Companies Can't Raise Equity

Earlier today, Hostess Brands (maker of the twinkie) filed for bankruptcy protection.  Such a sad headline got me thinking of bankruptcy in general, and why companies that may be worthwhile enterprises can't raise equity when confronted with financial distress.

First, I want to clarify that bankruptcy is not necessarily a doomed result to be avoided.  Its entirely possible the company seeks bankruptcy protection to free itself of overly burdensome contracts that inhibit its success.  Nevertheless, bankruptcy can be costly.  Many distressed companies would seek to avoid bankruptcy but cannot--even if they show an optimistic future.

Why is this?  I've learned that the reason many companies can't raise equity capital when experiencing difficulty is a product of:

1) distinctions between debt and equity capital

2) uncertainty in future firm value 

An example can illustrate how both of these  factors interact to leave some companies shut out of equity markets.

Consider a firm with $90 million in par value of debt capital.  We'll assume that the future of this firm will take one of two distinct outcomes, each with 50% chance of occurring.  In outcome U (U = "up"), the firm is worth $130.  Firm value is equal to debt value plus equity value.  In outcome D (D = "down") the firm is worth $70.  For our purposes, we'll ignore any time value of money.  What is the current equity worth?

Firm value = (50% * firm value in outcome U) * (50% * firm value in outcome D) = $100
So the firm value is $100.  Does this mean that equity value equals firm value - debt capital?  Well, yes, as long as the debt capital is measured at market value.

In this case, debt capital is worth less than its par value.  I know this by applying the same approach to determining current value of the firm.  Specifically, debt capital in outcome U is worth its full par value of $90. In outcome D, debt is worth only $70.  At 50% probability for each scenario, debt capital is currently worth $80.  Thus, equity capital is worth $20.

Such a company is quite leveraged, having a debt/equity ratio of 4.  Lets say that the company is losing customers and suppliers due to its high leverage.  It wants to raise an extra $10 in equity capital to reduce their debt/equity ratio from 4 to less than 3 (using the assumption that equity value will obviously go from $20 to $30 with $10 of equity contribution).  What actually happens?

Adding $10 to our firm value in both outcome U and D will provide our answers.  Firm value, debt value, and equity value in outcome U will now be $140, $90, and $50, respectively.  In outcome D, firm value, debt value, and equity value will now be $80, $80, and 0.  So, at 50% probability, we see that total firm value increases by $10 to $110.  Debt capital is now worth $85, and equity value is now worth $25.  Of the $10 equity contribution, $5 increased equity value, while $5 increased debt value.  Said differently, 50% of the equity contribution value was simply transferred from equity capital to debt capital.

If you were a potential equity investor, would you want to invest where 50% of your investment went to helping a different set of investors?  Neither would I.

This situation occurs when equity capital gets a large percentage of its value from its option-like features.  Equity possesses option like features because it gets the opportunity participate in the upside, but has a floor of zero on the downside.  Options become valuable when volatility (or uncertainty) is high.  Volatility becomes more valuable when firm value and debt capital are similar.  This means that volatility is valuable for equity holders as the debt burden grows.  Although volatility is valuable to these equity holders, it becomes a double edge sword as described above.  The equity holders trade the "option value" inherent in their share price for the risk that the company will likely not be able to raise further equity even if desperately needed.

When reflecting on the financial crisis, banks and other financial institutions were subject to much of what has been discussed above.  These firms were leveraged so highly, debt capital was approximately equal to firm capital.  Many banks and financial institutions escaped, and their common stock investors saw huge returns.  Those companies that needed equity to restore confidence, however, were left empty handed, even if they represented a potentially valuable, long term business franchises. 

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.