Cross currency basis (Stuyvesant)

CFA Level III Derivatives
#1

Vignette: “The fixed-income assets of the plan include US$10 million invested in one-year US Treasury bonds. Stuyvesant’s evaluation of global bond and currency markets indicates that she can increase the yield on the portfolio by selling the Treasury bond position and buying Japanese government bonds of the same maturity. The data she uses for her assessment show that the US bonds pay 1.75% and Japanese bonds pay –0.40% annualized. She plans to fully hedge the currency risk. The YEN/USD spot rate is 106.85, the one-year YEN/USD forward rate is 104.15, and the one-year YEN/USD cross currency swap basis is –0.63.”

Q: Does Stuyvesant’s proposal to buy Japanese bonds most likely increase the yield on the portfolio?

  1. Yes, it increases the yield.
  2. No, because the yen appreciation does not compensate for the lower Japanese rate.
  3. No, because paying the basis would further erode the return on the Japanese government bonds.

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Answer

  1. Correct. Stuyvesant can sell US$10,000 converted at a spot rate of 106.85 to invest proceeds of ¥1,068,500 at –0.40%. After one year, the Japanese bonds are sold (1,068,500 × 0.9960 = 1,064,226.00) and converted at the forward rate of 104.15, for proceeds of US$10,218.20. The fund has earned 10,218.20/10,000 – 1 = 2.18%. The 2.18% yield is higher than the 1.75% she could have earned in US Treasury bills. The difference is due to the basis given a high demand for US dollars.
  2. Incorrect. The exchange rate reflects not only the interest rate differential implied by interest rate parity but also receiving the basis.
  3. Incorrect. Stuyvesant is actually receiving the basis for lending US dollars.

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I’m struggling to understand the answers provided for (2) and (3). Can someone help…?

#2

(2)

  • Looking at interest rates alone
  • -0.4% JPY +1.75% you would expect to lose money on this trade. -2.15%
  • But the forward rate is not what interest rate differences would predict. The yen is appreciating. c. 2.59%
  • This is more than loss on rates. so gain made

(3)

  • It is the non-USD person who has the basis. Here basis is negative so on a swap JPY leg would receive JPY MRR - 0.65%, equivalent to USD leg receiving 0.63%
#3

Thanks @MikeyF , I still don’t understand the following.

Why would a cross currency swap be used?

  • The vignette says Stuyvesant can sell the Treasury bond position to get USD. Then the answer for (1) says that Stuyvesant can simply convert USD to JYP at the spot rate, invest in JPY bonds, then covert back to USD at the forward rate. Why would a swap be needed here?
  • Or, are we saying that Stuyvesant can sell the Treasury bond position to get USD, then enters into a cross currency basis swap (‘lend’ USD; ‘borrow’ YEN). So Stuyvesant is paying (YEN MRR - 0.63%) on the YEN leg, and using the YEN obtained to invest at -0.4%. So Stuyvesant’s net position on YEN is 0.23% (0.63% - 0.4%). Then the YEN appreciates by 2.52%, so total gain is now 2.75% (2.52% + 0.23%). But how do I reconcile this with the 2.18% net yield the answer for (1) mentions?

Also, is it correct to say that once we see that there is a basis, we should use uncovered interest rate parity? Since covered interest rate parity assumes that there is no basis.

Thanks so much!

#4

I put answers in your reddit post

https://www.reddit.com/r/CFA/comments/1mk3k1l/cross_currency_basis/