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# Lecture18 - MGMT 4370 MGMT 7760 Risk Management Aparna...

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11/5/2010 1 MGMT 4370 / MGMT 7760 Risk Management Aparna Gupta Lally School of Management and Technology Office: PITTS 2104 Email: [email protected] Phone: x2757 Back to Interest Rate Risk Assessing Risks in Fixed-Income Instruments - Sensitivities A popular risk measure among traders is “ DV01 ”, meaning change in value of a bond due to change in yield of 1 basis point or 0.01% . A more rigorous definition of measuring sensitivity of price of a Bond w.r.t. interest rates (YTM) is defined by Duration . 23 1. 2. 3. .( ) ..... 1 ( 1)( 1) ( n cF cF cF n cF F yy y y D P + +++ + ++ + + = Duration (or Macaulay Duration) is the weighted average of the dates (in years) of each cash flow, where weights are the present value of the cash payment divided by the sum of the weights, i.e., the price of the bond. Duration of a coupon paying Bond is less than the maturity of the bond – It is exactly equal to the maturity of the bond if there are no coupons. – Longer the maturity of a bond, higher its duration. Assessing Risks in Fixed-Income Instruments - Sensitivities Modified Duration, D* = D/(1+y), and modified duration has a better interpretation: Higher the duration, greater the sensitivity of the Bond price to change in yield. But the price-yield relationship for a Bond is Nonlinear ! Duration is 1 * P D Py Δ −≅ Δ only the first-order approximation of impact of change in yield on the price of a bond, so works for sensitivity of price to yield only in small variations of the yield. Convexity of the Bond price : A second order adjustment to more accurately predict change in value of a bond due to larger changes in yield comes. 2 2 1 P C Δ Δ Assessing Risks in Portfolio of Fixed-Income Instruments Price sensitivity of instruments from the same yield curve can be aggregated from individual sensitivities by calculating weighted- average duration of the instruments held in the portfolio. But this is restrictive for a general portfolio. ** 12 11 2 2 () PP PD yyy ΔΔ ΔΠ =+≅ − + ΔΔΔ For a general portfolio of fixed-income instruments the robust method is the VaR methodology – This requires models for future term-structures of interest rate – Determine price of the instruments in the portfolio under this modified term-structure – Compute the change in value of the portfolio, and – Determine the 1-day or 10-day VaR.

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Lecture18 - MGMT 4370 MGMT 7760 Risk Management Aparna...

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