Purchasing Power Parity

Over the past decade consumer prices in Aurelia have risen roughly 7% a year while consumer prices in Norvik have risen roughly 1% a year. Both countries let their currencies float freely and neither restricts capital flows. All else equal, purchasing power parity predicts that over this period the Aurelian currency will:

1. A.Appreciate against the Norvik currency, because higher inflation signals faster underlying economic growth.Incorrect. Inflation is a price-level measure, not a growth measure, and high inflation weakens rather than strengthens a floating currency.
2. B.Hold its value against the Norvik currency, because floating exchange rates offset inflation differences the instant they arise.Incorrect. Floating rates adjust toward parity over long periods, but they do not neutralize inflation gaps instantly or perfectly.
3. C.Appreciate against the Norvik currency, because Aurelian exporters collect more nominal revenue as prices rise.Incorrect. Nominal revenue rising with domestic prices does not create foreign demand for the currency; it simply reflects the same loss of buying power.
4. D.Depreciate against the Norvik currency, because each Aurelian unit buys steadily less than it used to.Correct. The currency with the persistently higher inflation rate loses relative purchasing power, and the exchange rate adjusts downward over time.

Why: Purchasing power parity says that a currency losing domestic buying power faster than another currency must, over time, fall against it. Aurelia is running about six percentage points more inflation each year, so an Aurelian unit buys steadily less at home and abroad. Currency markets adjust by pricing the Aurelian unit lower against the Norvik unit. This is a long-run tendency, not a day-to-day rule, and it explains why chronically high-inflation currencies tend to weaken.

Corentin Delahaye, 60, will retire in five years to Portugal and expects to spend essentially all of his money in euros for the rest of his life. His $1,600,000 portfolio and his pension are entirely dollar-denominated. His adviser should point out that:

1. A.He should hold only U.S. Treasury bills, which are the safest possible holding for an investor in any currencyTreasury bills carry no credit risk but full currency risk for a euro-spending investor, and they will not fund a multi-decade retirement.
2. B.He should convert the entire portfolio to euros immediately, because matching currency always outweighs diversification and transaction costA wholesale conversion five years ahead of the move concentrates timing risk and abandons diversification; a gradual, partial approach is the standard answer.
3. C.His true risk is measured in euros, so a portfolio that looks safe in dollars can lose purchasing power if the dollar weakens, and he should build euro-denominated or euro-hedged assets and income over time to match his liabilitiesCorrect. Match the currency of the assets to the currency of the spending.
4. D.Currency movements are irrelevant, because the portfolio is reported in dollars and he remains a U.S. taxpayerTax residence and reporting currency do not change the currency in which he will buy groceries.

Why: Risk should be measured in the currency of the liabilities being funded. Once Delahaye living costs are euro-denominated, a portfolio that looks conservative in dollars can still lose a large share of its purchasing power if the dollar weakens against the euro. The sensible response is gradual: build euro-denominated or currency-hedged assets and, where possible, euro income, so that assets and liabilities move together. Converting everything at once concentrates timing risk and can be expensive.

Short-term risk-free interest rates in Country A are 5% and in Country B are 1%. Both currencies float freely and capital moves without restriction between them. Under INTEREST RATE PARITY, how should the one-year forward exchange rate for Country A currency compare with its spot rate, and why?

1. A.The forward rate should equal the spot rate, because arbitrage forces all freely floating exchange rates to converge over time.Incorrect. Equal forward and spot rates would leave a riskless 4% arbitrage profit available, which traders would immediately exploit.
2. B.Country A currency should trade at a forward PREMIUM of roughly 4%, because its higher interest rate attracts capital and strengthens the currency.Incorrect and reversed. A forward premium on the high-rate currency would add to the interest advantage, creating an even larger arbitrage.
3. C.Country A currency should trade at a forward DISCOUNT of roughly 4%, so the interest advantage is exactly offset and no riskless arbitrage profit remains.Correct. The high-yielding currency must sell forward at a discount approximating the interest differential for the no-arbitrage condition to hold.
4. D.The relationship is indeterminate, because forward exchange rates are set by expectations of future spot rates rather than by arbitrage.Incorrect. Covered interest parity is enforced by arbitrage among observable spot, forward and interest rates, independently of expectations.

Why: Interest rate parity is a no-arbitrage condition linking spot rates, forward rates and interest rate differentials. Consider an investor holding Country B currency. She could simply invest at home at 1%, or she could convert to Country A currency, invest at 5%, and simultaneously sell the proceeds forward to lock in the rate at which she will convert back. If both routes are genuinely riskless, they must produce the same return, because otherwise traders would borrow in one currency and lend in the other in unlimited size until the gap closed. The only way the two can be equalised is if the forward exchange rate for the HIGH interest rate currency is below its spot rate, so that the extra 4% of interest earned is exactly offset by an expected loss on the currency conversion. The high-yielding currency therefore trades at a forward DISCOUNT and the low-yielding currency at a forward premium, with the size of the discount approximately equal to the interest rate differential. The practical implication is that a hedged foreign bond position does not capture a foreign yield advantage: hedging away the currency risk also hedges away the excess yield.