Oil Futures

From NYMEX, Corrections displays light crude oil futures prices from 2015-2023 (click to enlarge). Note that we know that futures prices are not unbiased predictors of future spot prices (there are risk premia) but that they give an idea of the direction and magnitude of what future prices will be.

The Middle-Class Comeback Is Under Way

Wall Street Journal op-ed "The Middle-Class Comeback Is Under Way" (February 12th, 2015) makes a painful error while trying to pin the world's woes on the Fed.

The Fed’s easy-money policies were also slamming the middle class by encouraging speculation in—and thus pushing up the price of—commodities like oil and food, which are an incidental expense for the rich and a real burden for everyone else.

Normally of the left, this sort of talk belongs in the economic dark ages (60's, 70's).  Markets are driven by supply and demand.  Speculators essentially never take delivery of their product: they purchase a contract for future delivery with the intent to sell later.  They can, of course, sell to other speculators, but eventually speculators must sell to an agent that will actually take delivery of oil.

Assume first there is no storage market.  Agents who take delivery inelastically supply oil, and demand determines price.  This price determines what the delivery agent is willing to pay, which pins down the price they are willing to buy from speculators.  Whatever heights the oil may reach during speculation is pinned down by what it will actually be worth when it arrives.  Speculation can't impact prices at the pump in this world.  (One might say: "but maybe they can sell at a higher price to the agent and he will pass it on to consumers!"  The question this raises is "if he could sell at a higher price to consumers, why wasn't he before?  They don't care about his costs, only their value and the price.")

There is little difference with a storage market.  With a storage market, speculators can actually temporarily bring up prices, but only at a loss to themselves, if they brought it up incorrectly.  Say speculators anticipate (or act like they anticipate) a demand shock: oil will be pricier, they think.  They purchase many shares and drive the price up because they think it will be valuable in the future.  This causes less oil to go on the market today, and the price at the pump to rise today, and less oil is consumed.

After this, there will be a sharp plunge in oil prices, as storage capacity is sold but demand hasn't gone up.  (That is, speculators could potentially shift supply down and then up.  If there is no fundamental demand shift, this will cause a rise, then a fall in prices, easily mappable to storage).

Inventories did not change enough, and prices were not sharply changing enough, to allow speculation to have any role in the rise in oil prices.  Instead according to Knittel and Pindyck (2013), it seems that (as economic theory would predict) speculation lead to the smoothing of oil supply over demand shocks, actually reducing the price volatility (but not changing the level: changing the level over the long run is highly unrealistic, for the reason discussed earlier).

While theory and empirics line up to tell a clear story (viz., speculators are not to blame for price rises the way you ever read in newspapers), February 12th's Wall Street Journal's op-ed page doesn't just seem to abandon coherence of multiple signals, but even a sensible signal to begin with.  For shame.

Theory: the Federal Reserve is a liberal "long con."  The idea is to drive conservatives to heights of irrationality, causing the party to twist itself in knots to blame the Fed for each new and imagined ill, bringing them to the point of making up easily refuted historical and current "facts."

Quantitative easing: giving cash to the public would have been more effective

The Guardian article "Quantitative easing: giving cash to the public would have been more effective" (10/29/2014) offers rhetorical flourishes rather than understanding when discussing Quantitative Easing.

Central banks have always been wary of “helicopter money” on the grounds that QE is temporary while giving cash to the public is permanent. But the temporary has become permanent. What was once unconventional has now become conventional.

As with most casual commentary about monetary policy, which trades understanding for catchphrases, sophistry, and silliness, this is phenomenally foolish.

QE is temporary in the sense that the Federal Reserve traded one asset for another asset (cash for Mortgage-Backed Securities and U.S. Treasuries).  The Federal Reserve "created money" and purchased these interest-bearing assets.  As these interest-bearing assets bear fruit, they can un-create the money they created (plus some more thanks to interest, if they so desired).  It is in this sense that QE is temporary.

Simply giving money away isn't trading money for an interest-bearing asset: it's giving money away.  Not only would it be illegal for the Federal Reserve to do this (this is fiscal policy, not monetary policy, the purview of Congress), but it would be permanent because the Federal Reserve has no way to "un-do" it, absent taxes which go unspent.

The distinction between "permanent" and "temporary" is not in the timeframe, it's the net change in assets.  The writer of the Guardian's article either misunderstands this meaning of temporary and permanent or ignores it: without this distinction, the article loses coherence.

Long-Run Geometric Annual Return by Industry: 1970-2012

Below, Corrections depicts the long-run geometric annual return by industry, from January 1970-December 2012, from Kenneth French's industry data.

Treasury Yield Curves

Below, Corrections plots selected Treasury yield curves: 1 year, 5 year, 10 year, 20 year, and 30 year Treasury yields are all historically quite low (click to enlarge).

Time Series and Distribution of S&P 500 Returns by Timespan

Below, Corrections depicts the time series of net percent return on the S&P 500 from January 1926 to March 2013 by day, month, and yearly observation (click to enlarge).

