History of money and gold

David Beckworth has some interesting comments on the gold standard and monetary history.

Excerpt:

 Silver actually was the dominant metallic standard for hundreds of years before gold. The main reason it was displaced by gold is not that gold was inherently better, but that important countries, including the U.K. and the U.S., introduced bimetallism—legally minting silver and gold into money—and did so at exchange rates that inadvertently led to the undervaluation of silver. This undervaluation eventually drove silver out of circulation as money. Gold became the money standard largely by accident.

February 2014 Employment Report

I kind of expect a positive surprise from the employment report Friday.

Initial unemployment claims are flat, but they are near the cyclical trough level.  There isn't much room left to fall.

Continued claims have stagnated, and in fact kicked up a notch in the past month.  This seems like a bad sign.  It would signal that unemployment durations are increasing again.  I suspect, however, that the end of Emergency Unemployment Insurance (EUI) has led to a renewed competition for jobs from workers with longer unemployment durations, so I think this temporary kick up in regular unemployment insurance could be, ironically, a sign of the supply-side benefits of the end of that program.

I've posted this graph before, showing the unusual improvement in unemployment in North Carolina after they ended EUI in June 2013.

In every month of the 5 months we have data for since the end of the program, the monthly change in North Carolina unemployment was significantly more than one standard deviation below the mean for the 50 states.  Most of this decrease came from employment growth.

					Aug 2013	Sep 2013	Oct 2013	Nov 2013	Dec 2013
Avg. State UE % Change					0.01	-0.10	-0.06	-0.24	-0.20
Standard Deviation of State UE % Change					0.12	0.13	0.14	0.15	0.16
North Carolina UE % Change					-0.20	-0.40	-0.30	-0.60	-0.50
North Carolina UE Change, # of SD					-1.73	-2.37	-1.67	-2.45	-1.85

Unemployment was at 8.9% in North Carolina in July 2013, so there was a lot more room to drop, but all else being equal, I think we should expect a 0.1-0.2% drop each month for the next several months, from this effect, relative to what we might otherwise expect.

Another interesting recent development has been the recent increase in Commercial & Industrial Loans.  I had noticed a trend where this measure of credit from commercial banks has tended to flatten during QE's and recover between QE's.  I have been watching to see if the same pattern might emerge as we exit QE3.  The expansion has come much more quickly and more strongly than I expected.

In all of 2013, Commercial & Industrial Loans (red line) increased by about $110 billion.  These loans have increased by $35 billion in just the first 3 weeks of February and $50 million since the beginning of the year.  Real estate loans on commercial bank balance sheets have also shot up in the last month (blue line).

Bill McBride at calculatedrisk has a rundown of indicators.  They are oddly bearish this month.  This month's indicators seem especially mixed.

Stock/Bond Allocation (Part 5) - Modeling the Mortgage/Bond Hedge

After writing part 3, I decided to add a home & mortgage element to my historical data, to see if my intuition was correct.  So, for each 20 year portfolio, I added to option of putting a 20% down payment down on a home, at portfolio inception.

Here are the effects this had on the presumed optimal asset allocation, where the 20-year outcome variance is estimated with the historical worst case scenario, which helps to account for the non-normal distribution of outcomes in the historical data.

The lines with white diamonds are the stock/bond (red) and stock/cash (green) portfolio allocation lines from the previous analysis.  The light blue capital allocation line (CAL) identifies the optimal allocation for the stock/cash portfolio.  As I described in the earlier post, bonds do not provide effective long-term hedging against stocks, so the optimal stock/bond allocation is to 100% stocks.  Cash works a little better, so that a risk averse investor who does not want to allocate 100% to stocks can reduce risk more effectively with a cash allocation than she can with a bond allocation.

The lines with light gray diamonds and the blue CAL show the optimal allocations for a household that has purchased a house where the 20% down payment is 50% of the size of their at-risk portfolio.  This reduces the risk in all efficient portfolios, with little change in the recommended allocations.

If the household purchases a home where the down payment is equal in size to their at-risk portfolio (dark gray diamonds and purple CAL), we see several changes.  A house of this size no longer effectively improves the risk profile of the stock/cash portfolio.  Now, the stock/bond portfolio is the optimal portfolio, and now the optimal portfolio holds a 20% bond allocation.  Here, I think we are beginning to see the effective hedge between the long bond position in the at-risk portfolio and the short bond position represented by the mortgage on the home.

This becomes even more clear as the home increases so that the down payment is 150% of the at-risk portfolio.  The combined performance of the home/stock/cash portfolio continues to decline.  For the home/stock/bond portfolio, the optimal combined portfolio doesn't perform quite as well as it does with a smaller home, but the home and the stock/bond portfolio do continue to provide hedging value, providing better returns than the household that doesn't buy a home.  And, the optimal at-risk portfolio in this scenario now holds around 50% of the portfolio in bonds.

