A Song of Gold and Iron
I wrote this short story a couple of years ago and I parked it in a dusty corner of the hard drive. The first spark of this story lit up while I was reading the fourth book of the saga “A Song of Ice and Fire”, also known as Game of Thrones by TV-series addicted.
I had almost forgotten it when I read a long Twitter thread published by Prof. Fabio Ghironi of Washington University. Prof. Ghironi made use of ducks (Ludwig von Drake and Uncle Scrooge) to explain a few basic concepts of international finance. He reminded me of my tiny hoax grounded in the imaginary worlds of Westeros which was amassing grime in my laptop.
If you are not a big fan of fantasy novels, do not be too scared and keep reading. Stat rosa pristina nomine, nomina nuda temenos, or in other words, once you read beyond the names, you will discover the universal and immortal meaning of things.
The world created by George R. R. Martin shows two continents, Westeros and Essos, separated by the Narrow Sea. King’s Landing is the capital of the Seven Kingdoms, a group of territories which live and frequently die through wars (many) and truces (few) in the Westeros continent.
One key feature of King’s Landing, that immediately caught the financial corner of my eye, is that the city is highly indebted. The three largest creditors are the Iron Bank of Braavos, the House Lannister (the richest and most powerful family of Westeros) and a Church called Faith of the Seven God.
When I read about the distressed finances of the capital city, I began transposing kingdoms, territories and families to the real world. Westeros can be seen as a union of western developed countries, King’s Landing resembles the United States and the Faith of the Seven God is the Catholic Church. What about Braavos?
Initially I fancied that the Iron Bank was a sort of Federal Reserve but I soon realized that my first intuition was inaccurate. Not by chance, the author settled Braavos in the Essos continent, on the other side of the Narrow Sea. Geographically, Braavos looks like an ancient Asian city, similar to a Phoenician harbor, where sailors and merchants govern business and politics.
In modern era, the Iron Bank mimics the People’s Central Bank of China, a mighty institution that stores the fortunes of exporters and buys the debt issued by the United States.
With all these good premises, I began fantasizing about the economy of this imaginary world.
King’s Landing has its own currency, the Dragon, divided in moons, stags, stars, groats and pennies. The value of the Seven Kingdom’s coins, minted out of gold, silver and copper is given by their intrinsic value. The Iron Bank of Braavos issues iron coins that, we assume, have a very low or close to zero intrinsic value. Therefore, Braavos, the richest and financially most powerful city, makes use of a fiat currency, a monetary system that relies on the reputation of its Central Bank, with a very loose connection to precious metals. I could not find the name of the currency in the book, but allow me to be a bit ironic and let me call it Irony.
Fiat money, gold-backed currencies, public debt, distressed assets. The game seems to be more and more intriguing and quite familiar.
Imagine a Braavosi (a Braavos’ inhabitant that we may call Stavros) who sells silk to King’s Landing and buys armors and weapons. P(S) and P(W) are the prices of silk and weapons in Braavos while K(S) and K(W) are the prices of silk and weapons in King’s Landing.
By using draconian rules and assumptions (no tolls, no frictions, no legal constraints), the price in Ironies of silk must be equal to the price in Dragons times the exchange rate.Similarly:
Putting everything together:
The allocation between silk and weapons between the two countries depends on the previous formula, that takes the name of Law of One Price and it is the basis of Purchasing Power Parity, an economic theory that compares the currencies of two or more countries through a basket of good. If for any reason the production of silk in Braavos increases, the price will go down. If the price is not allowed to go down, the exchange rate will be adjusted to reflect the impact of the excess of supply. But what happens when the market players are allowed to add complexities, like different prices for goods that are sold domestically and externally, transaction costs and trade barriers? Well, the simple Law of One Price stops working.
Let’s go one step further and imagine that Stavros wants to invest his savings either in bonds issued by his own city, denominated in Ironies, or in the debt of King’s Landing, denominated in Dragons.
His own city, financially solid and highly rated, will offer a small interest rate, that we can identify with “i”.
Braavosis are financially literate and they know the concepts of real value and inflation. They know that, in the future, what is important is not the nominal values of capital (C) and interests (i), but their real value, once adjusted by inflation (I).
Our Braavosi evaluates the purchase power (PP) of his future domestic capital according to the following formula:
Stavros has an idea of the future real value of his investment, but this is still only an idea and cannot be determined with certainty. It is therefore recommendable to write the previous formula in terms of expectations (E).The Iron Bank of Braavos offers another investment to his client: instead of buying local debt, Stavros can purchase bonds from King’s Landing, at a higher interest rate (z), accepting the currency risk of investing in Dragons. Please note that z>i, due to the credit spread that exists between the two economies: Westeros’ capital must pay a higher interest rate when its governors want to borrow. The capital must then be converted at the current exchange rate (*), it will be invested in highly risky treasuries and finally discounted by a different inflation rate (K). And do not forget to convert back the Dragons into Ironies (5).Allow me a short digression.
King’s Landing is conquered by the Lannister’s family and for a short period of time by the Faith of the Seven Son. What is the impact of those events on the variables z, X and K?
The three variables are economically linked: the inflation risk is embedded in the forward exchange rate and into the expected interest rate.
Do not forget that both the Lannisters and the Church are co-creditors together with the Iron Bank of Braavos: they can all be seen as senior bondholders of King’s Landing. From a financial point of view, when the Lannisters take control of the Iron Throne, they swap their credit into an equity participation. The credit risk of the Iron Bank is expected to decrease, z will be lower for the new debt and the price of the current debt stored in the vaults of the Iron Bank goes up. Does it not resemble a Greek-type restructuring?
While reading of King’s Landing conquerors, I was wondering why the Bravoosis did not say a word when the debtor’s treasure changed hands from Robert Baratheon to the Lannisters first and to the Faith of the Seven Son at a second stage. The change of credit seniority perfectly explains their behavior: with the Lannisters or the Church taking the equity risk of the Throne, the bankers will be better off.
But let’s go back to our main story.
The investment in a foreign country’s debt implies the creation of new variables that the investor can only estimate today based on his expectations, like we did before:The Iron Bank may offer an option to its clients who want to invest in King’s Landing: they may hedge the currency risk by entering in a forward FX transaction. Mathematically:And more precisely:The investor transforms the uncertainty of the future currency exchange rate into a deterministic and known rate differential between the short-term risk-free rates of the two cities. Keep in mind that z, K, B and KL are, once again, strictly connected.
I am pretty sure you did not get lost. The next point is to answer a simple but essential question: should the Braavosi invest in the highly indebted King’s Landing or should he keep its money in the more peaceful and safe debt of Braavos?
Also in this case the answer is pretty straightforward. He will invest in foreign debt if:or:We have already shown how we can hedge the currency risk by using a forward contract to balance out the exposure. We made use of the covered interest rate parity. Risk-neutral investors will be indifferent among the available interest rates in two cities because the exchange rate between those cities is expected to adjust such that the domestic return on domestic debt is equal to the Irony return on King’s Landing debt once the credit risk is netted out. In a nutshell:In the actual world, other variables and barriers play against these formulas, among them: taxation regimes, transaction costs and irrational expectations.
It is important to highlight how credit spreads, currency rate, inflation and interest rates are bound together to express the real risks of an investment in different cities and currencies.
By Andrea Luzzi
CEO of Ayaltis, a Swiss asset management company specialized in funds of hedge funds.
Andrea has a Masters degree in Economics, a Master in Quantitative Finance from the Bocconi University in Milan and he is a PRM and a CAIA charter holder.