Why is it that the lower the coupon of a bond, the greater the price fluctuation caused by the same

Because the coupon rate of a bond is inversely proportional to the volatility of the bond** for a given yield to maturity, the lower the coupon rate, the greater the volatility of the bond**.

Bonds are issued by debtors such as enterprises and banks in accordance with legal procedures in order to raise funds and promise creditors to repay principal and interest on a specified date.

Bonds (bonds debenture) is a kind of financial contract, which is a creditor's rights and debt certificate issued to investors when financial institutions, industrial and commercial enterprises, etc. directly borrow funds from the society, and promise to pay interest at a certain interest rate and repay the principal according to the agreed conditions. The essence of a bond is a certificate of debt, which has the force of law. The bond purchaser or investor and the issuer are in a creditor-debt relationship, with the bond issuer being the debtor and the investor (bond buyer) being the creditor.

A bond is a valuable one**. Since the interest rate on a bond is usually determined in advance, a bond is a type of fixed interest rate (fixed rate). In countries and regions with developed financial markets, bonds can be listed and circulated.

In fact, this sentence needs to be changed, otherwise there will be a misunderstanding of the yield to maturity.

When changing to the same maturity time and yield to maturity, it is recommended that you refer to the entry in the encyclopedia in detail: "Duration, in fact, can be simply understood by the duration theorem as if the maturity time and yield to maturity are the same, the lower the coupon rate of the bond, the longer the duration (this can refer to the duration theorem 4 in the encyclopedia duration entry, but the complete statement of duration theorem 4 should also be that under the same conditions of maturity time and yield to maturity, the higher the coupon rate, the shorter the duration), Duration is an approximation of the change in units that reflect the yield to maturity of a bond, and the longer the duration, the greater the volatility caused by the same fluctuations in the time to maturity and the yield to maturity.

All other things being equal, the lower the coupon rate of the bond, the greater the volatility of the bond** and the expected yield.

For example, there are 5 types of bonds with a maturity of 20 years and a face value of $100. The only difference is the coupon rate, i.e. the coupon rate is 4%, 5%, 6%, 7% and 8% respectively.

If the expected yield of these bonds is 7%, the intrinsic value can be calculated separately. If the expected yield changes, the new intrinsic value of these five bonds can be calculated accordingly.

Under the same change in expected yield, the internal value of the five bonds with the lowest coupon rate fluctuates the most, regardless of whether it is related to the increase or decrease of the yield, and the change in the internal value of the five bonds gradually decreases as the coupon rate increases. Therefore, the lower the coupon rate of the bond, the more volatile the bond**.

The coupon rate and yield of bonds differ in three ways:

The overview of the two is different. Overview of bond coupon rate generally refers to the annual interest rate of a bond.

a percentage of the face value of the bond;

Bond yields.

Overview: refers to the ratio of the total income generated by investing in bonds to the total investment principal amount each year;

The two types are different.

Bond coupon rate type: It can be a fixed coupon rate, floating, that is, a fixed interest rate.

The decision is based on a reference rate, such as the Hong Kong Interbank Offered Rate or the London Interbank Offered Rate + Profit, or zero interest rate. In the case of foreign exchange** bonds, for example, the coupon rate is paid semi-annually.

The types of bond yields are:

Current yield. The current yield, also known as the direct yield, refers to the income generated by interest income. It is usually paid twice a year, which accounts for corporate bonds.

Most of the revenue generated. The current yield is the annual interest rate of the bond divided by the yield of the current market**. It does not take into account the capital gains or losses on bond investments, but only measures the ratio of the cash gains received by the bond over a certain period of time to the bond**;

Yield to maturity: The so-called yield to maturity refers to the income obtained from holding the bond to the repayment period, and the lease includes all interest on the maturity date. The yield to maturity, also known as the final yield, is the internal rate of return on an investment.

The purchase of government bonds, that is, the future cash flow obtained.

The present value of the investment is to buy U.S. Treasury bonds.

The discount rate is equal to the bond's current market**. It is equivalent to the average annual yield that an investor would receive by buying at the current market** and holding it to maturity.

No, the coupon rate of the bond is fixed and will not be less.

Bond** refers to the current market price of the bond, and the bond interest rate is fixed, that is, the interest is fixed!

Yield to maturity refers to the income earned by holding a bond until the maturity period, including the full interest at maturity.

Yield to maturity = [annual interest i + (value of income to maturity - market price) term n] [(m+v) 2] 100%.

m=face value; v = market price of bonds; i = annual interest income; n = holding period.

All other things being equal, bonds** fall and yields to maturity rise; Bonds** go up, yields to maturity go down, and vice versa!

In fact, it is the market price of bonds that affects the yield to maturity, and the market price of bonds is related to the interest rate of the market, the market interest rate is higher than the bond interest rate, the market price falls, the market interest rate is lower than the bond interest rate, and the market price rises!

Extended information: 1. There is only one basic and reliable way to price bonds, which is market pricing. Of course, the premise of market pricing is that bonds do have a trading market (only the secondary market is discussed here), that is, there is a certain amount of liquidity. Bonds issued by the same issuer, even if other characteristics are the same, will generate a relative premium or discount due to differences in liquidity.

