Interest Rates and Bond Analysis

Definition: Interest rates represent the price for holding money.
Market Mechanics: The rate is determined as a function of money demand and money supply.
Economic Context: Shadow interest rates occurred in the United States following the liquidity trap that emerged post the onset of the US subprime crisis.
Investment Influence: Interest rates serve as a primary determining factor in investment decisions.
Financial Stability: Rates can be utilized as a tool to prick asset price bubbles to shun off potential financial crises.

Nominal interest rates: The stated rate of interest without adjustment for inflation.
Real interest rates: The interest rate adjusted for the effect of inflation.
Fixed interest rates: Rates that remain constant for the duration of the loan or investment.
Floating interest rates: Rates that fluctuate over time based on market conditions.
Key Repo Rate: Specifically used in Mauritius, this serves as the main stance for monetary policy.
Interbank Market Rate: The rate at which banks lend to and borrow from one another in the interbank market.
Repo and Reverse repo rates: The rates used for repurchase agreements and their counterparts.

Motivational Drivers:
- Precautionary demand: Holding money as a safety cushion for unexpected expenses.
- Transactionary demand: Holding money to cover regular, planned transactions.
- Liquidity demand: The desire to hold money for its immediate spendability.
Impact Factors:
- Price level: Has a positive relationship ( $+$ , as demand increases to restore purchasing power).
- Real GDP: Has a positive relationship ( $+$ , as more transactions occur in a larger economy).
- Financial innovation: Has a negative relationship ( $-$ , as it reduces the overall demand for physical money).
- Interest rates: Causes a movement along the demand curve rather than a shift of the curve.

Expansionary Policy (Buying Securities):
- The Fed buys securities in the open market.
- Bank reserves increase, and the quantity of money increases.
- Interest rates fall.
- The dollar falls in the foreign exchange market.
- Consumption, net exports, and investment increase.
- Aggregate demand increases.
- Real GDP and inflation rise.
Contractionary Policy (Selling Securities):
- The Fed sells securities in the open market.
- Bank reserves decrease, and the quantity of money decreases.
- Interest rates rise.
- The dollar rises in the foreign exchange market.
- Consumption, net exports, and investment decrease.
- Aggregate demand decreases.
- Real GDP and inflation fall.

The relationship between nominal rates, real rates, and expected inflation is expressed as: $Nominal \text{ risk-free interest rate} = \text{Real risk-free interest rate} + \text{Expected inflation rate}$

Definition: A bond is a financial instrument having fixed claims. It serves as a secured source of income for the investor and a source of funding for companies.
Issuer Types: Corporate bonds versus government bonds.
Seniority and Rights:
- Seniority of claims: Bondholders have priority over shareholders in the case of bankruptcy.
- Income Type: Bonds provide coupons, whereas equity provides dividends (which are at the discretion of management).
- Voting Rights: Bondholders have no voting rights compared to shareholders.
- Period: Bonds have a fixed maturity period, while equity lasts for the lifetime of the company.
- Risk: Bonds generally represent low risk compared to equity.
- Investor Identity: Bondholder versus shareholder.

Key Features:
- Maturity period.
- Coupon rate.
- Yield rate.
- Nominal value.
- Frequency of coupon payments (considered the key element).
Valuation Model:
- $\text{PV of a bond} = \sum \text{discounted values of series of cash inflows} + \text{Discounted value of its principal}$
Annuity Multiplying Factor: To calculate the sum of discounted values for coupons only, use: $\frac{1}{r} \times [1 - \frac{1}{(1+r)^n}]$
Example Calculation Data:
- Nominal value: $\$1000$
- Maturity period: $3\,years$
- Coupon rate: $5\%$
- Yield rate: $10\%$
- Frequency: Yearly payments.
Trading Status:
- Premium: Coupon rate $>$ Yield rate.
- Discount: Coupon rate $<$ Yield rate.
- Par: Coupon rate $=$ Yield rate.

Corporate bonds: Issued by companies.
Government bonds: Issued by national governments.
Inflation-indexed bonds: Bonds where the principal or interest is adjusted for inflation.
Mortgage bonds: Involve the offer of collaterals when using bonds.
Junk bonds: High-risk, speculative bonds.
Investment grade bonds: High-quality bonds rated as $AAA$ , $AA$ , $A$ , or $BBB$ .

Definition: The relationship between yield to maturity and time.
Shapes and Interpretations:
- Upward sloping: Indicates a booming economy.
- Downward sloping: Indicates a recession.
- Flat: Not considered highly practical for standard interpretation.
Theories:
- Unbiased Expectations Theory: The yield curve reflects the market's current expectations of future short-term rates. For example, the return on a 7-year bond should equal the return on 7 successive investments in a 1-year bond: $(1+i)^7 = (1+i_1) \times (1+i_2) \times (1+i_3) \times (1+i_4) \times (1+i_5) \times (1+i_6) \times (1+i_7)$
- Liquidity Premium Theory: To induce investors to hold longer-term bonds, a liquidity risk premium needs to be paid.
- Market Segmentation Theory: Participants operate in segmented markets. Banks have mainly short-term liabilities, so investments tilt toward shorter-term instruments. Insurance companies have mainly long-term liabilities, so investments are skewed towards long-term instruments.

Yield Curve Specifics: Modeling typically compares the 3-Month Treasury to the 30-Year Treasury.
Historical Benchmarks:
- Inverted Curve: Occurred on November 24, 2000.
- Flat Curve: Occurred on March 2, 2006.
- Normal Curve: Occurred on January 11, 2010.
- Recent Snapshot: Data from December 31, 2019, shows the progression across maturities from 0 to 30 years.

Cornett, Adair and Nofsinger, 2015. Finance: Applications & Theory. McGraw-Hill International Edition. Specifically Chapter 6 and Chapter 7.