Cheap or Expensive Currency? PPP, the Big Mac Index and Why It Can't Time Trades

Whether a currency is “cheap” or “expensive” can actually be measured, with an idea called PPP (Purchasing Power Parity). The idea is simple: if the same item sells for very different prices in two countries, the currency that makes it dearer is “expensive”. The catch is that an expensive currency can stay expensive for years. This article explains how to measure it, works through an example, then simulates what happens to a trader who fades a currency because “it’s already expensive”.

What PPP is

PPP comes in two forms.

• Absolute PPP (price levels): the exchange rate “should” equal the price in one country divided by the price of the same item in the other.
• Relative PPP (changes): the currency of the country with higher inflation should weaken by roughly the inflation gap.

The logic behind it is arbitrage: if something is cheaper abroad, people buy it there and sell it at home until prices or the exchange rate line up. In real life there are shipping costs, taxes and many things that can’t cross a border (haircuts, shop rent), so PPP never holds exactly.

The Big Mac Index: PPP in a burger

The Economist started the Big Mac Index in 1986 as a light-hearted guide. It uses the price of a Big Mac in each country instead of a basket of goods, because the recipe is the same everywhere. A version adjusted for GDP per person was added later, for the Balassa–Samuelson reason explained below.

Worked example (made-up prices, not current ones)

Say a Big Mac costs 130 baht in Thailand and 5.00 dollars in the US, and the actual exchange rate is 34 baht per dollar.

1. PPP rate = 130 ÷ 5 = 26 baht per dollar
2. Gap = 26 ÷ 34 − 1 = −23.5%
3. A negative number means the baht is 23.5% “cheap” against PPP versus the dollar

Check: change 130 baht at 34 and you get 3.82 dollars, not enough for a 5-dollar Big Mac in the US, and 3.82 ÷ 5 − 1 = −23.5%. It matches.

Relative PPP: inflation moves fair value

Fair value doesn’t stand still. Say Thai inflation is 1% a year and US inflation 3% a year.

• PPP rate next year = 26 × 1.01 ÷ 1.03 = 25.50 baht
• Change per year = 1.01 ÷ 1.03 − 1 = −1.94% (the shortcut 1% − 3% = −2% is close)
• After 5 years: 26 × (1.01 ÷ 1.03)⁵ = 23.57 baht

So if the actual rate stayed at 34 for five more years, the baht would look ever “cheaper” without the price moving at all. Fair value is a moving target. Relative PPP works best for very high-inflation countries and over decades. Over short horizons it explains almost nothing.

REER: many trading partners at once

The Big Mac Index looks at one product against one currency, the dollar. The REER (Real Effective Exchange Rate) does two more things.

1. It compares the currency with a basket of trading partners, weighted by their share of trade (this part is called the NEER), much like the dollar index DXY but covering far more partners.
2. It adjusts for the domestic price level relative to the partners’ price levels.

The Bank for International Settlements (BIS) publishes REERs for dozens of economies, Thailand included. The thing to know is that a REER is an index against a base year. A reading of 105 does not mean 5% expensive. It only tells you how high it sits relative to its own past. People usually look at how many percent it is from its long-run average.

Why rich-country currencies always look “expensive”

On the raw Big Mac Index, high-income countries’ currencies tend to look expensive and middle- and low-income countries’ currencies tend to look cheap. That’s no accident. The standard explanation is the Balassa–Samuelson effect (put forward separately by Bela Balassa and Paul Samuelson in 1964).

1. Rich countries are highly productive in goods that trade across borders (cars, chips, machinery), so wages are high.
2. Those high wages spill over into services where productivity isn’t much different, such as barbers and restaurant staff.
3. Those services can’t be shipped abroad, so arbitrage doesn’t pull their prices together.
4. The result is a higher overall price level in rich countries, so their currencies look “expensive” by PPP.

A Big Mac contains beef and bread (tradable) as well as wages and rent (not tradable), so its price reflects local wages too. A gap like this is structural. It can last for decades and is not a signal that the currency will come back.

Context for the Thai baht

Thailand is a middle-income country with lower wages and cheaper services than the US, so raw PPP tends to make the baht look “cheap” against the dollar, by the Balassa–Samuelson logic, like many emerging-market currencies. That number gives no direction. In the short to medium term the baht moves more on other things: tourism and export income, capital flows, the gap in policy interest rates and the dollar’s broad strength or weakness. If you want to judge whether the baht is cheap or expensive, a REER compared with its own history means more than a burger price.

