[Quantitative Course] 02_2. Basic Concepts of Monetary Finance

2.2_Basic Concepts of Monetary Finance

overview

1. Financial market : A market in which funds are transferred from surplus to deficit. Both the supply and demand sides of funds conduct financial intermediation through the financial market to achieve effective allocation of financial resources and improve economic efficiency.
2. Bond Market : One of the major financial markets.
   1. Meaning: A place where bonds are issued and traded.
   2. A bond is an "IOU for borrowing money," in which the borrower promises to make regular cash payments in the future. The interest rate is the cost paid (the cost of debt) or the price paid (usually expressed as a ratio of interest to principal over a period of time) to borrow money.
3. **Stock Market:** One of the major financial markets.
   1. Meaning: the place where issued stocks are traded, transferred and circulated.
   2. Stocks are "certificates of ownership". Holders of stocks have the right to claim certain company income and assets, which is equivalent to owning a part of the company.
4. Money and Inflation
   1. Money: An item generally accepted in economic activities such as making payments or paying off debts.
   2. Inflation: refers to the continuous increase in the price level (the average price of goods and services in an economy), which can be measured by indicators such as CPI and PPI.
5. Monetary Policy and Fiscal Policy
   1. Currencies can have an impact on many vital economic variables.
   2. Monetary policy is the policy that a country's central bank (in the US, the Federal Reserve) uses to manage that country's currency and interest rates.
   3. Fiscal policy refers to government spending and tax revenue decisions. According to the relationship between expenditure and income, there are three situations in a country's fiscal operation: budget deficit (expenditure > income), budget surplus (expenditure < income) and budget balance (expenditure = income).
6. Foreign exchange market
   1. It is a place where currencies of various countries are exchanged. In order to transfer funds across borders, the domestic currency and foreign currency must be exchanged in the foreign exchange market.
   2. An exchange rate is the price of one currency expressed in another currency. When reporting the exchange rate, it is usually calculated by how much the foreign currency is converted into the local currency. For example, the onshore renminbi is quoted at 7.2525, which means that 1 U.S. dollar is exchanged for 7.2525 yuan. An increase in the value indicates a depreciation of the RMB.

financial system

1. **Financial Markets:** Shift funds from surplus to deficit.
2. direct financing and indirect financing
   1. Direct financing: The borrower directly sells securities (such as stocks) to the lender in the financial market to obtain funds directly.
   2. Indirect financing: the presence of financial intermediaries (such as banks). Intermediaries make loans to borrowers and borrow funds from lenders.
3. Structure of Financial Markets
   1. Divided by the way of raising funds: bond market and stock market.
   2. Divided by hierarchy: primary market and secondary market.
      • Primary Market: The issuance market or primary market. A market that forms when borrowers sell securities for the first time.
      • Secondary market: securities circulation market or secondary market. It is a market for buying, selling, transferring and circulating issued securities.
   3. Divided by the maturity of the securities traded: money market (trading short-term debt instruments maturing in one year) and capital market (trading long-term debt instruments maturing in one year)
4. financial market instruments
   1. Money market instruments: Less than one year to maturity, lower risk (such as short-term treasury bonds).
   2. Capital market instruments: more than one year away from maturity, with high risk (such as stocks, corporate bonds).
5. financial intermediaries
   1. Divided into: depository institutions (commercial banks, etc.), contract savings institutions (insurance companies, etc.), and investment intermediaries (mutual funds, etc.)
   2. Function: reduce transaction costs; share risks; reduce information asymmetry (will be discussed later).

currency

1. **Currency:** An item generally accepted in economic activities such as payment or debt repayment
2. function of money
   1. Medium of exchange: Refers to money that can be used to purchase products or services.
   2. Unit of Account: A currency that can be used to measure the value of a good or service.
   3. Store of value: It can store value and convert it into purchasing power in the future (that is, you can make money now and spend it later).
3. measurement of money
   1. M0: Cash in circulation
   2. M1: M0+corporate futures deposits+organizational deposits+rural deposits+personal credit card deposits
   3. M2: M1+ savings deposits of urban and rural residents + corporate time deposits + foreign currency deposits + trust deposits
   4. M3: M2+financial bond+commercial paper+CDs, etc.
   5. From M0 -> M3, the liquidity becomes worse and worse. M1 is narrow money and M2 is broad money. It can be understood that M1 is a property that is relatively common in life and can be used for payment almost immediately.

interest rate

1. Present value

   1. That is, how much a future income is worth today. Expressed in PV.

   2. The calculation formula is: $$PV=\frac{CF}{(1+i{)}^n}$$

   3. Among them: CF is the future cash flow (of the nth period), i is the interest rate (discount rate) used for discounting, and n is the time span of discounting.

