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.