Tower Private Advisors
- Asymptotes…remember those?
- A rant about duration
Capital Markets Recap
Here’s a little different version, showing 1-week, 1-month, and year-to-date returns…
At a recent seminar we conducted I threw a Hail Mary pass in response to a question. I think my answer was directionally correct, but that’s about it. Then I saw a variation of the chart below on Twitter, and I thought I’d include this. The question–more a request–was along the lines of, can you comment on the level of margin debt. I said I thought it was high and was another indication of enthusiasm for stocks, which suggested caution. The chart below show margin debt over the last thirty years, along with the S&P 500. I think there are three observations to be made about the chart. First, the new high in margin debt in 2007 was not confirmed by a new high in stock prices. That should have been a warning. Then, in March 2006, the new low in stocks was not confirmed by a new low in margin debt. That should have a been a heads-up signal. Finally, both of the prior peaks in margin debt and, in turn, stocks, were spiky. The current level of margin debt has been arrived at more gradually and in fits and starts. While that’s a positive, we would feel a lot better if margin debt was lower. If it were it would suggest potential demand for stocks. This is an indication of an all-in investor.
Maybe that last one was a top story. Only time will tell. Here is a small collection of stories from this week.
- JPMorgan Chase came to a $13 billion settlement with the U.S. Department of Justice. This settlement encompasses a couple of others the company has agreed to. According to Reuters, there are nine other government inquiries still going on. The company has set aside $23 billion to settle all charges. Its stock is approaching its practically-speaking all-time high of 2000. Go figure. To be fair, these charges were, at least in part, a result of actions by Bear Stearns and Washington Mutual, both companies that were acquired by Chase…at the government’s behest, I seem to recall.
- Treasury Secretary Jack Lew repeated what his predecessors have said: eliminate the U.S. debt ceiling. I don’t know…seems sorta reckless…the kind of behavior that would get a bank into trouble…”I think, Mr. Borrower, a solution to your problem of being late and not able to balance your checkbook–not to mention your budget–would be to give you an unlimited line of credit. ‘Sound good?”
- Ben Bernanke has your back. In a speech today, he said the Fed’s objectives, “are squarely tied to Main Street,” and that rates would stay near zero even after the Fed’s bond buying program has ended.
- Speaking of Gentle Ben, his likely successor, Janet Yellen, is for a vote before the Senate Banking Committee tomorrow. That will likely lead to a full Senate vote yet this year.
U.S. stock markets were listless today, waiting for the 2:00 release of minutes from the Federal Open Markets Committee meeting of October 29-30…
Here’s a word cloud of the minutes. Not much new.
Ever since…oh, about May 1,when some interest rates nearly doubled over the ensuing months and bond prices fell, investors, including many of our clients, have been using a new word–rather, an old word differently…duration, as in, “what’s the duration of my portfolio’s bonds [or bond funds]?” Naturally, we dutifully turn to our Bloomberg terminals and/or Morningstar and get to work. Here’s how the conversation might go.
Q: So what’s the duration of my portfolio?
Q: 3.5 what?
A: 3.5 years
Q: Is that bad?
A: Well, it depends on what you mean by bad…bad compared to what?
Q: Okay, well what does it mean, since you’re going to play mental tiddlywinks with me?
A: It means that for a given change in interest rates the value of your portfolio is likely to change by a negative 3.5 times the change in interest rates. So, if interest rates go up by 1% your portfolio’s value is going to down by (-)3.5%…sorta.
Q: And, Mr. Obfuscator, what do you mean…sorta?
A: Uhh…do you have a little while? The price of a bond is a many-splendored thing.
** Warning: This next part’s going to run a little long and be a little dry**
The chart on display below captures a number of things. First, the curved line reprents the price and yield relationship of a bond. For the bond represented by the curved line, every possible combination of prices and yields is shown. The relationship of price to yield is inverse; prices go up when yields (interest rates) go down. Second, duration is measured by the slope of the line that is tangent (touching) to the curved line at the given price/yield point. The steeper the line, the greater the duration.
As with many prescription medications, however, duration comes with at least one caution, namely, duration math only works for small changes in interest rates. This can be seen in the chart above. Imagine that price/yield is at P1/Y1. Now imagine that interest rates move to Y2. The duration line says that prices should fall to P2. Instead, they fall to only P2*. Obviously, the reason prices don’t fall to P2 is because the price/yield relationship line is curved; specifically, it’s convex. If memory serves, duration is the first derivative (rate of change) of the curved price/yield relationship. Convexity is the second derivative (change in the rate of change.)
With this, we come to the first drawback of duration: it only tells part of the story.
