Help, CFA Level 1 Arbitrage Question (Can't Find Correct Forum Topic)
I was working on a practice test for Level 1 when I came across this bugger. The answer provided makes absolutely no sense to me. I honestly think they made an error. If I don't get to the bottom of this it will really bother me. Please give it a shot and let me know. Should be very simple.
Question:
An investor examines the following rate quotes for the Brazilian real and the Australian dollar and shorts BRL 500,000.
Spot rate BRL/AUD 2.1128 BRL 1-year interest rate 4.1%
-----------------------------------------------------------------------------------------
Forward rate BRL/AUD 2.1388 AUD 1-year interest rate 3.1%
Question:
The risk-free arbitrage profit that is available is closest to:
a) BRL6,405.
b) BRL1,344.
c) –BRL6,327
b) is the Correct answer...somehow
This is how I got my answer:
Scenario 1(invest locally) vs Scenario 2(invest abroad then convert back):
Scenario 1.
Step 1: Simply invest 500,000 BRL locally @ 4.1%
= 500,000 * 1.041 = 520,500 BRL
VS.
Scenario 2.
Step 1: Convert 500,000 BRL to AUD, @ BRL/AUD = 2.1128 (2.1128 AUD for every 1 BRL)
500,000 * 2.1128 = 1,056,400 AUD
Step 2: Invest that 1,056,400 AUD @ 3.1% for 1 year
1,056,400 * 1.031 = 1,089,148 AUD
Step 3: Convert that 1,089,148 AUD back to BRL @ BRL/AUD 2.1388 (Locked in Forward Rate)
2.1388 AUD for every 1 BRL, so 1,089,148/2.1388 = 509,233 BRL
RESULT: Scenario 2 - Scenario 1
Arbitrage Profit = 509,233 BR - 520,500 BRL = -11,267 BRL
Ergo, no arbitrage profit, you are better off keeping those BRL and investing locally
Am I missing something here?? or is it an error?
______________________________________________________________________________________________________________
This is what the answer key gave me:
Left side of equation: BRL500,000 × (1+.041) = BRL520,500
Right Side:
1
BRL500,000 × (1/2.1128AUD/BRL) = AUD236,653
**500,000 BRL= 1,056,400 AUD not 236,653 AUD wtf?**
Convert domestic to foreign
2
AUD236,653 × (1.031) = AUD243,989
Invest foreign @ foreign rate
3
AUD243,989 × 2.1388 = BRL521,844
Convert foreign to domestic
Arbitrage profit = BRL521,844 – BRL520,500= BRL1,344
Thanks in advance!
They definitely gave you the BRL/AUD rate and called it AUD/BRL. Does it seem logical to you that the Brazilian real would be stronger than Aussie dollars?
Though it's the other way around - they gave you the AUD/BRL rate but called it BRL/AUD.
Yes
Aut quia et modi qui libero. Provident nisi reprehenderit sit alias dolorem. Voluptas porro minima et provident. Soluta sit est repellat quis consequuntur.
Cupiditate similique qui quaerat velit assumenda voluptatibus. Voluptates vitae expedita aut suscipit aliquid.
Autem velit nesciunt voluptatem deserunt repudiandae quo non ut. Repellendus voluptas molestiae corrupti voluptate perferendis. Corrupti in quae voluptatem ut accusantium sed.
Praesentium occaecati sed totam soluta aspernatur esse voluptatem. Et harum explicabo et eum quibusdam. Doloribus iure et ut et repudiandae quidem rem. Nostrum non ipsa ipsum tenetur ut quia aut. Dignissimos quis voluptatem quas iure aut.
See All Comments - 100% Free
WSO depends on everyone being able to pitch in when they know something. Unlock with your email and get bonus: 6 financial modeling lessons free ($199 value)
or Unlock with your social account...