R20 - Total Return + Immunization

Question 1

What is the Horizon Price of a bond?

Answer 1

PV of bond if cashflows reinvested at current yield

Question 2

Two ways to match liabilities?

Answer 2

Cash flow match - buy zero coupon default free bond; riskless; matches cashflow exactly; but expensive

Immunization - match duration of assets and liabilities;

Question 3

Requirements and assumptions of single-liability immunization:

Answer 3

Duration of asset and liability = horizon date
PVa = PV of liability
FV of asset = face value of liability to be paid

Assumptions:

• one small immediate parallel shift in yield curve
• liability amounts and dates don’t change
• no assets default

Question 4

Why is rebalancing necessary when matching duration of assets and liabilities?

Answer 4

Because interest rates change over time (i.e. There is not just one parallel shift in yield curve)

Question 5

Dollar Duration (DD) equation:

Answer 5

DD = Value x Duration x 0.01

Question 6

Rebalancing ratio (RR) equation:

Answer 6

DesiredDDp/newDDp = RR

If RR < 1, then sell bonds at 1-RR (percent to sell)
If RR > 1, then buy bonds at RR - 1 (percent to buy)

Question 7

Types of spread duration?

Answer 7

Nominal - spread between treasury and non treasury
Zero-volatility - spread added to spot curve to equate cash flows and price
Option-adjusted spread - spread accounting for embedded options