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. 直接将ytm的变化加入valuation model 看对price的变化，如果对于多个要一个一个试
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,倾向单对单且option free的bond
a.iv. Example
题目给出条件：N,PMT,FV,Y/I  Cpt PV
要求改变Y/I xxbps，对PV的影响，直接在计算的时候改Y/I即可，然后与原价格相比较
b. Duration/convexity approach – approximation of the actual interest rate sensitivity of a bond or bond portfolio. (相对full valuation 简单，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. (笑脸的左半边)
b. Duration of a bond is the slop of the price-yield function (和前面的A-c联系)从左往右移时slope下降
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 是negative convexity, at higher yield the callable bond is positive convexity （乙字）
c.iii. At low yield 很有可能被call, 则有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. (前快后慢)
C. Effective duration of a bond
a. Effective duration – the avg of price change in response to equal increase
Effective duration = / D. 知道effective duration and change in yield, 算percentage price change
a. Percentage change in bond price = -effective duration *change in yield in percentage
E. Definition of duration &如何适用于embedded option
a. Macaulay duration – estimate of a bond’s interest rate sensitivity based on the time, in years, until promised cash flows will arrive. (适用于option 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=
注意算weight的时候是用(par value*market price)/total par*maket
b. Limitation of portfolio duration: yields may not change equally on all the bonds in the portfolio (所以说是适用于parallel change in yield curve)
G. Convexity
a. Convexity is a measure of the curvature of the price-yield curve. (弧度越大convexity越大，则与duration所预测出来的价格差别越大)
b. 用duration and convexity 预测price
Percentage change in price=duration effect +convexity effect
={[-duration*Δy]+[convexity*(Δy)^2]}*100
c. 如果只有duration，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