Purchasing Power Parity: A quick introduction

After the familiar introduction on PPP (Big Mac Index), we can start by introducing Rudiger Dornbusch’s NBER Paper on PPP published in March 1985. In his working paper, Professor Dornbusch states that the PPP theory of exchange rate has ‘the same status in the history of economic thought and in economic policy as the Quantity Theory of Money (QT)’. The QT version most commonly used is the Fisher Identity (Economist Irving Fisher in his book The Purchasing Power of Money) defined by:

M.V = P.T, where

M = Money supply, or stock of money in coins, notes and bank deposits

V = Velocity of circulation

P = Some measure of the Price level (i.e. CPI)

T = Volume of Transactions in the economy

1. Historical context
The notion of purchasing power parity PPP can be traced to the 16-century Spanish Salamanca school, but the protagonist of the theory is the Swedish Economist Gustav Cassel. During and after WWI, he observed that countries like Germany or Hungary a sharp depreciation of the purchasing power of their currencies in addition to hyperinflation. Therefore, he proposed a model of PPP that became a benchmark for long run nominal exchange rate determination.

2. Statement of the PPP theory:
Let Pi and Pi* be the price of the ith commodity at home and abroad respectively (both in local currencies) and e the exchange rate. Let P and P* represent the price level at home and abroad.

In an integrated, competitive market (no cost for transport and no barriers to international trade for the good), the concept is based on the Law of one Price where identical goods will have the same price in different markers when quoted in the same currency.

For unless Pi = e.Pi*        (1)

There will be an opportunity for profitable arbitrage.
Arbitrage:  Recall that arbitrage is the possibility to make a profit in financial market without risk and without net investment of capital. A portfolio π has an arbitrage opportunity if there exists T > 0 such that Xo = 0, Xt >= 0 (P – a.s.), P(Xt > 0) > 0.

For instance, if Pi < e.Pi*, then an arbitrageur will buy the good domestically for Pi, sell it abroad for Pi* and realize a risk-free profit as Pi*.e – Pi > 0. Such arbitrage, purchasing the cheap good and selling it where it is dear, would continue until the equality (1) held.

As we said, equation (1) states that the price of the ith commodity must be the same in both markets (i.e. two different countries, for instance US and UK). The Equation is known as Commodity Price Parity (CPP).

Example: Let’s say that the price of one ounce of gold sold in London is 846 GBP, whereas it is sold of for USD 1,290 in New York. If we apply equation (2), we can conclude that the implied rate for Cable (GBP/USD) is 1.5248 (as a result of 1,290 / 846).

Limits:  As we all know, in the real world, CPP may not hold for different reasons:
– Transactions costs (transportations costs, insurance fees)
– Non-traded Goods: items such as electricity, water supply, or goods with very high transportation costs such as gravel.
– Restraints of Trade
– Imperfect Competition

3. Purchasing Power
In an economy with a collection of commodities, ‘purchasing power’ is defined in terms of a representative bundle of goods. We evaluate purchasing power by constructing a price index based on a basket of (consumption) goods.

3.1. Absolute purchasing power parity
Let P = f(p1,…, pi,…,pn) and P* = g(p1*,…,pi*,…pn*) be domestic and foreign price indices.
Then, if the prices of each good (in dollars) are equalized across countries, and if the same goods enter each country’s market basket with the same weights, then Absolute PPP prevails.

e = P/P* = ($ price of a standard market basket of foods) / £ (price of the same standard basket)     (2)

If pi / pi* = k for i = 1,…,n , then

e = P/P* = k     (3)

There can be no objection to equation (2) as a theoretical statement. However, as we mentioned it earlier (limits), objections arise when equation (2) is interpreted as an empirical proposition (Tariffs, transportation costs make it difficult for the spot prices of a commodity i to be equal in different location at a given time).

Strong (Absolute) PPP implies that whatever monetary or real disturbances in the economy, the price of a common market of basket of goods will be the same, i.e. P/e.P*=1.

