CFA CFA Level 2 FX Rates: which direction to gain arbitrage?

# FX Rates: which direction to gain arbitrage?

• Author
Posts
• vincentt
Participant
• CFA Level 3
22

The following are spot rates quoted in the interbank market:
USD/GBP 1.5462/1.5467
JPY/USD 89.34/89.36
JPY/GBP 139.02/139.10

An analyst suspects that the JPY/GBP exchange rate is mispriced. After calculating the no arbitrage rate the analyst would most likely:

A Conclude that the exchange rate is not mispriced.
B Conclude that there is a mispricing and exploit it by selling GBP and buying JPY.
C Conclude that there is a mispricing and exploit it by selling JPY and buying GBP.

After doing the cross rate calculation USD/GBP * JPY/USD you’ll get —> JPY/GBP 138.137508 138.213112 which clearly shows that it is mispriced so A is out of the question.

However, which “direction” do you usually use to gain the arbitrage?

As i feel both B and C are correct:

B

Sell base * bid –> Â£100 * 139.02 —> Yen 13,902
Sell var / ask –> Yen 13,902 / 138.213 —> Â£100.584

C

sell var / ask –> Yen 10000 / 138.213 —> Â£72.35
sell base * bid –> Â£72.35 * 139.02 —> Yen 10058.39

So would that means both ways are possible or am i missing something?

• Zee Tan
Keymaster
• CFA Charterholder
6

@vincentt @diya Here’s how my thinking works. I’ve been told that this doesn’t necessarily make sense to some people because my thinking is a little weird, but here goes.

Imagine there is an FX trader willing to trade at that mispriced rate. The way I figure out what to do is to ask this question: how do I screw this poor mispriced trader over?

So if the mispriced rate is 139.02/139.10 and the true rate is 138.14/138.21, this means that in order to screw this FX trader over, I need to buy JPY from him (since he’s undervaluing JPY i.e. giving me too much JPY per unit GBP). Therefore I buy JPY and sell GBP.

If say the mispriced rate is 137.02/137.10, he’s willing to take too little JPY per unit GBP (i.e. he’s overvaluing JPY for what it really is). So I’ll sell him JPY (as he’s not taking enough as he should) and buy GBP (elsewhere).

This logic works beautifully for me, although I know it doesn’t for everyone. But hope it helps you!

• 5

@Zee when I was working out the solution I was reasoning it out the same way you do. Which way do I screw over this misguided FX trader…

• vincentt
Participant
• CFA Level 3
4

thanks for the explanation @zee !

The part where I got confused was that I thought I could buy GBP cheaply (with JPY) from the actual price (138.14/138.21) by getting USD from (JPY/USD) and then GBP from (USD/GBP).

After that with the GBP, I’ll buy the undervalued JPY from the ‘poor mispriced trader’.

But by looking at a couple of examples and based on both of your explanation (@zee and @diya), i realised the cross rate is just a guideline to decide whether to buy (sell) if it’s undervalued (overvalued).

• 4

yup that’s right @Vincentt. Somehow I got confused at the same areas as you did too ðŸ™‚ @zee’s analogy is pretty helpful

• vincentt
Participant
• CFA Level 3
2

@diya u got it right, I guess i sort of got the concept right after i posted.

Basically, the “no arbitrage rate” is just a guideline to tell you what you should be doing (buy or sell the base currency) to the base currency of the actual rate. E.g. since “no arbitrage rate” is less than the actual rate, which implies that the actual rate is overpriced hence sell gbp.

But based on my explanation in the first post, you could start with either Â£ or Yen and you would still make a profit by arbitrage.

• Zee Tan
Keymaster
• CFA Charterholder
2

@diya Finally someone who thinks alike!

• 2

Hi everyone.

I just made a video explaining triangular arbitrage.

I have a very useful and straightforward way of calculating it, as I felt that curriculum and third party prep providers didn’t explain it well enough.

Let me know what you think and if you found it helpful.

Regards

• 2

Thanks for sharing this with all of us @Coen! Definitely helpful to see the steps to avoid all the confusion ðŸ™‚

• 0

If you recall for the triangular arbitrage section, you can earn a profit only going one way around the triangle. That means only B or C are correct.

I feel that this is a triangular arbitrage question and would solve it by employing a triangle. But that takes too long.

JPY/GBP 139.02/139.10
JPY/GBP 138.1375/138.2131 (no arbitrage rate)

So you want to buy JYP at a price of 138.1375 GBP and then sell it at 139.02 GBP you make a profit.

Therefore the right answer is B, right?

It doesn’t work the other way since if I buy GBP at 139.10 JYP I’d have to sell it at 138.1375 you would make a loss.

disclaimer: I don’t feel 100% confident with my answer