Interest Rates Notes PDF

**Interest Rates Notes** **[Measuring Interest Rates]** - **Present Value**: a dollar paid to you one year from now is less valuable than a dollar paid to you today **[Simple Present Value]** PV = Today's (present) value CF = Future cash flow (payment) i = the interest rate PV = CF/(1+i...

**Interest Rates Notes** **[Measuring Interest Rates]** - **Present Value**: a dollar paid to you one year from now is less valuable than a dollar paid to you today **[Simple Present Value]** PV = Today's (present) value CF = Future cash flow (payment) i = the interest rate PV = CF/(1+i)^n^ **[4 Types of Credit Market Instruments]** 1. Simple Loan 2. Fixed Payment Loan 3. Coupon Bond 4. Discount Bond Yield to maturity: the **interest rate** that equates the present value of cash flow payments received from a debt instrument with its value today **[YTM on a Simple Loan]**  **[YTM on a Fixed Payment Loan]** The same cash flow payment every period throughout the life of the loan LV = Loan Value FP = Fixed Yearly Payment *n* = number of years until maturity A math equations with black text Description automatically generated **[YTM on Coupon Bond]** Using the same strategy used for the fixed-payment loan: P = Price of Coupon Bond C = Yearly Coupon Payment F = Face Value of the bond *n* = years to maturity date  Facts on YTM vs Coupon Rate ( P vs F): - When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate - The price of a coupon bond and the yield to maturity are negatively related - The yield to maturity is greater than the coupon rate when the bond price is below its face value **Consol or Perpetuity**: a bond with no maturity date that does not repay principal but pays fixed coupon payments forever P = C/i~c~ P~c~ = price of the consol C = yearly interest payment I~c~ = yield to maturity of the consol Can rewrite above equation as this: i~c~ = C/P~c~ For coupon bonds, the equation gives the **current yield**, an easy to calculate approximation to the yield to maturity **[YTM on a Discount Bond]** For any one-year discount bond i = F -- P/P F = Face value of the discount bond P = Current price of the discount bond YTM equals the increase in price over the year divided by the initial price YTM is negatively related to the current bond price **[Interest Rate vs Return]** **Rate of return (realised, ex post):** The payments to the owner plus the change in value expressed as a fraction of the purchase A math equations with black letters Description automatically generated RET = return from holding the bond from time *t* to time *t* +1 P~t~ = price of bond at time *t* P~*t*\ +1~ = price of the bond *t* +1 C = coupon payment C/P~t~ = current yield = i~c~ P*t* ~+1~ -- P~t~/P~t~ = rate of capital gain = g **[Supply and Demand in the Bond Market]** - At lower prices (higher interest rates), ceteris paribus, the quantity demanded of bonds is higher: negative relationship - At lower prices (higher interest rates), ceteris paribus, the quantity supplied of bonds is lower: positive relationship **[What Shifts Bond Demand?]** Holding all othe factors constant: - The Qd of an asset is positively related to **wealth** - The Qd of an asset is positively related to its **expected return** relative to alternative assets (works via **expected interest rate & expected inflation**) - The Qd of an asset is negatively related to the **risk** of its returns relative to alternative assets - The Qd of an asset is positively related to its **liquidity** relative to alternative assets **[What Shifts Bond Supply?]** - **Expected profitability of investment opportunities**: in an expansion, the supply curve shifts to the right - **Expected inflation**: an increase in expected inflation shifts the supply curve for bonds to the right - **Government budget**: increased budget deficits shift the supply curve to the right **[What Determines Heterogeneity across the Same Maturity Bond Yields?]** - **Default risk**: profitability that the issuer of the bond is unable or unwilling to make interest payments or pay off the face value - US Treasury bonds are considered default free ( Gov can raise taxes) - **Liquidity**: the relative ease with which an asset can be converted into cash - Cost of selling a bond - Number of buyers/sellers in a bond market - **Income tax considerations** - Interest payments on municipal bonds are exempt from federal income taxes **[Term Structure of Interest Rates]** Bonds with identical risk, liquidity, and tax characteristics may have different interest rates because the time remaining to maturity is different - **Yield curve**: a plot of the yield on bonds with differing terms to maturity but the same risk, liquidity, and tax considerations - **Upward-sloping**: long-term rates are above short-term rates - **Flat**: short and long-term rates are the same - **Inverted**: long-term rates are below short-term rates The theory of the term structure of interest rates must explain the following 3 facts: - Interest rates on bonds of different maturities move together over time - When short-term interest rates are low, yield curves are more likely to have an upward slope; when current short-term rates are high, yield curves are more likely to slope downward and be inverted - Yield curves almost always slope upwards Three theories to explain the three facts: **Expectations theory**: - **The interest rate on a long-term bond will equal an average of the short-term interest rates that people expect to occur over the life of the long-term bond** - **Buyers of bonds do not prefer bonds of one maturity over another; they will not hold any quantity of a bond if its expected return is less than that of another bond with a different maturity** - Bondholders consider bonds with different maturities to be perfect substitutes - explains the first two facts but not the third **Segmented markets**: - Bonds of different maturities are not substitutes at all. - **The interest rate for each bond with a different maturity is determined by the demand for and supply of that bond.** - Investors have preferences for bonds of one maturity over another. - If investors generally prefer bonds with shorter maturities that have less interest-rate risk - theory explains the third fact but not the first two **Liquidity premium (or preferred habitat) theory**: - **The interest rate on a long-term bond will equal an average of short-term interest rates expected to occur over the life of the long-term bond plus a liquidity premium that responds to supply and demand conditions for that bond.** - Bonds of different maturities are *partial* (not perfect) *substitutes*. - combines the 2 theories to explain all 3 facts where l~nt~ is the liquidity premium for the n-period bond at time t l~nt~ is always positive Rises with the term to maturity **Relationship between the Liquidity Premium and Expectations Theory:**