3.2. Relative Purchasing Power Parity
The relative version of PPP restates the theory in terms of changes in relative price levels and exchange rate: e = C. P/P*,

where C is a constant that reflect the trade obstacles. The difference in the rate of change in prices at home and abroad – difference in the inflation rate – is equal to the percentage depreciation or appreciation of the exchange rate:

ê = π – π*   (4)

where ^ denotes a percentage change, π – π* the inflation differences between two markets (i.e. countries) reflected in percentage changes in the exchange rate. For instance, if the inflation rate is π = 2% in the US and π* = 1% in the UK, then the British Pound (GBP) should appreciate by ê = π – π* = 1% against the USD.
Prices in the US are rising faster than in the UK, therefore UK exports are becoming more competitive (compare to US ones), raising importers’ interest. This should generate a higher demand for GBP (relative to USD), hence sending Cable (GBP/USD) higher.

Equation (4) was applied by Gustav Cassel to an analysis of exchange rate changes during World War, as according to PPP, the fair value of an  exchange rate between two countries is determined by the two countries’ relative price levels.

4. Opening
Since the early 1980s (after the collapse of Bretton Woods), advances in econometrics and longer time series covering the period of floating exchange rates were two important developments in the new generation of fair value models. The next article will focus on the two dominating families of currency fair values widely used today: the Behavioural Equilibrium Exchange Rate (BEER) models and Underlying Balance (UB) models adopted for flexible exchange rates.


Dornbusch, Rudiger (1985), “Purchasing Power Parity”. NBER Working Paper No. 1591.

Isaac, Alan G. Lecture in Purchasing Power Parity.

Jerry Coakley and Stuart Snaith (2004), “Testing for Long Run Purchasing Power Parity”.

Purchasing Power Parity: The Big Mac Index

When it comes to FX long-term projections, I do believe that you already heard of the PPP (Purchasing Power Parity) model. A popular one was introduced in The Economist in 1986 (September 6) by Pam Woodall and is called the Big Mac Index (or Big Mac PPP). Basically, the BMI index measures the Purchasing Power Parity between nations using the price of a Big Mac as the benchmark. The Big Mac PPP between two countries is obtained by dividing the price of a Big Mac in one country by the price of a Big Mac in another country (both in local currencies).

The Big Mac Index for 2015 has not been published yet and the latest index was published on July 24 last year.

In July 2014, the average price of a Big Mac in the US was $4.80. In Norway, the hamburger costed 48 NOK at that time, which obviously gives you an implied exchange rate of 10 NOK for 1 USD. The actual rate chosen on that day by The Economist was 6.19NOK / 1USD. Therefore, the implied FX rate was approximately 61.6% higher than the actual FX rate, bringing the Big Mac price to $7.76 in Norway.

The chart below (on the right) represents which currency is overvalued (blue) or undervalued (red) against the select base currency, in this case the US Dollar. As you can see, Switzerland and Norway were the two expensive countries with the NOK and CHF overvalued by 61.6% and 42.4% against the Dollar, while Ukrainian Hryvnia UAH was undervalued the most by 66.1%.

Capture d’écran 2015-01-22 à 10.11.44(Source: The Economist)

More elaborate models take into account economic indicators depending on the major activities of the country (export-driven nation, developed or EM economy, …).

Even though we agree that there is no explicit answer regarding which model delivers the correct fair value of a currency (the Art of predicting), I believe that it is interesting to visit  the work that has been done by some brilliant academicians and major institutions (Banks, Investment Managers).

A CB surprise…

After October 15th last year, yesterday was another insane day in the market. We know approximately the impact of a lower (or higher) NFP report on the US dollar or a lower (resp. higher) than expected EZ inflation rate on Euro bonds; however when the surprise comes from a central bank, we saw the consequences…
But first, I am going to have just one quick digression before going for it, concerning the OMT.

OMT is legal

Almost a year ago, the German Federal Constitutional Court (GFCC) found ECB’s OMT bond-buying program illegal and incompatible with EU and German law. Given that the GFCC only has jurisdiction on matters of German domestic law, it decided to leave judgement to the European Court of Justice (ECJ). In his Opinion on Wednesday, the Advocate General Cruz Villalon observed that the program is compatible with the EU Law and that the ‘objectives are in principle legitimate and on consonant with monetary policy’. He added that the program is ‘necessary as well as proportionate in the strict sense, since the ECB does not assume a risk that will necessarily make it vulnerable to insolvency’. As a reminder, the Advocate General’s Opinion is not binding on the Court of Justice. THe judges are now deliberating and the Opinion is expected to reach its judgment by May.

