Bond Portfolio Management Strategies债券投资组合管理的策略共30页
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Bond Portfolio Management Strategies
Active, Passive, and Immunization Strategies
Alternative Bond Portfolio Strategies
1. Passive portfolio strategies 2. Active management strategies 3. Matched-funding techniques 4. Contingent procedure (structured active
Where: m = number of payments a year YTM = nominal YTM
Duration and Price Volatility
Bond price movements will vary proportionally with modified duration for small changes in yields
Not symmetrical change
As yields increase, the rate at which prices fall becomes slower
As yields decrease, the rate at which prices increase is faster
1. Bond prices move inversely to bond yields (interest rates) 2. For a given change in yields, longer maturity bonds post
larger price changes, thus bond price volatility is directly related to maturity 3. Price volatility increases at a diminishing rate as term to maturity increases 4. Price movements resulting from equal absolute increases or decreases in yield are not symmetrical 5. Higher coupon issues show smaller percentage price fluctuation for a given change in yield, thus bond price volatility is inversely related to coupon
Convexity
Modified duration approximates price change for small changes in yield
Accuracy of approximation gets worse as size of yield change increases
0.08
0.981 4.254 7.286 11.232 15.829
Source: L. Fisher and R. L. Weil, "Coping with the Risk of Interest Rate Fluctuations: Returns to Bondholders from Naïve and Optimal Strategies," Journal of Business 44, no. 4 (October 1971): 418. Copyright 1971, University of Chicago Press.
Where: t = time period in which the coupon or principal payment occurs Ct = interest or principal payment that occurs in period t i = yield to maturity on the bond
Result – convexity is an attractive feature of a bond in some cases
Positive convexity Negative convexity
Convexity
The measure of the curvature of the priceyield relationship
Second derivative of the price function with respect to yield
Tells us how much the price-yield curve deviates from the linear approximation we get using MD
Indexing methodologies
Full participation Stratified sampling (cellular approach) Optimization approach Variance minimization
Determinants of Price Volatility
Active Management Strategies
Potential sources of return from fixed income port:
1. Coupon income 2. Capital gain 3. Reinvestment income
A composite measure considering both coupon and maturity would be beneficial
Duration
n Ct (t)
D t1 (1i)t
n
t PV(Ct ) t1
n Ct
t1 (1i)t
price
Developed by Frederick R. Macaulay, 1938
underestimates price increases So convexity adjustment should be made to estimate
of % price change using MD
Convexity
Convexity of bonds also affects rate at which prices change when yields change
Duration in Years for Bonds Yielding 6% with Different Terms
COUPON RATES
Years to
Maturity 0.02
0.04
0.06
1 0.995 0.990 0.985 5 4.756 4.558 4.393 10 8.891 8.169 7.662 20 14.981 12.980 11.904 50 19.452 17.129 16.273
Expect rate declines (parallel shift in YC), increase average modified duration to experience maximum price volatility
Expect rate increases (parallel shift in YC), decrease average modified duration to minimize price decline
Duration and Price Volatility
Longest duration security gives maximum price variation
Active manager wants to adjust portfolio duration to take advantage of anticipated yield changes
Performance analysis involves examining tracking error
Passive Portfolio Strategies
Advantages to using indexing strategy
Historical performance of active managers Reduced fees
An estimate of the percentage change in bond prices equals the change in yield time modified duration
PP100Dmodi
Where: P = change in price for the bond P = beginning price for the bond Dmod = the modified duration of the bond i = yield change in basis points divided by 100
management)
Passive Portfolio Strategies
Buy and hold
Can be modified by trading into more desirable positions
Indexing
Match performance of a seleห้องสมุดไป่ตู้ted bond index
Duration
Since price volatility of a bond varies inversely with its coupon and directly with its term to maturity, it is necessary to determine the best combination of these two variables to achieve your objective
Characteristics of Duration
Duration of a bond with coupons is always less than its term to maturity because duration gives weight to these interim payments A zero-coupon bond’s duration equals its maturity
An inverse relation between duration and coupon A positive relation between term to maturity and duration,
but duration increases at a decreasing rate with maturity An inverse relation between YTM and duration Sinking funds and call provisions can have a dramatic
effect on a bond’s duration
Duration and Price Volatility
An adjusted measure of duration can be used to approximate the price volatility of a bond
modid fiu erdat io M nacad uu lary ation 1YTM m
WHY? Modified duration assumes price-yield relationship of
