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yield to maturity
Yield to maturity (YTM) is the internal rate of return on investment in purchasing government bonds, that is, it can make the present value of future cash flow of investment in purchasing government bonds equal to the discount rate of the current market price of bonds. It is equivalent to the average annual rate of return that investors can get by buying at the current market price and holding it until maturity.
Y is yield to maturity.
situation
Assume that the coupon rate of the national debt due after 1 year is 3% and the face value is 100 yuan. The current price is 98 yuan (full price), and there is no interest before maturity. Due Japanese gold is paid together with the interest of the previous year. Yield to maturity's calculation is as follows: 98 = (100+3)/(L+Y), the solution is y, and yield to maturity's solution is 5. 102%.
Yield to maturity is the interest rate that makes the present value of debt instruments equal to the future present value, which needs to be considered: purchase price, redemption price, holding period, coupon rate and the length of interest payment interval. Yield to maturity assumes that the reinvestment rate of return is the same as that of yield to maturity.
Yield to maturity's calculation standard is the basis of bond market pricing, and establishing a unified and reasonable calculation standard is an important part of market infrastructure construction. To calculate the yield to maturity, it is necessary to determine the days of accrued interest and the days of interest payment cycle during the bond holding period. From the perspective of the international financial market, three standards are generally used to calculate the days of accrued interest and the days of interest payment cycle: actual days/actual days, actual days /365 and 30/360. Among them, the "actual days/actual days" method, which calculates the accrued interest days according to the actual days of the bond holding period, has the highest accuracy. Many countries that adopt the method of "actual days /365" begin to use the method of "actual days/actual days" to calculate the bond yield to maturity. China inter-bank bond market has always adopted the calculation method of "actual days /365" since 200 1 adopted yield to maturity to calculate bond returns. With the continuous enrichment of bond products and the increasing trading volume in the inter-bank bond market, market members have higher and higher requirements for the accuracy of yield to maturity calculation. Therefore, the People's Bank of China decided to adjust the yield to maturity calculation standard of the inter-bank bond market to "actual days/actual days". The adjusted yield to maturity calculation standard is applicable to the issuance, custody, trading, settlement and payment of all inter-bank bond markets in China.
skill
The People's Bank of China issued a notice specifically for the inter-bank market, and published a unified bond yield formula. In the Notice, the calculation method of national debt yield to maturity is given according to three situations.
1. For interest-bearing bonds (including fixed-rate bonds and floating-rate bills), discount bonds and one-time debt service bonds with a remaining circulation period of less than one year (including one year), yield to maturity adopts simple interest. The calculation formula is:
In which: y is yield to maturity;
PV is the full price of the bond (including the transaction price and accrued interest, the same below);
D is the actual number of days from the bond delivery date to the bond redemption date;
FV is the sum of the due principal and interest, in which, the discount bond FV= 100, the one-time due principal and interest bond FV=M+N×C, and the interest-bearing bond Fv = m+c/f;
M is the face value of the bond;
N is the bond repayment period (year);
C is the annual interest of the bond;
F is the annual interest rate of the bond.
2. The yield to maturity of the one-time debt service bonds with the remaining circulation period of more than one year shall be calculated according to compound interest. The calculation formula is:
In which: y is yield to maturity;
PV is the full price of the bond;
C is the annual interest of the bond;
N is the bond repayment period (year);
M is the face value of the bond;
L is the remaining circulation period of bonds (years), which is equal to the actual number of days from the delivery date to the maturity date of bonds divided by 365.
For example, for bonds due after 1.5 years, interest is calculated once every six months, but interest is not paid. The annual interest rate is 5%, and the principal and interest are repaid at maturity, with a face value of 100 yuan. Full price 97 yuan now. Yield to maturity is 7.09%.
3. The yield to maturity in fixed-rate interest-bearing bonds and floating-rate bills that are not in the final interest-paying cycle shall be calculated according to compound interest. The calculation formula is:
In which: y is yield to maturity;
PV is the full price of the bond;
F is the annual interest-paying frequency of bonds;
w = D/(365÷f)；
M is the face value of the bond;
D is the actual number of days from the bond delivery date to the next interest payment date;
N is the number of remaining interest payments and n- 1 is the number of remaining interest payments;
C is the annual coupon interest of this bond. When calculating the rate of return of floating rate bills and floating rate bills, yield to maturity calculates according to the current income, and pays more attention to the reflection of the spot income level. In each period, the formula needs to be adjusted according to the change of parameter C.
The bond price in the market is often inconsistent with the face value. When calculating bond yield to maturity, both coupon rate and bond price will be considered. If the bond price is equal to the face value, yield to maturity is equal to coupon rate. If the bond price is higher (lower) than the face value, yield to maturity is lower (higher) than coupon rate.
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Spot interest rate
Spot interest rate refers to the interest rate indicated on the face of the bond or the ratio of the discounted income obtained when buying the bond to the current price of the bond. It is an interest-free security in yield to maturity at a specific point in time.
There are two basic types of bonds: interest-bearing bonds and interest-free bonds. When buying interest-bearing bonds issued by the government, bondholders can get a one-time repayment of principal and interest from the government after the bond expires. The ratio of one-time income to principal is the spot interest rate. Investors can buy interest-free bonds issued by the government at a price below the face value. After the bond expires, the bondholder can get a one-time payment according to the face value. The ratio of the discount of the purchase price to the face value is the spot interest rate.
