# Uncovered Interest Rate Parity and Capital Flight

For a moment, lets assume a world made up of two countries, U.S. and Canada, where Canada is in fact a top trading partner of the U.S. The exchange rate between the two currencies, US$/ Can$ is approximately 1.2602, as of today. In other words, it takes USD1.2602 to purchase a Canadian dollar.

Lets also assume that there is no capital control and one can move money freely. I have two options: Invest my money in a U.S Series EE Bonds that has a rate of return of 0.1% annualy or, convert my US dollars into Canadian dollars and invest in, say, Canada Premium Bonds Series that clearly has a higher return of 1% annually.

Well according to Interest Rate Parity, interest rates (savings yield) will adjust so that a person is indifferent between holding U.S dollars or Canadian dollars, or assets denominated in U.S dollars/Canadian dollars.

Lets work out this example and se if IRP holds and if no, what does it take to ensure it does. We start with 1 U.S. dollar as our initial investment portfolio. Given the current exchange rate of US$/Can$=1.2602, we will end up with Can$0.7935. We invest Can$0.7395 into a Canadian Premium Bond that offers a return of 1% annually. AT the end of the year, we have Can$0.7935(1+1/100)^1=Can$0.8014

Now, lets convert that amount back to U.S. dollars. Can$0.08014 = US$1.0099.

Can we do better ( or worse) if we invested the dollar in a U.S. EE bonds instead of the Canadian one?
1 US$invested in a bond that pays a return of 0.1% gives us 1(1+0.1/100)^1= US$1.001

So, it turns out that we are slightly better off investing our money in a Canadian bond by 1.0099-1.001=0.0089 cents!

What should the U.S. interest rate be so as to prevent capital flight from the U.S. to Canada? In other words, 1US\$ ( 1+r/100)= 1.0099, at the very least. r turns out to be 0.99 % or at least 9.9 times higher than the current one.

This is a simplistic view of IRP and capital flight with 2-country world. Do you believe that IRP holds true in the real world? Are there any strong evidence, or the lack there of, that currency arbitraging does indeed happen between world currencies?

Note by Venture Hi
6 years ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

There is a lot of evidence for that, and (even perceived) interest rate movements have the ability to drastically shift the world currency markets.

Countries do fight capital flight in terms of currency controls, IE restricting the amount of money that can be moved in / out.

Staff - 6 years ago

Currency controls, and restrictions, as oppose to free market system, will only exacerbate the problem further. The tighter the rein on restrictions will only be thought of as one's inability to maintain the current regime, and running very low on foreign reserves.

- 6 years ago