Stuck on CFA Example Question

CFA Level I Economics
#1

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 x (1+.041) = BRL520,500

Right Side:

1

BRL500,000 x (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 x (1.031) = AUD243,989

Invest foreign @ foreign rate

3

AUD243,989 x 2.1388 = BRL521,844

Convert foreign to domestic

Arbitrage profit = BRL521,844 - BRL520,500= BRL1,344

Thanks in advance!

#2

First, you misunderstand CFA Institute’s exchange rate quoting convention. BRL/AUD 2.1128 means:

BRL2.1128 = AUD1.0

If he shorts BRL, he borrows BRL today. Here are the steps:

  1. Borrow BRL500,000 @ 4.1% for one year.
  2. Convert BRL500,000 to AUD236,653 @ BRL/AUD 2.1128.
  3. Invest AUD236,653 @ 3.1% for one year.
  4. Enter into a 1-year forward contract to deliver AUD243,989 @ BRL/AUD 2.1388.
  5. Wait one year. Watch a movie.
  6. Your AUD236,653 will have grown to AUD243,989 (= AUD236,653 × 1.031).
  7. Convert AUD243,989 to BRL521,844 @ BRL/AUD 2.1388.
  8. Pay off the loan for BRL520,500 (= BRL500,000 × 1.041).
  9. Your net gain is BRL1,344 (= BRL521,844 − BRL520,500).

I wrote an article on this that may be of some help: http://financialexamhelp123.com/covered-interest-rate-parity-irp-pricing-currency-forwards/

#3

Obviously not my question, but just wanted to say thanks for the great and concise answer S2000magician.

#4

Thank you mag, very good example, in my finance class the convention was the other way around, but that wasn’t my only problem…

I will pay it forward when I get my CFA, I appreciate it!

#5

My pleasure.

CFA Institute’s convention is the opposite of the norm. Welcome to the CFA curriculum.

#6

I have tried using this formula to solve the above question but somehow i could not get the right answer.

So my working is basicly like this: 1.F(f/d) = S(f/d) * (1+f) / (1+d) = 2.1128 * 1.041 / 1.031 = 2.13329

  1. Minus the difference between the calculated value above (2.13329) and the given Forward value (2.1388) to get 0.00551*500.000 = 2755.

Anyone can tell me where i made mistakes?

Thanks.

#7

Thank you for your detailed explaination. I totally got the idea of the question after reading your solution.

But please look at my working and tell me where is my mistake.

I have tried using this formula to solve the above question but somehow i could not get the right answer.

So my working is basicly like this:

1.F(f/d) = S(f/d) * (1+f) / (1+d) = 2.1128 * 1.041 / 1.031 = 2.13329

  1. Minus the difference between the calculated value above (2.13329) and the given Forward value (2.1388) to get 0.00551*500.000 = 2755.

Anyone can tell me where i made mistakes?

Thanks.