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Chapter 13 Interest Rate: The Financial Magic Wand That Turns All Beings Upside Down (2)
Dawei bought a lottery ticket and won a first prize of 2000 million yuan.Organizers promised that he would receive 20 million yuan a year for the next 100 years.Dawei was very excited.But did he really get 2000 million yuan?From a present value point of view, poor Dawei was fooled by the organizers.Assuming that the interest rate is 10%, the first payment of 1 million yuan is obviously equal to today’s 100 million yuan, but the second year’s payment of 100 million US dollars is measured by today’s value, only 100 million / (100+1) = 0.10 yuan , far less than 909090 million yuan.Subsequent payments will be even less. Adding up these present values, it is actually only 100 million yuan. This figure is far from the promised 940 million yuan, and it is less than half.But most people who don't understand the concept of present value will undoubtedly be as excited as David.

Therefore, it is very necessary to understand the concept of present value for the measurement of interest rate.If you don't understand the price of money, how can you trade money?
There are usually several ways to calculate interest rates, and the present value is the simplest way.The most important of these is the yield to maturity.Because the yield to maturity reflects significant economic meaning, economists believe that it is the most accurate measure of interest rates.

The so-called income at maturity refers to the income obtained by holding the bond until the repayment period, including all interest on maturity.The yield to maturity, also known as the final rate of return, is the internal rate of return for investing in treasury bonds, that is, the discount rate that makes the present value of the future cash flow obtained by investing in treasury bonds equal to the current market price of bonds.It is equivalent to the average annual rate of return that investors can obtain by purchasing at the current market price and holding it until maturity.

The formula for calculating the yield to maturity is:
Yield to maturity = [I×100+(MV)/N]/ [(M+V)/2]×100%

M=face value; V=market price of bonds; I=annual interest income; N=holding period
假设某债券为10年期，8%利率，面值1 000元，贴现价为877.60元。计算为 [80+(1000-877.60)/10] / [(1000+877.60)/2] ]×100％ =9.8%。

The yield-to-maturity calculation standard is the basis for bond market pricing, and the establishment of a unified and reasonable calculation standard is an important part of market infrastructure construction.To calculate the yield to maturity, it is first necessary to determine the days of accrued interest and the number of days of the interest payment cycle during the bond holding period. From the perspective of the international financial market, the calculation of the number of days of accrued interest and the number of days of the interest payment cycle generally adopts the "actual number of days/actual number of days" method, "Actual days/365" method, "30/360" method and other three standards, in which the accrued interest days are calculated according to the actual days of the bond holding period, and the interest payment cycle is calculated according to the actual days "actual days/actual days" method highest accuracy.In recent years, many countries that use the "actual days/365" method have begun to use the "actual days/actual days" method to calculate bond yields to maturity.

Equilibrium Interest Rates: How to Match Money Supply and Demand

Jiang Chao, a well-known financial columnist, once wrote in an analysis article on the global bond market in 09:

In fact, long-term inflation expectations in the United States have remained stable at 10% for nearly a decade.Based on stable long-term inflation and economic growth, we believe that there is a long-term equilibrium level of long-term bond interest rates. Taking the United States as an example, the equilibrium real interest rate is 2.5%, and long-term inflation is 2%. Therefore, the equilibrium level of long-term bond interest rates is 2.5%. China's long-term inflation is 4.5%, the equilibrium real interest rate should not be lower than that of the United States, and the equilibrium interest rate of 2-year long-term bonds should be above 10%.

央行主导下的短债利率波动改变的是长债利率的阶段均衡水平。以中国为例，假定央行维持2年的低利率环境，则10年期金融债的阶段均衡利率应为3.4％。即当前配置2年期1％利率短债并在未来配置4%利率的8年期长债的组合与直接购入3.4%的10年期长债回报相当。

The "equilibrium interest rate" is mentioned many times in this small text, which seems a bit difficult to understand.What is the "Equilibrium Interest Rate"?What's so special about it?
Equilibrium interest rate refers to the interest rate when the money supply and money demand in the currency circulation are kept in line.It corresponds to the specific interest rate of each bank for different situations.

And its special feature is that the factors that affect the change of interest rate are mainly reflected by the equilibrium interest rate.For example: the impact of expectations on future interest rates on interest rates.If people expect interest rates to rise in the next year, the suppliers of funds will not buy long-term bonds, but choose short-term investments, so that they can withdraw funds in time for more profitable investments when interest rates rise.In this way, the capital supply curve of long-term bonds will shift to the left, and the equilibrium interest rate will rise.Conversely, the expected decline in future interest rates means that long-term bonds become a more favorable investment, thereby increasing the demand for long-term bonds and increasing the supply of funds at various interest rate levels.This shifts the money supply curve for long-term bonds to the right and lowers the equilibrium interest rate.