We can alternatively look at the distribution of returns by day, month, and year (click to enlarge):

Inflation Expectations over Time by Duration

Below, Corrections depicts two different of the 10-year expected inflation rate (that is, the average yearly rate of inflation over the next ten years).  The first comes from the Cleveland Fed, and the second comes from the TIPS break-even rate.

First, we depict three different Cleveland Fed inflation expectations series (click to enlarge):  for the most part, from the 1980's onwards it took time for people's inflation expectations to fall from the highs of the 1970's and they currently range around 1 to 2 percent.

Below, we look at the break-even rate for 10-year TIPS vs. 10-year government bonds (click to enlarge).  Note that TIPS fell dramatically against bonds during Fall 2008, perhaps because of their relative illiquidity during a time when liquidity was highly valued (and are therefore probably not useful as a measure of expected inflation during that period).

 Finally, we look at the two measures together (click to enlarge):  they both suggest that over the next ten years, the yearly inflation rate ranges between 1.5 and 2.5%.

Inflation, Stock Market, and Bond Market Returns

Below, Corrections depicts value-weighted one-year stock market returns (including distributions), one-year Treasury bond returns, and the one-year inflation rate (click to enlarge).  We display each one year lagged return by month, from 1951-2012 (inclusive).

Obviously, unexpected inflation takes away from an already-issued bond's return while having an unclear impact on already-owned stock returns.  Interestingly, simple regression on non-overlapping periods suggests a:

• 3.46% return on one-year bonds with 0.57% increase above and beyond that baseline for each one percent of inflation experienced that year.  
• 15.28% return on stocks with a -.76% loss for each one percent of inflation experienced that year

This may be seen in light of:

• One-year bond's arithmetic (geometric) average return of 5.57% (5.49%) with a standard deviation of 3.76%
• Value-weighted stock market's arithmetic (geometric) average return of 12.49% (11.13%) ( (including distributions) with a standard deviation of 16.36%
• The CPI's arithmetic (geometric) average level of 3.67% (3.68%) with a standard deviation of 3.00%

It is interesting and surprising that while bonds return less than stocks (on average) they return more in periods of higher inflation.  This is counter to the fact that a one log-point fall in unexpected inflation impacts the log return of already purchased bonds by one log-point.

Expected Inflation and Treasury Bond Yields

Below, we plot the Treasury bond yields against the Cleveland Fed's estimates of expected inflation (click to enlarge).  It is important to note that the Cleveland Fed's estimates may be a noisy measure of "true" expected inflation.

A simple model in finance would suggest a one-to-one correlation between expected inflation and interest rates.  More complex models may deviate from this.  For example, they may allow for pricing of uncertainty about inflation (and therefore an inflation risk premium) that correlates with the level of inflation.

10-Year Stock Market Return

Corrections has been perennially dissatisfied and unclear about the "average" long-run stock market return.  We've always had in our mind a 7% number, but looking at Center for Research on Security Prices (gated) data, or other online sources, numbers seem to vary quite a bit, from 4% to 13%.  The reasons for variance are generally 1)  inclusion of inflation to get real returns, 2)  use of returns based on price but not dividends, 3)  use of different time periods, and 4)  use of different portfolios.

Consequently, we produced two graphs that show real stock market returns.  They take a 10-year portfolio and ask "what is the compounded rate of return over that 10-year window?"  The two graphs reflect the inclusion of distributions (generally dividends, but including other direct payouts to shareholders).  Within each graph there are four lines:  two nominal returns, and two corresponding real returns, crossed with equally-weighted returns vs. value-weighted returns.  The idea behind value-weighted returns is that it reflects the return if you had to hold the market portfolio:  more money in larger market caps, less money in smaller market caps.  The equal-weighted simply buys $1/(Total Number of Stocks) of every stock, rather than $1*(Company Market Cap)/(Market Market Cap).

The four numbers at the bottom of each graph are the average compounded 10-year growth rate.  So, for instance, if you purchased $1 in stock, split evenly across all companies in the NYSE/NASDAQ/AMEX in March 2003 and held it for 10 years through to March 2013 (our final data point), reinvesting dividends all the way and re-balancing each month, you would have received an compounded yearly return of about 11.7% (click to enlarge).  Without including dividends, it would have been about 5% (see second graph below).  

While a graph excluding distributions is less informative, it helps some understand why their personal calculations based only off price are too low (click to enlarge).

Distribution of Market Equity

Below, Corrections displays the distribution of (log) market equity (price times shares outstanding) of the NYSE, NASDAQ, and AMEX in 2012 (click to enlarge).  As always, log means natural log.  Note that the graph would be essentially unreadable if it were transformed into levels:  the skew in market equity is very large.

The large cap nature of the NYSE is evident:  the breakpoint denoting the NYSE's 20th percentile is around the NASDAQ's 60th, and AMEX's 80th percentile.

Benefits of Diversification

Below, Corrections displays the benefits of diversification.  Returns from the the 1990-1991 stock period, we display the simulated standard deviation from a randomly-chosen portfolio of a given number of stocks and holding it for a year (click to enlarge).