bond is linear when in actuality it is convex. Result – MD overestimates price declines and
Active, Passive, and Immunization Strategies
Alternative Bond Portfolio Strategies
1. Passive portfolio strategies 2. Active management strategies 3. Matched-funding techniques 4. Contingent procedure (structured active
Where: m = number of payments a year YTM = nominal YTM
Duration and Price Volatility
Bond price movements will vary proportionally with modified duration for small changes in yields
Not symmetrical change
As yields increase, the rate at which prices fall becomes slower
As yields decrease, the rate at which prices increase is faster
1. Bond prices move inversely to bond yields (interest rates) 2. For a given change in yields, longer maturity bonds post
larger price changes, thus bond price volatility is directly related to maturity 3. Price volatility increases at a diminishing rate as term to maturity increases 4. Price movements resulting from equal absolute increases or decreases in yield are not symmetrical 5. Higher coupon issues show smaller percentage price fluctuation for a given change in yield, thus bond price volatility is inversely related to coupon
Convexity
Modified duration approximates price change for small changes in yield
Accuracy of approximation gets worse as size of yield change increases
0.08
0.981 4.254 7.286 11.232 15.829
Source: L. Fisher and R. L. Weil, "Coping with the Risk of Interest Rate Fluctuations: Returns to Bondholders from Naïve and Optimal Strategies," Journal of Business 44, no. 4 (October 1971): 418. Copyright 1971, University of Chicago Press.
Where: t = time period in which the coupon or principal payment occurs Ct = interest or principal payment that occurs in period t i = yield to maturity on the bond
Result – convexity is an attractive feature of a bond in some cases
Positive convexity Negative convexity
Convexity
The measure of the curvature of the priceyield relationship
Second derivative of the price function with respect to yield
Tells us how much the price-yield curve deviates from the linear approximation we get using MD
Indexing methodologies
Full participation Stratified sampling (cellular approach) Optimization approach Variance minimization
Determinants of Price Volatility
Active Management Strategies
Potential sources of return from fixed income port:
1. Coupon income 2. Capital gain 3. Reinvestment income
A composite measure considering both coupon and maturity would be beneficial
Duration
n Ct (t)
D t1 (1i)t
n
t PV(Ct ) t1
n Ct
t1 (1i)t
price
Developed by Frederick R. Macaulay, 1938
underestimates price increases So convexity adjustment should be made to estimate
of % price change using MD
Convexity
Convexity of bonds also affects rate at which prices change when yields change
Duration in Years for Bonds Yielding 6% with Different Terms
COUPON RATES
Years to
Maturity 0.02
0.04
0.06
1 0.995 0.990 0.985 5 4.756 4.558 4.393 10 8.891 8.169 7.662 20 14.981 12.980 11.904 50 19.452 17.129 16.273
Expect rate declines (parallel shift in YC), increase average modified duration to experience maximum price volatility
Expect rate increases (parallel shift in YC), decrease average modified duration to minimize price decline
Duration and Price Volatility
Longest duration security gives maximum price variation
Active manager wants to adjust portfolio duration to take advantage of anticipated yield changes
Performance analysis involves examining tracking error
Passive Portfolio Strategies
Advantages to using indexing strategy
Historical performance of active managers Reduced fees
An estimate of the percentage change in bond prices equals the change in yield time modified duration
PP100Dmodi
Where: P = change in price for the bond P = beginning price for the bond Dmod = the modified duration of the bond i = yield change in basis points divided by 100
management)
Passive Portfolio Strategies
Buy and hold
Can be modified by trading into more desirable positions
Indexing
Match performance of a seleห้องสมุดไป่ตู้ted bond index
Duration
Since price volatility of a bond varies inversely with its coupon and directly with its term to maturity, it is necessary to determine the best combination of these two variables to achieve your objective
Characteristics of Duration
Duration of a bond with coupons is always less than its term to maturity because duration gives weight to these interim payments A zero-coupon bond’s duration equals its maturity
An inverse relation between duration and coupon A positive relation between term to maturity and duration,
but duration increases at a decreasing rate with maturity An inverse relation between YTM and duration Sinking funds and call provisions can have a dramatic
effect on a bond’s duration
Duration and Price Volatility
An adjusted measure of duration can be used to approximate the price volatility of a bond
modid fiu erdat io M nacad uu lary ation 1YTM m
WHY? Modified duration assumes price-yield relationship of
bond is linear when in actuality it is convex. Result – MD overestimates price declines and