Practice Quiz 8 Solutions — Carry Trades & Hedging
Setup: S = $/Yen = 0.0067 (1 USD ≈ 149 Yen). US 1-year rate 4.5%, Japanese 1-year rate 0.5%. Fund borrows 100 million Yen.
(a) Dollars received today? Yen owed after one year?
Dollars received:
\[100{,}000{,}000 \times 0.0067 = \$670{,}000\]Yen owed after one year (principal + interest):
\[100{,}000{,}000 \times (1 + 0.005) = 100{,}500{,}000 \text{ Yen}\]The fund invests $670,000 in US Treasuries at 4.5%.
(b) Yen strengthens to S = $/Yen = 0.0075. Profit or loss?
Dollar value of US Treasury investment after one year:
\[\$670{,}000 \times 1.045 = \$700{,}150\]Dollar cost of repaying Yen debt at the new exchange rate:
\[100{,}500{,}000 \times 0.0075 = \$753{,}750\]Profit/loss:
\[\$700{,}150 - \$753{,}750 = -\$53{,}600\]The carry trade lost approximately $53,600. The 4% interest rate differential was far more than wiped out by the ~12% appreciation of the yen. The fund earned extra yield but the currency moved sharply against the trade.
(c) Why do carry trades generate small steady profits but occasionally large losses? How does this relate to July 2024?
Carry trades profit when the high-yield currency does not depreciate as much as the interest rate differential would predict — and empirically, high-yield currencies tend to appreciate slightly, violating UIRP. This generates small, steady returns most of the time. However, when risk appetite collapses or the funding currency strengthens suddenly (as when the Bank of Japan unexpectedly raised rates in July 2024), the yen surged and carry traders faced massive losses as they unwound positions simultaneously. This is the “peso problem” — the returns look like a free lunch in normal times, but carry traders are being compensated for bearing rare but severe crash risk (negative skewness).