Fixed Income Flashcards
Spot Rate
Market discount rate for a default-risk-free zero-coupon bond
Par Rate
A market discount rate for a specific maturity that would result in bond priced at par
Forward Rate
Incremental return for extending time-to-maturity of a bond for additional time period. Basically it represents breakeven reinvestment rate.
Spot curve relation with Par & Forward curve
If Spot curve is upward sloping, Forward - SPOT - PAR
If Spot curve is downward sloping, PAR - SPOT - Forward
what are 3 sources of return on a FI bond?
- Coupon & Principal
- Reinvestment of coupons
- capital gain/loss with pre maturity sale of bond
Macaulay Duration
Time at which reinvestment gain/loss is offset by one time instantaneous parallel shift in the yield curve
What are different risks for bond investments
- Reinvestment Yield (only risk for buy & hold)
- Price risk
why Macaulay duration is calculated at one time parallel shift of the curve
Every time the spot rate curve is shifted, price changes, changing the Macaulay duration. If the shift is not parallel, we have to consider slope and curvature.
relation b/w Macaulay duration and Investment horizon
- Investment H>MD gives reinvestment risk (falling interest rates is a problem)
- Investment H<MD gives price risk (rising interest rate is a problem)
- Investment H = MD, means reinvestment risk = price risk
What is duration gap?
= Macaulay D - Investment H
The duration gap for a bond is the difference between its Macaulay duration and the investor’s investment horizon.
negative gap = falling rate is a risk
positive gap = rising rate is a risk
Macaulay duration formula
= (1-t/T)(PMT/(1+r)^(1-t/T))/PVfull + (2-t/T)(PMT/(1+r)^(2-t/T))/PVfull + ….. + (N-t/T)*((PMT+FV)/(1+r)^(N-t/T))/PVfull
t/T = time in between coupon payments
Macaulay duration closed formula???
= ((1+r)/r-
Carrying value of a bond??
idk
Modified duration
first derivative of Macaulay duration
= MD/(1+r)
Bond price yield elasticity
=-Mod Duration * delta(yield)
6yr 5.8% annual coupon priced at par. Immediately after the purchase of the bond, interest rates rise to 6.5%. The family office sells the bond after three years. total annualized return on the investment was?
5.28%.
5.80%.
6.50%.
A
Bond has 2 years to maturity, a coupon of 4% paid semiannually, and a YTM of 4.60%. Assuming it is 63 days into the first coupon period and a 30/360 basis, the bond’s annualized Macaulay duration is closest to:
0.9419 years.
1.7666 years.
1.9416 years.
B
https://study.cfainstitute.org/app/cfa-program-level-i-for-may-2025#read/section/introduction-54
What’s MacaulayDuration for a Zero Coupon bond?
No calculation is required, because the Macaulay duration of a zero-coupon bond is its time-to-maturity unless it is between coupon dates.
How to calculate return on FI bond? what is Horizon Yield.
https://study.cfainstitute.org/app/cfa-program-level-i-for-may-2025#read/section/sources-of-return-from-investing-in-a-fixed-rate-bond
- Calculate FV of reinvested coupons
=FV(Rate,nper,PMT,PV,type)
here rate is interest rate (=coupon rate if bought at par), pmt=coupon*100,PV=0 - Calculate PV of price if the bond is sold before maturity =PV(rate,nper,PMT,FV,type)
YOU HAVE TO DO TIME JUMP - calculate realized yield r=(FV/PV)^1/T-1
FV=FV of coupon + bond sell price
This realized yield is also called as Horizon Yield.
What are the different yield based bond duration measures?
Macaulay duration
Modified duration
Money duration
Price Value of Basis point
