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Practicals Flashcards

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1
Q

Bond at premium or discount

A

Compare Mkt price with face value or discount rate with coupon rate

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2
Q

When a bond is traded between coupon dates

A

additional amt must be added for int accrued that buyer must pay to seller

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3
Q

Bond’s accrued int

A

Coupon x Days elapsed / total days in coupon period. Use actual/actual (Used with GB) or 30/360 (Used with CB). AI = t/T x PMT. Doesn’t depend on YTM

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4
Q

Govt equivalent yield

A

Used to restate the YTM on a corporate bond to obtain the spread over government YTM. To restate a corporate bond yield from the 30/360 day count basis to the actual/actual day count basis multiply bond yield calculated on 30/360 day count basis by 365/360

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5
Q

Effect of change in YTM

A

Coupon effect - Lower the coupon rate (high amt is going to be received at maturity) greater the % change in price.
Maturity Effect - Longer the time to maturity, greater the % change in price. Exception to this maturity effect is there for low coupon (not zero coupon) long term bonds trading at discount

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6
Q

Matrix pricing (also used to calculate required yield spread)

A

Price estimation process for new or illiquid bonds that uses yields on securities with the same or similar features. Matrix pricing is widely used in price quotations for bonds. Identify actively traded comparable bonds, Calculate YTM for each of comparable bonds & calculate average YTM for each maturity yr, Use interpolation to calculate yield of new bond, then find mkt price. If new bond tenor is 4 yrs take 2 or 3 yr bond & 5 or 6 yr bond for YTM calculation

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7
Q

Int payment not in yearly basis

A

To find Price of bond, interest shall be taken per period not annually, discount rate shall be period, n shall be per period

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8
Q

Flat Price (Quoted or clean price)

A

Full price (-) Accrued Interest. Bond is usually quoted at its Flat price

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9
Q

Full price (Invoice or dirty price)

A

PV as of trade settlement date which involves partial payment period because we’re between coupon dates. Amt actually paid by buyer

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10
Q

To find full price in between int date

A

PMT / (1+r)^1-t/T, where t - elapsed date from last int payment date & T days between 2 int payment date. Alternatively, PV (Full) = PV calculated as usual x (1+r)^t/T. Page 136

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11
Q

Constant-Yield Price Trajectory

A

Bond price change even when YTM is constant as bond moves to maturity

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12
Q

Convexity Effect

A

% change in a bond’s price will also vary depending on how the yield changes. The percentage price increase is greater, in absolute value, than the percentage price decrease. This implies that the relationship between bond prices and yields is not linear; instead, it is curved and “convex.”

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13
Q

YTM

A

single measure to compare bonds with varying maturity & coupons. When YTM is calculated using formula multiply the YTM with periodicity to find annualized YTM (Page 160)

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14
Q

Yield mentioned in qn

A

Semiannual bond equivalent yield of 1.88% means annualized yield. 1.88% yield per semiannual basis means not annualized yield.

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15
Q

Value of call option in a bond

A

Price of the option-free bond minus the price of the callable bond. So option adjusted price = Flat price - Call option value. If COV is +ve then option adjusted price is lower than flat price

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16
Q

For capital mkt securities maturing after a year

A

investors want an annualized & compounded YTM

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17
Q

Periodicity

A

Frequency of coupon payt in a year

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18
Q

Effective annual rate

A

Has periodicity of 1. When calculating YTM of strip (Zero coupon bond), periodicity is arbitrary (can be any 1, 2, 4) because there are no coupon payments

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19
Q

Semi annual bond basis yield or semi annual bond equivalent yield

A

Has periodicity of 2

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20
Q

For a given pair of CF, annual rate (annualized YTM) & Periodicity

A

are inversely rated

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21
Q

Convert annualized yield using one periodicity to another periodicity

A

(1 + APRm/m)^m = (1 + APRn/n)^n

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22
Q

Current yield

A

Bond’s annual coupon / Flat Price. Crude measure of return because it ignores periodicity, time value of money (interest on interest) & accrued interest

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23
Q

Street Convention vs True yield

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A

Do not account for weekends and holidays (Commonly used in practice) vs account for weekend. True yield can never be higher than street convention

