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Tom Guttenberger
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  • Fed Model For Disequilibrium In Markets Explored

    A very commonly cited valuation metric is the stock market's P/E ratio. It describes the price of stocks relative to their earnings. A recent article by economist John Huston brings attention to a different way of measuring the price of stocks. It compares the P/E with the yield one can receive on a 10-year Treasury note. The ratio proposed is i*(p/e), where i is the yield on the 10-year bond. This ratio adds yield to measure the relative attractiveness of bonds vs. equities. As a matter of behavioral indifference, this ratio is proposed to signal equilibrium when it is at its mean which should be constant throughout time. Other than our own irrational behavior, are there fundamental forces that could cause this metric to drift?

    Before examining the possibilities, a fundamental illustration of the relationship and the theory behind it:

    It is supposed that equilibrium in this metric is achieved when this series is at its mean, and that mean is stationary over time. That is to say, increases or decreases in the yield of Treasury bonds should offset changes in the price to earnings ratio of stocks. When there are deviations from the ratio, demand will have a tendency to return to equilibrium in the asset pair and the ratio will correct to the mean.

    As a demand problem - demand for Treasuries and demand for equities should be the same directionally at any given time. Divergences in demand would cause the rate to move from equilibrium, or the long-term mean. For example, if rates are low (high bond demand), the price to earnings ratio of stocks should be high (high equity demand) to offset it. These assumptions are required for the series to be stationary, as proposed.

    To make a reasonable guess about the validity of the theory, we should try to identify forces that affect demand from all angles of the market.

    First, the Federal Reserve has been actively involved in the credit economy, and will impact the demand equilibrium on Treasury bonds. The Fed not only controls the baseline interest rate, but it has buoyed credit markets with QE purchases. By purchasing both long and short-term Treasuries, the Fed directly invests into government credit. So there are two ways the Fed can impact at least one variable in the relationship:

    1. With the Fed Funds target rate, it directly controls the risk-free interest rate on the USD
    2. Equilibrium in the Treasury market. More QE buying means less private demand needed to balance the market at a lower rate.

    So Fed open market participation and control of the risk-free rate have a direct impact on this model. Would the model be more a meaningful indicator of private demand indifference if we could normalize for the Fed's non-market controls? Would using the interest rate expressed as the spread above the risk-free rate be an improvement to the equation?

    When studying the ^TNX-minus-Fed Funds rate series, we see that this metric is unusable in the analysis. This is because of time periods with an inverted yield curve - when longer maturity government debt yields less than short dated. Negative series values do not make sense, and directionally a more negative yield would impact our test ratio incorrectly.

    Still, it seems like normalizing for the Fed Funds rate's direct impact on yield in our equation could be a helpful improvement to the model - after all, the equation should reflect demand indifference. So for the sake of this analysis, I am creating a new interest rate metric: An average of ^TNX and ^TNX minus the Fed Funds rate. I propose substituting this interest rate metric in the Fed model for i. A 1954-2012 time series of the metric is shown below, in addition to the Shiller CAPE10 model and the Fed i*(p/e).

    As indicators, these series are intended to be mean-reverting. That is, when assets are "overpriced" or "underpriced", market participants will buy what is cheap, and cause the ratio drift back to the mean. To compare the diffusion rates, and thus the mean-reverting tendencies of each model, I used a coefficient of variation test - standard deviation divided by mean. Without going into the mathematical proof, this is a good test to compare relative stationarity for multiple series. This is because by definition a mean-reverting series' up/down conditional probabilities would be impacted by its location relative to the mean. Disequilibrium points will possess drift opposite to their location relative to the mean, and increase the conditional probabilities of low residual measurements continuously. Therefore, a more stationary series should display a lower coefficient of variation. As shown below, averaging ^TNX with its spread above the Fed Funds rate made the model slightly more mean-reverting. This model also implies a nice discount in equities currently.