   4. Explanation: How much a certain income in the future is worth today can be understood from another perspective: how much money needs to be invested today to generate that income in the future. Therefore, the money invested today is PV (that is, the present value), multiplied by the income that can be generated in n years KaTeX parse error: Expected group after '^' at position 6: (1+i)^̲ , which is equal to the future income CF . The formula can be obtained by shifting terms.

2. credit market instruments
   1. Ordinary loan: A loan that repays the principal and pays additional interest to the lender when it matures.
   2. Fixed payment loan: A loan in which the borrower repays a fixed amount (principal and interest) every period (such as every month) over a certain period of time. (It can be understood as: paying interest while repaying the loan)
   3. Coupon bond: A bond that pays the holder a fixed interest rate each year and repays the principal at maturity. (It can be understood as only paying interest, and finally repaying the loan)
   4. Discount bond (zero-coupon bond): A bond whose purchase price is lower than the face value and which is repaid at face value at maturity. (It can be understood that no interest is paid, and the loan is finally repaid)
   5. Perpetual bond: a bond with no maturity date, no requirement for principal repayment, and a fixed amount of interest paid by the borrower indefinitely. (It can be understood as paying interest all the time, but not necessarily repaying the loan)
3. Yield to maturity
   1. Meaning: The rate of return that can be obtained by purchasing a bond at a specific price and holding it until maturity.
   2. In essence, it is an interest rate that requires that the present value of future income obtained when discounted at this rate is equal to the current purchase price of the bond.
4. Calculation of Yield to Maturity (i stands for Yield to Maturity)

   1. 

   2. Note: For the calculation of the yield to maturity, it is necessary to solve the i in the above equation to obtain.

   3. explain:

      • From the above explanation of the present value calculation, the explanation of the yield to maturity can be extended. In the calculation of yield to maturity, we are equivalent to knowing the future cash flow CF and the current value PV, and we need to calculate an equivalent discount rate i (ie, yield to maturity) to match CF and PV. In the calculation, cash flows are generated in different periods, so they need to be discounted in turn and summed.
      • Perpetual bonds are special: if the principal is not repaid, the discounted future cash flow in the equation is an infinite geometric series. The above calculation formula can be obtained by using a certain mathematical transformation.
5. Nominal vs. Real Interest Rates
   1. Nominal interest rate is the interest rate announced by the central bank and not adjusted for inflation.
   2. The real interest rate is the rate adjusted for expected changes in the price level (inflation). Reflects the true cost of borrowing funds.
   3. Even if nominal interest rates are high, real interest rates can be low if inflation is high. For example, if the rate at which bonds generate income cannot keep up with the rate at which the price level rises, then the real interest rate is negative, and saving money means losing money.
   4. Fisher's theorem: The nominal interest rate is equal to the sum of the real interest rate and the expected inflation rate.

Risk Structure and Term Structure of Interest Rate

1. Interest Rate Risk Structure
   1. Default Risk: The risk that a borrower will not be able to make interest or principal payments. Treasury bonds are generally considered to have no default risk.
   2. Risk premium: The difference in interest rates between a bond with the same maturity and a bond with no risk of default. That is to say, in order for the lender to be willing to bear the risk that the principal or interest will not be recovered, under the same period of time, bonds with default risks need to provide higher yields.
   3. The risk premium for bonds with a default risk is always positive; and the risk premium increases as the default risk rises.
   4. Liquidity: Refers to the ability to quickly convert into cash at a relatively low cost. Bonds that are less liquid are less likely to be liquidated and therefore less popular. This requires less liquid bonds to offer higher yields (similar to risk premiums), resulting in a spread called a liquidity premium.
   5. Income tax factors: bonds with higher tax rates generally have higher pre-tax interest rates; bonds with tax incentives generally have relatively lower interest rates.
2. The Term Structure of Interest Rates and the Yield Curve
   1. Term structure of interest rates: refers to the relationship between the interest rates of various bonds with the same other characteristics but different maturities
   2. Yield curve: A curve formed by connecting the yields of bonds with different maturities but the same attribute category. (upward sloping: long-term rates are higher than short-term rates; flat: both are equal; downward sloping: long-term rates are lower than short-term rates)
   3. Empirical facts about the term structure of interest rates:
      • Interest rates on bonds of different maturities change over time
      • The yield curve is more likely to slope upward when short-term interest rates are low;
      • Yield curves generally slope upward (short-term rates are generally lower than long-term rates).

