Chapter 3 "What do Interest Rates Mean and What Is Their Role in Valuation?"

Relationships between Rates and Returns

1. only bond whose return = yield is one with maturity = holding period 2. for bonds with maturity greater than the holding period, if interest goes up, the prices goes down, implying capital loss 3. longer is maturity, greater is price change associated with interest rate change 4. longer is maturity, more return changes with change in interest rates 5. bond with high initial interest rate can still have a negative return if interest rates rise

Maturity and the Volatility of Bond Returns

1. prices and returns are more volatile for long-term bonds because they have higher interest-rate risk 2. no interest-rate risk for any bond whose maturity equals holding period

Formula for Duration

1. the higher the coupon rate on the bond, the shorter the duration of the bond 2. duration is additive: the duration of a portfolio of securities is the weighted-average of the durations of the individual securities, with the weights equaling the proportion of the portfolio invested in each security

Interest Rates (YTM)

- among the most closely watched variables in the economy. Yield to Maturity is the most accurate measure of interest rates!

Present Value (present discounted value)

- based on the commonsense notion that a dollar of cash flow paid to you one year from now is less valuable to you than a dollar paid to you today. You could invest the dollar in a savings account that earns interest and have more than a dollar in one year - PV can mean the PV of a single cash flow or the SUM of a sequence or group of cash flows

Perpetuity/ Consol

- fixed coupon payments of $C forever P = C/I I = C/P

Fixed-Payment Loans

- loans where the loan principal and interest are repaid in several payments, often monthly, in equal dollar amounts over the loan term

Reinvestment Risk

- occurs if investor holds a series of short bonds over long holding period - gain from interest rates rising (reinvest at higher rate), lose when interest rate drops (reinvest at lower rate)

Simple Loans

- require payment of one amount which equals the loan principal plus the interest

Cash Flows

- streams of cash payments to the holder - debt instruments are evaluated against one another based on the amount of each cash flow and the timing of each cash flow - present value analysis: the analysis of the amount and timing of a debt instrument's cash flows lead to its YTM or interest rate

Installment Loans (fixed-payment loan examples)

- such as auto loans and home mortgages are frequently of the fixed-payment type

Loan Principal

- the amount of funds the lender provides to the borrower

Interest Payment

- the cash amount that the borrower must pay the lender for the use of the loan principal

Maturity Date

- the date the loan must be repaid - Loan Term = from initiation to maturity date

Duration and Interest-Rate Risk

- the greater the duration of a security, the greater the percentage change in the market value of the security for a given change in interest rates - the greater the duration of a security, the greater its interest-rate risk

Simple Interest Rate

- the interest payment divided by the loan principal - the percentage of principal that must be paid as interest to the lender - convention is to express on an annual basis, irrespective of the loan term

Yield to Maturity (YTM)

- the interest rate that equates today's value with present value of all future payments (not the same as return)

Rate of Return

- we can decompose return into 2 pieces :current yield and capital gains Return = C + [P(t+1)- Pt] / Pt or C/Pt (current yield) + (Pt+1 - Pt)/ Pt (capital gains)

Four Basic Credit Instruments (with present value concepts)

1. Simple Loan - one payment 2. Fixed Payment Loan - multiple payments 3. Coupon Bond - multiple payments 4. Discount Bond - one payment

Yield on a Discount Basis

1. Understates yield to maturity; longer the maturity, greater is understatement 2. Change in discount yield always signals change in same direction as yield to maturity

Relationship Between Price and YTM (coupon bonds)

1. When bond is at par, yield is equal to coupon rate 2. Price and yield are negatively related (if interest rates go up, price of bond goes down) 3. Yield is greater than coupon rate when bond price is below par value (discount) * if the interest rate increases, the PV of any given cash flow is lower; hence the price of the bond must be lower

Key Facts about Duration

1. all else equal, when the maturity of a bond lengthens, the duration rises as well 2. all else equal, when interest rates rise, the duration of a coupon bond fall

Present Value Formula

FV / (1+i)^n

Current Yield (CY)

I = C/P - an approximation for YTM that is easy to calculate 1. If a bond's price is near par and has a long maturity, then CY is a good proximation (perpetuity) 2. a change in the current yield always signals change in same direction as yield to maturity

Real Interest Rate

I(r) = I - expected inflation 1. interest rate that is adjusted for expected changes in the price level (inflation) 2. real interest rate more accurately reflects true cost of borrowing 3. when the real rate is low, there are greater incentives to borrow and less to lend * we usually refer to this rate as the ex ante real rate of interest because it is adjusted for the expected level of inflation. After the fact, we can calculate the ex post real rate based on the observed level of inflation

Coupon Bond Formula

PV = C/ (1+i) + C/ (1+i)^2......+ C/ (1+i)^n + F/ (1+i)^n

Fixed Payment Loan Formula

PV = FV/ (1+i) + FV/ (1+i)^2 + ....FV / (1+i)^n