    Unfortunately the statistics suggest that the model is only maybe a tiny improvement. Below is a comparison of the means and confidence intervals for squared residuals divided by squared means in each model (the same as coefficient of variation squared, used to account for negative residuals and give the statistic a sample size). This shows that the mean-reverting properties of all three models are more or less the same, with the fed model likely a better incremental improvement than my tweaked interest rate variable. Still, normalizing for the risk-free rate gave us the most mean-reverting equation from July 1954- June 2012 when tested with monthly observations.

    (click to enlarge)

    So are any of these series actually stationary? I don't know if it can be proven one way or the other, but I tend to think that they are not. Perhaps on a long enough time horizon. Dr. Shiller displays a dotplot of P/E against 20 year returns on his page, but these test points include overlapping yearly return and valuation inputs. This makes the relationship look a bit stronger than it actually is, the price paths are 95% shared and the earnings predictors are 90% shared. Maybe if they are mean-reverting, it could be to a much smaller degree than their stochastic components.

    Logically, why do I think these series are not necessarily stationary?

    For the Shiller CAPE model, I think that earnings variance is an important factor that could cause trends in the series. Consistent with the capital asset pricing model, earnings variance serves as a risk adjustment to the P/E ratio. Curiously enough, there was a decently strong relationship (R-squared ~.31) that suggested variance up, P/E up - the opposite of my intuition. While this contradicts theory, it appears the regression was trumped by high variance, high multiple-growth observations from the dot-com bubble. High variance can also be manifested through high sequential earnings-growth observations, and could easily be perceived as a trend. I would expect P/E ratios to be less instructive in a high earnings variance environment. The other caveat is already expressed through the intention of the Fed model revision - there is no comparison to other domestic, yielding, paper assets. Shown below is the 10-year moving coefficient of variation for S&P500 earnings.

    For either of the interest-rate-adjusted models, there is not complete independence of factors. Total credit market debt owed in the U.S. economy stands at nearly 55 trillion dollars today. So any significant increase in borrowing costs would have a pronounced negative effect on underlying corporate earnings. It follows that in a low rate environment, earnings from our equation would be directly improved by lower credit costs, therefore related. It could, however, be argued that the interest rate is an assumption of economic growth prospects, therefore offsetting credit costs through business opportunity. While I am sure it does to an extent, this is an implicit assumption whereas the cost of credit can be explicitly measured and is accounted for in net earnings. This would suggest less mean-reversion in the Fed model than the rate spread model because the non-market interest rate forces are not being discounted from its equation at all. In my view, both exacerbate the interest rate factor, double counting it to a degree.

    For investors who think these series are inherently stationary, the Fed model is giving the strongest S&P500 buy signal, followed by the Guttenberger i=(^TNX+(^TNX-Fed Funds Rate))/2 model, while the Shiller model suggests equities are slightly overpriced. Finally as a word of caution - both models suggesting equities are cheap are probably overly sensitive to interest rate moves. That means without future QE, these ratios could easily correct because of rising interest rates, as opposed to higher equity valuations.

    Jul 03 11:36 AM | Link | 4 Comments
  • Historic Volatility Divergence from Implied Volatility as a Broad Market Sell Signal
    Using volatility to forecast market direction is a commonly used technique.  In this post, I show an observation that has peaked by attention along with the some theoretically justification for my directional call.

    Below is a three series chart of SPY underlying price (beige), calculated historic volatility (red), and implied volatility (blue).

    The first observation that I want to draw attention to is that SPY 30 day historic volatility has flat lined right around 30% over the past 2+ months.  Historic volatility is a measure of the variance of underlying asset price changes.  Historic volatility is important to note because this is the amount of variance the underlying has actually experienced over a given time interval, in this example calculated based on the trailing 30 days. 

    Notice that historic volatility is not necessarily subject to fall when the equity markets rise.  It is entirely dependent on the price path of the underlying. 

