# Greek yield curves

The Greeks certainly yielded, but that's not what I'm talking about. No, this is about bond yields, specifically the inverted yield curve that Greek bonds show at the moment. And its jolly interesting (no, really, don't go... oh).

I should begin by saying I don't know what I'm talking about. I started off thinking I did, a bit, and then I read NOTES ON THE BANK OF ENGLAND UK YIELD CURVES and realised just how little I knew. But I discussed the Greek stuff a bit in the previous post, and the inverted yields came up, but not with a good explanation. The convention answer to an inverted bond yield... oh, hold on. First of all, the current yield on Greek 2-year bonds is about 12%. Whereas on 10 year bonds its about 9%. At the peak of the crisis this summer, 2-year yields were 57%, and 10-year 20%. And yet normally, longer term yields are higher, as people demand a premium for locking their money in; and for risks. Well, you can read wiki on the shape, and on the meaning of inverting, and similar elsewhere.

But none of that seems applicable to the Greek situtation. Timmy pointed me at The Mysterious Greek Yield Curve from 2012, which looks like its full of scary maths, but actually it isn't. This post if essentially nothing but a gloss on that article; if you're up to it, go read that instead. The point is that (removing trivia like inflation and interest payments) the bond yield is defined by:

```     market_price = nominal_redemption_price / (1 + yield)^n
```

where n is the number of years to maturity, market_price is what you could buy or sell it at today, and nominal_redemption_price is what the issuing government has promised to pay when it matures. Of course, the nominal redemption price is known, and so (at any given time) is the market price. (For the less mathematically inclined Yes this does, or can be interpreted to, define the yield, even if it isn't on the left-hand-side). In our case, n=2 or n=10. And this can be trivially re-arranged into

```    yield = (nominal_redemption_price / market_price)^(1/n) - 1
```

Now (and this is where we get to the Key Insight), suppose there is a risk of default (as there very clearly is, in the case of the Greeks). Then the markets are likely to price that in. To make it simple, suppose that everyone thinks that there will certainly be another "haircut", and that the actual redemption price will be half the nominal. Then, suddenly, the market price halves. And therefore - if you're using the formula above - the calculated yield shoots up: if you continue to use the nominal values - as, of course, the official calculations do. But if you use the adjusted-aka-expected redemption price, the yield remains unchanged, as it should.

But amusingly, because of the 1/n, the unadjusted calculated yields change differently at different maturities. So as that article says (and you, like me, can verify on a messy spreadsheet) if you have a "typical" 2-year bond, par 100, priced at 80, then the implied yield is 11.8% (because ((100/80)^(1/2)-1)*100 = 11.8). Supposing everyone expects that to pay off at 50 not 100, then the implied yield - based on the nominal payoff value - is 58% (oddly enough, almost exactly what the Greek bonds did hit). However the implied yield of a 10-year bond, with the same assumptions, only rises to 20%; significantly less than 58%; and hey presto, we have our inverted yield curve.

So, in this case, the inverted yield is a clear sign of expectation of default or haircut. And the recent narrowing of the inversion is a sign that expectations of default/haircut have fallen.

### Refs

* Alexis Tsipras calls for a snap election - Economist, The prime minister remains popular, but his government is unstable. Aug 20th 2015

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That's a nice pix, anyway.

By David B. Benson (not verified) on 14 Aug 2015 #permalink

Good description!

I know you've got this right here but I still don't understand it. In the sense that yes, I read through it, it all makes sense, but it doesn't then slot into that little bit of the brain that says "Yes, I understand that".

Sigh.

[I could tell by the way that you pointed me at that PDF that you hadn't grokked it in its fullness :-) -W]

By Tim Worstall (not verified) on 15 Aug 2015 #permalink

Thought you might be interested in betting markets on Greek Eurozone Exit. Matchbook have a Greek Eurozone 2015 Exit market. Unfortunately I cannot find rules or a graph of prices. The no bet currently pays 1.027 * bet amount. I think this was over 1.1 six weeks ago or so. The range is from 1.027 to 1.059 (or 18 to 37 on the yes bet). 1.027 is more than a good rate of interest over 4.5 months so suggesting a small amount of risk for an exit still to occur in 2015. Still the reduction from 1.1 to 1.027 agrees with your conclusion that "the recent narrowing of the inversion is a sign that expectations of default/haircut have fallen".

[I almost did the reverse calculation, which I think you can do, to invert the spread and turn it into the implied risk of default; but I suspect there are fiddly bits that get in the way -W]

> (removing trivia like inflation and interest payments)

That would greatly benefit my household accounts.