I think the effectiveness of the mortgage/bond hedge is also visible in the way that the return-risk profile looks much more smooth and normal as the home allocation increases.  In fact, at the 150% allocation to the home, the worst-case method of measuring risk actually recommends a larger bond allocation than the normal standard deviation does, suggesting that the mortgage somehow turns the persistency of bond market risks into an advantage.  (I should note that I didn't include rent savings as a benefit of home ownership in my model, which I don't think effects the shape of these relationships much, but would generally cause the graphed returns of the home-owning households to be understated.)

I'm working with a pretty simple model, and it would take a lot more work to confirm all the details here.  But, what this suggests is that a stock/cash allocation still seems most effective as an optimal long-term investing strategy.  But, for households that use home ownership as a tool in their long-term savings strategy, especially in areas where high home prices require home equity to be a large portion of the household's overall net worth, a significant bond allocation may be prudent.  This is not as a hedge against the stock allocation, however.  This is a hedge against the short bond position represented by the mortgage on the home.  And, in this regard, it may be a very effective hedge.

In fact, this helps solve the transitional problem of moving from a long term, risk-seeking portfolio to a more risk-averse retirement portfolio.  Looking at bonds as a hedge against the mortgage, a young household with a new house and a portfolio mixed between stocks and bonds would have a beginning exposure to a highly leveraged piece of real estate and a portfolio of stocks (the mortgage and bonds would roughly hedge away bond exposure).  This is probably not a bad set of exposures for a young household.  Over time, as the mortgage is paid down, the exposures would evolve, so that at the point where the mortgage is paid off, the household would have a comprehensive portfolio roughly split between unleveraged real estate, stocks, and bonds, which is probably a decent allocation for an older household.


A Caveat

This conception of the household lifecycle is dependent, though, on the behavior of real estate as a near cash asset.  That has usually been the case, in the past, since, outside the 2000's, either high inflation, high real long term interest rates, or a crippled credit market have limited entry into the homeowner's market, reducing the convexity of home values relative to long-term real interest rates.  This meant that if you could clear the hurdle to become a leveraged home owner, it would almost certainly provide you with above-market returns on capital.  If credit markets continue to recover, and we remain in a low-inflation, low-real rate environment, home values should become more convex again, leading to more pure bond-like behavior in home prices, which would mean exceptionally high home prices, again.  In that case, the highly leveraged real estate begins to mimic long-duration bonds in the household's comprehensive portfolio, and the young household that buys a home now holds a comprehensive portfolio that looks like a highly leveraged portfolio that is very heavy in bonds.  That is a recipe for disaster.


An Alternative View of the Housing Boom

The colloquial approximation of this problem would just see unusually high home prices as a "bubble", and would lead to conception of the housing market as an inefficient market where buyers should avoid buying during the "bubble".  I don't agree with that conception.  I think the high home prices of the past decade were justifiable, in and of themselves.  But, the change in character of homes in this context means that they aren't appropriate for some buyers.  Just like a retired 80 year old shouldn't put their entire portfolio into stocks - in a low rate environment with a functional credit market, a young household shouldn't buy a home on a mortgage.  Maybe there isn't much difference between the colloquial approximation and my description of the housing market, in practice.  On the other hand, if banks conceived of the housing market the way I do, they wouldn't be approving mortgages as if they were consumer credit.  It would be more appropriate to treat mortgage debt like a sort of margin credit, with standards that change with market conditions - like the Chicago Mercantile Exchange might do with margins on futures contracts.  It's understandable that they don't, since before the 2000's, the heuristics banks used for home financing erred on the conservative side, and kept the housing market inefficient, and home prices too low.  I'm afraid that the consensus views the high prices of the 2000's as a market failure, when the real failure may be the lack of sophistication in our banking conventions regarding mortgages.  This tendency for the consensus to see "bubbles" in hindsight may prevent us from learning from history, and doom us to continually repeat it.

Another comparison of what I think we've seen in housing is commodity markets.  For some time, some sophisticated institutions earned excess profits on alternative investments, like commodities.  Several new methods of portfolio construction have been proposed around their methods, claiming to boost risk-adjusted returns.  However, some observers suspect (I among them) that those extra returns were a product of the limited access investors had to those asset classes, preventing them from being efficiently included in the broadly diversified market portfolio.  As access to those asset classes is expanded, through ETF's, etc., their prices will be bid to efficient levels, and returns will be a function of their non-diversifiable risk.

The same thing might be said of housing.  Our conventional ideas about the profitability of owning a home are based on a history where access to home ownership was limited.  So, much as the Yale Endowment Fund could earn excess profits on alternative investments, a family with an income that pulled them over the hurdle of mortgage approval could earn excess profits on a leveraged home.  But, now that we have commodity ETF's and 4% fixed mortgage rates with a plethora of optional terms, entrance into these markets isn't limited, and there are no longer excess returns to be gained.

