PowerPoint Presentation
Chapter 21: Bond Immunization Strategies
Copyright By PowCoder代写 加微信 powcoder
What is immunization?
Usually applied to bonds
Definition 1: Financial strategy that portfolio value is not affected by changes in interest rates.
Definition 2: Financial strategy that values of assets and liabilities are equally affected by changes in interest rate.
Usually: Immunize by keeping the duration of the assets equal to the duration of the liabilities.
The big names in immunization:
(1945) wrote an article about protecting banks against changes in interest rates.
(1952) wrote an article about protecting insurance companies against changes in interest rates.
Immunization for a life insurance company
Receives premiums from and promises future benefits to policyholders
Invests premiums in a portfolio of assets to fund the promised future benefits to policyholders. Portfolio assets are typically bonds.
How do we immunize the insurance company’s investment portfolio against changes in interest rates?
Set DURATION of the bond portfolio = DURATION of promised future benefits to policyholders
Immunization for a bank
Loan portfolio (loans made)
Liabilities and Shareholder Equity
Borrowed money (debt/bonds issued)
If interest rate the value of loans made
If interest rate the value of borrowed money
How do we keep the two sides of the balance sheet balanced?
Immunize: Set DURATION of the Loans Made = DURATION of the Borrowed Money
Why immunize?
Cash flows for a 30-year bond, face value $1,000, coupon 7%, paid annually
Year 1 – 29: 7% * $1,000 = $70
Year 30: 7% * $1,000 + $1,000 = $1,070
Reinvest cash flow
Reinvest cash flow
Reinvest cash flow
Reinvestment rate of return?
Why immunize?
You buy bonds today to fund a future obligation. You would like to hedge against changes in interest rates. This is the immunization problem.
You’ve decided to buy a 30-year bond to fund an obligation in year 10.
The funding of the future obligation is composed of two parts:
Reinvested coupons during years 1-10
Selling the bond in year 10
Three bond immunization problem
Parameters:
3 bonds, each with different coupon, maturity, and duration
Future obligation in year 10 of $1,790.85
Each bond has Yield to Maturity (YTM) of 6%
Question 1: How much of each bond to buy in order to fund the future obligation?
Answer: $1,000
Proof of Question 1
Suppose you buy $1,000 face value of Bond 2
15-year maturity, 6.988% coupon
Reinvest coupons for years 1-10 at 6%
Future value in year 10:
% Bond 2 purchased at t = 0
Reinvested coupons at YTM of 6% for years 1 – 10
Bond price in year 10 assuming YTM does not change
Calculation for each of 3 bonds
What if the YTM falls from 6% to 5%?
If the YTM falls to 5%:
Bond 3 fails to fund the future obligation
Bond 1 overfunds the future obligation
Bond 2 is immunized (note that this bond has duration = 10 = duration of the obligation)
What have we shown so far?
To fund an obligation with duration N, pick a bond (or bond portfolio) with duration N
Along the way—we showed how to choose the amount of the bond needed to fund the future obligation
When choosing a bond portfolio
We can choose a portfolio of bonds 1 and 3 with duration = 10
This portfolio has more convexity (meaning: at worst it guarantees funding of the obligation, maybe does better)
When the interest rate increases:
When the interest rate decreases:
THE IMMUNIZATION PROBLEM
Illustrated for the 30-year bond.
0Year 10:Future obligation of $1,790.85 due.30Buy $1,014 face value of 30-year bond.Reinvest coupons from bond during years 1-10.Sell bond for PV of remaining coupons and redemption in year Value of reinvested coupons increases.Value of bond in year 10 decreases.Value of reinvested coupons decreases.Value of bond in year 10 increases.
Yield to maturity 6%
Bond 1Bond 2Bond 3
Coupon rate 6.70%6.988%5.90%
Maturity 101530
Face value 1,0001,0001,000
Bond price $1,051.52$1,095.96$986.24
Face value equal to $1,000 of market value 951.00$ 912.44$ 1,013.96$
Duration 7.665510.000014.6361
New yield to maturity 6%
Bond 1Bond 2Bond 3
Bond price $1,000.00$1,041.62$988.53<-- =-PV($B$14,D6-10,D5*D7)+D7/(1+$B$14)^(D6-10)
Reinvested coupons $883.11$921.07$777.67=-FV($B$14,10,D5*D7)
$1,883.11$1,962.69$1,766.20<-- =D17+D18
Multiply by percent of face value bought 95.10%91.24%101.40%<-- =D10/1000
1,790.85$ 1,790.85$ 1,790.85$ <-- =D21*D19
New yield to maturity 5%
Bond 1Bond 2Bond 3
Bond price $1,000.00$1,086.07$1,112.16<-- =-PV($B$14,D6-10,D5*D7)+D7/(1+$B$14)^(D6-10)
Reinvested coupons $842.72$878.94$742.10=-FV($B$14,10,D5*D7)
$1,842.72$1,965.01$1,854.26<-- =D17+D18
Multiply by percent of face value bought 95.10%91.24%101.40%<-- =D10/1000
1,752.43$ 1,792.97$ 1,880.14$ <-- =D21*D19
1,5001,7001,9002,1002,3002,5002,700
1,5001,7001,9002,1002,3002,5002,7002,9000%2%4%6%8%10%12%14%16%Immunization Properties of the Three BondsBond 1Bond 2Bond 3
1,5001,6001,7001,8001,9002,0002,1000%2%4%6%8%10%12%14%16%Performance of Bond 2 versus Bond PortfolioBond 2Bond portfolio
/docProps/thumbnail.jpeg
程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com