For example, newly issued Treasury bonds have better liquidity than old Treasury bonds, so they are higher (i.e., lower yields), which is the liquidity premium. An important tool for bond pricing is the yield curve. Changes in the yield curve reflect changes in bonds of various maturities**.

2. What is the coupon rate How to calculate the coupon rate.

Coupon rate: Refers to the annual interest rate of a bond, which is equivalent to a percentage of the face value of the bond. Coupon rates can be fixed (i.e. the rate of interest is fixed over the life of the bond, as is the case with foreign exchange** bonds), variable (i.e. the rate is fixed at regular intervals based on a reference rate, such as the Hong Kong Interbank Offered Rate or the London Interbank Offered Rate plus a spread) or zero interest rate.

In the case of foreign exchange** bonds, for example, interest calculated at the coupon rate is paid semi-annually.

The coupon rate is the interest rate determined at the time of issuance of the bond, and the coupon is generally paid semi-annually. Refers to the annual interest rate that the bond issuer promises to pay to the bondholder on the face value of the bond.

The effective interest rate (yield) of a bond > the coupon rate (coupon rate), and the issuance of a bond** is below par value.

For example: the face value is 1000 yuan, the coupon rate is 5%, the effective interest rate is 6%, and the term is 1 year.

Issuance**=1000 (1+6%)+1000*5% (1+6%)=

No, it is paid at face value.

In many people's impressions, **of**, represents an increase in expected returns. Both are true, but bonds are the opposite. bonds****, their expected yield will be **, and vice versa.

So, why is that? Let's talk about it below, if you are interested, please see below.

Why is the expected yield decreasing?

First, we need to understand what the expected yield of a bond is. There are three major elements of a bond, which are the face value of the bond, the repayment period and the coupon rate (equivalent to the principal, investment period, and interest).

The face value of the bond is the face value of the bond**, which is generally 100 yuan. The repayment period is the amount of time during which the bond will repay the Principal Tour, and is generally used to calculate the number of interest payments. The coupon rate is used to calculate the interest income of bonds.

In many cases, the expected return of a bond is not only interest, but also the bid-ask spread. Many investors who buy bonds will not hold them forever and get back the principal and interest when they mature, but will get them to the bond market.

Buy and sell and earn the difference.

For example, if the face value of a bond is 100 yuan, assuming that the repayment period is 1 year and the coupon rate is 5%, then its original expected rate of return is 5 100 * 100% = 5%. If someone is in a hurry to realize, with 95 yuan of ****, when the investor buys a bond with a face value of 100 yuan at 95 yuan, after holding the maturity, the investor will earn interest and 5 yuan of differential income, at this time the expected yield of the bond is (5 + 5) 95 * 100% = Therefore, when the ** bond ** is higher, that is, the bond ****, since the maturity principal is fixed is 100 yuan, then the investor will have less income from the price difference, plus the fixed interest, the less its total expected return, The expected yield on bonds will decrease, and vice versa.

Summary. The reason is very simple, that is, there are more people who buy it, which leads to the **** of the bond, and the interest that needs to be paid on the bond has not increased, the principal of the investment has increased, the interest has not increased, and the yield has naturally declined.

Why a drop in bond yields causes bonds** to rise.

The reason is very simple, that is, there are more people who buy it, which leads to the **** of the bond, and the interest that needs to be paid on the bond has not increased, the principal of the investment has increased, the interest has not increased, and the yield has naturally declined.

What I asked was why there were still so many people buying sovereign bonds issued by the state when the yield was negative.

Okay, wait a minute.

And the more negative the yield, the more people buy.

In fact, I just want to buy low and sell high.

When the yield is negative, the buying price must be low, and then when the yield is high, you will make a profit.

Well, that makes sense.

Can you help explain the inverse relationship between bonds** and yields?

Have you read the above explanation?

Is there a formula for calculating bonds**?

Some. The issuance of bonds** is determined based on the face value of the bonds, the coupon rate, the market interest rate, and the maturity of the bonds. It is calculated as follows:

Bond issuance** = par value * compound cash value (market interest rate) + interest per period (par value * coupon rate) * annuity cash value (market interest rate).

After the issuance of the bond, the maturity date and interest rate of the bond have been determined, and the implied income of the bond listed on the trading market** is in proportion to the interest rate income of the bank deposited in the same amount of currency, so as to achieve the investment income in the market sense.

Balance. When the bank interest rate increases, the interest rate income of the same amount of currency deposit bank increases, and the interest rate of the bond cannot be increased flexibly, so it can only be a decline in the transaction, maintaining the implied income of the bond and the interest rate of the same amount of currency deposit bank in the original proportion, and maintaining the balance of investment income. And vice versa, when bank rates fall, bonds** rise.

After the issuance of the bond, the maturity date and interest rate of the bond have been determined, and the implied income of the bond listed in the trading market is in a certain proportion with the interest rate income of the same amount of currency deposited in the bank, so as to achieve a balance of investment income in the market sense.

When the bank interest rate increases, the interest rate income of the same amount of currency deposit bank increases, and the interest rate of the bond cannot also be flexibly increased, so it can only be a decline in the transaction, and the implied income of the bond is maintained in the original proportion with the interest rate income of the same amount of currency deposit bank, so as to maintain the balance of investment income. And vice versa, when bank rates fall, bonds** rise.