The answer to this isn't to return to inefficiency.  The answer isn't to outlaw mortgage products or to hamstring bank underwriters even while enforcing the same outdated underwriting conventions.  We just need to recognize that homes need to be assessed as investments without the old assumptions, and that they may not be the right asset for every household.

The paradigm that ignores all of this and just blames the situation on predatory banks is like an old map with "Here be monsters" scrawled across the frontier.  It might seem like a good rule of thumb for a while, but it's not a real guide to the landscape.

PS.
Below is a similar graph as the one above, using the conventional standard deviation to measure risk.  The same tendencies appear here, with the stock/bond portfolios improving as the home size increases.  The recommended bond allocation increases along with the home size.

Stock/Bond Asset Allocation (Part 4) - Schrödinger's cat's pension

When considering portfolios with different holding periods, as I have in recent posts, I find a paradox.  I wonder if anyone has a solution to this paradox.

Consider this graph.  This compares the outcomes of 3 portfolios over time - a stock portfolio, a long-duration bond portfolio, and a 50/50 mixed portfolio.

This seems like pretty straightforward standard analysis to me.  The longer your investment horizon, the more exposure you can withstand to temporary fluctuations, and the more risk you would want to position yourself with.

Here, we can see that, historically, the worst 20 year period for the stock portfolio was better than the worst periods for both the bond and the mixed portfolios.  So, given this binary choice, I recommend holding 100% stocks for those holding periods.  If a friend asked for my free advice, I would say, "Look, over that time frame, stocks have never done worse than these other options.  Put all your money in a low-cost stock index, and don't look at it for twenty years.  It's going to have big up years, and big down years.  You are getting paid for your lack of concern about those fluctuations."

In fact, when I invest in volatile small cap stocks, this phenomenon happens in a much shorter time frame.  A family member may invest in the small cap, and if it goes down 40%, I might get a phone call, and I say, "When you bought this, you were saying, implicitly, that the price was incorrect.  So, now the price is more incorrect.  Or, maybe the price is correct, and by the time we realize we were wrong, it will be too late to escape our losses.  So, you committed to losing all of your money the day you bought those shares.  Don't look at the price.  Just figure that money's gone.  If, by chance, a year from now, that stock is up 500% and it hits our target, we'll figure that, as best as we can tell, the price has corrected itself.  Then, we can look, and we will sell.  Until then, DON"T LOOK."

It's amazing how much our portfolios change, just as a product of us looking at them.

But, this isn't just a battle with our cognitive and emotional challenges.  As with the holding period portfolios above, our looking actually changes the portfolio.  Let's say that, having bought into my analysis above, you put all your retirement savings into a diversified set of stock funds, to be recalibrated in 20 years, when you will start to plan for eventual cash withdrawals.  This analysis depends on holding through potential volatility.

So, what happens if in 15 years, you decide to look at your portfolio to see how it's doing?  As soon as you open the file, that 20 year portfolio becomes a 5 year portfolio.  Now, you're thinking, this is too risky, I need to prepare to recalibrate this in 5 years, and if stocks take a dive, I'm going to be in big trouble.

It seems like we should plan for that transition ahead of time, but the problem is, every extra step along the life of that portfolio that we add, changes the context of the portfolio.  If we say, look, in 15 years, the portfolio is going to need to start being more safe to prepare for a recalibration, then we might say, ok, let's do all stocks for 15 years, and then see what changes we need to make to make sure we are ok in 20 years when we recalibrate.  But, now we can make the same observation about that 15 year portfolio that we did about the 20 year portfolio, and very quickly, this becomes turtles all the way down.

It doesn't take a lot of effort to start at the end point, and work our way backward, and decide that we need to be in all cash.  I don't see a hard and fast way to avoid this paradox.  Do we just create heuristics that treat portfolios as slightly shorter in duration than they really are?  Is that why we don't generally concern ourselves with the suboptimality that comes from assuming normal distributions in our stock/bond analysis?  Because the end result of that error is simply to construct portfolios with a bias toward a shorter holding period, and this solves the paradox through conservative portfolio construction policies?

If my analysis concerning the stock/bond allocation problem is correct, American households could be sorely mis-allocating their long-term investments, because this bias would not lower both risk and returns, as one might expect.  An inappropriate match between asset classes and investment horizons may be increasing risk with no benefit at all for longer-horizon portfolios.

On the other hand, my solution, which is to not look, hardly seems prudent as a systematic rule.

Follow up post.

Stock/Bond Asset Allocation (Part 3) - Short Duration with a mortgage! (Oh, you already are?)

...in which I find that two wrongs may make a right....

In my previous posts, I dug into the non-normal behavior of historical stock & bond portfolios, and decided that bonds had no place in individual long-term portfolios.  Portfolios with a cash allocation will almost always do better than portfolios with bonds that have duration risk.