money supply process

1. Money supply : refers to the process by which a country's banking system invests, creates, and expands (shrinks) money into the economy
2. Money supply : the sum of the currency (currency in circulation) held by enterprises other than banks, individuals, foreign countries, and other deposit currencies that can be withdrawn at any time. That is $$M=C+$$ , where M represents the money supply, C represents the currency in circulation, and D represents deposits.
3. Three Participants in the Money Supply Process
   1. Central Bank: Oversees the banking system and is responsible for implementing monetary policy
   2. Bank (depository institution): acts as a financial intermediary, accepts deposits and makes loans
   3. depositor
4. Reserve : The cash in the commercial bank's inventory (from deposits, etc.) is deposited in the central bank at a ratio (not less than the statutory reserve ratio).
   1. Reserves are kept by the bank to ensure that the bank has sufficient solvency when encountering a large amount of short-term withdrawal of bank deposits.
5. Assets and Liabilities of Central Banks and Commercial Banks
   1. commercial Bank:
      • Assets include: reserves, loans, government securities
      • Liabilities include: bank deposits, discounted loans, capital (i.e. bank capital)
   2. central bank:
      • Assets include: government securities, discounted loans
      • Liabilities include: cash in circulation, reserves
   3. explain:
      • About the cash in circulation: it is the amount of currency held by the public, which is equivalent to the IOU issued by the central bank to the holder.
      • Reserves are deposits and cash held by commercial banks at the central bank.
6. Base currency : the sum of cash in circulation (C) and total reserves (R), ie $$MB=C+$$
7. Open market operation : refers to the means by which the central bank buys and sells secondary market bonds in the open market to increase or decrease the money supply. It is one of the main ways for the central bank to control the base currency.
   1. Such as: open market purchase: central bank purchases bonds -> inputs reserves to the banking system -> base money increases
8. Loans to financial institutions : The central bank provides loans to financial institutions in the form of discounted loans, which is also one of the main ways to control the base currency.
   1. For example: lower rediscount rate -> increase in loans -> increase in reserves -> increase in base money
9. multiple deposit creation
   1. It means that the increase of reserves in the banking system will lead to a multiple increase in deposits.
   2. Example: A bank obtains a deposit of 100 yuan, reserves 10 yuan (statutory) and then uses 90 yuan to lend; 90 yuan for lending flows into another bank through various channels, and the other bank leaves 9 yuan as a statutory reserve Use 81 yuan to lend, and so on. Finally, deposits in the entire banking system will increase by 1,000 yuan.
   3. The simple deposit multiplier is the multiple of the deposit increase relative to the initial deposit under the above circumstances, and is the reciprocal of the statutory deposit reserve ratio.
   4. The above is an ideal state: in fact, the public chooses to hold cash, which will stop the creation of deposits; and banks will choose to keep a certain amount of excess reserves.
10. determinants of the money supply
    1. Participants: Central Bank
       • Non-borrowed base money (base money minus reserves borrowed by commercial banks): Positively related to money supply.
         • Such as: open market purchases -> non-borrowed base money rises -> base money and reserves increase -> monetary expansion
       • Required Reserve Ratio: Negatively Correlated with Money Supply
         • Such as: reduction of statutory reserve ratio -> increase of simple deposit multiplier -> expansion of money supply
    2. Participants: Banks
       • Reserves to borrow: positively related to the money supply
       • Excess reserves: Negatively related to the money supply
         • Such as: increase in excess reserves -> decrease in loans -> contraction of money supply
    3. Participants: depositors
       • Cash holdings: Negatively related to money supply
         • Such as: increase in cash holdings -> weakening of multiple expansion capabilities -> contraction of money supply
11. money multiplier
    1. Indicates the proportion of changes in the money supply caused by changes in the base currency. Expressed with m.
    2. Relationship with base money and money supply: $$M=m\ast MB$$
    3. calculate:
       • KaTeX parse error: Unexpected end of input in a macro argument, expected '}' at end of input: …rac{1+c}{rr+e+c
       • Among them, c represents the currency deposit ratio (C/D) determined by the willingness of depositors to hold cash, e represents the excess reserve ratio (ER/D) determined by the bank, and the statutory deposit reserve ratio determined by the central bank ( rr).