By Hank Roberts (not verified) on 15 Aug 2015 #permalink

Or in other words, we could flatten the yield curve by creating the expectation that short-term bonds will get less of a haircut than long-term bonds.

[No, that's not the interpretation I have. What I've said (copying the PDF, but I believe it) is that the market pricing in the risk of a haircut (which applies to both 2-year and 10-year debt) makes the yield calculation "wrong", and the curve "appear" skewed. I believe that if there was a hair-cut it would apply equally to short and long term debt. On the face of it, that would make long term debt more subject to a hair cut, since it has monger to happen; but one might guess that the risk is greatest over the next few years anyway -W]

To me a proposal along that line would make a lot of sense beyond its effect on the yield curve.

By Raymond Arritt (not verified) on 15 Aug 2015 #permalink

According to a report in the French press Germany has benefited to the tune of 100 billion Euros because of the Greek crisis. Because of the uncertainty their bonds were seen as safe, so demand increased, allowing Germany to borrow at a lower interest rate.

[Timmy has pushed the same idea. The report this is based on is here. Despite being titled "Germany’s Benefit from the Greek Crisis" its very first sentence backs this off to "the European/Greek debt crisis". I'm not convinced they make a good case for Germany benefiting specifically from Greek as opposed to European woes; or even European as opposed to global -W]

By turboblocke (not verified) on 15 Aug 2015 #permalink

I see that Greece has sold the concession of 14 airports to a German consortium. Well that's a surprise: I thought the Greeks were supposed to have the money to keep the privatisations in country.

[You mean http://www.theguardian.com/world/2015/aug/19/germans-to-run-greek-regio…? Sounds reasonable. I don't really know what you mean by "supposed to have the money to keep the privatisations in country"; you thought that they would be privatised into Greek private hands? I'm not sure why -W]

By turboblocke (not verified) on 19 Aug 2015 #permalink

Funny, but when I mentioned that an obligation to privatise would lead to a foreign take over of Greek assets I was informed that Greek businesses had plenty of money to buy them. Don't you recall that too?

At least the Germans are more subtle that the Americans who when they want to steal a country's assets, sorry, I mean bring democracy and liberate the population, declare it to be a dictatorship and declare war on it.

By turboblocke (not verified) on 21 Aug 2015 #permalink

For anyone wondering what was actually said from http://scienceblogs.com/stoat/2015/07/10/greek-pm-drops-trousers-again/… it was:

turboblocke: They’re also being obliged to privatise their infrastructure to, obviously, foreign investors. We all know how that works out in tax revenues don’t we? So that’s going to lead to more government cuts, reduced services, so more pressure to accept any job…

W: [The Greeks clearly need their clientist state shaken up. If privatisation helps to do that, then good. Once upon a time we thought it was a sensible thing for government to run car factories. The idea now seems ludicrous. Why should they run docks? -W]

turboblocke: And you ignored my point that the privatisations will be to foreign investors, as the Greeks don’t have the money. In addition, these are forced sales, so the Greeks are in a weak bargaining position.

W: [The Greek state doesn’t have the money; but there’s plenty of money in Greece outside the state. Failing to collect taxes has been one of their problems. You, however, ignored my point: The Greeks clearly need their clientist state shaken up. If privatisation helps to do that, then good -W]

W main point seems shake up of clientist state is more important. There being money outside the state does not appear to be a strong statement claiming privatised assets will stay in Greek control.

Unless you provided evidence that Greeks are being excluded from bidding for assets then I think you can make a good case that Greek businesses may have been able to afford to buy such assets but if foreign investors are willing to pay more for the assets it is better for the state to sell to the highest bidder rather than do some clientist deal.

Problems with foreign ownership of business not paying enough tax often happens with particularly software companies based in other countries or where a case can be made that payment is made due to foreign assets. In the case of a Greek company owning regional airport concessions being owned by German company also running other airports, I am not sure the scope to move profits to where they are taxed at the lowest rate is all that great a problem. Maybe you lose a little but if there is a big difference in the amount that foreign vs Greek bidders are willing to pay and the state cannot afford to take a much lower bid why is this such a disaster?

[Thanks for finding what I said. That sounds about right. I should admit that my actual knowledge of the amount of spare money in Greece is very thin and only based on fleetingly remembered comments -W]

>"sensible thing for government to run car factories" did we ever think that? Wasn't it more that these manufacturers were, in their day, considered too big to be allowed to fail so not ideal for government to run them but better than going bust very much like govt ownership of banks today. Plus ca change ...

[Hmm. I'm not sure that's true; at least in my memory of childhood British Leyland existed for decades. However https://en.wikipedia.org/wiki/British_Leyland tells me it was only nationalised in 1975, and lasted about a decade -W]