The Euro plummeted by 100 pips to 1.1730 (9-year low) after the news, but came back above 1.1840 on the back of poor US retail sales figures. As a reminder, retail sales dropped 0.9% MoM on Wednesday, the most since June 2012, and missed expectations of a 0.1% decline.

However, the ‘recovery’ didn’t last very long as the single currency is currently trading at 1.1630 against the greenback. How come?

Definitely unexpected…

Yesterday morning, slightly before lunch time (Swiss local time), the Swiss National Bank announced that it was discounting the minimum exchange rate of 1.20 per Euro (that it has been ‘defending’ for the past 3-1/2 years). It also announced that it would go further into NIRP policy, pushing its interest rate on deposit balances to even more negative from -0.25% to -0.75%.

By letting the exchange rate float ‘naturally’, the consequence were brutal and EURCHF, which had been flirting with the 1.20 over the past couple of months, crashed to (less than) 75 cents per Euro, wiping out every single long EURCHF position, before ‘recovering’ to parity (now trading at 1.0140).


USDCHF is now trading around 0.8700 (back from above parity levels, 1.02 to be precise), and EURUSD was sold to 1.1568 before rebounding.

A Stressed Market

The Swiss curve is now trading in the negative territory for all the maturities until 10 years; the swiss market index tumbled to (less than) 8000 (almost 15 drawdown) and then stabilized around 8,400.

US yields are still compressing, with the 5-year, 10-year and 30-year trading at 1.18%, 1.72% and 2.37% respectively. I added a table below that shows the 10-year overall and definitely summaries the current ‘environment’. As you can see, Greece is the only EZ country where yields are trading at astronomic levels on the fear of a Grexit scenario in 10 days (See article here). I like the expression ‘the Japanization of Global Bond yields’ used by some analysts I read.

Capture d’écran 2015-01-16 à 10.35.47


Our favorites, AUDJPY and USDJPY, both reacted to the SNB comments ‘bringing down’ the equity market with them. AUDJPY plunged from (almost) 97 to 95.30 and is now trading at 95.60. USDJPY broke below 116.60 and dropped to 116.28; before that, it reached a daily high of 117.92 during the ‘early’ Asian hours.

The S&P500 index followed the general move and broke the 2,000 level (closing at 1,992), and is now trying to find a new low. Is it going to be a buy-on-dips scenario once again? Clearly, the equity market is ‘swingy’, however I don’t think we are about to enter a bearish momentum yet and I still see some potential on the upside. Therefore, USDJPY should also help the equity market levitate and we should see the pair back to 120.

Discrete poor US fundamentals

Yesterday was also marked by a poor jobless claims report in the US, which was totally forgotten of course but surged to 316K (vs. expectations of 290K). In addition, the Philly Fed, an index measuring changes in business growth, crashed from a 21-year high of 40.2 in November to 6.3 in January (missing expectations of 18.7), the lowest since 2014. I know these figures are quite not relevant for traders and investors, however I do think it is worth noticing it. As a reminder, US inflation rate (watched carefully by US policymakers) decreased from 1.7% to 1.3% in November and is expected to remain at low levels (between 1 and 1.5 percent).

Overall, the global economy still looks weak, and we saw lately that the World Bank decreased this year’s growth projections to 3% in 2015 (down from 3.4% last June). Major BBs declined their forecasts on oil and expect prices to remain low in the first half of this year. We heard Goldman’s Jeff Currie lately saying that prices of crude oil may fall below the bank’s 6-month forecast of $39 a barrel. Remember the chart I like to watch (oil vs. inflation vs. yields vs. equities).

The next couple of event to watch are of course the ECB meeting on January 22nd, followed by the Greek national elections on January 25 (see below). For the ECB meeting, it is hard to believe that the central bank will do nothing after the SNB’s announcement.