T-year spot interest rate calculation formula:
Pt is the current market price of T-year interest-free bonds, Mt is the maturity value, and st is the T-year spot interest rate.
For example, the price of a three-year 1 zero coupon ticket is 97 yuan. So what is the spot rate of return for three years?
S3 is obtained, and the spot yield is 1.0 1%.
Considering the change of interest rate with the length of the term, people have adopted such a method, that is, discounting cash flows with different terms with different interest rates. This interest rate that changes with the term is the interest rate. The spot interest rate changes with the term, forming a mathematical curve with continuous fluctuation, which is called YieldCurve.
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forward (exchange) rate
Forward interest rate refers to the interest rate implied in a given spot interest rate from one point to another in the future.
If we have determined the yield curve, then all forward interest rates can be obtained according to the spot interest rate on the yield curve. Therefore, the forward interest rate is not an independent set of interest rates, but closely linked to the yield curve. In mature markets, some forward interest rates can also be directly observed from the market, that is, calculated according to the market price of interest rate forward or futures contracts.
Forward interest rates can be classified as follows:
(1) 1×2 forward interest rate, that is, the forward interest rate with a term of 1 month from 1 month.
(2)2×4 forward interest rate, that is, the forward interest rate with a term of 2 months after 2 months.
situation
Calculate forward interest rate.
In 20 19, the one-year interest rate of bank deposits in China was 4. 14%, the two-year interest rate was 4.68%, and the sum of principal and interest of 10000 yuan a year was10000× (1+0.046538). Deposit for two years is10000× (1+0.0468× 2) =10936 yuan. If the interest rate in the first year should be 4. 14, then the interest rate in the second year is: (10936- 14.
If investors choose not to save for two years, they will directly save for one year and then continue to save for another year. If the annual interest rate in the second year is lower than 5.0 125%, the accumulated income of investors will be lower than that of saving for two years.
Forward interest rate is difficult to observe directly, but it does affect investors' rate of return. In the financial market, there are interest rate futures (such as Eurodollar futures) and forward interest rate agreements, which can hedge forward interest rate risks.
skill
1. Functions of Forward Interest Rate Agreement (FRA)
Forward interest rate agreement is a kind of forward contract. The buyer and the seller (between the customer and the bank or between two banks) agree on the agreed interest rate for a certain period from a certain point in the future (referring to the value date), and specify which interest rate to use as the reference interest rate. On the future value date, one party will pay the other party the discount of the interest difference between the agreed interest rate and the reference interest rate according to the agreed interest rate, term and principal amount.
According to this agreement, both parties agree to borrow a nominal principal with a fixed interest rate and a fixed amount in a specific currency for a specific period from a certain date in the future. The buyer of the forward interest rate agreement is the nominal borrower. If the market interest rate rises, he will pay interest according to the interest rate determined in the agreement, thus avoiding interest rate risk. However, if the market interest rate falls, he still has to pay interest at the agreed interest rate and will suffer losses. The seller of the forward interest rate agreement is a nominal lender, and interests are charged according to the interest rate determined in the agreement. Obviously, if the market interest rate drops, he will benefit; If the market interest rate goes up, he will suffer.
The role of 2.2. The Federal Railroad Administration.
The role of FRA is to avoid the risk of interest rate changes by fixing the actual interest rate to be delivered in the future.
Interest rates are settled by spreads, and the capital flow momentum is small, which provides an effective tool for banks to manage interest rate risks without changing the structure of assets and liabilities.
Forward interest rate agreement has the advantages of simplicity, flexibility and no need to pay margin.
3. General terms and conditions of forward interest rate agreement
Contract amount-the nominal principal amount of the loan.
Contract currency-currency currency.
Trading day-the date when the forward interest rate agreement is reached.
Settlement date-the date when the nominal loan starts.
Determine Date-The date when the reference interest rate is determined.
Expiration date-the date when the contract ends.
Contract term-the number of days from the settlement date to the expiration date.
Contract interest rate-the interest rate agreed by both parties in the agreement.
Reference interest rate-some market interest rates.
4.4 Price and quotation. The Federal Railroad Administration.
The price of FRA refers to the agreed interest rate within a certain period from the interest date. The quotation method of FRA is similar to the expression method of money market loan interest rate, but the FRA quotation stipulates the interest rate term more in the contract. The specific FRA market can be obtained through the FRAT screen of Reuters terminal. The FRA market pricing changes with the market changes every day, and the actual transaction price is determined by each quotation bank.
5. Use FRA's risk management skills
FRA is a financial tool to prevent the risk of future interest rate changes, which is characterized by locking the future interest rate in advance. In the FRA market, the buyers of FRA hope to lock in the future financing costs now to prevent the risk of rising financing costs caused by rising interest rates. Using FRA to prevent the risk of future interest rate changes is essentially to offset the risk of spot capital market with the profit and loss of FRA market, so FRA has the function of determining financing cost or investment return in advance.
6.6 the connection and difference between. FRA and interest rate futures.
Formally, FRA and interest rate futures have similar advantages, that is, they avoid the risk of interest rate changes, but there are also differences between them, which are summarized in the following table.
Comparison of advantages between on-balance-sheet forward interest rate agreement and interest rate futures
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What is the relationship between interest rates and bonds?
Generally speaking, bond and market interest rates change in the opposite direction, that is, interest rates rise and bond prices fall; On the contrary, bond prices will rise. This reverse change makes the bond price clearly reflect the change of market interest rate. As the carrier of market interest rate, bond price can reflect the change of market interest rate in time and effectively.