FIXED INCOME SECURITIES - MANAGING BOND PORTFOLIOS
Introduction
Two management strategies are most commonly used:
1. Passive Management
• assumes that market prices are fairly set.
• only seek to control the risk of their bond portfolio
2. Active Management Strategies are based on the belief that the market misprices
securities.
• trade on market inefficiencies
• to predict market movements (interest rate movements)
• Key source of return is capital gain
o Both are concerned with concepts of interest rate risk
INTEREST RATE RISK
Introduction
- Driven by fluctuations in interest rates
- Forms of interest rate risk:
• Reinvestment risk - affects the income from the reinvestment of coupons.
• Price risk - affects capital gains/losses. The variability in bond prices caused by
their inverse relationship with interest rates.
o The magnitude of the gains/losses - B.P/I.R sensitivity, B.P volatility
P
o The B.P variability/sensitivity= [P1] − 1
0
o a high price change/high Capital gains/losses means…
o Properties of bond price sensitivity
- What do you make of these two forms of IR risks
Properties of interest rate risk: Price risk
- Property 1: Inverse relationship between bond price and yields
- Property 2: For small changes in yields, the price sensitivity of a given bond is roughly
the same - for an increase/decrease in yield
- Property 3: For large changes in yields, the price sensitivity is not the same for an
increase and a decrease in the required yield.
- Property 4: For large changes in yields for a given bond, the % price increase > price
decrease - convexity
- Property 5: The price sensitivity [price change] is not the same for all bonds.
,Factors that affect bond price sensitivity
1. Time to maturity
2. Coupon
3. Yield to Maturity (YTM)
NB:
- Knowledge of how these factors affect bond price sensitivity is important to passive
and active managers. Help you to know if a bond is high/lowly sensitive
- Pave way for consolidated measures of IR risk
Time to maturity:
- Proposition 1: Prices of long-term bonds tend to be more sensitive to changes in
interest rates than short-term bonds (in general)
- Implications of proposition 1 to a bond trader who is forecasting interest rates to
decline
- Proposition 2: any observations from the table
Coupon rate:
Bond name Maturity Coupon Price @ Price @ Price
(years) rate 10% YTM 11% YTM change as %
T 5 10% R1 000 R963.04 -3.696%
M 5 12% R1 075.82 R1 036.96 -3.612%
- Proposition 3: Prices of low-coupon bonds tend to be more sensitive to changes in
interest rates than high-coupon bonds (interest rate risk is inversely proportional to
coupons)
, Yield to maturity:
Bond name Maturity Coupon rate YTM Price (R) at
(years) given YTM
A 1 10% 5% R1 047.62
B 1 10% 10% R1 000.00
C 1 10% 15% R956.52
Bond name Maturity Coupon rate YTM Price (R) at Price
(years) given YTM change
A 1 10% 6% R1 047.62 -0.94%
B 1 10% 11% R1 000.00 -0.90%
C 1 10% 16% R956.52 -0.86%
- Proposition 4: Sensitivity of a bond’s price to a change in its yield is inversely related
to the yield to maturity at which the bond currently is selling
MEAURING INTEREST RATE RISK: DURATION
- Duration is a measure of bond price sensitivity
- Duration is applied in
1. Trading strategies (simple trading decisions and immunization)
2. Estimate bond price changes when yields change, accurate only for small
changes in yields
- Formula:
• 𝐷 = ∑𝑇𝑡=1 𝑡 × 𝑤𝑡
1
𝐶𝐹𝑡 [(1+𝑟)𝑛 ]
• 𝑤𝑡 =
Price
• CFt = cash flow at time t (coupons and face value)
- The weighted average term to maturity of the discounted cash flows, with the
weights proportional to the present value of the payments (Macaulay’s duration).
EXAMPLE 1
Introduction
Two management strategies are most commonly used:
1. Passive Management
• assumes that market prices are fairly set.
• only seek to control the risk of their bond portfolio
2. Active Management Strategies are based on the belief that the market misprices
securities.
• trade on market inefficiencies
• to predict market movements (interest rate movements)
• Key source of return is capital gain
o Both are concerned with concepts of interest rate risk
INTEREST RATE RISK
Introduction
- Driven by fluctuations in interest rates
- Forms of interest rate risk:
• Reinvestment risk - affects the income from the reinvestment of coupons.
• Price risk - affects capital gains/losses. The variability in bond prices caused by
their inverse relationship with interest rates.
o The magnitude of the gains/losses - B.P/I.R sensitivity, B.P volatility
P
o The B.P variability/sensitivity= [P1] − 1
0
o a high price change/high Capital gains/losses means…
o Properties of bond price sensitivity
- What do you make of these two forms of IR risks
Properties of interest rate risk: Price risk
- Property 1: Inverse relationship between bond price and yields
- Property 2: For small changes in yields, the price sensitivity of a given bond is roughly
the same - for an increase/decrease in yield
- Property 3: For large changes in yields, the price sensitivity is not the same for an
increase and a decrease in the required yield.
- Property 4: For large changes in yields for a given bond, the % price increase > price
decrease - convexity
- Property 5: The price sensitivity [price change] is not the same for all bonds.
,Factors that affect bond price sensitivity
1. Time to maturity
2. Coupon
3. Yield to Maturity (YTM)
NB:
- Knowledge of how these factors affect bond price sensitivity is important to passive
and active managers. Help you to know if a bond is high/lowly sensitive
- Pave way for consolidated measures of IR risk
Time to maturity:
- Proposition 1: Prices of long-term bonds tend to be more sensitive to changes in
interest rates than short-term bonds (in general)
- Implications of proposition 1 to a bond trader who is forecasting interest rates to
decline
- Proposition 2: any observations from the table
Coupon rate:
Bond name Maturity Coupon Price @ Price @ Price
(years) rate 10% YTM 11% YTM change as %
T 5 10% R1 000 R963.04 -3.696%
M 5 12% R1 075.82 R1 036.96 -3.612%
- Proposition 3: Prices of low-coupon bonds tend to be more sensitive to changes in
interest rates than high-coupon bonds (interest rate risk is inversely proportional to
coupons)
, Yield to maturity:
Bond name Maturity Coupon rate YTM Price (R) at
(years) given YTM
A 1 10% 5% R1 047.62
B 1 10% 10% R1 000.00
C 1 10% 15% R956.52
Bond name Maturity Coupon rate YTM Price (R) at Price
(years) given YTM change
A 1 10% 6% R1 047.62 -0.94%
B 1 10% 11% R1 000.00 -0.90%
C 1 10% 16% R956.52 -0.86%
- Proposition 4: Sensitivity of a bond’s price to a change in its yield is inversely related
to the yield to maturity at which the bond currently is selling
MEAURING INTEREST RATE RISK: DURATION
- Duration is a measure of bond price sensitivity
- Duration is applied in
1. Trading strategies (simple trading decisions and immunization)
2. Estimate bond price changes when yields change, accurate only for small
changes in yields
- Formula:
• 𝐷 = ∑𝑇𝑡=1 𝑡 × 𝑤𝑡
1
𝐶𝐹𝑡 [(1+𝑟)𝑛 ]
• 𝑤𝑡 =
Price
• CFt = cash flow at time t (coupons and face value)
- The weighted average term to maturity of the discounted cash flows, with the
weights proportional to the present value of the payments (Macaulay’s duration).
EXAMPLE 1