Chinese Monetary Policy Tools

Some of the main tools:

1. Repurchases (open market operations):
   1. Positive repurchase, that is, the People's Bank of China sells securities to the market and agrees to buy back the securities on a certain date in the future. During the positive repurchase, the central bank withdraws liquidity from the market and releases liquidity to the market when it expires. A reverse repo is the opposite.
2. Reserve ratio:
   1. Adjust the statutory deposit reserve ratio:
      1. The money supply can be affected by affecting the money multiplier.
      2. Comprehensive RRR cuts and targeted RRR cuts (large financial institutions and small and medium-sized financial institutions have different deposit reserve ratios)
   2. Adjust the excess deposit reserve interest rate:
      1. Affect the income of banks holding excess reserves, affect the ratio of excess reserves, and thus affect the money multiplier.
3. Interest Rate Policy:
   1. By affecting the benchmark interest rate, it will affect the savings rate of residents in commercial banks and the quoted interest rate of the loan market.

monetary policy effect

1. Linkages between central bank instruments, policy instruments, intermediary indicators, and monetary policy objectives
   1. Central bank tools: open market operations, discount policy, statutory reserve ratio, reserve interest, large-scale asset purchases...
   2. Policy instruments: total reserves (reserves, non-borrowed reserves, base money, non-borrowed base money), interest rates (short-term interest rates, etc.)
   3. Intermediate indicators: monetary aggregates (M1/M2), interest rates (short and long term)
   4. Goals: price stability, high employment, economic growth, financial market stability, interest rate stability, foreign exchange market stability
2. Taylor rule : refers to the method by which the central bank's short-term interest rate tools are adjusted according to the state of the economy (taking the Federal Reserve as an example)
   1. Fed funds rate indicator = inflation rate + equilibrium real federal funds rate + KaTeX parse error: Unexpected end of input in a macro argument, expected '}' at end of input: \frac1 inflation gap + KaTeX parse error: Unexpected end of input in a macro argument, expected '}' at end of input: \frac1 output gap
   • Inflation Gap: Current Inflation Rate - Target Inflation Rate
   • Output Gap: Real GDP Growth - GDP Growth at Potential (Natural) Level
   2. Implications: The nominal interest rate should follow changes in the inflation rate and be adjusted according to the gap between output and inflation in order to keep the real interest rate stable.

Quantity Theory of Money, Inflation and Money Demand

1. Quantity Theory of Money
   1. Assuming that other factors remain unchanged, commodity price fluctuations are directly proportional to the amount of money, and the value of money is inversely proportional to the amount of money.
2. velocity of money
   1. Transaction speed KaTeX parse error: Unexpected end of input in a macro argument, expected '}' at end of input: …=\frac{(P*Y)}{M
   2. P represents the price level, Y represents total income (total output), P*Y represents the nominal income of the economy, and M represents the total amount of money (money supply)
3. inflation
   1. Under the quantity theory of money, the inflation rate is equal to the difference between the growth rate of the money supply and the growth rate of total output.
   2. Hyperinflation: The price level rises rapidly and completely out of control, and the currency depreciates sharply.
4. money demand
   1. People hold money from: daily transaction motivation, accident prevention motivation, and motivation to speculate in the securities market.
   2. Interest rates are negatively related to the demand for money because the opportunity cost of holding money increases when interest rates rise
   3. Income is positively correlated with money demand as the value of transactions increases
   4. Other asset risk is positively correlated with money demand, because other asset risk increases and currency risk decreases relatively.
   5. Inflation risk is negatively correlated with money demand, as inflation risk increases and the relative risk of currency depreciation increases.

Aggregate Demand and Aggregate Supply Analysis

1. Aggregate Demand (AD): $$Y^{ad}=C+I+G+NX$$

   1. The aggregate demand curve is a downward sloping curve that shows the relationship between aggregate quantity demanded and the rate of inflation. It can also be expressed as the relationship between total demand and price, which are equivalent.

   2. 

   3. Consumer ExpenditureC: Total Expenditure on Goods and Services

   4. Investment Spending I: Spending on Real Assets and New Homes

   5. Government PurchasesG: Government Department Expenditures on Specified Goods and Services

   6. Net Exports NX: Net foreign demand for domestic goods and services, equal to exports minus imports.

2. Factors that affect the shift of the aggregate demand curve

   1. Explanation of the curve shift: When the aggregate demand curve shifts to the right, it means that for a given level of inflation (prices remain the same), aggregate demand increases.

   2. Autonomous monetary policy: changes interest rates, affects investment, shifts the curve

   3. 政府购买增加：政府支出增加，曲线右移

   4. 税收增加：影响可支配收入，消费减少，曲线左移

   5. 净出口增加：直接增加总需求，曲线右移

   6. 消费意愿更强：消费增多，曲线右移

   7. 投资增加：直接增加总需求，曲线右移

   8. 金融摩擦加剧：借款实际成本上升，投资减少，总需求下降，曲线左移

3. 总供给（AS）

   1. 总供给曲线是表示总供给量和通货膨胀率之间关系的曲线。
   2. 短期总供给曲线（SRAS 或 AS）向上倾斜，因为受预期通货膨胀率、产出缺口、通货膨胀冲击影响。
   3. 长期总供给曲线（LRAS）是一条过自然产出率水平（KaTeX parse error: Expected group after '^' at position 2: Y^̲）的垂直线。长期中，经济体的产出量受资本量、劳动力和技术决定。此时的失业率称为自然失业率。
   4. 

