Parities and Carry Trade

Currency Parities and Strategies The theory of exchange rates offers several concepts of equilibrium: purchasing power parity and interest rate parity. These concepts, though imperfect empirically, provide guidance for currency assessment and a foundation for investment strategies.

Purchasing Power Parity (PPP)
Purchasing power parity states that the exchange rate should equalize the purchasing power of currencies.
Absolute PPP: $E = P / P^*$, the rate equals the ratio of price levels.
Relative PPP: the change in the rate equals the difference in inflation rates.
Empirically, PPP works poorly in the short term. Rates can deviate from PPP for years and decades. However, in the very long run (decades), there is a tendency to revert to PPP. The PPP rate is used for cross-country comparisons of living standards and economic size. GDP by PPP adjusts for differences in prices and provides a more accurate comparison of real output.

Interest Rate Parity
Uncovered interest rate parity (UIP) links the difference in interest rates to the expected exchange rate change:
$i - i^* = \frac{E^e - E}{E}$, where $i$ is the domestic rate, $i^*$ is the foreign rate, $E^e$ is the expected future rate.
According to UIP, a higher rate is offset by the expected depreciation of the currency.
Covered interest rate parity (CIP) uses the forward rate instead of the expected one: the rate differential equals the forward premium/discount. CIP holds under conditions of free capital movement due to arbitrage.

Carry Trade
Carry trade is a strategy of borrowing in a low-interest currency and investing in a high-interest currency. The profit arises if the high-yield currency does not depreciate by the amount of the rate differential.
Empirically, UIP is systematically violated: high-yield currencies depreciate less than predicted by UIP, or even appreciate.
This creates the profitability of carry trade.
Risks of carry trade include sharp reversals in exchange rates (unwinding), especially during periods of rising volatility and risk aversion. Carry trade has the characteristics of "picking up pennies in front of a steamroller": small steady profits with occasional large losses.

Currency Crises and Sudden Stops
Currency crisis — a sharp depreciation of the currency, often accompanied by attacks on reserves, banking crisis, recession. Causes include policy incompatibility (fixed rate with expansionary policy), accumulation of external imbalances, contagion from crises in other countries.
Sudden stop — abrupt cessation of capital inflow into a country with a current account deficit. Leads to devaluation, recession, financial stress. Countries with large foreign-currency debt are especially vulnerable.

Application for Investors
PPP provides a guideline for long-term currency valuation. Significant deviations from PPP create preconditions for future correction, though the timing of correction is uncertain.
Carry trade can be a source of additional yield, but requires risk management. Diversification by currencies, volatility monitoring, stop-losses help limit losses.
Assessment of vulnerability to currency crises includes analysis of current account deficit, foreign-currency debt, reserves, exchange rate regime, political stability.