Below the fold, I explore that idea some more, consider the role of home ownership in these allocations, and discuss the financial semantics that result from our peculiar treatment of real estate ownership.

Stock/Bond Asset Allocation - Don't bother with duration risk. (Pt. 2)

I want to look some more at asset allocations between stocks & bonds, because I think there might be some subtle but powerful issues to think about here regarding portfolio construction.  (Here's my previous post.) I find evidence that argues while a cash allocation can provide diversification and asset rebalancing benefits, bonds with duration risk have not provided useful downside portfolio risk mitigation, given historical maturity premiums.

More below the fold.

Stock/Bond Asset Allocation

A friend asked me about stock & bond allocations, and I decided to review the data.  Of course you're all doing it wrong.  I explain below.  Make sure you read to the end....You're welcome.  :-)

Data

For bonds I have used the Moody's AAA bond rate series, from Fred, not adjusted for defaults, and adjust the value of the bond portfolio monthly, based on the monthly rate, assuming average bond duration of 30 years.  For stocks, I use Robert Shiller's historical S&P500 data.

Here is a graph of cumulative gains (rebalanced monthly) for different allocations:

The following two graphs are comparisons of the returns to these allocations over time, for a 10 year holding period and for a 20 year holding period.

There is a dispute in finance about the size and persistence of the equity risk premium (the additional return that an investor gets by taking on the extra risk of owning equities instead of bonds).  One issue is that these relationships just aren't stationary enough for a century's worth of data to give us an answer.

As can be seen in these graphs, almost all of the excess gains to equities came in the period from 1940 to 1965.  At shorter holding periods, there is a significant amount of variance in equity returns.  But, with a longer holding period, returns revert to long-term trends, so that with very long holding periods, there are two distinct eras:

(1) holding periods beginning from 1940 to 1965 where equities earned a tremendous premium with much less risk than bonds.

(2) all other periods, where equities earned a slightly higher return with slightly more volatility and the occasional crisis.

So the allocation decision boils down to two questions.

1)   Are we about to see another 1940-1965?  This is impossible to answer.  We are currently in a period of very low interest rates.  My intuition wants to say that in a low interest rate environment, bond allocations should be very low, because (a) in a low rate environment it would be very difficult for bond yields to match the combined growth and income value of stocks and (b) the risk profile would skew very negatively for bonds since bonds have defined income potential and a limit on valuation gains due to the zero lower bound on interest rates.

The one era of high interest rates that we have seen in the past century was associated with relatively high returns with relatively low variance for long holding periods, along with a modest equity premium.

Eras of low interest rates have had a more bifurcated set of outcomes, with periods of either very high equity premiums or periods of very negative returns on equities compared to bonds.  This is largely because the most damaging economic crises have come during deflationary liquidity crises associated with monetary policy.  These episodes have been associated with low interest rates.  (The graph at right shows the difference between stock and bond returns <blue line> overlaid on top of the 10 year treasury yield <red>.)

So, the current level of interest rates isn't as useful of an indicator as I would hope.  This is again due to the fact that the serial correlations we see in these broad market behaviors mean that over a century there have only been a few separate regimes of return behavior, with no clear forward indication of when the regimes might switch again.

2) What is your holding period?  This is a question that we can answer.  And, considering the lack of a definitive answer to number 1, the answer to this question should generally guide our decisions.  The decisions here are going to be imprecise, but the good news is that we can get a pretty good idea of the appropriate allocation within 10% to 20%, and over the holding period, the differences between the outcomes of allocations within that range are going to be pretty marginal.  As the two line charts to the right demonstrate, as the holding period is extended, the number of periods where stocks underperform bonds declines.  At a 20 year holding period, there are just a few times where stocks slightly underperformed bonds during the last 94 years.

This is the classic chart of returns for portfolios with different allocations.  These three return/risk curves assume annual rebalancing and reflect the average returns and variance of holding periods with start dates after 1919 and end dates prior to 2013.

Equity returns can have large annual variance, but they tend to revert to long term trends.  The effect that we can see from this is that, as the holding period is extended, the standard deviation of holding period returns of equity heavy portfolios is mitigated, and these return/risk curves rotate counterclockwise with longer holding periods.  The extra returns available from equities can be captured during these long holding periods without taking on so much extra risk.

In any holding period, there are very high expected costs from being too highly-weighted in bonds.  Even at short holding periods, holding more than 70% bonds is suboptimal.  But, once a portfolio reaches the efficient frontier where there is a reasonable trade-off between higher risk and higher return, there isn't that much difference between portfolios.  Even at 20 years, the difference in expected returns between a 70% equity allocation and a 100% equity allocation is about 1% annually.

So, here's where I would say that as long as you pick an allocation to stocks in the 40% to 90% range (lower for shorter holding periods and higher for longer holding periods), depending on your risk aversion, you'll be fine.  But, I would be wrong.