The PPP puzzle: gaps close very slowly

Kenneth Rogoff’s article “The Purchasing Power Parity Puzzle” (1996) summed up the research of the time: deviations from PPP take about 3–5 years for half of them to disappear (the half-life). It’s called a puzzle because exchange rates swing hard month to month, yet the pull back to fair value is very slow, and it’s hard to explain both with the same story.

An “expensive” currency does feel a pull back, but the pull is so weak that monthly noise easily drowns it out. Knowing it’s expensive doesn’t tell you when.

Simulation: how long does a 20% overvaluation last

We built an AR(1) model in node, the standard model for a gap that slowly decays towards zero. The settings:

• Start with the currency 20% above fair value
• Half-life of 4 years (the middle of Rogoff’s range), which per month is φ = 0.5^(1/48) = 0.9857
• Monthly shocks of 2.5% (volatility of about 8.7% a year, similar to major pairs)
• Fair value stays fixed, no costs, 20,000 random paths of 10 years each

This model guarantees a pull back, which is kinder than the real market, where fair value itself is uncertain and moves. The results:

What we measured	Result
Expected gap after 1 year	still 16.6% expensive
Expected gap after 4 years	still 9.5% expensive (half, in log terms)
Time to reach fair value (median, among the 79% that get there within 10 years)	45 months
Fastest 25% / slowest 25% (same group)	within 26 months / over 73 months
Never back to fair value within 10 years	20.9%
Still more than 10% expensive after 2 years	62.6%
Reached 30% expensive or more along the way	48.4%

Signal against noise: in the first year the pull back is expected to move price about 2.9%, while yearly volatility is 8.7%. The noise is roughly three times the signal.

What happens to a trader who fades it with leverage

Say a trader sees a 20% overvaluation and sells (shorts) the currency at different leverage levels (position size relative to account equity), holding until price reaches fair value or until the loss hits 50% of the account and the trade is cut. Same 20,000 paths.

How far price has to move against you to lose 50%: 1x = 50% · 2x = 25% · 3x = 16.7% · 5x = 10% · 10x = 5%. If the target is reached, the gain at 1x is 1 − 1 ÷ 1.2 = 16.7% of the position size.

What these numbers show:

• At 10x, 57.5% are stopped out before the target, with a median stop-out in month 9, even though the direction is “right” in the long run.
• The average ending equity at 10x is 1.46 times the starting stake, which looks good, but the median is 0.5: most traders lose half. A lucky minority drags the average up.
• At 1x you are almost never stopped out, but 20.8% have to hold for more than 10 years, and the most you make is 16.7% over several years.
• The real market is harsher. An expensive currency is often a high-interest currency, so the short pays swap every night, the mirror image of a carry trade, and real fair value doesn’t sit still the way it does in the model.

“Expensive” is a good reason not to chase a currency higher, and a terrible reason to short it with high leverage. A market can stay mispriced longer than your account can stay alive.

How to use this when trading

1. Use PPP and REER as context, not an entry signal. A very large gap tells you risk is building on one side. It doesn’t tell you the timing.
2. Compare with its own history. A REER unusually far from its long-run average means more than the raw Big Mac Index, which is mixed up with the Balassa–Samuelson effect.
3. If you fade it, wait for price to confirm. For example, wait for the trend to turn instead of selling while it is still rising hard. See the comparison of riding versus fading in Price at the old high: ride or fade.
4. Low leverage, sized from the Stop loss distance. If your Stop loss is 10% of price away, the position must be small enough that hitting it costs only 1% of the account. Use the lot size calculator and read Wide or tight Stop loss.
5. Put swap into the plan. Holding for years means counting every overnight fee. See Swap and overnight fees.
6. Understand why it’s expensive. Higher interest rates, capital inflows or higher productivity. If the reason is still there, the gap can stay too.

To see how to measure whether price tends to revert to the mean or keep running, read The Hurst exponent and mean reversion, and if waiting keeps costing you, read Risk of ruin.

Common mistakes

• Reading the Big Mac Index as a forecast. Gaps of 20–30% can last for decades, especially between rich and middle-income countries.
• Forgetting that fair value moves. The inflation gap shifts PPP every year. A “cheap” currency can get cheaper without its price moving.
• Reading REER as a direct percentage of over- or undervaluation. It is an index against a base year, so compare it with its own average.
• Fading with high leverage. In a model where the return is guaranteed, 10x was still stopped out more than half the time. The real market guarantees nothing.
• Looking at the average instead of the median. A strategy’s average result can look fine because of a few survivors while most people lose.
• Ignoring swap. Expensive currencies often pay high interest, so a long-term short has a holding cost that eats into profit every night.