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Fixed-Income securities. Outline. Mortgages Types Mortgage Risk The Mortgage Backed Securities Market History Types of Securities. A mortgage is a loan with real estate as collateral. The lender, called the mortgage originator , often charges

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  • Mortgages
    • Types
    • Mortgage Risk
  • The Mortgage Backed Securities Market
    • History
    • Types of Securities

A mortgage is a loan with real estate

as collateral. The lender, called the

mortgage originator, often charges

points as a fee for preparing and

placing the mortgage.


It is quite common for the lender to sell the mortgage to another party.


Mortgages: Types

  • A fixed rate mortgage is one with payments

based on a set interest rate that does not change.

  • An adjustable rate mortgage (ARM), also

called a variable rate mortgage, has an interest rate that moves with some market interest rate, such as the Treasury bill rate.

  • Most ARMS have an annual reset to the

interest rate. Many also have either a cap or a floor on the interest rate.


Mortgage Risk

  • Default risk is the risk that the borrower is

unable or unwilling to repay the debt as agreed.

  • Interest rate risk is the risk that the general

level of interest rates rises, such that the value of the mortgage’s cash flow stream declines.

  • Prepayment risk is the risk of an early

payment of the original mortgage, such as when the home is sold or when the mortgage is refinanced at a lower rate.


The Mortgage Backed Securities Market

  • The Federal National Mortgage Association (Fannie Mae), the Government National Mortgage Association (Ginnie Mae), & the Federal Home Loan Mortgage Corporation (Freddie Mac) support the US mortgage market by providing liquidity, buying conforming mortgages from banks across the country for resale elsewhere.
  • The term mortgage-backed securities refers to all products based on mortgage loans.

Individual Individual Individual

Mortgages Mortgages Mortgages

Mortgage Pool

Pass Through Security

Types of Securities

  • A pass-through security is a share of a pool

of mortgages.

  • The holders receive a monthly check for their

portion of the scheduled principal and interest payments, plus their share of any prepayments that may occur.


Types of Securities

  • Pass-through securities may be issued and guaranteed by a government agency, or they may be private label.
  • Two types of derivative securities that spring from pass-through securities are collateralized mortgage obligations and stripped mortgage-backed securities.

Types of Securities

  • A collateralized mortgage obligation (CMO) is

a security backed by a pool of mortgages and structured to transfer prepayment or interest rate risk from one group of security holders to another.

  • A given pool of mortgages backs two or more

classes of securities called tranches.


Individual Individual Individual

Mortgages Mortgages Mortgages

Mortgage Pool

A Tranche B Tranche C Tranche Other Tranches

Types of Securities

Collateralized Mortgage Obligation


Types of Securities

  • With a sequential pay CMO, all the tranche

holders receive monthly interest payments based on the principal amount outstanding in their tranche.

  • All principal payments go to the A tranche

until the A tranche principal is completely returned. Only then will the investors in the next tranche begin to receive principal.


Individual Individual Individual

Mortgages Mortgages Mortgages

Mortgage Pool

Interest Only Security Principal Only Security

Types of Securities

  • There are two types of stripped mortgage

backed securities, or strips.

  • All the interest goes to the interest only (IO)

security holders, while the entire principal goes to the principal only (PO) holders.


Considerations in

Pricing Mortgage Backed Securities

  • The price risk of a MBS comes from the

uncertainty about the timing of cash flows.

  • Prepayments can affect the realized return on

a MBS substantially.

  • The offering memorandum for a MBS will

state the assumptions used in estimating cash flows from the mortgage pool.

  • A benchmark assumption for the rate of

mortgage prepayment is offered by the Public Securities Association (PSA).


The Risk of Collateralized Mortgage Obligations

  • Declining interest rates will increase the

value of a cash flow stream and will lead to prepayments.

  • If a mortgage pool sells at a discount,

prepayments will increase the value of each of the tranches, with the higher duration tranches benefiting the most.

  • If the pool sells at a premium, then

prepayments will reduce everyone’s yield, with the effect most pronounced for the holders of the longer duration tranches.


The Risk of Stripped Mortgage Backed Securities

  • Prepayment has different consequences for

IO and PO strips. An extension of the mortgage decreases the value of the principal payments but increases the value of the interest payments.

