金融机构管理Chap009.pptVIP

Immunization and Regulatory Concerns Regulators set target ratios for an FI’s capital (net worth): Capital (Net worth) ratio = E/A If target is to set ?(E/A) = 0: DA = DL But, to set ?E = 0: DA = kDL Limitations of Duration Immunizing the entire balance sheet need not be costly Duration can be employed in combination with hedge positions to immunize Immunization is a dynamic process since duration depends on instantaneous R Large interest rate change effects not accurately captured Convexity More complex if nonparallel shift in yield curve Convexity The duration measure is a linear approximation of a non-linear function. If there are large changes in R, the approximation is much less accurate. All fixed-income securities are convex. Convexity is desirable, but greater convexity causes larger errors in the duration-based estimate of price changes. *Convexity Those who are familiar with calculus may recognize that duration involves only the first derivative of the price function. We can improve on the estimate using a Taylor expansion. In practice, the expansion rarely goes beyond second order (using the second derivative). This second order expansion is the convexity adjustment. *Modified Duration Convexity DP/P = -D[DR/(1+R)] + (1/2) CX (DR)2 or DP/P = -MD DR + (1/2) CX (DR)2 Where MD implies modified duration and CX is a measure of the curvature effect. CX = Scaling factor × [capital loss from 1bp rise in yield + capital gain from 1bp fall in yield] Commonly used scaling factor is 108 *Calculation of CX Example: convexity of 8% coupon, 8% yield, six-year maturity Eurobond priced at $1,000 CX = 108[DP-/P + DP+/P] = 108[(999.53785-1,000)/1,000 + (1,000.46243-1,000)/1,000)] = 28 *Duration Measure: Other Issues Default risk Floating-rate loans and bonds Duration of demand deposits and passbook savings Mortgage-backed securities and mortgages Duration relationship affected by call or prepayment provisions *Contingent Claims Interest rate cha