4. 总供给的影响因素

   1. 短期：预期通货膨胀率上升，短期总供给曲线左移；产出缺口存在时，短期总供给曲线向潜在产出回归；通货膨胀；通货膨胀冲击也会移动短期总供给曲线。
   2. 长期：由经济中资本总量、劳动供给量增加，自然失业率水平降低，科学技术进步等缺口下，长期供给曲线右移。

5. 总供给，总需求分析的均衡

   1. AD与SRAS的交点形成短期均衡，此状态下有均衡的总产出水平和均衡的通货膨胀率。

   2. 

   3. 如果均衡的产出水平不等于潜在水平，说明该经济没有达到长期均衡。短期均衡点此时会不断移动，直到达到潜在产出水平。

      • 解释：以短期均衡的产出高于自然产出为例。此时劳动力市场存在供不应求情况，这会推高工资水平，提高通货膨胀预期，使短期总供给曲线上移，直到短期和长期均衡重合。
        -

6. 均衡的变动

   1. 总需求冲击：引起总需求曲线右移的冲击（反之左移）
      1. 自主性宽松货币政策
         • AD曲线右移，短期产出增加，物价上升；
         • 中期内AS左移，产出逐渐回到潜在水平；
         • 长期内产出回到潜在水平，但物价水平永久升高
      2. 政府购买增加
      3. 税收减少
      4. 净出口增加
      5. 自主性消费支出增加（消费意愿提高）
      6. 投资增加
      7. Financial Friction Ease
   2. Temporary supply shocks: the equilibrium remains unchanged in the long run, affects only the short run, and will gradually adjust back in the medium run
      1. A temporary negative supply shock shifts the short-run aggregate supply curve to the left. If the weather is not good in the current season, the crops will not be harvested.
   3. Permanent supply shocks: affect both long-run and short-run equilibria.
      1. A long-run negative supply shock shifts both the long-run and short-run aggregate-supply curves to the left. such as desertification.

Monetary Policy Theory

Most of the content in this part requires specific drawing analysis, and most of the following cases only provide conclusions.

1. In the face of negative shocks to aggregate demand:

   1. If the government does not act, the economy will first go through a period of real aggregate output below potential levels and unemployment problems; in the long run, output recovers, but inflation is permanently lower.

   2. 

   3. In order to eliminate the output gap and inflation gap in the short term, the central bank implements an autonomous loose monetary policy and lowers the real interest rate level, thereby stimulating investment and shifting the AD curve to the right. At this point, the government acted to stabilize both inflation and economic activity.

   4. 

2. In the face of permanent negative supply shocks:

   1. The government can adopt voluntary tightening monetary policy to push the aggregate demand curve to the left until the output gap is zero.
   2. Stabilizing inflation and stabilizing the economy do not conflict at this time.
   3. The analysis is the same as above.

3. In the face of temporary negative supply shocks:

   1. If there is no policy response, the short-term aggregate supply curve will shift to the left, the unemployment rate will rise and inflation will be serious, and the aggregate output will be lower than the potential output. long-term recovery.

   2. 

   3. At this point there is a trade-off between stabilizing inflation and stabilizing economic activity.

   4. Stabilizing inflation: Adopting a tightening monetary policy can bring inflation back to the target value, but compared with no policy response, the deviation of total output from potential output in this case is more serious and cannot stabilize economic activities.

   5. 

   6. Stabilize output: adopt loose monetary policy to bring output back to potential output, but compared with no policy response, inflation in this case is more serious and cannot stabilize inflation.

   7. 

Monetary Policy Transmission Mechanism

1. Traditional interest rate channel : money supply M affects interest rate r, and changes in interest rate r affect investment I by affecting financing costs, and ultimately affect total expenditure and total income

   1. Take loose monetary policy as an example:

   2. Money supply increases –> Real interest rate falls –> Funding costs decrease and investment increases –> Aggregate demand rises

   3. Interest rates play a major role in the transmission mechanism.

2. Other asset price channels:
   1. The exchange rate affects net exports and thus aggregate demand
   2. Tobin's q theory: Affects new investment by firms, thereby affecting aggregate demand
3. Credit channel: The central bank can affect reserves through monetary policy operations, thereby affecting the issuance of bank loans, affecting the raising of funds by borrowers, and affecting the level of investment and total expenditure.