24
Q

Simple Yield

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A

Sum of the coupon payments plus the straight-line amortized share of the gain or loss, divided by the flat price. Simple yields are used mostly to quote Japanese government bonds

25
Yield to worst
Lowest of sequence of yield to call and yield to maturity. Page 170
26
Yield spread
Difference between YTM & Benchmark yield. Benchmark rate captures top down factors while spread captures bottom up
27
Benchmark Spread
The yield spread over a specific benchmark. It represents the risk premium for the credit and liquidity risks and possibly the tax impact of holding a specific bond. Spread = Taxation + Liquidity + Credit Risk. Benchmark = Expected Inflation Rate + Expected Real Rate
28
G spread
Corporate Bond Yield − Government Bond Yield (of same maturity).
29
I spread (Calculate credit risk)
Bond Yield − Swap Rate (same maturity)
30
Z spread (Static spread coz it is constant & has zero volatility)
Rate that must be added to benchmark rate to make PV of bond's CF = Mkt price. Z spread used to calculate Option adjusted spread on a callable bond. Add z spread with each spot benchmark rate to find YTM of each yr. power is reqd. pg 179
31
Option Adjusted Spread
Z spread - Option value in basis point per yr
32
In FRN
MRR + Quoted margin = Int rate. Quoted margin constant. Required margin (Discount margin) is spread required by investors. If floater trades at par, quoted & required margin are equal. If quoted & required margin are same flat price of FRN will be pulled to par as the next reset date nears. During period between two int date it wont trade at par even if 2 margins are same due to MRR.
33
FRN Price fluctuation
Floater has stable price even during volatile int rate period because CF adjust for int rate change. Floaters with longer reset periods may be more exposed to interest rate and price volatility. The longer the reset period, the more a floater will behave similarly to a short-dated fixed-rate security and the more its price will potentially fluctuate.
34
Valuation of FRN
Requires pricing model. PMT = (MRR + QM) x FV. R = MRR + RM (DM). All 3 rates are quoted in annual % so divide it by periodicity while calculating price. No accrued int so Flat price = Full price
35
Money mkt instruments
Quoted using different conventions than bonds (which are quoted using YTM). So to compare it with long term bonds we need to standardize them. Discount rate = Interest income / Face value x 360 (or) 365 / Time to maturity. But this doesn't reflect actual money earned. Disc rate understate return when price is less than FV & overstate it when P > FV.
36
Add on rate (Bond Equivalent Yield) (Year is always assumed to have 365 days)
(Year / Days to settlement) × (FV - Price/P). Where Price = FV x {1 - (Days x Disc Rate/yr)} FV is the Face value at maturity & Price is price at issuance. Using add on rate we can compare with other instrument's YTM. DR = (Yr/Days) x (FV - PV / FV)
37
Price calculation
Using DR = FV x {1 - (DR x Day/yr)} Using AOR = FV / {1 + (AOR x Day/yr)}
38
When qn gives discount rate calculated based on 360 days
to find Price use year as 360. But to calculate AOR use 365
39
Bond's YTM vs Money mkt yield
Annualized & compounded vs Annualized. Stated for common periodicity for all time to maturity vs Money mkt instrument with different time to maturity have different periodicity for annual rate.
40
Comparing money mkt instrument on BEY basis
If disc rate is given first find price = FV x {1 - (Days x Disc rate/year)}. Then find add on rate = (FV - PV / PV) x Year / Day to maturity. This BEY is comparable with YTM
41
Spot curve (Zero or strip curve)
Used to derive Par curve & Forward curve. The shape of the spot curve is closely related to the shape of the par and forward curves. Spot rates are market discount rates on default-risk-free zero-coupon bonds, sometimes referred to as zero rates. By using a sequence of spot rates in calculating bond prices, a no-arbitrage bond price is obtained. Spot curve is created by calculating the YTM on recently issued coupon-paying government bonds of varying maturities but zero-coupon government risk-free bonds would be preferable
42
Par curve (Par rate = YTM)
Bond yield for hypothetical benchmark securities priced at par. A par rate is the market discount rate for a specific maturity that would result in a bond priced at par. So Coupon rate = Par rate (YTM). Qn gives spot rate. Then assume PV is 100 which shall be equal to FV (100). Use that to find PMT. From that find coupon rate. Page 222