These models are based on normal distributions and linear correlations with homoscedastic errors.  Both of these assumptions are surprisingly wrong.


Buy Equities, but not for the reason you think you should.

Looking again at the cumulative holding period returns for different portfolios, you can see that bonds have a bifurcated return distribution.  There are long periods with low returns and long periods with high returns, and not much in the middle.  I thought maybe all of this would disappear with inflation adjustments, but the nominal and real data are surprisingly similar.

Here is a histogram of real bond returns over a 20 year time horizon.  Instead of providing a large basket of moderate return outcomes, bonds provide a bunch of relatively poor outcomes and a bunch of relatively good outcomes, without much in the middle.  The relatively low average returns from bonds are supposed to be the cost we incur for their moderating influence.  I would say that for the past century, bonds have not been doing that job well.

Next is the histogram of real stock returns over a 20 year time horizon.  There is a similar bifurcation here, but less pronounced than with bonds.  Out of 74 holding periods, a full 32 bond return outcomes are worse than any stock outcomes.  Bonds aren't just failing at mitigating failures at the left end of the outcome distribution - they are creating them by the bushel.

And, it's even worse than that.  Over 20 year holding periods, there is little correlation between stocks and bonds, so you would think that at least bonds would provide diversification benefits.  But this is not the case either.  Holding periods with low bond returns have no correlation with stock returns.  But, as bond returns increase, they tend to correlate relatively strongly with stocks.  In other words, bonds only perform well when you don't need them to perform well, and when you do need them to perform well, they never perform well.

On these scatterplots, the diagonal line represents equivalent outcomes between the two portfolios.  Outcomes above the line are outcomes where 100% stock allocations outperformed the other portfolios.

I have included two additional graphs comparing the fully invested stock portfolio with a 80/20 mix and a 60/40 mix.  In both cases, we can see again that the allocation to bonds has not provided any systematic protection against relative losses over the 20 year time frame.  As the bond allocation is increased, the average return decreases substantially, with no improvement in the number of poor outcomes.  There is one holding period that begins in 1930 where bonds provide a 70% return compared to 25% for stocks.  One holding period out of 74.

Even for a 10 year holding period, the past 94 years (84 holding periods) provides little reason to utilize bonds for stability related to the holding period.

For 10 year holding periods, I show the comparison between stocks & bonds, and between stocks and a 60/40 and 40/60 portfolio.  There are two holding periods (the two starting in 2000 and 2001) where bonds provide significantly positive returns while stocks provide significantly negative returns.  But, outside of these two holding periods, for every period where a bond allocation would have provided a boost, there is at least one other holding period where a bond allocation created a similarly negative outcome.

The final graph below shows the cumulative distribution of returns for a portfolio of 100% stocks and a portfolio of 60/40 stocks and bonds.  There is very little gain at the bottom of the outcome distribution from the 60/40 portfolio with which to justify so many holding periods in the heart of the distribution where significant losses are taken, relative to a 100% stock portfolio.



cumulative

Some analysis of portfolio allocations might suggest a relatively large bond allocation, because on an annual basis, bonds and stocks do provide significant diversification.  Portfolios with a higher bond allocation will produce a higher annual Sharpe Ratio.  So, the paths these 10 and 20 year stock portfolios take en route to their final values will probably tend to be more volatile than the diversified portfolios.  And that is probably an important factor to consider if you have to deal with agency issues that come along with managing other people's money.  But, the non-normal distribution of outcomes, the heteroskedastic behavior of the correlations, and the mean reverting nature of these asset classes are strong enough influences on the performance of long term portfolio behaviors, that if you can commit to these longer holding periods without risking capital flight during potentially volatile return paths, the past century's experience gives absolutely no reason to allocate to bonds on a 20 year time scale, and scant reason to do it even at a 10 year horizon. (follow up post).





What is the expected date of the first interest rate increase?

I was reading this econbrowser post , and I was surprised to see this graph, from the San Francisco Fed, of the median expected exit from the zero lower bound.

Here is how it compares to my very basic estimate, using treasury yields:

Now, the estimate I show in this graph is from a very broad analysis of treasury yields, with a blunt adjustment made to account for the asymmetry of the yield curve near the zero lower bound (ZLB).  I have a more rigorous model that starts with Eurodollar futures data in September 2012, but the blunt estimate from treasury data fits the estimate from that model surprisingly well.  (Below is a comparison of my two estimates since September 2012.)  The graph above is similar to this previous graph that I posted.  Keep in mind that the two graphs above measure the distance to the ZLB exit at any given time, whereas the graph in my previous post, and this little graph comparing my two models are showing the expected exit date on a fixed calendar.

