L05 - International Financial Management

5.1 Foreign Exchange (FX)

5.1.1 Spot Trade

Spot price = instantaneous price. But then it’s actually delivered 2 days later. (or you pay up).

51.2 FX: Forward

If you know in advance, you could lock in a rate via a forward. But then you lose upside if one currency goes up.

Also note, the forward rate $F=S\times 1+\frac{1+r_{\text{USD}}}{1+r_{\text{EUR}}}$ is spot price * the interest rate differential (i.e. opportunity cost of converting now).

If USD rates > EUR rates → USD is weakening faster than EUR.
Thus forward rate for EUR/USD (number of USD per EUR) will be higher than spot = more dollars per euro in the future.

5.1.3 Interest Rates & Forward Prices

Forward Premium and Discount

Let $S$ be the spot rate and $F$ be the forward rate, both quoted as units of foreign currency per 1 unit of home currency. The annualised forward premium/discount on the foreign currency over a period of $\frac{1}{n}$ years is

$$n\times \left(\frac{S}{F}-1\right)$$

• If the result is positive, the foreign currency trades at a forward premium (expected to appreciate).
• If the result is negative, the foreign currency trades at a forward discount (expected to depreciate).

Note the quoting convention matters: because $S$ and $F$ are expressed as foreign per home, the ratio $S/F$ captures the change in the foreign currency’s value. Reversing numerator and denominator gives the premium on the home currency instead.

Example: The Brazilian real spot rate is $5.1101$ BRL/USD and the 3-month forward rate is $5.1273$ BRL/USD. The annualised forward discount on the real is

$$4\times \left(\frac{5.1101}{5.1273}-1\right)\approx -1.34\%$$

The real is at a forward discount of $1.34\%$ per year. Equivalently, the dollar is at a forward premium of $1.34\%$.

To see concretely what this means: at spot, $1$ USD buys $5.1101$ BRL. In the forward market, $1$ USD buys $5.1273$ BRL — so a holder of reals needs more reals to buy one dollar in 3 months. The real has weakened forward.

Covered Interest Rate Parity (CIP)

Let $r_d$ and $r_f$ be the risk-free interest rates in the home and foreign country respectively, over the same horizon as the forward contract. Then in the absence of arbitrage,

$$\frac{F}{S}=\frac{1+r_f}{1+r_d}$$

Equivalently, the forward premium on the foreign currency equals the interest rate differential:

$$\frac{F-S}{S}\approx r_f-r_d$$

Proof (by arbitrage): If the forward traded at the same price as today

• Borrow $1,000 in the US at 4%
• Convert to reals at spot, invest in Brazil at 8%
• In one year, collect your 8% return
• Convert back to dollars at the same rate, repay your 4% loan
• Pocket the 4% difference — risk free

High Interest Rate ↔ Forward Discount

A currency with a relatively high interest rate trades at a forward discount; a currency with a relatively low interest rate trades at a forward premium.

5.1.4 Worked Example

Dollar loan:
The rate of interest on 1-year dollar deposits is $5\%$. At the end of the year:

$$1,000\times 1.05=\text{USD }1,050$$

RUR loan:
The current exchange rate is RUR $50$ / USD $1$. For \1{,}000$ you can buy:

$$1,000\times 50=\text{RUR }50,000$$

The rate of interest on a 1-year RUR deposit is $15.5\%$. At the end of the year:

$$50,000\times 1.155=\text{RUR }57,750$$

• You don’t know the exchange rate in 1 year’s time, but can fix today the price if you sell your RURs forward.
• The one-year forward rate is RUR $55$ / USD $1$.
• Selling forward, you receive:

$$\frac{57,750}{55}=\$1,050\text{at end of the year}$$

Both strategies yield exactly USD $1,050$ — the higher RUR interest rate is fully offset by the forward depreciation of the ruble, consistent with covered interest rate parity.

5.1.5 Exchange Rate & Inflation

If a currency is expected to be more prone to inflation than another, we expect it’s spot exchange rate to be higher in the future.
The market makes sure of this through arbitrage opportunities if not conserved.

In general the following holds: higher interest rate ←> higher inflation rates for a country.

5.2 Exchange Risk and International Investment Decisions