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Chapter 3 Understanding Interest Rates PowerPoint PPT Presentation


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Chapter 3 Understanding Interest Rates. Four Types of Credit Instruments. 1.Simple (Interest) Loan 2.Fixed Payment Loan (Amortizing) Coupon Bond Face or Par Value ($1,000 increments) Maturity Coupon Rate (% of the Face Value) Discount Bond (Zero Coupon)

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Chapter 3 Understanding Interest Rates

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Chapter 3 understanding interest rates

Chapter 3

UnderstandingInterest Rates


Four types of credit instruments

Four Types of Credit Instruments

1.Simple (Interest) Loan

2.Fixed Payment Loan (Amortizing)

  • Coupon Bond

    • Face or Par Value ($1,000 increments)

    • Maturity

    • Coupon Rate (% of the Face Value)

  • Discount Bond (Zero Coupon)

    • Purchased at a Discount (Below Face Value)

    • Matures to Face Value


Present value

Present Value

Concept of Present Value

Simple loan of $1 at 10% interest

Year123n

$1.10$1.21$1.33 $1´(1 + i)n

$1

PV of $1 =———

(1 + i)n

Calculating Present Value is Referred to as Discounting


Yield to maturity loans

Yield to Maturity: Loans

Yield to maturity = interest rate that equates today’s value with present value of all future payments

1.Simple Loan (i = 10%)

$100 = $110/(1 + i) Þ

$110 – $100$10

i = ————— =——= .10 = 10%

$100$100

2.Fixed Payment Loan (i = 12%)

$126$126$126$126

$1000 =——— + ——— + ——— + ... + ———

(1 + i) (1 + i)2(1 + i)3(1 + i)25

FPFPFPFP

LOAN =——— + ——— + ——— + ... + ———

(1 + i) (1 + i)2(1 + i)3(1 + i)25


Mortgage payments table

Mortgage Payments Table


Bond table

Bond Table


Yield to maturity bonds

Yield to Maturity: Bonds

3.Coupon Bond (Coupon rate = 10% = C/F)

$100 $100 $100$100$1000

PB =——— + ——— + ——— + ... + ——— + ————

(1 + i) (1 + i)2 (1 + i)3 (1 + i)10 (1 + i)10

CCCCF

PB =——— + ——— + ——— + ... + ——— + ————

(1 + i) (1 + i)2 (1 + i)3 (1 + i)N(1 + i)N

Perpetuity: Fixed coupon payments of $C forever (No Payback)

CC

Pc = —— i =——

iPc


Yield to maturity bonds1

Yield to Maturity: Bonds

4. Discount Bond (Pd = $900, Face = $1000)

$1000

$900 = ——— Þ

(1 + i)

$1000 – $900

i = —————— = .111 = 11.1%

$900

F – Pd

i =———

Pd


Relationship between price and yield to maturity

Relationship Between Price and Yield to Maturity

Three Interesting Facts in Table 1

1.When bond is at par, yield equals coupon rate

2.Price and yield are inversely related

3.Yield is greater than the coupon rate when the bond price is below par value


Current yield

Current Yield

  • C

  • ic = ——

  • PB

  • Two Characteristics

  • 1.Is better approximation of yield to maturity, the nearer the bond price is to par and the longer the maturity of bond

  • 2.Change in current yield always signals change in same direction as yield to maturity


  • Yield on a discount basis

    Yield on a Discount Basis

    (F – Pd)360

    idb =————´————————————

    F(number of days to maturity)

    One year bill, Pd = $900, F = $1000

    $1000 – $900360

    idb =———————´——= .099 = 9.9%

    $1000365

    Two Characteristics

    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


    Bond page of the newspaper

    Bond Page of the Newspaper


    Distinction between interest rates and returns

    Distinction Between Interest Rates and Returns

    Rate of Return

    C + Pt+1 – Pt

    RET =——————= ic + g

    Pt

    C

    where: ic = ——= current yield

    Pt

    Pt+1 – Pt

    g =———= capital gain

    Pt


    Key facts about relationship between interest rates and returns

    Key Facts about RelationshipBetween Interest Rates and Returns


    Maturity and the volatility of bond returns

    Maturity and the Volatility of Bond Returns

    Key Findings from Table 2

    1.Only bond whose return = yield is one with maturity = holding period

    2.For bonds with maturity > holding period, i­ PB ¯ 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 rate

    5.Bond with high initial interest rate can still have negative return if i­


    Maturity and the volatility of bond returns1

    Maturity and the Volatility of Bond Returns

    Conclusion from Table 2 Analysis

    1.Prices and returns 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


    Reinvestment risk

    Reinvestment Risk

    Reinvestment Risk

    1.Occurs if an investor holds a series of short term bonds over long term holding period

    2.i at reinvestment is uncertain

    3.gain from an i­, lose when i¯


    Calculating duration i 10 10 yr 10 coupon bond

    Calculating Duration, i = 10% 10-yr 10% Coupon Bond


    Calculating duration i 20 10 yr 10 coupon bond

    Calculating Duration, i = 20% 10-yr 10% Coupon Bond


    Formula for duration

    Formula for Duration

    Key facts about duration

    Everything else equal,

    1.when the maturity of a bond lengthens, the duration rises as well.

    2.when interest rates rise, the duration of a coupon bond falls.

    3.the higher the coupon rate on the bond, the shorter the duration of the bond.

    4.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.


    Duration and interest rate risk

    Duration and Interest Rate Risk

    %DP – DUR´Di/(1 + i)

    i­ 10% to 11%:

    Table 3—10% coupon bond

    %DP= 6.76 ´ .01/(1 + .10)

    = –.0615 = –6.15%.

    Actual decline = 6.23%

    20% coupon bond, DUR = 5.72 years

    %DP= – 5.72 ´ .01/(1 + .10)

    = –.0520 = –5.20%

    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. Therefore, the greater the duration of a security, the greater its interest-rate risk.


    Distinction between real and nominal interest rates

    Distinction Between Real and Nominal Interest Rates

    Real interest rate

    Interest rate that is adjusted for expected changes in the price level

    ir = i – pe

    1.Real interest rate more accurately reflects true cost of borrowing

    2.When real rate is low, greater incentives to borrow and less to lend


    Distinction between real and nominal interest rates1

    Distinction Between Real and Nominal Interest Rates

    Real interest rates an Example

    if i = 5% and pe = 0% then

    ir = 5% – 0% = 5%

    if i = 10% and pe = 20% then

    ir = 10% – 20% = –10%


    U s real and nominal interest rates

    U.S. Real and Nominal Interest Rates


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