Question 23.6: For May 23, 2008, The Financial Times reported a spot ruble—...
For May 23, 2008, The Financial Times reported a spot ruble—dollar exchange rate of R23.5937/$ and a one-year forward exchange rate of R24.2316/$. At the time, the yield on short-term Russian government bonds was about 5.7%, while the comparable one-year yield on U.S. Treasury securities was 2.1%. Using the covered interest parity relationship, calculate the implied one-year forward rate. Compare this rate to the actual forward rate, and explain why the two rates differ.
PLAN
Using the covered interest parity formula, the implied forward rate is:
Forward Rate = Spot Rate × \frac{(1+r_R)}{(1+r_\$)}
Thus, we need the spot exchange rate (R23.5937/$), the dollar interest rate ( r_\$ = 0.021 ), and the ruble interest rate (r_R = 0.057).
EXECUTE
Forward Rate = Spot Rate × \frac{(1+r_R)}{(1+r_\$)} = (R23.5937/$) \frac{1.057}{1.021} = R24.4256/$
The implied forward rate is higher than the current spot rate because Russian government bonds have higher yields than U.S. government bonds. The actual forward rate, however, is lower than the implied forward rate. The difference between the implied forward rate and the actual forward rate likely reflects the default risk in Russian government bonds (the Russian government defaulted on its debt as recently as 1998). A holder of 100,000 rubles seeking a true risk-free investment could convert the rubles to dollars, invest in U.S. Treasuries, and convert the proceeds back to rubles at a rate locked in with a forward contract. By doing so, the investor would earn:
\frac{R100,000}{R23.5937/\$ \text{today}} \times \frac{\$1.021 \text{ in } 1 \text{ yr}}{\$\text{today}} × (R24.2316/$ in 1 yr) = R104.860 in 1 yr
The effective ruble risk-free rate would be 4.860%.
EVALUATE
The higher rate of 5.7% on Russian bonds reflects a credit spread of 5.7% – 4.860% = 0.840% to compensate bondholders for default risk.