(Source: MS Research)

Quick update on the ‘Grexit’

Not only last year was a bad year for Greek market, Greece Athex is one of the worst 2014 performers (total return) with a 29% drawdown, but the country has suffered from political instability since the beginning of June. Since Syriza’s triumph in European elections on May 25th, the 10-year bond yield has soared from a low of 5.5% on June 10 to over 10% on ‘Grexit’ fears (the 3-year bond yields trading at 13.6%, up 10% over the past four months). The – Hellenic Republic – 5-year CDS, a good measure of the country’s default risk, is up more than 1000 bps, now trading around 1500bps. There has been some speculation of a possible ‘Grexit’ scenario; and as Der Spiegel news reported lately, German Chancellor Merkel is ‘prepared to let Greece leave the euro zone’ if the country abandons fiscal discipline and does not repay debts to its creditors.

2015: another difficult year for Greece

This year, according to Nomura’s analysts, Greece will face total payments (Principal + Interests) of 22.3bn Euros; €8bn scheduled to be paid to the ECB (mainly in July and August). As you can see it on the chart below published by Eurostat, which shows EuroZone debt and deficit by country, with a debt-to-GDP ratio standing at an all-time-high of 175% (despite the debt ‘haircut’ back in March 2012) and a deficit of 12.7% in 2013, there is no doubt that the country’s debt is unsustainable.

EZfiscal(Source: Eurostat)

There is nothing to stop it growing except haircuts, i.e. ‘partial’ default. Even though Greece’s recession has ended last year after almost six years of misery (the economy is now 30% less than in 2008), financial conditions (unemployment rate at 26% in total and 50% for youth, deflation for the past two years) will weigh on the economy longer than many analysts expect, especially now with the global macro conditions.

How strong is the anti-austerity party in Greece?

To sum up briefly the events of the past few weeks, Greece failed to approve a president (Stavros Dimas) nominated by PM Antonis Samaras as the number of votes didn’t reach 180 after three consecutive rounds (in the last round, 168 Greek lawmakers voted in favor of Dimas, 132 against). Therefore, as the Parliament failed to elect the President, Greek Constitution provides that the Parliament is being dissolved and snap earlier elections.
Greek elections will take place in a couple of weeks (on January 25) and the question is What could it look like?

In the last days of 2014, I remember that a first poll done by Alco for Proto Thema suggested that no party will have a clear majority in the new parliament (as one party will need roughly 35% of the Greek votes in order to gain an absolute majority). At that time, Syriza, a leftist anti-austerity party led by Alexis Tsipras, was ‘leading’ the league with 28% of the votes, followed by liberal-conservative New Democracy (ND) with 23%.

The market’s reaction was quite brutal as I said earlier as many investors fear that Greece may be forced to leave the Euro. The Syriza party wants to abandon the austerity measures imposed by the Troika as part of the €240bn bailout and wants a writedown on the nominal value of Greek Debt. I like the chart below (Source: Bloomberg) that gives you an idea of the government exposures to Greek’s public debt. The main bloc is held by official creditors (Euro-area governments: 62%; followed by the IMF, 10% and the ECB 8%). As you can see it in the chart, Germany is the major government-creditor of Athens and has more than €60bn in total exposure.

GreeceExpo(Source: Bloomberg Brief)

Greece bank shares (Alpha bank, Piraeus) all collapse over the past few weeks as fear of bank solvency and bank runs surged (Cyprus ‘bail-in’ regime continental template?). As a matter of fact, interruption of liquidity by the ECB to Greek banks will potentially lead to a ‘Cyprus type’ bank holiday.

Latest update: An article from the WSJ came up earlier this morning, and says that in nine separate opinion tools that were published in the Greek media in the last couple of days, Syriza is still on top and would garner ‘between 27.1% and 31.2%’ of the votes.

ECB meeting and consequences on the Euro.

As we know, any spike in Euro peripheral (or core) bond yields has usually bad consequences on the single currency. Even though Greece doesn’t represent a major risk for the 19-nation economy, I strongly believe Greece is and will be the ‘hot’ topic of the next couple of weeks (with the Yen as usual). And at the moment, Greece makes ECB policymakers’ life complicated, concerning the central bank’s introduction of its public QE in order to counter deflation now (yes, you read it, deflation of -0.2% in December).

EUR/USD broke its 1.20 psychological support earlier this year and is now trading slightly above 1.1800 (a 9-year low). The next support that traders will target now stands at 1.1640, which corresponds to 2005 low.

I don’t think the market will react aggressively at the next ECB meeting on January 22nd, and even though we don’t hear any update concerning its QE, the Euro is still capped on the topside. I added below a timeline from Morgan Stanley that sums up the Key risk events for the EZ this quarter.

