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I understand it is common sense that treasury yield goes up, the dollar goes up as well due to the fact that domestic/foreign money are attracted to the higher yield therefore they need to buy more US dollars to get into the bond market (higher demand of the dollar).

On second thought though, given the inverse relationship between bond yield and bond price (when yield goes down, the price goes up, and vice versa), doesn't it also make sense that when bond yield goes down there's more money flowing in, meaning people have a higher demand of dollar (which naturally pushes up the dollar against other currencies)?

This baffles me. Does anyone know why bond yield falls together with the dollar? the more I think about it the more it confuses me.

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I'll try my best to provide an explanation of the link between treasury yield and exchange rates. However, my answer is not a reference, but just a piece of a dialogue.

First, I'll start by explaining the most simple model I can think of. Let's suppose there's an open economy with only two country (A and B), with a simple portfolio choice between bills and money. Will be able to describe this economy with a finite set of equations, including:

$$Hha = Va - Ba - Bb(1/xa)$$

This is the wealth constraint of the country $A$, where the holdings of domestic currency $(Hha)$ is equal to household wealth $(Va)$ minus the holdings of domestic bills $(Ba)$ and foreign bills ($Bb$ - is adjusted according to exchange rate). To fully understand the impact of change in treasury yield, will also need this other equation:

$$CAa = (Xa - IMa) - RaBa + RaBb(1/xa)$$

This means that the current account of country $A (CAa)$ is equal to it's trade balance plus income transfer (because the two country trade securities and not only goods).

..............

Using the previous equations we can better understand the impact of treasury yield on exchange rate. First of all, let's suppose there's an increase in country A treasury yield (and that this increase leads to an increased demand for country A's bills). Following the wealth constraint, this mean that we can expect an appreciation of country A currency. However, if we use the current account equation, we'll see that this impact is only on the short-term. The appreciation of country A currency leads to an increase in imports, which decrease the current account value. In turn, this progressive decrease in current account will put pressure on the exchange rate, and eventually depreciate Country A currency.

I'm not the best at explaining, but I would suggest reading Carnevali 2021.

References

Emilio Carnevali (2021): A New, Simple SFC Open Economy Framework, Review of Political Economy, DOI: 10.1080/09538259.2021.1899518

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