Alex Stomper, HU Berlin
This is a lecture collecting some tools for sovereign credit risk analysis.
We, however, start with a motivation for sovereign credit risk analysis: Carry trading in foreign exchange markets.
Definition: Carry trading is a strategy of investing in a currency with a higher risk-free interest rate and financing the investment by borrowing in a currency with a lower risk-free rate.
What about the risk of changes in the exchange rate? To get rid of this risk, the proceeds of the foreign currency investment can be sold "forward". This in itself locks in a profit (or loss) because the forward price of the foreign currency will typically differ from the spot price.
Definition: The forward premium is the discount rate at which the NPV of spot-buying/forward-selling a foreign currency equals zero:
$$-X_0+\frac{X_T}{(1+\rho_T)^T}=0.$$The forward premium is an internal rate of return. It measures the appreciation of the foreign currency in the forward market relative to the spot market. Another measure is simply the ratio of the forward exchange rate and the spot exchange rate. We use the above-stated measure because we will compare the forward premium to per-annum interest rates. We will do this using Covered Interet Rate Parity.
Covered Interest Rate Parity (CIP) is a "no-arbitrage" argument for setting the forward price of a foreign currency (in units of a home currency) so that setting up a forward contract does not require a payment from either counterparty to the other.
Covered Interest Parity:
$$X_T=X_0\left (\frac{1+R_T}{1+R_T^*}\right )^T.$$where we have used the following notation:
What´s the idea here?
CIP implies:
$$(1+R_T)^T=\frac{X_T}{X_0}(1+R_T^*)^T,$$$$(1+R_T)^T=(1+\rho_T)^T(1+R_T^*)^T.$$The forward premium is akin to an additional return earned in the foreign currency. This return can be positive or negative:
$$\rho_T=\frac{1+R_T}{1+R_T^*}-1.$$If the risk-free rate of the foreign currency is higher than that of the home currency, then the forward premium must be negative: The price of the foreign currency must be lower in the forward market than in the spot market. The price difference implies a capital loss incurred by investors who invest in the foreign currency and thus earn more interest income than by investing in the home currency.
It is tempting to interpret CIP as a theory of exchange rates:
If the foreign currency interest rate increases, the forward premium must decrease, i.e. the foreign currency must appreciate in the spot market relative to the forward market.
If the home currency interest rate increases, the forward premium must increase, i.e. the foreign currency must depreciate in the spot market relative to the forward market and the home currency must appreciate in the spot market relative to the forward market.
However: There is no causality. Moreover, it is not possible to interpret the CIP as a theory of exchange rate dynamics. The CIP is nothing more than a statement regarding the relationship between spot and forward exchange rates at the same point in time.
CIP can be used to distinguish between different components of the "carry", i.e., the interest differential of two currencies. To flesh this out, we first define the "cross-currency basis".
CIP implies the following approximation:
$$R_T=(1+\rho_T)(1+R_T^*)-1\approx \rho_T+R_T^*.$$The risk-free rate in the home currency can be compared to a synthetic rate that is the sum of the risk-free rate in the foreign currency and the forward premium:
$$\hat R_T=\rho_T+R_T^*.$$Definition: The cross-currency basis is the difference
$$\Delta_T=R_T-\hat R_T=R_T-R_T^*-\rho_T.$$The CIP can be used to decompose the carry earned by investing in a foreign currency and borrowing at home:
$$R_T^*+\rho_T-R_T=-\Delta_T, \mbox{ so that } R_T^*-R_T=(-\rho_T)+(-\Delta_T).$$The carry has two components, i.e. the two terms stated in brackets. The first component is the depreciation of the foreign currency in the forward market relative to the spot market.
What´s the second component? These could be arbitrage opportunities due to a possible violation of the CIP. Carry traders try to profit from these arbitrage opportunities. But, are they really earning arbitrage profits?
Definition: arbitrage opportunities are investment opportunities...
Ok, so how about investing in a high-interest currency and financing the investment by borrowing in a low-interest currency?
What if we use a forward sale of the investment proceeds to deal settle the repayment in the low-interest currency?
The cross-currency basis should be zero given that we are comparing a risk-free investment in a (high-interest) foreign currency to the cost of (low interest) borrowing at home. But, what if the foreign risk-free rate is not really a risk-free rate? In this case, the cross-currency basis could be a return differential due to credit risk!
$$R_T^*+\rho_T-R_T=-\Delta_T$$What´s the most risk-free investment in a foreign (high-interest) country?
If the answer is "sovereign bonds", we need to understand sovereign credit risk...
In my course "Financial Economics for Citizens", we dive into the world of sovereign credti rating. As a consequence, I have come across some interest resources for analyzing sovereign credit risk. The resources cover different aspects of sovereign credit worthiness:
The internet contains a few interesting resources for assessing the above-listed characteristics of countries.
The World Governance Indicators:
Governance consists of the traditions and institutions by which authority in a country is exercised. This includes
- the process by which governments are selected, monitored and replaced
- the capacity of the government to effectively formulate and implement sound policies, and
- the respect of citizens and the state for the institutions that govern economic and social interactions among them.
The indicators concern the following indices:
The Harvard Atlas of Economic Complexity profiles countries with respect to their economic structures, mainly concerning the complexity and diversification of their export baskets. It also contains a wealth of related information:
Missing profits is a website showing where corporations "shift" their profits, and the extent to which countries gain or loose due to this profit-shifing.
The World Inequality Database shows the evolution of income inequality among countries´ citizens: pre vs post tax.
This was but a start!
I will keep updating/adding to this set of resouces.
Please let me know if you have suggestions for what to include!
I finish with a platform for analyzing sovereign credit risk. This platform will be used in my course "Financial Economics for Citizens". I will report on the experience.