Interest rates should also be viewed in logarithmic charts.

ເຈົ້າໄປກັບໃພ Interest rates should also be viewed in logarithmic charts.

If you look at the 10-year U.S. interest rate, let's say you're going to go 10% from where you are now. If you go from 0.5% to 2%, you're going to go up four times, but even if you go up to 10% from where you are now, you're going to go up a little more. It's not going to go up that much.

I don't think it's going to go 10% and if it goes up a lot, it's 6.75%. It's going to go up roughly 50%. Then how much should we lower the bond price?

Someone who knows bonds well, please let me know.

"Gemini: Yes, it's often more appropriate to see interest rates as log charts. Log charts are especially useful when identifying long-term trends or comparing the past to the present. The reason is that, as you said, if interest rates rise from 0.5% to 2%, they will quadruple (300% higher), while if they rise from the current 4.5% level to 10% they will increase a little more than double (122% higher). In other words, log scales are appropriate to intuitively understand the rate of change in interest rates.
Let's assume that the current 10-year U.S. interest rate is around 4.5%, and calculate how much the bond price will fall when the rate rises to 6.75%. A rise in interest rates to 6.75% means a 2.25%p rise, or about 50%.
Bond prices move inversely to interest rates, so when interest rates rise, bond prices fall. However, the change in bond prices due to changes in interest rates is not just a 1:1 ratio. You have to consider the concept of duration of bonds. Duration is an indicator of the sensitivity of bond prices to changes in interest rates, and generally, the longer the maturity, the longer the duration. In other words, the longer the maturity, the more sensitive it is to changes in interest rates.
For simple calculations, a Modified Duration formula can be used. Modified Duration is used to estimate the rate of change in bond prices.
Bond Price Change Rate ≈ - (Amendment Duration) * (Rate Change)
Let's assume that the duration of the 10-year U.S. Treasury note is now about 7.5 years. (The actual duration is subject to market conditions.) And let's calculate the case where interest rates rise by 2.25%p from 4.5% to 6.75%.
First, you need to get a correction duration.
Correction duration = duration / (1 + (expired return / number of interest payments))
In general, U.S. government bonds pay interest twice a year. So the number of interest payments is two.
Correction Duration = 7.5 / (1 + (0.045 / 2) ≈ 7.33
You can now calculate the rate of change in bond prices.
Bond Price Change Rate ≈ - (7.33) * (0.0225) ≈ -0.165
In other words, a 2.25%p rise in interest rates is expected to reduce the price of the 10-year U.S. Treasury by about 16.5%.
In conclusion, if the U.S. 10-year interest rate rises by about 50% from 4.5% to 6.75%, the price of the 10-year U.S. Treasury is expected to fall by about 16.5%.
Precautions:
The above calculation is a simplified example, and actual bond price fluctuations may be affected by several factors.
The duration is subject to change depending on interest rates, maturity, interest rates, etc.
Bond investments always come with risks, and it is recommended that you consult an expert before investing.
I hope this answer was helpful, and if you have any further questions, please feel free to contact me." Gemini: Yes, it is often more appropriate to look at interest rates as a log chart. Log charts are especially useful when identifying long-term trends or comparing the past to the present. The reason is that, as you said, if interest rates rise from 0.5% to 2%, they will quadruple (up 300%), while if they rise from the current 4.5% level to 10%, they will increase a little more than double (up 122%). In other words, to intuitively understand the rate of change in interest rates, log scales are appropriate.

Let's assume that the current 10-year U.S. interest rate is around 4.5%, and calculate how much the bond price will fall when the rate rises to 6.75%. A rise in interest rates to 6.75% means a 2.25%p rise, or about 50%.

Bond prices move inversely to interest rates, so when interest rates rise, bond prices fall. However, the change in bond prices due to changes in interest rates is not just a 1:1 ratio. You have to consider the concept of duration of bonds. Duration is an indicator of the sensitivity of bond prices to changes in interest rates, and generally, the longer the maturity, the longer the duration. In other words, the longer the maturity, the more sensitive it is to changes in interest rates.

For simple calculations, a Modified Duration formula can be used. Modified Duration is used to estimate the rate of change in bond prices.

Bond Price Change Rate ≈ - (Amendment Duration) * (Rate Change)

Let's assume that the duration of the 10-year U.S. Treasury note is now about 7.5 years. (The actual duration is subject to market conditions.) And let's calculate the case where interest rates rise by 2.25%p from 4.5% to 6.75%.

First, you need to get a correction duration.

Correction duration = duration / (1 + (expired return / number of interest payments))

In general, U.S. government bonds pay interest twice a year. So the number of interest payments is two.

Correction Duration = 7.5 / (1 + (0.045 / 2) ≈ 7.33

You can now calculate the rate of change in bond prices.

Bond Price Change Rate ≈ - (7.33) * (0.0225) ≈ -0.165

In other words, a 2.25%p rise in interest rates is expected to reduce the price of the 10-year U.S. Treasury by about 16.5%.

In conclusion, if the U.S. 10-year interest rate rises by about 50% from 4.5% to 6.75%, the price of the 10-year U.S. Treasury is expected to fall by about 16.5%.

Precautions:

The above calculation is a simplified example, and actual bond price fluctuations may be affected by several factors.
The duration is subject to change depending on interest rates, maturity, interest rates, etc.
Bond investments always carry risks, investments