And, the pattern fits the pattern of the estimate from the Fed pretty well, too, up to QE3.  We both see a spike before QE2, which is reversed during QE2, before spiking again at the end of 2011 and moving sideways into 2012.

But, after that, they seem to move in opposite directions.  My model shows the exit moving back, from 2.5 years to 1.5 years, from the beginning of QE3 until September 2013, when it levels off at about 1.5 years.  The Fed model shows the exit date remaining fairly level, around 2 years, until September 2013, after which it declines steeply toward 1 year.

This is an important difference.  My data would support what I would call the market monetarist version of events.  The expected exit date had been moving ahead over time, so that we were not making progress on escaping ZLB.  But, QE3 improved economic and inflation expectations, which stabilized the expected exit date until economic improvements in early 2013 caused the exit date to move toward us.  Taper talk in June 2013, followed by the establishment of a tapering schedule later in the year, reversed some of these expansionary expectations, which moved the expected exit date back into late 2015.  Continued improvements in the economic outlook, in spite of the taper, have continued to have a positive influence on the expected exit date.  This is my interpretation, and I expect the exit date to remain fairly stable.  I expect continued economic progress pulling the exit date back a little more, and my main fear is that the economy's inherent growth won't maintain enough momentum to overcome the slightly disinflationary effect of the taper, and the expected ZLB exit date will start to recede again.  (Here is a more detailed review of summer 2013 rate changes.)

But, the Fed data would tend to support what I call the "Wizard of Oz" view of the Fed, which ascribes a powerful ability to target interest rate levels over time to the Fed.  With this data, and in this view, QE3 signaled a plan from the Fed of holding rates lower for longer, so the expected exit date kept moving into the future, but with the talk of taper in June 2013 and the subsequent implementation after September 2013, the Fed has signaled that they will raise rates sooner than they had previously planned, so the expected date of the exit has moved back toward us.

What's Up?

My model is constructed by assuming that the range of possible dates for the ZLB exit is described by a normal curve.  My model fits the forward yield curve to a curve defined by that normal distribution's mean and standard deviation, combined with the expected slope of the yield curve from that date.  I am reporting the mean expected date of the ZLB exit, which, by assumption, is the same as the median expected date.

The Fed's model is much more sophisticated than mine, and they are measuring a set of inputs that, through Monte Carlo simulations, produce unique distributions of the expected exit date.  These distributions tend to have a positive skew, which should be expected.  The Fed is reporting the median expected date of the exit, which because of the skew, is sooner than the mean expected exit.  This is why the Fed's expected median dates tend to be earlier than my expected mean dates.

It looks to me like the mean exit date from my model is stable, regardless of the shape of the distribution, at least within the range of skew that we have experienced.  If the positive skew did become so excessive that a measurable percentage of potential ZLB exits would happen in the range of the yield curve where the slope levels off to the long term yield levels, it should cause my model to report a future yield curve slope that is slightly understated, and possibly slightly understate the amount of time to the mean.  And some of the skew would increase the measured standard deviation of the distribution of the expected exit date, which makes the yield curve less convex around the exit date.  I don't believe that these distortions were significant.

Now, while both the mean and the median would be useful if you are trying to assess the shape of expected outcomes and risks of taking positions on the yield curve, the mean date would be the more important measure for determining the intrinsic value of forward rate contracts.  So, I believe that my measure is useful.

But, looking at both the mean and the median might allow a more fine interpretation of market reactions to Fed policies since the beginning of QE3.

Here is the mean from my model, compared to the median (estimated from the Fed graph above).

For a period in 2013, the median date of the ZLB exit was farther away than the mean date.  That suggests a negatively skewed distribution, which seems implausible.  I don't have the Fed's data, but either I am misunderstanding something here, or there seems to be either an error in the published chart or something wrong with the Fed data.

y-axis is Eurodollar contract price, which is 100 minus the interest rate.
It is inverted, so that the graph represents the yield curve.

The next chart compares the forward Eurodollar yield curve for the three dates noted in the mean vs. median chart.  On May 1, 2013, forward rates were very low, signifying both a distant exit from the ZLB and a low slope rising from the ZLB.  By September 6, the date had moved much nearer and the subsequent slope had steepened.  By December 16, 2013, the expected date of the ZLB exit had reverted into the future, but the slope of the post ZLB curve had continued to steepen.

Following are three charts comparing each of these specific yield curves, showing the estimated locations of the mean date of the exit from ZLB (from my model) and the median date of the expected exit from ZLB (estimated from the Fed's graph).

(A brief note on these charts. 

The mean date appears to be shifted by 3 months, because these are 3 month Eurodollar contracts.  So, if the first rate increase is in September 2015, the June 2015 contract would be the last contract settled at the ZLB and the September contract would reflect the higher rate.)

