The Incomplete Currency. Marcello Minenna

Figure 1.6 Probability distribution of the values at maturity of a 2-year floating-rate bond issued by State D

      Now let's imagine a state that's not so “solid”, where there are serious doubts that it can fulfil the obligation to repay the capital at the maturity and/or pay the eventual periodic coupons (for example, Greece today). The government of this state (GR) issues a bond that pays the same rate as solid State D, which is still 1.1 % per annum.

Intuitively, the bond issued by GR looks riskier, but pays the same rate as that of State D. How will the probability distribution of this bond look and what would be the fair price that the investor would have to pay? Figure 1.7 answers our questions.

Figure 1.7 Probability distribution of the values at maturity of a 2-year floating-rate bond issued by State GR

      Figure 1.7 shows that in a number of cases it is possible that State GR doesn't pay back the capital at maturity and doesn't pay some coupons, going into default. Since in these cases the investor will get much less than the promised return, it is fair that today the bond is cheaper, since he bears the risk of possible losses.

      Conclusion: a riskier bond as a result of the possibility of default of the issuer, with the same return offered, is worth less than a risk-free bond.

      Now it is clear that a bond from GR that only pays 1.1 % per annum is not very attractive to investors. There is only one possibility for the State GR in order to raise funds on the markets: to make bonds more appealing for the investor by increasing the interest rate offered.

      It's clear that if profit rises, the fair price that an investor would have to pay to buy the bond would rise too. If the profit increases sufficiently to bring the fair price to the value of the risk-free bond of State D (100), the investor will be completely compensated for the credit risk of the State GR by higher yields.

      Conclusion: a riskier bond as a result of the possibility of the issuer's default pays more than a risk-free bond with the same fair price.

      At this point of the analysis a question arises: how can market participants measure the credit risk of a specific issuer?

      The default risk of a sovereign issuer can be observed and measured through complex statistics on the health of the economy and public finances; clearly these data provide estimates subject to a certain variability and implemented in a given moment, while operators need constantly updated and trustworthy information in order to close their financial transactions in real time. Other indicators are therefore needed for their businesses.

The solution is simpler than one can imagine: we said that a riskier bond, to be successfully sold, must pay more. Consequently, the differential (the so-called credit spread) of yield between a risky bond issued by State GR and a risk-free bond like that issued by State D is an immediate and safe measure of the credit risk perceived by the operators. This reasoning is summarised in Figure 1.8.

Figure 1.8 Probability distribution of the values at maturity of a 2-year fixed rate bond issued by State D and of a 2-year fixed rate bond issued by State GR

The more that an issuer is considered risky, the more it will have to pay in order to sell his bonds at an issue price equal to that of the risk-free bond of State D (see Figure 1.9).

Figure 1.9 Probability distribution of the values at maturity of a 2-year fixed-rate bond issued by State D, of a 2-year fixed rate bond issued by State GR, and of a further 2-year fixed rate bond whose issuer is riskier than GR

      1.1.4 The Credit Default Swap (CDS)

      In the previous section, we learned that the credit spread measures the extra return necessary to compensate the holder of a specific bond of the perceived credit risk of the issuer; this is an indicator which assumes that the investor is materially the owner of the bond and bears the risks of insolvency.

      On the financial market at the beginning of the 90s, operators started negotiating the financial derivative products–so-called Credit Default Swaps or CDSs–that allow you to acquire (and sell on) the risk of default of an issuer without having to be the holder of the underlying asset. In simple words, the buyer of a CDS gets insurance against the default of a given issuer in exchange for the payment of a periodic premium. If all goes well, the CDS buyer only pays the premiums and doesn't receive anything until the expiry of the contract; but if the issuer defaults, the CDS seller must refund the buyer with a sum that covers the loss in the value of the bond. It is reasonable to assume that the higher the perceived credit risk of the issuer, the higher the periodic premium required by the seller to provide the insurance. This premium (the CDS spread) is therefore a further measure that operators use, alongside the credit spread, to assess the credit risk of a particular subject (banks, companies, sovereign states).

Figure 1.10 presents a summary of the definition of CDS.

Figure 1.10 Credit Default Swap contract (CDS)

      Later we will explore the similarities and the differences between these two different measures. At the moment it is enough to remember that in one case (credit spread) the material possession of the bond is assumed while in the other (CDS spread) the presence of the bond is not necessary.

1.2 Sovereign Credit Risk, Public Debt and Inflation

      The credit risk on bonds issued by a state is also known as sovereign risk. One of the main factors that impact on the magnitude of sovereign risk (and, accordingly, the associated default probability) is the size of the government debt. Intuitively, the bigger the debt, the higher the probability of not paying it (in terms of capital at maturity or interests coupons).

      Let's explore now in details the structure and the evolution of the public debt. To this purpose, it's useful to think at the state as a firm whose accountability presents obviously positive financial flows (the fiscal revenues) and negative ones (the public expenditures). The difference between revenues and expenditure is known also as primary balance. The public debt accumulates when this difference is negative, since in this case part of the expenditure has to be financed through government bond issues. As it can be expected, the government debt is characterised by the payment of interests to the investor that compensate him for the risks borne. From the government point of view, these flows of interests represent an expense known, in technical jargon, as the cost of debt servicing. It follows that the debt grows over time if the government produces primary deficits or if the primary surplus is not sufficient to cover the interests expense on the accumulated debt.

      In the following we will assume for the sake of simplicity that the primary balance of the government will be always zero, i.e. that at every moment the tax revenues match exactly the public expenditure. However, a debt exists since it has been inherited from the past. It's not so difficult to argue that under this hypothesis the debt dynamics are influenced only by the interest burden; for example, if at a given year the debt is equal to €2,000 billion and its servicing cost is €100 billion, the year after the debt will grow to €2,100 billion.

      Hence,