    This differs from implied volatilty. Implied volatilty is calculated based on the price premiums of options on the underyling.  Implied volatilty almost always moves opposite the direction of the underlying - SPY up, VIX down, and visa versa.  This is because the put premiums signal fear in the market as investors look to buy protection for their long positions on the underlying.

    Now that we have covered the basic background of each indicator, time to get into the premise of why this would be a good time to sell out of stock positions, buy puts, or perhaps buy VIX calls.

    If you accept that the actual variance of the SPY is going to remain right  around 30% for the time horizon you choose through you position, buying puts serves as a worthwhile insurance policy for a long position in the market.  If the market continues on its upward ascent with a variance measure still near 30%, you will be able to capture a profit from the spread between what you paid for the volatility and the actual variance of your portfolio (assumed to be the same as the SPY).  While the put positions you initiate would expire worthless, your portfolio gains will outpace the cost of insurance, again returning to the constant 30% historic volatility assumption.

    If you accept that implied volatility costing less than our historic flatline level of 30 is a bargain, it logically follows that this would be a time for a portfolio manager to "accumulate variance".  This is to say, buy more puts or get long implied volatility, in one way or another.

    Now here is the theory behind my direcitonal prediction:  If you accept that funds will accumulate variance when it is cheap, as it has been for the past few days, a sell reaction in the market would follow, if it ever was going to come to fruition.  It is a problem of order of operations. 

    Why would a (for the sake of argument) HUGE fund want to sell out of equity positions before they buy implied volatility?

    They wouldn't.  They would be raising their own cost of insurance.

    To maximize their own gains, they would want to buy the implied volatility, while it remains cheaper than historic.  Additionally, if they plan to be a net-seller into the market (in a medium term), any selling pressure is only going to act as a sell-defeating feedback loop to their own cost of insurance.  This leads to the conclusion that any large fund that uses volatility to hedge AND plans on liquidating net-long exposure, will follow this order of operation: Buy volatility first, sell equities second.  By following anything other than this sequence, they only shoot themselves in the foot.

    Anecdotally, the observation has proven to be correct.  When implied dipped below historic volatility in late October, a sharp sell-off followed.  Obviously there are 10,000 reasons to be either long or short this market and the headline risk is another reason to be long the upcoming calculated volatility, but I think as a technical signal this observation shouldn't be ignored.  The logical sequence of events for how large market participants would buy volatility is clear, at least in my mind, and this observation makes me bearish on the direction of S&P 500 equities in the upcoming weeks.
    Dec 08 9:18 AM | Link | Comment!
  • Exchanging Life Settlements for Mortgages as a Federal Stimulus Alternative

    The link is a short elevator pitch a friend and I made in January 2010.  It never developed beyond what is there in the video. In terms of being a private start-up, there were good reasons it did not - relatively large initial investment, relatively low ROI upside, and it could take a many years to see returns.

    That being said, it seems like a perfect business for the Federal government to carry out (not kidding).  Let me explain why.

    Just like HUD offers people reverse mortgages, the government could tap into another financial asset many Americans have - their life insurance policy. During the period 1995 to 2008, life insurance sold to individuals totaled over $20.9 trillion and the lapsed and surrendered life insurance over that same period totaled $9.3 trillion.   Life settlements are the secondary market for life insurance that involves the policy holder forfeiting their policy in exchange for cash.  The total outstanding life insurance policies held as settlements approximated $31 billion as of 2008. That is a mere 0.26% of the estimated total $10.25 trillion of individual in-force life insurance.

    When one financial asset class bubbles, others tend to bubble along with it.  Putting this amount of money into perspective:

    • The market cap of all publicly traded companies in the world is roughly ~$50 Trillion
    • The world annual GDP is ~$75 Trillion

    Life insurance in America was a bubble, a bubble that has unwound ~.26%.

    Rather than a need for cash, a great many Americans have the need for help with their mortgages.  As the labor market remains weak, and people are locked into underwater, or at a minimum, financially inopportune mortgage deals, many are struggling to pay their mortgages. Residential real estate delinquencies were 10.18% in Q2 2011, more than double their 2008 rate.

