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6 October 2011 By Hugo Dixon, Neil Unmack

Italy could cut its yields to 3.7 percent. First-loss insurance from the euro zone’s bailout fund should do the trick, according to Breakingviews calculations. Even after adding an insurance fee, Rome’s all-in cost would be around 5 percent.

The euro zone is working on several plans to enhance the European Financial Stability Facility, but the most likely appears to be for the EFSF to write “first loss” insurance on Italian debt. Assuming a 20 percent first-loss, the EFSF’s firepower would increase five times – making it big enough to help both Italy and Spain.

With first-loss insurance, investors would only be exposed to losses on the uninsured debt. To value such bonds, investors will need to know what the likely losses could be, and what the chances are of them suffering those losses.

Assume one of two scenarios will happen: Italy will either repay the bond, or it will default. The payout from both scenarios, weighted by their probability of occurring, should in theory equal the payout from investing in risk-free assets. If one knows the payouts in the two scenarios (as well as the risk-free payout), one can then reverse engineer the probability of default.

The Breakingviews calculator starts by working out that probability before there is any insurance from the EFSF. Assume an undisturbed 10-year yield of 6.2 percent – where Italian bonds were trading before the European Central Bank started buying them in August. Assume too a risk-free rate of 1.9 percent, Germany’s cost of funds. If the recovery rate without a guarantee is 50 percent, the probability of default works out at 7.7 percent.

First-loss insurance, though, would benefit Italy in two ways: bondholders would lose less if there was a default; and the chance of default would also drop as market access should improve. Assume first loss insurance of 20 percent and that the protection cuts the probability of default by 30 percent. The yield that would have to be offered on such protected bonds to give investors the same probability-weighted payout as a risk-free German bond would be 3.7 percent.

But that would leave the rest of the euro zone on the hook for no return. So Italy must pay a fee. The minimum it should pay is the risk transferred to the EFSF. This can be calculated by multiplying the probability of default by the loss the EFSF suffers in such a scenario. With all the above assumptions that comes to 1.1 percent.

Using such a fee, Italy’s all-in cost would be 4.8 percent. Even if Rome had to offer bondholders a premium for buying such an unusual security and had to give the EFSF a slightly higher fee, the all-in cost should come in around 5 percent – enough to keep it from the jaws of financial hell.

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