# Stuck on CFA Example Question

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

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?

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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

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/

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

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!

My pleasure.

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

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.

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.