Module 56: Interest Rate Risk and Return Flashcards
(18 cards)
What are the three sources of returns from investing in a fixed rate bond?
- Coupon and Principal Payments
- Interest earned on coupon payments reinvested
- Any capital gain or less if the bond is sold before maturity
- The last two are affected by changes in interest rate
What is the horizon yield?
It’s the annual return earned from the bond over the investment horizon, based on the absolute total return (incl: Sale of Bond/Redemption, Reinvestment of Coupons)
What is the investment horizon
The time that the bond is held by the investor
How do you work out the Horizon Yield?
Get the PV for both timelines (different YTMs)
On Calculator: FV = Price of Redemption + Reinvested Coupons, PV = bought Price of Bond, N = years, PMT = 0
Other way: (Price of redemption, coupons, etc / price of bond)^1/n - 1
What is a capital gain?
Ir arises if a bond is sold for a price that is different than it’s carrying value (above/below it’s constant yield trajectory
What is the constant yield trajectory?
It’s the trajectory of a bond towards its par value, assuming that YTM is constant
What happens to the horizon yield if Interest rates/YTM doesnt change
The horizon yield is the same irrespective of interest rates going up or going down if the bond’s duration is the macauley duration
What is the macauley duration?
It is the holding period that balances the coupon reinvestment risk and price risk (the two offest each other), where the Horizon Retrun is equal to the original YTM regardless of changes in YTM of the bond
It only works for a parallel
What happens if an investor has a horizon longer than the macauley duration
Then the reinvestment risk (risk with reinvesting the coupon a long time), may prevail over the price risk
This becomes a problem if interest rates fall, as you won’t make as much on the reinvestment of coupons, and this will be bigger than the capital gain increase
What happens if an investor has a horizon shorter than the macauley duration
The price risk will be the more dominant risk, so if interest rates go up, the investor will have a capital loss as bond prices drop, but if your investment horizon is not long enough then your gain from reinvesting the coupon at the higher rate
What is a duration gap?
Macauley Duration - Investment Horizon
(1) if > 0 (so Macauley is higher than investment horizon) then dominant risk is price risk, trouble if interest rates increase, because the drop in bond price will be bigger than the gain in reinvesting in a higher rate as Investment Horizon is too short
(2) if < 0 (so Investment Horizon is larger than Macauley Duration) then dominant risk in reinvestment risk, trouble if interest rates decrease as the reinvestment of the coupon turns out to be loss making to the price yield trajectory
How do you caclulate the reinvestment coupon money on the calculator
N = investment horizon, PMT = Coupon, PV = 0, I/Y = Yield, FV = Coupons
What are the 5 key results
Constant YTM: Holding a bond to maturity yields the initial YTM only if market interest rates (and thus the reinvestment rate) remain unchanged.
YTM Increase (Long-term): If YTM increases after purchase, holding to maturity results in a realised return higher than the initial YTM.
YTM Increase (Short-term): If YTM increases after purchase, selling before maturity results in a realised return lower than the initial YTM.
YTM Decrease (Long-term): If YTM decreases after purchase, holding to maturity results in a realised return lower than the initial YTM.
YTM Decrease (Short-term): If YTM decreases after purchase, selling before maturity results in a realised return higher than the initial YTM.
How do you compute Macauley Duration?
Cash Flows & Timing: Identify all future bond cash flows (coupon payments & principal) and their payment times.
YTM: Determine the bond’s yield to maturity (YTM).
Present Values: Discount each cash flow to its present value using the YTM: PV = CF / (1 + YTM)^t
Weights: Calculate the weight of each cash flow: Weight = PV / (Sum of all PVs)
Macaulay Duration: Calculate the weighted average time: Duration = ∑ (Weight * Time)
How do you compute Macauley Duration for semi annual periods?
Each relevant period would be 1, e.g. 6 months would be period 1, 1 year would be period 2
But need to divide the final result by 2 (as it’s done in semi annual periods)
What is a positive Duration Gap?
If a bond’s Macaulay duration exceeds the investor’s investment horizon, the bond is more sensitive to interest rate changes. Increases in interest rates will lead to a larger price drop, potentially outweighing any gains from reinvesting coupon payments at the higher rates.