Obviously, choosing a random number of stocks gives the same expected return.  But choosing more stocks reduces the expected noise around that return.  Choosing only one stock will yield a more noisy process than another.  As more stocks are included, the standard deviation of portfolio returns converges down to the market's standard deviation of returns (around 18% for annual returns).

Size-Based Portfolios

Below, Corrections mimics the "size" part of Fama-French (1992), replicating 99.7% of the return variation in Kenneth French's size-based portfolio results in Kenneth French's website using raw CRSP data.

Imagine, each year, after markets close on the last day of June, you form a portfolio based on market equity (market cap).  Take the NYSE and find the size decile breakpoints (smallest 10%, smallest 20%, and so on).  Then, apply those breakpoints to the NYSE, NASDAQ, and AMEX, form an equally-weighted portfolio of all stocks in that size category.

We can form those portfolios at the end of each June and then look at the average returns (price appreciation as well as reinvested dividends included) from 1926-2012.  The results of each strategy are depicted graphically below (click to enlarge).

As one can see, the lowest decile of stocks returns approximately 18%, while the rest return only 11%.  We can also see this small-cap premia evolve over time if we look at the yearly returns of these portfolios, rather than taking the average over many years.  While yearly returns are volatile, I compare the 10-year results of rebalancing on size each year (click to enlarge).  Again, returns include dividends, producing an equally-weighted 14.5% average yearly return from the stock market rather than 12% from price appreciation alone.  Further, the returns are 10-year returns and are net and in percent (e.g. 30 on a certain date means that rebalancing to a certain-sized portfolio for the 10 years leading that date would yield a 30% net return (you would possess 1.3*original assets).  To be clear about dating, the last  date of December 2002 represents the return of a strategy of holding the June 2002 portfolio from December 2002 to end of June 2003, and then reforming the portfolio for every year until liquidation in December 2012:  yielding a return around 14% for the small-cap portfolio.

It is important to remember that this is in no way indicative of an "inefficient" market:  if some stocks are more risky, they should have more rewards.  If the smallest 10% of stocks are illiquid in times when liquidity matters, then they should have a higher average return, to compensate for their bad qualities.

Options Price vs. Spot Price

Below, Corrections took the price, over nine months, of an option to buy a share of GE stock for $15.  We graphed the price of the option plus $15 against the spot price (click to enlarge).

P/E Ratio Portfolios

Below, Corrections depicts ten different portfolios, organized based on P/E ratios.  For instance, one takes the lowest 10% of P/E ratios and puts them in one portfolio, and looks at the average return of that portfolio, and then takes the next 10% and puts them in another.

We then compare the returns, organized by decade (click to enlarge).

TIPS Yield Spreads

Below, Corrections depicts different Treasury-TIPS yield spreads.  The plots take the yield of a regular treasury security of maturity X and subtracting the yield of an inflation-indexed treasury security of maturity X (click to enlarge).

The plot shows not only a remarkable consistency in inflation expectations but the dramatic flight to liquidity during the 2008 crisis.

IQR and Percentile of Stock Returns by Month

Below, Corrections plots three percentiles of monthly stock returns (NASDAQ, AMEX, and NYSE) over time.  A 1 corresponds to a 100% gain.  A 0 corresponds to no gain, and a -1 corresponds to a 100% loss (click to enlarge).  

Similarly, we plot the interquartile range (75th percentile minus the 25th percentile) of stock returns in each month (click to enlarge)

Distribution of Stock Market Returns

Below, Corrections displays the distribution of daily holding period returns in all non-delisted stocks in the U.S. NYSE, NYSE-AMEX, NYSE-ARCA, and NASDAQ (click to enlarge).  Holding period returns include dividends.

We do the same thing but cumulate the net returns over the course of the month (click to enlarge):

What are the Long-Run Returns on Sovereign Bonds of defaulting countries?

Bondholders of defaulting sovereigns often take haircuts between 5 and 70 percent (typically around 20%) of the net present value of their bonds, but they often get large risk premia in the years running up to a default.  What are the long run returns of a portfolio that specializes in bonds of countries that are likely to default?

The answer seems to be that there looks to be a positive but small benefit to holding the bonds, though there is high variance in the outcomes.  Lindert and Morton (1989) look at 1,522 bonds over the course of 150 years and find a 0.42% premium of their portfolio against a portfolio of British and U.S. bonds.  Eichengreen and Portes find that U.S. bonds beat default-prone sovereign bonds, but default-prone sovereign bonds bean U.K. bonds during the 1930's round of defaults.  Klingen, Weder and Zettelmeyer (2004) estimate long run premia of between -0.17% and 0.46%, using various methodologies.

Below, from the book Debt Defaults and Lessons from a Decade of Crises (Sturzenegger and Zettelmeyer), Corrections depicts the degree to which a portfolio of sovereign bonds beats a portfolio of "safe" (U.S. or U.K.) bonds over long time periods for 32 country-time periods (click to enlarge).

10-year Eurozone Bond Yields: January 1993-April 2012

Below, Corrections displays 10-year Eurozone Bond Yields from January 1993-April 2012 (click to enlarge).  Did Ireland's "austerity" measures work like Iceland's did?  10-year bond yields have fallen dramatically.