EZrecaps(Source: MS Research)

Below is another chart posted by SG Research that shows the ‘global macro’ euro are agenda for January and the downside/upside risk scenarios. As you can see, it includes the (forgotten) OMT case with the European Court of Justice’s decision on the legality of the ECB program for sovereign bonds.


(Source: SG Research)

The Fed’s 2015 dilemma: Equity market VS Oil prices

Even though the FX market is usually considered as an esoteric asset class, it happens that a lot of opportunities were in currencies last year. I mainly think about the Yen and the Euro, but the chart shows the main currency performances against the Dollar.


(Source: Hard Assets Investors)

We saw a couple of weeks ago that the economy increased at an annual rate of 5 percent according to the third estimates, the highest print since Q3 2003 when GDP rose by an outstanding 6.9.%. In addition, we saw in October that the final numbers for FY2014 federal deficit was $486bn (or 2.8% as a share of GDP), $197bn lower than the $680bn recorded in FY2013 and the lowest deficit since 2008 as you can see it on the chart below.


(Source: CBO)

On the top of that, the unemployment rate stands at a multi-year low of 5.8%, down 2.1% over the past couple of year. The only scary figures is US debt [like any other country], which now stands at a record high of 18tr+ USD, up 70% under Obama (10.6tr USD back in January 2009).

Another Good Year for equities…

I have to admit that with the Fed’s exit at the end of October, I was a bit anxious on the consequences it could have on the equity market, especially after the several ‘swings’ we saw (January, October). In my article Could we survive without QE (Part II with US yields), I added a chart (S&P 500) where you can see the impact on the equities each time the Fed stepped out of the bond market. Clearly not good.

But it didn’t. And after the 2013 thirty-percent rally, the S&P500 increased by another 11 percent in 2014 [and closed at records 53 times].

It looks to me that there are a lot of positive facts and the Fed can eventually start its tightening cycle. However, the collapse in oil prices will weigh on US policymakers’ decision in my opinion.

I think the question now is: which one will weigh more on US policymakers’ decision to tighten (or not)?

I strongly believe that the two main indicators the central bank is watching are the equity market and oil prices. An increasing equity market tends to have a positive effect on consumer spending (through the wealth effect). As a reminder, consumer spending represents 60 to 70 percent of GDP for most of the well-developed economies.

However, falling oil prices, with now Crude Oil WTI Feb15 Futures trading at $51.80 per barrel, is problematic. First of all, problematic for oil exporters’ countries (i.e. Chart of the Day: Oil Breakeven prices). We saw lately that Saudi Arabia announced that it will face a deficit of $38.6bn in FY2015, its first one since 2011 and the largest in its history (no projected oil price was included in the 2015 budget, but some analysts estimated that the Kingdom is projecting a price of $55-$60 per barrel).

I am just back from Kuwait City where I met a few investors there with a friend of mine (Business Developer in the Middle East), and most of them agreed that there were comfortable with a barrel at $60.

To me, falling oil prices reflect the weakening global demand and real economy effects. With the Chinese economy slowing down (GDP growth rate of 7.3% in Q3 is the slowest in five years), major economies back into recession (Triple-dip recession for Italy and Japan) and rising geopolitical instability, forecasts are constantly reviewed lower and problematic for debt stability [and sustainability]. I like the chart below (Source: ZeroHedge) which clearly explains that oil prices and global demand are moving together. In fact, lower growth projections combined with low oil prices and [scary] low yields are problematic for the Fed.


(Source: ZeroHedge)

Moreover, falling oil prices is problematic as it will drive US [and global] inflation lower. The inflation rate is slowing in most of the developed economies: in November, UK inflation fell to a 12-year low of 1% in November, EZ policymakers are still working on how to counter rising deflation threat (prices eased to a 5-year low of 0.3%) and US CPI fell at the steepest rate in almost six years to 1.3%. Most of the countries whose central banks target inflation are below their target.

2015: New Board, new doves…

In addition, as you can see it below, the ‘hawks’ members – Fisher and Plosser – are out this year and this could change the tenor of debate within US central bank’s policy-setting committee.


(Source: Deutsche Bank)