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Fixed-Income Portfolio Management

Fixed-Income Portfolio Management. Strategies Risk Management Trade on interest rate predictions Trade on market inefficiencies. Duration. A measure of the effective maturity of a bond

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Fixed-Income Portfolio Management

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  1. Fixed-Income Portfolio Management • Strategies • Risk Management • Trade on interest rate predictions • Trade on market inefficiencies

  2. Duration • A measure of the effective maturity of a bond • The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment • Duration = the 1st-order derivative of bond price with respect to yield. • Duration = bond’s sensitivity to interest-rate risk

  3. Duration Formula

  4. Properties of Duration • The longer a bond’s maturity, the longer its duration and hence the more risky. • Duration is shorter than maturity for all bonds (except zero coupon bonds) • Duration = maturity, for zero -coupon bonds

  5. 8% Time Payment PV of CF Weight t*wt Bond years (10%) .5 40 38.095 .0395 .0198 1 40 36.281 .0376 .0376 1.5 40 34.553 .0358 .0537 2.0 1040 855.611 . 8871 1.7742 sum 964.540 1.000 1.8853 Duration: Example

  6. Duration/Price Relationship Price change is proportional to duration and not to maturity P/P = -D {(1+y) / (1+y) } or, P/P = - D* y where D* = D / (1+y), modified duration

  7. Rules for Duration Rule 1 The duration of a zero-coupon bond equals its time to maturity Rule 2 Holding maturity constant, a bond’s duration is higher when the coupon rate is lower Rule 3 Holding the coupon rate constant, a bond’s duration generally increases with its time to maturity Rule 4 Holding other factors constant, the duration of a coupon bond is higher when the bond’s yield to maturity is lower

  8. Passive (Risk) Management • Bond-Index Funds • Immunization of interest rate risk • Net worth immunization Duration of assets = Duration of liabilities • Target date immunization Holding Period matches Duration • Cash flow matching and dedication

  9. Price Pricing Error from convexity Duration Duration and Convexity Yield

  10. Adjusting for Convexity Thus, adjusting for Convexity, we have

  11. Better Risk Management • For the previous types of funds/portfolios • Duration Matching duration of assets = duration of liabilities • Convexity Matching:convexity of assets = convexity of liabilities

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