Understand why you should care about the US 10-year interest rate – 08/21/2023 – Grain to Grain

If we had to choose a single asset that accounted for at least part of the result of all the others in the world, this would be the US 10-year federal government bond (T10). That rate reached a 16-year high today. In the last 30 days, it rose from 3.87% per year to 4.34% per year. I explain the relevance of this rate and its variation.

The fair value of virtually all assets is calculated by discounting future cash flows to present value. Let’s illustrate this with an example.

Consider an asset that has only a cash flow of $30.00 over the next 3 years. You will agree with me that R$30 in 3 years is worth less than R$30 today.

In order to understand the fair value of these R$30 each year, we adjust this value by the price of money in time, which is the interest rate, plus a premium for the risk of not receiving this flow.

Thus, assume that the appropriate interest rate and premium for this stream are 10% and 5% per year, respectively. Therefore, the rate to discount the flow would be 15% per year.

Therefore, to know the fair value of the asset above, just perform the following calculation:
Value = 30/(1+15%)+30/(1+15%)^2 + 30/(1+15%)^3 = 26.09 + 22.68 + 19.73 = 68.50.

But where does the T10 come in?

It is the basis for calculating the 10% rate we used in the calculation above.

Assets such as stocks, real estate and developments in general have term cash flows that extend beyond 10 years. I won’t go into the mathematical details, but the average maturity of a long-term flow, that is, more than 20 years, is usually close to 10 years.

Thus, the US 10-year rate is practically the basis for building all asset discount rates around the world.

For example, when an analyst calculates the interest rate to discount assets in Brazil, he starts with the US 10-year interest rate, adds the rate that represents the Brazil risk and adds what he believes to be the rate that would represent the variation of the exchange rate in the long run.

So when T10 goes up, all discount rates go up. However, because discount rates are used in the denominator of the value calculation, when discount rates go up, the fair value of assets goes down.

The T10 interest rate rose by almost 0.5% in 30 days. This rise is like an earthquake that occurs in the middle of the sea and causes a tsunami whose wave spreads across the world, affecting all discount rates.

See the effect in Brazil. 30 days ago, the interest rate on the 10-year Brazilian interest rate futures contract traded on the B3 was at 11% per annum. Today, the same contract trades at 11.4% per annum. An increase of 0.4% in the period.

See an example of the impact of this rise. Consider a stock that pays a flow, for example, a constant dividend of $10 per year indefinitely. To calculate fair value, we use the sum formula of an infinite geometric progression. Thus, the fair value of this share would be the ratio between the flow and the rate. We will disregard the risk premium for flow uncertainty.

Doing the calculation, 30 days ago, the fair value of this share was R$90.91.

With the new interest rate of 11.4% per annum, the new fair value is R$87.72. Therefore, a drop of 3.51%.

Do you know how much the Ibovespa devalued in 30 days?

On July 21, the Ibovespa ended the trading session at 120,267 points. Today, the Ibovespa ended the day worth 114,429. A devaluation of 4.85%.

Obviously, the interest rate is not the only factor influencing the variation of the Stock Exchange, but it was an important variable in this fall.

The rise in US 10-year interest rates is a risk for all assets around the world, as it could trigger a correction in these assets.

Therefore, their behavior must be closely monitored. However, more important than following its level today is trying to predict how it will be in the coming months, as it will be this variation that will influence asset prices around the world.

Michael Viriato is an investment advisor and founding partner of Investor House.

Talk directly to me via email.

Follow and like De Grão em Grão on social networks. Follow the investment lessons in Instagram.

PRESENT LINK: Did you like this text? Subscriber can release five free hits of any link per day. Just click the blue F below.