How is the money market equilibrium achieved?
1. The realization of monetary equilibrium under market economy conditions depends on three conditions, namely a sound interest rate mechanism, a developed financial market and an effective central bank regulation mechanism. 2. Under the conditions of a complete market economy, the most important mechanism for realizing monetary equilibrium is the interest rate mechanism.In addition to the interest rate mechanism, there are four other factors: ① the central bank's control means; ② the state's fiscal revenue and expenditure; ③ whether the structure of the production sector is reasonable; ④ whether the international balance of payments is basically balanced. 3. Under the condition of market economy, the interest rate is not only an important signal of whether the money supply and demand are balanced, but also has an obvious regulating function on the money supply and demand.Therefore, monetary equilibrium can be achieved through the action of the interest rate mechanism.

As far as the money supply is concerned, when the market interest rate rises, on the one hand, the public will reduce cash withdrawals due to the increase in the opportunity cost of holding money, which will reduce the cash ratio, increase the money multiplier, and increase the money supply; on the other hand, Banks reduce their excess reserves to expand their loan scale due to the increase in loan income, which reduces the excess reserve ratio, increases the money multiplier, and increases the money supply.Therefore, there is a relationship between interest rate and money supply in the same direction.As far as money demand is concerned, when the market interest rate rises, people's opportunity cost of holding money will increase, which will inevitably lead to an increase in people's demand for financial interest-earning assets and a decrease in people's demand for money.Therefore, there is an inverse relationship between the interest rate and the demand for money.When there is an equilibrium interest rate level in the money market, money supply and money demand are equal, and the state of monetary equilibrium is achieved.When the market equilibrium interest rate changes, the money supply and money demand will also change accordingly, and finally a new monetary equilibrium will be achieved on the new equilibrium amount of money.

Interest Rate Fluctuations: Risk to Currency Prices
A piece of news about the bond market can help us understand the impact of interest rate fluctuations on financial markets:
Nov 2006, 11 (Reuters) - Mortgage-backed bonds (MBS) sold by companies including Fannie Mae and Freddie Mac rose this week, buoyed by strong overseas demand and volatile interest rates The drop also supported bond prices.

The spread over 5.5-year U.S. Treasuries narrowed about 10 basis points to 3 percentage points.

Analysts believe that the range-bound 10-year Treasury yield (yield rate) can prevent unexpected increases or decreases in mortgage refinancing activity, thus supporting MBS.

Rising overseas demand has been supporting MBS this week, according to traders.

房利美发行的票面利率为5.5%的MBS价格上涨11/32，至99 4/32，收益率报5.669%.10年期美国公债价格攀升17/32，收益率报4.61%。

As the year draws to a close, MBS traders and analysts are keeping a close eye on big investment banks including Goldman Sachs and Bear Stearns, noting the number of MBS held by the banks is at a more than three-year high.

(News excerpted from Financial Star Network)

Large fluctuations in interest rates will affect asset markets, especially capital markets, making them vulnerable to relatively small-scale international capital flows, and even market manipulation. From 1997 to 1998, Hong Kong's stock futures and foreign exchange markets were manipulated across markets, forcing the Hong Kong government to intervene in the stock market on a large scale, and took measures to allow banks to obtain liquidity through the discount window with exchange fund bills and bonds as collateral.The seven technical measures launched by the Hong Kong Monetary Authority in 1998 and the three optimization measures in 7 are all aimed at curbing interest rate fluctuations while maintaining the stability of the exchange rate.

Therefore, banks and capital markets must pay attention to avoiding interest rate risks.

Clear and limited exchange rate flexibility can help reduce interest rate volatility.Unlike the case where the exchange rate is only fixed at one point, under a flexible exchange rate regime, capital inflows or outflows do not immediately cause interbank fluctuations.Managing interest rate and other risks is part of a bank's day-to-day operations.Depending on the interest rate risk profile of individual banks, such as the degree to which they are net lenders or net borrowers in the interbank market, their profitability will be affected to varying degrees.Some banks may change their business strategies to reduce the impact of interbank fluctuations on them.What is more concerning is that if the interest rate gap at the wholesale level is transferred to the retail level, both depositors and borrowers will be affected. I am afraid that they may not be as good at managing interest rate risk as banks.

The banking industry is highly competitive and it is understandable that banks may pass the risk on to customers when managing interest rate risk.Banks may also use different pricing strategies to protect profitability.This just reflects the power of the free market, but we cannot ignore the possible negative impact of banks' actions on the public, because they may not be as good at identifying, assessing and managing interest rate risks as banks.

The Fisher Effect: Expected Inflation and Interest Rates
If the interest rate on bank deposits is 5%, and someone’s savings will increase by 5% after one year, does it mean that he is rich?This is just an assumption in an ideal situation.If the inflation rate was 3%, he would only be rich by 2%; if it was 6%, the things he could buy with 100 yuan a year ago would cost 106 now, and the money he saved for a year would only be 105 yuan No, he can't afford this thing anymore!

This can be said to be a popular explanation for the Fisher effect.The Fisher effect was the first discovery by the famous economist Irving Fisher to reveal the relationship between inflation rate expectations and interest rates. It pointed out that when inflation rate expectations rise, interest rates will also rise.

Expressed in a formula, it is: real interest rate = nominal interest rate - inflation rate.

Swap the left and right sides of the formula, and the formula becomes: nominal interest rate = real interest rate + inflation rate

(End of this chapter)