Last Wednesday afternoon, the Federal Reserve (FED), as the American Central Bank is known, released the minutes of its last meeting held on December 15, 2021. The document has a total of 14 pages, but the following sentence on the page 11 made the market shudder:

“…given their individual outlooks for the economy, the market, and inflation, it may become labor rate warranted to increase the federal funds rate sooner or at a faster pace than participants had earlier anticipated labor rate.” (given its outlook for the economy, labor market and inflation, it may be necessary to raise short-term rates **early** or in a rhythm **faster** than the participants had anticipated.)

A similar announcement was also made in Brazil by our Central Bank in the second half of 2021. The result was a sharp rise in the Brazilian yield curve and the consequent fall in equity markets.

I explain below the reason for the actions to suffer with the increase in the interest rate by the Central Banks.

The change in the short-term rate (the Selic in the Brazilian case) affects the market yield curve and this influences the pricing of shares.

Simply put, the market prices a share, bringing the future cash flow of a company to present value. For this, it uses the long-term interest rate implicit in the yield curve mentioned above. I’ll give an example, but first I’ll recall a concept from our high school to simplify.

If we consider that the cash flow of a company grows at a constant rate, the sum of the present value of the flows is represented by the sum of an infinite geometric progression, which we learned in high school when we are going to take the entrance exam.

This formula is presented below.

In the formula, the fair value (V) of a share today is the ratio of the cash flow (FC) to the difference between the discount rate (k) and the growth (g) of FC.

In the composition of the discount rate (k), the risk-free rate of the economy plus a premium for equity risk is considered. Thus, if the economy’s risk-free rate rises, the denominator gets higher and the present value of the stock falls. See the example.

Assume that a company has an expected cash flow (FC) of R$ 100.00 per year, that the discount rate (k) is 12% per year and the growth rate (g) of the flow is 4% per year. Thus, the fair value (V) of this share today would be R$ 1,250.00 (=100/ (12% – 4%)).

If the discount rate rises by 2% due to an unexpected move by the market, then the new discount rate jumps to 14% per year. Keeping the rest constant, the new fair value of the asset becomes R$ 1,000.00 (=100/ (14% – 4%)).

Therefore, a simple unexpected movement of interest rate increases can cause a fall in the fair value of assets. In our example, a 20% reduction in fair value.

This reduction in fair value may trigger a devaluation of the same magnitude as this action.

Part of the fall that the Brazilian market showed last year can be explained by the acceleration of interest rate hikes by our BC in the fourth quarter of 2021.

However, the unexpected upward movement in interest rates affects more than just the discount rate. It also negatively influences the future growth (g) of companies’ cash flows.

As rates rise, the opportunity cost for individuals to consume and for entrepreneurs to invest increases. This means that rising interest rates act as a handbrake on the economy.

Thus, the fair value of shares can be affected not only by a higher discount rate, but also by lower growth (g) when interest rates rise more than expected.

In our example, suppose the discount rate (k) went up by 2% and the growth rate (g) went down by 1%. Thus, the fair value of our hypothetical share would be R$909.09 (=100/ (14% – 3%)). That is, a drop of 27.27% of the initial fair value.

So this week’s stock market slump reflects investors’ fears about how much the Fed could raise rates.

The effect on our pockets of a stronger interest rate increase in the US could come, for example, from greater pressure on our exchange rate and, consequently, higher inflation and further interest rate increases in Brazil.

**Michael Viriato** is an investment advisor and founding partner of **Investor’s House**

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I have over 8 years of experience in the news industry. I have worked for various news websites and have also written for a few news agencies. I mostly cover healthcare news, but I am also interested in other topics such as politics, business, and entertainment. In my free time, I enjoy writing fiction and spending time with my family and friends.