On May 1, 2013, we can see the signatures of a positively skewed distribution of expected exits.  A median date that is sooner than the mean date, and a long stretch of curvature that reflects a wide range of expectations.  You can tell from the slope of the linear plot of my modeled forward curve that my model is able to pick up the expected slope of the post ZLB curve from the shape of the convexity, even though the slope of the actual yield curve never quite gets that high, because a measurable proportion of expected ZLB exits occur very far in the future.

By September 6, rates had risen substantially.  My model shows a quicker ZLB exit and a steeper subsequent slope.  Two issues are very clear in this graph.  Because at this point, the ZLB exit had become very near, the yield curve became very convex around the mean date of the exit, nearly mimicking my linear model of future rates.  The mean expected exit has to be at the center of that convex area.

I can't think of a plausible way for the mean and median dates to fall in these ranges in a way that leads to a yield curve with this shape.  I don't see how the Fed's stated median date at this point in time can be accurate.

By December 16, 2013, rates had fallen from the September levels, and the mean and median exit dates return to their expected positions.

Since December, the curve has flattened slightly, and the mean expected exit date has moved back to about August 2015.

CEO Candor

Rittenhouse Rankings is an attempt at quantifying the honesty and transparency of firm management.  Rittenhouse claims to be able to capture significant alpha by investing in firms with the highest scores.

I think this is an interesting idea, because even if these excess gains mainly come from avoiding unforeseen negative shocks to specific stock positions, you could say they come from a vulgar kind of market inefficiency.  If the market really is naïve and tends to buy into management obfuscations and overstatements about short term performance, then some of this alpha could come from mispricings among firms based on this inefficiency.  In other words, honest management causes their share price to decline.  This decline reflects a higher required return, and that return is showing up as alpha in the Rittenhouse portfolio.  Put yet another way, you could imagine this as a factor, with returns being a function of smallness, low market to book, momentum, and management honesty.

I would have hoped that markets would be functional enough that management honesty would create reputation, which would increase a firm's share price over time, manifest through a lower required return that would reflect a firm's earned reputational capital.

But, at least, if this is in an inefficiency, that means there are profits to be had for the discriminating speculator.

My experience has been that this is frequently an issue that can be very lucrative.  Micro caps that are coming off of extended periods of poor operating and share price performance, with managed turnarounds and conservative, honest management, can be very satisfying positions to own.  Frequently, these stocks will languish with very little trading volume, even after the turnaround becomes quite clear.  I used to own shares in Onyx Acceptance Corp, which has since been bought by Capital One.  They were a sub-prime auto loan firm, and they had really taken a hit in the 2000-2002 time period.  They made very extensive public reports of their monthly loan performance, so with just a little work, an investor could get a good idea of the differences between the expected values of their loan portfolios and the book values.  For some time, the market was discounting their book value, even though their new loans were clearly setting up to exceed book value.  Management would report perfectly honest, transparent results, with the tone of a palpable yawn, and take a part of their compensation in options.  Those were fun quarterly reports to get.  It was like knowing a secret hand-shake.  Management was putting it all out there, but they weren't cheerleading.  It just took a little patience to wait for the market to catch up.  It surprises me how those type of opportunities seem to be available to individual investors.

While management candor is good for share buyers, I don't know that we can always say it is good for existing shareholders or management.  There are a lot of agency issues here.  On this kind of topic, in addition to conflicting goals between shareholders, management, and other stakeholders, there are conflicting goals between long term shareholders, short term shareholders, and potential new shareholders.  And, while stock options might be associated in the popular mind with short term hucksterism among management, stock options may sometimes encourage management candor, at least for management that expects to have some permanence.

You can't analyze market interventions without considering sunk costs. (Yet another minimum wage post.)

Let's consider a new batch of capital investments in a competitive market.  And, let's make some basic assumptions, that while returns are unknown for any individual investment, the required return for this capital is 10%, and the aggregate return over the lives of the investments will be 10%, with a normal distribution around that outcome.

So, here is a picture of the ROIs of these investments:

This is the basic picture of finance.  There is some normal rate of return that emerges from the supply and demand of capital, and nobody knows exactly which operations will produce it, so we diversify investment capital among projects that meet our risk profile.

But, continuing to imagine this basket of investments, the returns don't come from a static set of operations.  Over time, losses gradually are represented by discontinued operations, so that, eventually, this set of assets evolves into something like this:

If the original set of investments represented $1 billion from a single firm, under our original assumption that on average these investments provided the required return, then the remaining operations would represent, say, 2/3 of the original investment.  These assets would show a very high ROI - 20% in the hypothetical numbers that come out of my example.  But, the ROI for the entire original set of investments remains 10%.  The market value of productive assets remains $1 billion.  The original investments in the failed operations and losses incurred during their operating lives are sunk costs now.

In the context of allocating capital within these projects, those sunk costs should be discarded now.  But, in the context of understanding capital and investment more broadly, those sunk costs are still important.

