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.