Fixed income


Weight on the exam = 12%

Number of formulas = 23

CFA formulas

quantitative economics financials

corpfin portfolio equity

fixedincome derivatives alternative


Full price

Full price is the price of a bond including accrued interest.


Pf - full price

Pc - clean price

AccInt - accrued interest

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Duration is the change in the value of a fixed income security that will result from a 1% change in interest rates.


D - duration

ΔPb - percentage change in bond price

ΔY - yield change in percent

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Yield on a risky bond

This equation demonstrates the relation between yield on a risky bond and default free bonds


Yrb - yield on a risky bond

Ydf - yield on a default free bond

DRP - default risk premium (credit spread)

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Value of a callable bond

Callable bond is a bond that can be redeemed by the issuer prior to its maturity. Usually a premium is paid to the bond owner when the bond is called.


Vcbond - value of a callable bond

Voption free - value of an option-free bond

Vcall - value of the call

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TIPS coupon payment

TIPS (Treasury Inflation Protected Security) is a treasury security that is indexed to inflation in order to protect investors from the negative effects of inflation.


CTIPS - TIPS coupon payment

Paradj - inflation-adjusted par value

Crate - stated coupon rate

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Absolute yield spread

Absolute yield spread measures the difference in spread between two bonds in terms of basis points.


AYS - absolute yield spread

Yhigher - yield on the higher-yield bond

Ylower - yield on the lower-yield bond

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Relative yield spread

Relative yield spread measures the yield spread relative to the reference bond.


RYS - relative yield spread

AYS - absolute yield spread

Ybm - yield on the benchmark bond

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Yield ratio

Yield ratio is the ratio of the yields between the two bonds.


YR - yield ratio

Ysubj - subject bonds yield

Ybm - yield on the benchmark bond

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After-tax yield

After-tax yield is the amount that an investor will actually get from that investment after all of the taxes have been taken out.


Yat - after-tax yield

Ytax - taxable yield

tm - marginal tax rate

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Taxable-equivalent yield

Taxable-equivalent yield is the pretax yield that a taxable bond needs to possess for its yield to be equal to that of a tax-free municipal bond.


Ytax eq - taxable-equivalent yield

Ytax free - tax-free yield

tm - marginal tax rate

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Zero-coupon bond value

Zero-coupon bond value is a debt security that doesn't pay interest (a coupon) but is traded at a discount, rendering profit at maturity when the bond is redeemed for its full face value.


Vzero - zero-coupon bond value

Vm - maturity value

i - semiannual discouint rate

n - number of years

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Bond price

Bond is a debt investment in which an investor loans money to an entity (corporate or governmental) that borrows the funds for a defined period of time at a fixed interest rate.


Pbond - bond price

C1 - semiannual coupon payment 1

C2 - coupon in year 2

C2N - coupon in year 2

Pbond - bond price

YTM - yield to maturity

Par - bond's par value


N - number of years to maturity

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Current yield

Current yield only considers the coupon interest and no other sources for an investors return.


Ycur - current yield

Can - annual cash coupon payment

Pbond - bond price

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Bond equivalent yield

Bond equivalent yield is used for a calculation for restating semi-annual, quarterly, or monthly discount-bond or note yields into an annual yield.



BEY - bond equivalent yield

CFYm - monthly cash flow yield

YTMap - annual-pay yield to maturity

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Effective annual yield converts holding period yield (HPY) to a compound annual yield based on a 365-day year to make the yield comparable with other investments.


EAY - effective annual yield

HPY - holding period yield

t - days to maturity

365 - days in a year

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Nominal spread

Nominal spread is simply the difference in basis points between the Treasury and non-treasury security.


Snom - nominal spread

YTMbond - bond's yield to maturity

YTMtreasury - treasury's yield to maturity

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Z-spread is the constant spread that will make the price of a security equal to the present value of its cash flows when added to the yield at each point on the spot rate Treasury curve where a cash flow is received . In other words, each cash flow is discounted at the appropriate Treasury spot rate plus the Z-spread.


Zspread - Z-spread

OAS- option adjusted spread

Costopt - option cost in percent

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Spot rate from forward rates

The equation shows how to determine spot rate from forward rates.


S3 - 3-year spot rate

1f0 - current 1-year forward rate

1f1 - 1-year forward rate one year from now

1f2 - 1-year forward rate two years from now

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Forward rate from spot rates

The equation shows how to determine forward rate from spot rates.


1f2 - 1-year forward rate two years from now

S3 - 3-year spot rate

S2 - 2-year spot rate

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Effective duration

Duration is the approximate percentage change in price for a 100 basis point change in rates. Effective duration takes into account the way in which changes in yield will affect the expected cash flows.


De - effective duration

P- - bond price when yields fall

P+ - bond price when yields rise

P0 - initial price

ΔY - change in yield in decimal form

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Percentage change in bond price

This equation simply shows how to calculate percentage change in bond price after the change in yield using effective duration.


%Pbond - percentage change in bond price

De - effective duration

ΔY% - change in yield in percent

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Portfolio duration

Portfolio duration equals the weighted average of the portfolio's bond's durations.


Dport - portfolio duration

w1 - weight of bond 1 (market value of bond 1 devided by the market value of the portfolio)

D1 - duration of bond 1

w2 - weight of bond 2

D2 - duration of bond 2

wN - weight of bond N

DN - duration of bond N

N - number of bonds in the portfolio

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Percentage change in price

Calculation of percentage change taking into account duration and convexity effects.



%P - percentage change in price

Effectdur - duration effect

Effectconv - convexity effect

D - duration

Δy - change in yield

Conv - convexity

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Price value of basis point

Price value of basis point is a measure used to describe how a basis point change in yield affects the price of a bond.


Pbp - price value of basis point

D - duration

Vbond - bond value

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