BUS307 Topic 3 - Topic 3 Interest Rate Risk Measurement Duration BUS307 Commercial Banking 1.0 Bond Prices Interest rate efect As interest rates

BUS307 Topic 3 - Topic 3 Interest Rate Risk Measurement...

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Topic 3 Interest Rate Risk Measurement Duration BUS307 Commercial Banking
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1.0 Bond Prices Interest rate effect As interest rates increase, bond prices decrease Maturity effect The longer the time to maturity, the greater the price change for a change in interest rates Coupon effect The larger the coupon, the less the price change for a change in interest rates
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1.1 Duration of a Bond Macaulay’s duration is the weighted average time to each cash flow from a bond The weights are the proportions that the present value of each cash flow comprises of the total value of the bond D txC t 1 r t nxFV 1 r n t 1 n C t 1 r t FV 1 r n t 1 n
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1.1 Duration of a Bond (Continued) The formula may be expressed more simply as: D cf t df t t cf t df t D cf t df t t P 0
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1.1 Duration of a Bond (Continued) Duration Calculation of a 5-year, 8% annual coupon bond when the discount rate is 9%. Period (t) Cash flow (cf) Yield = 9% Discount factor (df) Present value of cash flow (cf x df) Weighted cash flows (cf x df x t) 1 80 0.9174 73.39 73.39 2 80 0.8417 67.33 134.67 3 80 0.7722 61.77 185.32 4 80 0.7084 56.67 226.70 5 1080 0.6499 701.89 3,509.45 961.05 4,129.53 Duration (D) = 4,129.53 / 961.05 = 4.30 Years
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1.1 Duration of a Bond (Continued) Duration can be thought of as a weighted average life of a bond represented diagrammatically as follows:
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1.2 Bond Price Sensitivity to Interest Rates Duration captures interest rate sensitivity In BUS288 Treasury Management, it was shown that: D dP P dr 1 r
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1.2 Bond Price Sensitivity to Interest Rates (Continued) Re-arranging: dP P   D dr 1 r P   D . P . r 1 r
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2.0 Duration of Bank Assets and Liabilities The duration of fixed interest loans and deposits is determined as for bonds Floating rate instruments have duration equal to the time until interest rates are reset Perpetual bonds have a duration given by: Call deposits are sometimes assigned a duration equal to the turnover period D 1 r r
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2.1 Duration of a Portfolio
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