Next, pictured below is a depiction of yields and maturities, otherwise known as the yield curve. The line labeled “yc1″ represents, say, the current level of yields offered at each maturity level; “yc2″ and “yc3″ represent subsequent yields curves. YC2 is parallel to YC1, while YC3 is not. Notice that yields fall much further–for the furthest maturities–from YC1 to YC3
In the context of a bond portfolio, then, we come to another drawback of duration: it only applies in a parallel shift of the yield curve.
Duration regarding a single bond is a straightforward affair. It’s all math. Begin to add other bonds to the equation–literally–and duration increasingly becomes meaningless. Let’s take the first example, a two-bond portfolio. The chart below shows the price/yield curve for each bond, and at any given point in time the portfolio/fund duration is the weighted average duration of the bond holdings, as shown in the formula below the chart. With a spreadsheet it’s very easy to calculate an enormous portfolio’s duration, which, in the dialog above, was easy to convey to our client: 3.5 years. If we begin to think about the two drawbacks mentioned immediately above, the “sorta” adjective makes sense.
In just our two bond portfolio we have the inaccuracies of duration–it only tells part of the story and it’s only valid for parallel shifts of the yield curve–compounded by the fact that the bonds are likely to be represented by two different yield curves. Perhaps one is a government bond while the other is a corporate bond, both of which will have their own yield curves.
Okay, ready to see a very simple bond mutual fund?
Do you see any problems with duration? A multitude of bonds and a multitude of yield curves. An easy duration calculation, but a meaningless one.
Albert Einstein was famous for engaging in thought experiments, so let’s try one, ourselves. Let’s say we’re trying to find which of two pick-up basketball teams to cheer for, and just as in our bond experiment, we’ll only consider one aspect of our players, height (unlike our bond example, there’s a positive relationship between height and probability of winning.) Here are the two teams you can choose from. Team one has a 6-feet tall player and a 4-feet tall player; Team two has two 5-feet tall players. Which one do you choose? Does it change your mind if the 6-footer is wearing shoes made of concrete, or if one of the 5-footers is as wide as he is tall? Of course.
I asked my colleague and Tower Bank Treasurer, Zach Higgins, if he could come up with a higher-duration portfolio that outperformed a lower-duration portfolio in a period of rising rates. No problem, says Zach. Much like our basketball team example, Zach was able to construct a portfolio with a duration of 5.72 years that outperformed a portfolio with a duration of 2.9 years–and it outperformed by 50%!
- So, should duration be discarded as useless? No, but you wouldn’t use a hammer to fix a pair of eyeglasses. Duration is a very rough measure of interest rate sensitivity. Given two bonds in the same segment (i.e. both government bonds) and a parallel shift in the yield curve, the one with the higher duration will be more sensitive to a change in interest rates.
- Should you sell a mutual fund with a duration of five in favor of one with a duration of three. Not unless you know a whole lot more about a whole lot more about the funds.
- Will a mutual fund with a duration of twenty do worse than one with a duration of five if interest rates rise?–okay, probably, but absolutely not assuredly.
In the last week we’ve had the usual mixed bag of data. Initial Jobless Claims were released last Thursday. For almost all of 2013, we’ve been stuck in a range between 320,000 and 360,000 claims were week. From the peak level of claims on March 27, 2009 (670,000 claims!), claims dropped sharply over the the following 24 months and have since declined more lackadaisically. I have a remarkable memory for things that don’t make much difference, and word I’ll never forget–nor be able to work into everyday conversation–is from geometry–oh, how my parents wish I had remembered more in high school, especially on test days: asymptote. An asymptote is a level that never gets reached. For example, divide a positive number by 1/2, divide the result by half and repeat; you’ll approach zero but never get there; zero is the asymptote. Anyway, back to economics: aside from some storm-induced (i.e. government shutdown) or change in methodology (e.g. California’s), jobless claims can’t seem to get below 320,000. Last week’s figure was 339,000 claims versus expectations of 330,000 and a previous week’s reading of 341,000 (revised up from 336,000.) If this were the only thing the Fed was considering in its decision to taper, it would be tapering.
Ditto for the several regional economic indicators. The Empire State Manufacturing survey was released last Friday, and while the reading was negative–and an anomaly amongst the regional surveys–it’s likely to regroup with the others later, but they all look asymptotic–count on not getting that one into casual conversation–as the chart below shows.
The twin release of Capacity Utilization and Industrial Production also came out in the last week. It shows both evidence of an asymptote, one typical of many economic releases these days; the other troublingly similar to many other releases. I’ll leave it to you to determine which is which.
Consumer Price indexes were released today, and they showed very subdued inflation. Excluding food and energy prices, the price level was only up by 1.7% over the last 12 months. Add in food and energy, and prices are only up by 1.0%. That’s close enough to deflation to give the Fed a case of the heebie jeebies. It’s also what prompted The Economist to feature the cover below for last week’s issue.
Until next time,
Graig P. Stettner, CFA, CMT
Chief Investment Officer
Tower Private Advisors