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R41: INTRODUCTION TO FIXED-INCOME VALUATION - Coggle Diagram
R41: INTRODUCTION TO FIXED-INCOME VALUATION
Bond Valuation & Yield to Maturity
Price = PV of ( ∑PMT)
=> YTM ≈ discount rate of PV ≈ Ls nđt nhận khi nắm giữ đến đáo hạn
YTM incre => PV decre => Value decre
(Vice versa)
NOTE
: Semiannual:
Coupon / 2
YTM / 2
N (new) = N (old) * 2
Relationship
Bond price vs Market discount rate (YTM)
Inverse effect
Market discount rate
increases
(
decreases
) → the price of the bond
decreases
(
increases
).
Convexity effect
Bond price vs Coupon rate
a
LOWER
coupon bond is
MORE sensitive
to changes in the market discount rate than a higher coupon bond
HIGH coupon => ∆ YTM => LOW ∆ Price
LOW coupon => ∆ YTM => HIGH ∆ Price
=> coupon
bé
thì giá biến động
mạnh
Bond price vs Maturity
Maturity effect
LONG maturity => ∆ YTM ≈1% => HIGH ∆ Price
SHORT maturity => ∆ YTM ≈1% => LOW ∆ Price
=> Thời gian càng
dài
=> càng RỦI RO => giá biến động càng
mạnh
The constant-yield price trajectory
Bond value sẽ hội tụ lại tại Par value của bond có YTM = cp rate
Spot rates & Accrued Interest
Spot rate
Thay thế cho
lãi suất ko đổi
(YTM, discount rate) bằng
lãi suất thay đổi
Spot rate bond ≈ no-arbitrage value
Flat price
Accrued interest
Full price
AI = PMT(≈cpon) × t/T
Full price = PV( tại lúc t ngay trước) × (1+r)t/T
Flat price = Full price - AI
Matrix pricing
3-year YTM
is estimated as the
2-year YTM
+
one-third
of the
difference
between the
5-year and 2-year YTM
3-year YTM = 2-year YTM + [ (3-2) / (5-2) ] * (5-year YTM - 2-year YTM)
Yield Measure
Most important
EAR = (1+ (APR / n) )^(n-1)
Fixed-rate Bond
Option-free
Government equivalent yield
Current yield
= Annual cash cp pmt / Bond price
Street convention yield and True yield
(Scheduled cp pmt OR Actual cp pmt)
Simple yield
= ( Annual cash cp pmt + gain/loss (∗) ) / Bond price
Gain/loss
= the straight-line amortization of a discount/premium
Embedded option
Yield-to-call and yield-to-worst
Tính ra từng cái YTM (FV khác nhau, N khác nhau)
YT-1st call: FV = giá bán tại t=1, N = t1 - t0
YT-worst: Tính thêm YTM, YT-2nd call rồi chọn cái thấp nhất
Option-adjusted price
(Value of noncallable bond) = Flat price of callable bond + Value of embedded call option
Floating-rate Bonds
Quoted margin (QM)
:
Coupon rate
= MRR + quote margin (QM)
Required margin/Discount margin (DM):
Discount rate
= MRR + discount margin (DM)
QM để tính coupon
DM để tính discount
Money market instruments
Discount rate basis
Add-on rate basis
Yield Curve & Yield Spread
Yield curve
Spot rate YC
refers to YTMs on a series of zero-coupon government bonds at various maturities.
YC for coupon bonds
Par curve
YTMs for each bond trades at par.
Forward curve
the series of forward rates for bonds or money
market securities for the same maturities for annual periods in the future.
(1+Si)i = (1 + S1)(1 + 1y1y)(1 + 2y1y) ... (1 + (i-1)y1y)
Yield Spread
Benchmark Spread
G-spread (Government)
I-Spread (Interpolated)
Z-Spread (Zero-Volatility Spread)
OA-Spread (Option-adjusted Spread) = Z-spread − Option value
