Shorter-Term Bond Yields

There is a lot of focus every day on this site and in the media on the ten-year bond rate rate and Bloomberg’s web page showing the yield on this bond is regularly linked to. However, the movements in the ten-year bond only tell part of the story of the past couple of weeks. There have also been dramatic movements in the shorter-term bond yields.

Here‘s the Bloomberg page for the two-year bond yield and here‘s the page for the four-year bond yield. Also, here‘s NTMA’s daily bond report.

The four-year bond yield, which had been about 3% in early June, reached 5% in late October and, as I write, stands at 8.34%, not so far short of the 8.92% prevailing on the ten-year bond. This suggests that the market is pricing in a debt restructuring in the next few years. (See this earlier post for a discussion of the relationship between bond yields and default probabilities.)

Even more disturbing have been the movements in the two-year bond. The yield on this bond had been about 2% as recently as June. It started November at 4% and, as I write, has now soared to 6.66%. Given that pessimists are likely to be assuming that Ireland will be borrowing from the EFSF in two years time, the implicit pricing in of a high probability of a debt default\restructuring as early as 2012 strikes me as unwarranted. But it illustrates the scale of the current negative sentiment towards Ireland in the bond market.

As of yet, the government has not been able to turn this sentiment around. An optimist might argue that passing the budget, resolving the political uncertainty via a general election and the emergence of solid evidence of a return to sustained growth might, together, achieve the required improvement in sentiment. A pessimist would argue that it’s too late.

Whoever’s right, the government needs to at least play it’s role in providing the first step in attempting to make the optimistic scenario come about by passing the upcoming tough budget.  If it could achieve that goal, then after that point, there’s a strong argument that the best thing the government can do is deal with the second element of the optimistic scenario by resolving the political uncertainty as early as possible with a January general election. As to whether the third element of the optimistic scenario—the emergence of growth—occurs, one could argue that this is largely out of the government’s hands at this point

How Yields are Set in Bond Auctions

We’ve had lots of comments about yesterday’s bond auction, many of them from people confused by headlines about the “heavy demand” for the bonds. If the demand was so heavy, these folks are asking, why couldn’t we have sold the bonds at a lower interest rate? We’ve also had some good responses from people who know the answer but it’s perhaps worth putting the answer on the front page.

Take the €1 billion euro 8-year bond that was issued yesterday. The interest rates that we pay on these bonds are determined in an auction. People submit private bids detailing how much of the debt they want to acquire and what rate they are willing to pay. NTMA want to pay the lowest interest rates possible, so they allocate the bonds to those offering to take the lowest interest rates until they have handed out the full €1 billion of bonds.

Yesterday’s auctions featured €2.9 billion in bids (this is what is meant by the bid-cover ratio being 2.9) and the widely-advertised rate of 6.046% was the highest rate offered that received a full allocation of debt. The business about the “heavy demand” relates to the fact there were €1.9 billion in bids from people who were not allocated bonds. Pretty clearly, however, the existence of these bids can’t lower the rates that we are actually paying since these people weren’t willing to purchase the bonds at lower interest rates.

Also, we don’t know how serious all of these unsuccessful participants were. For all we know, some could have submitted bids at 10%: NTMA don’t release information about the nature of the unsuccessful bids. In the absence of this information, I’d recommend not reading too much into bid-cover ratios.

(Note, for those who want to be picky, I’m deliberately not getting into technicalities about Dutch and non-Dutch auctions and the like but informed commenters can fire away on this stuff if they wish.)

Implied Default Rates

Today’s bond auction has attracted a lot of media attention. However, quite a lot of the comment has been a bit confused. Let me set out the usual framework that economists use to think about bond yields. Our more financially sophisticated readers know this stuff anyway but it’s still worth briefly spelling out.

Consider an investor who has two options for their investment.

Option A is to purchase a risk-free bond which carries an interest rate of RF.

Option B is to purchase a bond with potential default risk. This bond delivers two possible outcomes. The first outcome occurs with probability p and in this case, the bond is defaulted on and the investor only recovers a percentage c of their original investment. The second outcome B occurs with probability 1-p and in this case the bond delivers the promised interest rate of RR and also repays the principal.

(Weighted) averaging over these two outcomes, the expected return from option B is

p(c-1) + (1-p) RR

Now assume that investors are risk-neutral, meaning they will pick the bond with the highest average return (and won’t shy away from option B just because it carries some uncertainty).

In this case, for investors to be willing to purchase both bonds, they must have the same average expected return. Setting the above return for option B equal to RF and re-arranging, this determines the interest rate on the risky bond as

RR = RF / (1-p) + p (1-c)

If one knows what the “recovery rate” parameter c is, then one can also back out the implied probability of default as

p = (RR – RF ) / (1 –c + RR)

Now to our current situation. As of this evening, the FT is reporting yields on ten-year Irish bond at annualised rates were 6.3% while the comparable German bond was yielding 2.46%. Let’s use 0.5 as the implied recovery rate should Ireland default. Now plug in RR = .063, RF = .0246, C = 0.5

p = (0.0630 – 0.0246) / .563 = .0682

When considering ten-year bond yields, this tells us the implied probability that the bond will not default over the 10 years is (1-.0682)^10 = 0.493.

In other words, this simplified calculation would suggest that investors are pricing in that a default is more likely than not at some point in the next ten years.

So, when one hears a Fianna Fail TD say on Prime Time say that if international investors didn’t have confidence in Ireland, they wouldn’t be willing to invest in the country (i.e. purchase sovereign bonds) it needs to be kept in mind that the rates on longer-dated sovereign bonds suggest that these investors believe that it’s as likely as not that the country will default over the next ten years. Not much of a vote of confidence.

Now, of course, the framework above is very basic. One can assume that investors are not risk-neutral which would mean there would be a risk premium in addition to the one related to default probability. This would lower the estimated default probability but it wouldn’t change the damage that perception of the possibility of default is doing.

Also, the 50% figure for recovery rate might be kind of low. A recovery rate of two-thirds would give a higher implied default probability of also about two-thirds from the above framework.

The other line I heard going round today was how we shouldn’t be surprised that the auction was successful because the rates being offered were “very attractive.” This is wrong on two counts. First, the rates were determined in an auction—the NTMA didn’t set a high minimum rate that they were willing to pay to attract interest. Second, once we know the market is factoring in default risk, there’s no point in judging bond yields as being “attractive” just because they are high. The high rates are compensation for the possibility that you might lose a lot of money if things go badly.

A key point to keep in mind is one that has been stressed recently by Willem Buiter. When perceived default probabilities rise there can be two possible self-confirming equilibria. In the good one, the government calms the nerves of the markets, borrowing rates decline and the day is saved. In the bad one, the high yields due to high default probabilities start to make fiscal stabilisation seem more difficult, which further raises estimated default probabilities until borrowing from the bond market becomes unfeasibly expensive or else simply impossible.