43
Forward curve
Rate for interest period starting in future. Implied forward rates are calculated using spot rates and can be interpreted as an incremental, or marginal, return for extending the time-to-maturity for an additional time period. As such, they reflect a breakeven reinvestment rate. (1 + ZA)^A × (1 + IFRA,B – A)^B – A= (1 + ZB)^B. Example, 3y1y to be found & 3yr & 4yr spot rate is given. A = 3, B = 4 find B-A = 1. Spot rate can be calculated using forward rate as well
44
Upward vs Downward sloping (Inverted yield curve)
In upward-sloping term structures, par rates will be lower than their corresponding spot rates and forward rates will be greater than spot rates. In downward-sloping term structures, par rates will be greater than spot rates and forward rates will be lower than spot rates.
45
3 yr spot rate using forward rate
(1+0y1y) x (1+1y1y) x (1+2y1y) = (1+Z3)^3. So if only forward rate is given we can use that in denominator as YTM. 3rd Year YTM = the above mentioned left side equation. Power is not applied because the left side equation represents power of 3
46
Spot rate vs forward rate in denominator
Power shall apply (Page 224)
47
Reinvestment risk vs Price risk
Types of int rate risk & both are inverse. Risk of decreasing reinvestment return on CF, which occurs when int rate fall vs Declining price occurs when int rate rises. When investment horizon = Macaulay Duration both risk setoff each other. When the investment horizon is greater than (less than, equal to) a bond’s Macaulay duration, coupon reinvestment risk is higher than (lower than, equal to) the bond’s price risk.
48
Duration
Can be used to estimate the change in the price of a bond in response to a change in yield, but it assumes a linear relationship between price and yield even though, in fact, the relationship is nonlinear. This is most evident when estimating price changes for large changes in yield and for bonds with certain features. Duration, for a given bond, is not static and decreases as the bond approaches maturity. All else equal, a longer (shorter) time-to-maturity, a lower (higher) coupon rate, or a lower (higher) yield-to-maturity results in higher (lower) duration or higher (lower) interest rate risk. For bond with one CF duration = Maturity
49
Duration gap for a bond
Difference between its Macaulay duration and the investor’s investment horizon
50
Yield Duration
a bond’s price sensitivity to changes in its own yield-to-maturity and assume underlying cash flows are certain. Macaulay duration, modified duration, money duration, and the price value of a basis point (PVBP) are yield duration measures.
51
Curve Duration
a bond’s price sensitivity to changes in benchmark yield curve, with less certain CF
52
Modified duration
The slope or first derivative of the price of a bond with respect to its yield-to-maturity, measuring the sensitivity of a bond’s price to changes in its yield-to-maturity. Modified duration can be calculated using a bond’s Macaulay duration and yield or through approximation.
53
Money duration
An extension of modified duration and incorporates the size of the bond position in currency terms. Related to this measure is the price value of a basis point, which is an estimate of the change in the price of a bond for a 1 bp change in the bond’s yield.
54
Capital Gain or Loss on a bond
Compare Sale price with Present value calculated using YTM
55
Formula related to duration
Duration - Find PV of each CF. Take weight of that based on sum. Multiply it with period (Yr x Periodicity). Sum it up. If periodicity is more than 1 divide final amt with periodicity Modified Duration - Macaulay Duration / (1+YTM). If M duration calculated was semi annual use that in numerator & divide YTM by 2. Ann Mod duration will be Semi Mod duration / 2. Approximate Mod Duration - (V_ - V+) / (2 x V0 x YTM Change) Money Duration - Mod duration x Full price Price Value of Basis Point - (V_ - V+) / 2
56
Formula related to Convexity
Convexity for each period = t x (t+1) / (1+r)^2. When periodicity is 2 divide r by 2. Multiply weight calculated for duration with convexity & final amt is annual convexity. If periodicity is more than divide the sum value by square of periodicity. Approximate convexity - (V_ + V+ - 2V0) / (V0 x YTM Change^2) Money Convexity = Annual Convexity x Full price

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