    This unfortunate situation leaves an opportunity in the life settlement market.  If an organization took the time to do analysis on life insurance holders who also have mortgages, I'm sure they could find a vast list of candidates whose current financial circumstances likely make them willing to surrender their life insurance policy for an up-front payment of their mortgage. 

    Mortgage Holder's Perspective

    For these people the piece of mind from finally having sole ownership of their most tangible asset (their home) would be invaluable.  In addition, it would free them of the burden of paying their mortgages and the premiums on their life insurance.  Rather than struggling with interest payments, their cash would be freed for discretionary spending, subsequently raising their standard of living.

    Investor's (Government's) Perspective

    From the investor's perspective, they would eventually be collecting the maturity of the insurance policy.  Because hypothetically, this could be a public program, the government could expand its' candidate list to include even expected-return-questionable clients.  If the pertinent analysis performed (longevity risk, interest rate risk) by the investing organization is at least roughly accurate, the profit distribution from these investments converge to an annualized rate as the number of total settlements in the portfolio increases. 

    Low interest rates means that the offers to people could be more enticing than otherwise, and it is my personal belief that many people would be interested in an exchange.  Compared to other federal stimulus programs the cost of these exchanges would be relatively low, and could even prove to be a profitable investment. 

    Some very high-level assumptions to make an estimate of maximum total up-front cost:

    Average value of mortgage exchanged: $100,000
    Number of American over 65 years old: 36 Million
    Percent Holding Life Insurance: 50%
    Percent 65+ year olds holding mortgages: 15%

    If every single person were eligible for the exchange, that would be a total initial investment of $270 Billion.  While this is obviously a daunting number, it is an absolutely maximum cost, and is still less than half the cost of either of the QE programs.  Further, it is an investment, and when the policies mature, the government would collect on the maturity value. The government could easily price offers so their expected portfolio return is greater than the returns from Treasuries. 

    The Perspective of Economic Greater Good

    Assets tend to bubble in tandem.  There is no doubt, in my mind, that as stock market assets were bubbling in the 90's and as real estate prices were bubbling after 2000, so did the value of life insurance policies.  In a strong labor market, people have a higher perception of their actual earnings potential.  Life insurance policies are sold indiscriminately, and if a person does have disposable financial assets, it does sound like a good idea - to assure your families financial security if something were to happen.  But if your own earnings power and circumstances are to change while you still are on this earth, you should be flexible enough to reallocate your assets.  In this case, the government just so happens to be the most able facilitator of this exchange. 

    The banks would finally get the certainty of placing values on these mortgage assets - they would be receiving cash.  This cash would help the banks capital ratios, allowing them to lend more.  By keeping people in their houses, supply would be taken off of the market, thus helping real estate prices.  The combination of banks lending more and decreased market supply, would help those who choose to keep their mortgages by buoying real estate values.  The newly freed liquidity, no longer being thrown by individuals at their own mortgages, would stimulate discretionary spending, and thus the economy.  The government could target settlements for a healthy future profit scenario, or depending on their focus, loosen their NPV models and help unleash liquidity by freeing people of their mortgage burden. Finally, the mortgage holders would still have the freedom to choose whether or not they accept the exchange offer, so if they weren't interested, "no harm, no foul".


    Mortgages were a bubble, life insurance was a bubble.  One has unwound the other has not.  An institution could help facilitate the balance of unwinding by exchanging mortgage cash-buyouts for life settlements.  I understand that there could be potentially huge conflicts of interests in terms of social programs, but from a strictly financial point of view it is a program that could make sense.  Certainly I realize that I am looking past intricacies of the life insurance and life settlement industries, but conceptually, I think it is something that could be explored.


    Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.
    Tags: LPHI
    Sep 19 9:55 AM | Link | 3 Comments
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