CFA review Essay

CFA review Essay CFA review Essay Los 58 Introduction to the measurement of interest rate risk A. Full valuation approach &the duration/convexity approach a. The full valuation approach (scenario analysis approach) – based on applying the valuation techniques for a given change in the yield. a.i. ç› ´Ã¦Å½ ¥Ã¥ °â€ ytmçš„å ËœÃ¥Å'â€"åŠ  Ã¥â€¦ ¥valuation model çÅ"‹å ¯ ¹priceçš„å ËœÃ¥Å'â€"ï ¼Å'Ã¥ ¦â€šÃ¦Å¾Å"Ã¥ ¯ ¹Ã¤ ºÅ½Ã¥ ¤Å¡Ã¤ ¸ ªÃ¨ ¦ Ã¤ ¸â‚¬Ã¤ ¸ ªÃ¤ ¸â‚¬Ã¤ ¸ ªÃ¨ ¯â€¢ a.ii. Stress testing a bond portfolio – using this approach with extreme changes in interest rates a.iii. Can be used to evaluate the price effects of more complex interest rate scenarios,å€ ¾Ã¥ â€˜Ã¥ â€¢Ã¥ ¯ ¹Ã¥ â€¢Ã¤ ¸â€option freeçš„bond a.iv. Example é ¢ËœÃ§â€º ®Ã§ »â„¢Ã¥â€¡ ºÃ¦  ¡Ã¤ » ¶Ã¯ ¼Å¡N,PMT,FV,Y/I ïÆ'   Cpt PV è ¦ Ã¦ ±â€šÃ¦â€ ¹Ã¥ ËœY/I xxbpsï ¼Å'Ã¥ ¯ ¹PVçš„å ½ ±Ã¥â€œ Ã¯ ¼Å'ç› ´Ã¦Å½ ¥Ã¥Å" ¨Ã¨ ® ¡Ã§ ®â€"çš„æâ€" ¶Ã¥â‚¬â„¢Ã¦â€ ¹Y/IÃ¥  ³Ã¥  ¯Ã¯ ¼Å'ç„ ¶Ã¥ Å½Ã¤ ¸Å½Ã¥Å½Å¸Ã¤ » ·Ã¦   ¼Ã§â€º ¸Ã¦ ¯â€Ã¨ ¾Æ' b. Duration/convexity approach – approximation of the actual interest rate sensitivity of a bond or bond portfolio. (ç› ¸Ã¥ ¯ ¹full valuation ç ®â‚¬Ã¥ â€¢Ã¯ ¼Å'only for estimating the effects of parallel yield curve shifts) c. Higher(lower) coupon means lower(higher)duration Longer(shorter) maturity means higher(lower)duration Higher(lower) market yield mean lower(higher)duration B. Positive convexity and negative convexity a. Option-free bond has positive convexity – curve is convex (toward the origin) price increases more when yield fall than it decreases when yields rise. (ç ¬â€˜Ã¨â€ž ¸Ã§Å¡â€žÃ¥ · ¦Ã¥ Å Ã¨ ¾ ¹) b. Duration of a bond is the slop of the price-yield function (å’Å'å‰ Ã©  ¢Ã§Å¡â€žA-cè â€Ã§ ³ »)ä »Å½Ã¥ · ¦Ã¥ ¾â‚¬Ã¥  ³Ã§ § »Ã¦â€" ¶slopeä ¸â€¹Ã©â„¢  c. Callable bonds, prepayable securities, and negative convexity c.i. Callable bond and prepayable securities have upside price appreciation, so price rise at a decreasing rate to decrease yield negative convexity c.ii. At lower yield the callable bond æ˜ ¯negative convexity, at higher yield the callable bond is positive convexity ï ¼Ë†Ã¤ ¹â„¢Ã¥ ­â€"ï ¼â€° c.iii. At low yield Ã¥ ¾Ë†Ã¦Å"‰å  ¯Ã¨Æ' ½Ã¨ ¢ «call, 则æÅ"‰risk reinvest at low yield d. The price volatility characteristics of putable bond d.i. Price increases at higher yields slow and decrease at lower yield fast. (å‰ Ã¥ ¿ «Ã¥ Å½Ã¦â€¦ ¢) C. Effective duration of a bond a. Effective duration – the avg of price change in response to equal increase Effective duration = / D. çŸ ¥Ã© â€œeffective duration and change in yield, ç ®â€"percentage price change a. Percentage change in bond price = -effective duration *change in yield in percentage E. Definition of duration &Ã¥ ¦â€šÃ¤ ½â€¢Ã©â‚¬â€šÃ§â€ ¨Ã¤ ºÅ½embedded option a. Macaulay duration – estimate of a bond’s interest rate sensitivity based on the time, in years, until promised cash flows will arrive. (适ç” ¨Ã¤ ºÅ½option free) b. Effective duration was appropriate for bonds with embedded options because the input (price) were calculated under the assumption that the cash flows could vary at different yields because of the embedded options in the securities. c. Modified duration = Macaulay duration/(1+periodic market yield) d. Interpreting duration d.i. Duration is the slope of the price-yield curve at the bond’s current YTM (first derivative) d.ii. A weighted average of the time(in yrs)until each cash flow will be received d.iii. Approximate percentage change in price for a 1% change in yield. F. Calculate the duration of portfolio a. Portfolio duration= æ ³ ¨Ã¦â€ž Ã§ ®â€"weightçš„æâ€" ¶Ã¥â‚¬â„¢Ã¦Ëœ ¯Ã§â€ ¨(par value*market price)/total par*maket b. Limitation of portfolio duration: yields may not change equally on all the bonds in the portfolio (所ä » ¥Ã¨ ¯ ´Ã¦Ëœ ¯Ã©â‚¬â€šÃ§â€ ¨Ã¤ ºÅ½parallel change in yield curve) G. Convexity a. Convexity is a measure of the curvature of the price-yield curve. (Ã¥ ¼ §Ã¥ º ¦Ã¨ ¶Å Ã¥ ¤ §convexityè ¶Å Ã¥ ¤ §Ã¯ ¼Å'则ä ¸Å½duration所é ¢â€žÃ¦ µâ€¹Ã¥â€¡ ºÃ¦  ¥Ã§Å¡â€žÃ¤ » ·Ã¦   ¼Ã¥ · ®Ã¥Ë† «Ã¨ ¶Å Ã¥ ¤ §) b. ç” ¨duration and convexity é ¢â€žÃ¦ µâ€¹price Percentage change in price=duration effect +convexity effect ={[-duration*Δy]+[convexity*(Δy)^2]}*100 c. Ã¥ ¦â€šÃ¦Å¾Å"Ã¥  ªÃ¦Å"‰durationï ¼Å'underestimate of the percentage increase in the bond price when yields fell, overestimate of the percentage decrease in the bond price when yield rose. [check p145 figure 4] d. For callable bond, convexity can be negative at low yield. Convexity adjustment will be negative for both yield increase and yield decrease. H. Modified convexity and effective convexity a. Effective convexity takes into account change in cash flows due to embedded options, while modified convexity does not, since it is based on