Several characteristics to note:

• The ROI of individual active projects in a competitive market will tend to be higher than the ROI for the market as a whole.
• So, seemingly monopolistic competition can arise from competitive markets because of deviations in ex post returns.
• The excess returns of successful operations may include excess returns from real options embedded in the operations that include follow-up investments.  But, additional other investments may continue to have an expected return of 10%, even though the existing and future pools of active investments will have returns on initial investments higher than 10%.
• This diversity of outcomes exists throughout a market, within and among firms.  In some ways, the categorization of projects among firms when analyzing the entire market is arbitrary.  Some failed projects will have been a part of failed firms, some will have been part of active operations within firms, and some will have been discontinued within active firms.  The complete ROI on all invested capital in a given market would be difficult to ascertain, and would tend to appear higher than the aggregate experienced return, because of extensive survivorship bias, whether at the project level or the firm level.

So, why is this a post about the minimum wage?

Much of the technical discussion about minimum wage effects appears to revolve around the idea that low wage employers reflect monopolistic competition.

Using the model I outlined above, I can graphically describe four effects of minimum wage increases on a low-wage employer market.  A minimum wage hike would increase costs, creating a first-order effect of lower ROI for all firms.

Immediate effects

1) Lost or reduced operations

Research that picks up employment losses is probably largely picking up this effect.  Added costs would lead more marginal firms and operations to be discontinued or reduced.  As the graph helps to visualize, even in a competitive market with relatively free entry of new capital, this probably tends to represent a small proportion of the set of affected firms at any given time.

2) Higher prices & lower profits

Firms that weren't marginal would initially move to a new equilibrium which might mostly involve continued operations at lower ROI's.  This probably includes most existing employers.  So, research following specific firms would probably pick up this effect, which would appear to point to minimum employment effects.

Long Term effects

The initial effect on operations would be an across the board reduction in ROI.  The combination of more failed operations and lower ROI among the successful operations drops the aggregate ROI.  Remaining operations would continue to have ROI's well above the required return for the market, but without fundamental adjustments in the entrance of new capital, the expected ROI of new capital would be less than the original 10%.

3) Expanded Operations

Existing employers who were not marginal might tend to experience some expansion, first due to the exit of marginal operators, and then due to the reduction of new entrants because of the lower ROI.  This could be the source of expanded employment that some research finds.  But this particular increase in employment would come about only as the result of shifting market share within a shrinking market.

4) Reduced New Investment

The original ROI would have been the result of an endlessly complex set of financial and cultural factors that would have settled on the original expected return.  Lower ROI's would lead to some new equilibrium that would involve some combination of changing capital mixes, prices, etc. which would settle at a new reduced level of investment that could again achieve 10% expected returns.

This effect might get picked up in macro-data time series, but it is probably difficult to see clearly with any method, because it would be part of complex long term processes.

This paper from the Chicago Fed finds increased firm exits after minimum wage hikes, but it finds that, increased firm entries mostly counter the negative employment from the exits in the short run.  So, the first effect above may not lead to extensive loss of economic activity.  This result seems plausible - an initial rush of replacement capital that was previously kept out by marginally productive existing capital.  Keep in mind, however, that this result involves capital destruction from the higher level of firm failures.  The new capital that replaces the obsolete capital in the given market has had to come from somewhere.  So, while in the measured market, there is an exchange of higher wage employment for previously lower wage employment, the capital allocation required in order to create that exchange has some unmeasured cost elsewhere in the economy.  (edit:  Hmm.  Thinking about this some more, if this effect is dominant, it would mean that employment losses would largely come from outside the markets for low wage labor, because of this shift in future invested capital.  It might explain an ironic outcome where measures tracking specific minimum wage employment levels don't show diminished employment from MW hikes, but measures of the broader economy do.)

I have found employment losses associated with the period of time from slightly before an initial federal minimum wage hike to about two years after.  This seems like a quick reaction if only the 4th effect above is leading to significant net employment losses.  But, I suppose the interplay between exiting firms, entering firms, and long term changes in capital allocation could have a net effect that leads to a variety of time series patterns.

In terms of measuring long-term employment levels, a labor market with flexible wages would be expected to grow to utilize substantially all available supply.  This couldn't necessarily be said of a labor market with a price floor.  But, again, the financial and cultural processes would be so complex, that it would be difficult to measure.  I suppose that over the very long term it could be possible for a new equilibrium to lead to widespread employment opportunities for employees formerly working below the price floor.  For normal products, we would expect to see a reduction in the quantity supplied after the implementation of a price floor, but reduced supply wouldn't need to result in only an increase of unemployment.  Changes in schooling, pre-job training, and labor force participation, in general, could lead to fundamental changes in types of labor that people are capable of providing.  Opinions about results that complex are likely to fall back on priors.

Added:  Patrick Sullivan points to this research, which seems to find some of the employment declines from outcome #4, above.