Lower interest rates lead to higher bond prices

“ Lower interest rates lead to higher bond prices ” It seems to be an iron law   A large number of materials found on the Internet all admit this conclusion by default . I'm very axial , I don't like passive acceptance , Even if it is true .

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Interest rates and money prices

The interest rate , This word can be called a pile of things , Including long-term interest rates 、 Short term interest rates 、 Nominal interest rate 、 Real interest rate and overnight lending rate, etc .

We don't bother with too complicated factors , Just assume that the interest rate is , And the interest rate cycle is . That is, the principal

After a cycle, it will increase in value to... According to the interest rate

If this is trading across a cycle , Is the lender who provides the principal , It is the borrower who returns the principal and interest , Then interest

On behalf of the use of these funds a cycle of “ The rent ”.

From this perspective , Interest represents the cost of using money . That is said , Interest rate is the price of money .

• about Fang said , Interest rate is the cost of using funds
• about Fang said , Interest rate is the expected return of funds

Abstraction of bonds

The next question to clarify is ,“ bond ” What is it? ？ We still use the simplest model to abstract it

It can be one cycle later , The issuer of a bond pays to the bondholder Voucher for yuan . It's that simple .

Contrast with the concept of interest rate , We can argue that Fang is the role of issuing bonds , and Fang is a bond holder .

The price of the bond

The price of bonds is naturally related to two factors ,

• One is face value , Value ;
• The second is the time limit , It's a cycle .

obviously , Because bonds represent future earnings , So it “ Now? ” The price is the holder of the bond How much do you think it's worth . So how much is it worth ？ Certainly .

When interest rates fall

We now assume that there are two interest rates and , And , Then we have this equation

obviously , There must be

such , So we get a set of inverse proportional relationships

The higher the interest rate , The lower the bond price ; The lower the interest rate , The higher the bond price .

So how to explain this phenomenon ？ I think we can think like this ：

• The lower the interest rate , Some money is still the money after a cycle , In fact, the current price of a long-term income is not much different from the value of the long-term income , So the price of the bond is about the same as its price ;

• When interest rates are high , We don't need a lot of money to invest now , You can get considerable profits in the long run , This means that the forward earnings are converted to the present , Actually, it's not worth much , Therefore, the price of the bond will be lower than its price , This leads to low bond prices .

Intermediate variable

therefore , We found that “ Lower interest rates lead to higher bond prices ” This thing is not inevitable , But there is an intermediate factor , This factor is actually

How easy it is for money to generate money in a cycle

• The easier money begets money , The less valuable the bonds are ;
• contrary , The harder money begets money , The more valuable the bond is .

Generally speaking , This factor is closely related to interest rates . But when the relationship between these two things is not so close , In fact, the interest rate has nothing to do with the bond price .