  • Declining interest rates will increase the

value of a series of known cash flows, as well as the likelihood of prepayment. Normally, the prepayment effect overwhelms the interest rate effect.


Key Features of a Bond

  • Par value – face amount of the bond, which is paid at maturity (assume $1,000).
  • Coupon interest rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par to get dollar payment of interest.
  • Maturity date – years until the bond must be repaid.
  • Issue date – when the bond was issued.
  • Yield to maturity - rate of return earned on a bond held until maturity (also called the “promised yield”)
  • Some bonds are callable
  • Call provision: Allows issuer to refund the bond issue if rates decline (helps the issuer, but hurts the investor)







100 + 1,000

VB = ?



What is the value of a 10-year, 10% annual coupon bond, if rd (discount rate)= 10%?


Fixed Income Security Risk

  • Default risk, or credit risk, is the possibility that a borrower will be unable to repay principal and interest as agreed upon in the loan document.
  • Reinvestment rate risk refers to the possibility that the cash coupons received will be reinvested at a rate different from the bond’s stated rate.
  • Interest rate risk refers to the chance of loss because of adverse movements in the general level of interest rates.

What is the Yield-to-Maturity or cost of debt capital?

  • A discount rate (rd )/cost of debt capital and the expected return for the debt holder if the investor holds the bond until the maturity

rd = r* + IP + MRP + DRP + LP

r* = real risk free rate

IP = inflation premium (rate)

MRP = maturity risk premium

DRP = credit risk premium

LP = liquidity premium


What is interest rate (or price) risk?

  • Interest rate risk is the concern that rising rd will cause the value of a bond to fall.

% change 1 yr rd 10yr % change

+4.8% $1,048 5% $1,386 +38.6%

$1,000 10% $1,000

-4.4% $956 15% $749 -25.1%

The 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk.


What is reinvestment rate risk?

  • Reinvestment rate risk is the concern that kd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income.

EXAMPLE: Suppose you just won $1,000,000 playing the lottery. You

intend to invest the money and live off the interest.

  • If you choose to invest in series of 1-year bonds, that pay a 8% coupon you receive $80,000 in income and have $1,000,000 to reinvest.

But, if 1-year rates fall to 3%, your annual income would fall to $30,000.

  • If you choose a 30-year bond that pay a 10 % coupon you receive $100,000 in income; you can lock in a 10% interest rate, and $100,000 annual income for 30 years

Interest Rate Risk : Malkiel’s Theorems

  • Malkiel’s theorems are a set of relationships among bond prices, time to maturity, and interest rates.
  • Theorem One : Bond prices move inversely with yields.
  • Theorem Two : Long-term bonds have more risk.
  • Theorem Three : Higher coupon bonds have less risk.

Interest Rate Risk : Malkiel’s Theorems

  • Bond A : matures in 8 years, 9.5% coupon Bond B : matures in 15 years, 11% coupon Which price will rise more if interest rates fall?
  • Apparent contradictions can be reconciled by computing a statistic called duration.

For a noncallable security, duration is

the weighted average time until a

    • bond’s cash flows are received.


  • Duration is not limited to bond analysis. It can be determined for any cash flow stream.
  • Duration is a direct measure of interest rate risk. The higher it is, the higher is the risk.

where D = duration

Ct = cast flow at time t

R = yield to maturity (per period)

P = current price of bond

N = number of periods until maturity

t = period in which cash flow is received

Duration Measures

  • Macaulay duration is the time-value-of-money-weighted, average number of years necessary to recover the initial cost of the security.

Duration Measures

  • Modified duration measures the percentage change in bond value associated with a one-point change in interest rates.

The bond price - bond yield

    • relationship is not linear.


yield to maturity

Problems with Duration

  • Graphically, duration is the tangent to the current point on the price-yield curve. Its absolute value declines as yield to maturity rises.
  • Duration is a first derivative statistic. Hence, when the change is large, estimates made using the derivative alone will contain errors.


  • Convexity measures the difference between the actual price and that predicted by duration, i.e. the inaccuracy of duration.
  • The more convex the bond price-YTM curve, the greater is the convexity.

bond price

yield to maturity

Using Convexity

  • No matter what happens to interest rates, the bond with the greater convexity fares better. It dominates the competing investment.