对外经济贸易大学：《银行管理学 Bank Management》课程教学资源（授课教案课件）Chapter 05 Managing Interest Rate Risk：Duration Gap and Market Value of Equity

卧的贸易孝 1951 Chapter 5 Managing Interest Rate Risk:Duration Gap and Market Value of Equity

Chapter 5 Chapter 5 Managing Interest Rate Managing Interest Rate Risk: Duration Gap and Risk: Duration Gap and Market Value of Equity Market Value of Equity

Duration and price volatility Maturity simply identifies how much time elapses until final payment. 目 It ignores all information about the timing and magnitude of interim payments. Duration is a measure of effective maturity that incorporates the timing and size of a security's cash flows. 目 Duration captures the combined impact of market rate,the size of interim payments and maturity on a security's price volatility. 爸封强的黄香+孝

Duration and price volatility Duration and price volatility † Maturity simply identifies how much time elapses until final payment. † It ignores all information about the timing and magnitude of interim payments. † Duration is a measure of effective maturity that incorporates the timing and size of a security's cash flows. † Duration captures the combined impact of market rate, the size of interim payments and maturity on a security’s price volatility

Duration versus maturity 1.)1000 loan,principal interest paid in 20 years. 2.)1000oan, 900 principal in 1 year, 100 principal in 20 years. 1000+int 10 20 900+int 100 +int 2 1 10 20 爸封强的黄香+孝

Duration versus maturity Duration versus maturity 1.) 1000 loan, principal + interest paid in 20 years. 2.) 1000 loan, 900 principal in 1 year, 100 principal in 20 years. 1000 + int |-------------------|-----------------| 0 10 20 900+int 100 + int |----|--------------|-----------------| 0 1 10 20 1 2

Duration ...approximate measure of the price elasticity of demand Price elasticity of demand =%A in quantity demanded /%4 in price ▣Price（vaue)changes Longer duration>larger changes in price for a given change in i-rates. ■ Larger coupon>smaller change in price for a given change in i-rates. 猫行贺影小号

Duration Duration …approximate measure of the approximate measure of the price elasticity of demand price elasticity of demand † Price elasticity of demand = %∆ in quantity demanded / %∆ in price † Price (value) changes „ Longer duration → larger changes in price for a given change in i-rates. „ Larger coupon → smaller change in price for a given change in i-rates

Duration ..approximate measure of the price elasticity of demand ▣Solve for△Price: ■△P≈-Duration x[△i/(1+i)]xP △P %△△ ■DUR≥ △ %△1 1+i Price (value)changes Longer maturity/duration larger changes in price for a given change in i-rates. 爸封强的黄香+孝

Duration Duration …approximate measure of the price approximate measure of the price elasticity of demand elasticity of demand † Solve for ∆Price: „ ∆P ≅ -Duration x [ ∆i / (1 + i)] x P „ † Price (value) changes „ Longer maturity/duration larger changes in price for a given change in i-rates. ∆i %∆∆ 1 +i ∆i P ∆ P DUR % ≅ − ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ≅ −

Measuring duration In general notation,Macaulay's duration (D): CF(t) D 含8州 CF PV of the Sec. 猫f的贺6号

Measuring duration Measuring duration † In general notation, Macaulay’s duration (D): PV of the Sec. (1 +r) CF (t) (1 +r) CF (1 +r) CF (t) D = n t = 1 t t k t = 1 t t k t = 1 t t ∑ ∑ ∑ =

Measuring duration Example:1000 face value,10%coupon,3 year,12%YTM 100×1 +100×2 ,100×3,1000×3 (1.12)1 (1.122（1.123 (1.123 2597.6 3100 2.73 years 1000 951.96 (1.12)3 的资5+号

Measuring duration Measuring duration † Example: 1000 face value, 10% coupon, 3 year, 12% YTM = 2.73 years 951.96 2597.6 (1.12) 1000 + (1.12) 100 (1.12) 1000 3 + (1.12) 100 3 + (1.12) 100 2 + (1.12) 100 1 D 3 t=1 t 3 1 2 3 3 = × × × × = ∑

Measuring duration ▣If YTM=5/O 1000 face value,10%coupon,3 year, 5%%YTM 100*1 +100*2+100*3+1000*3 (1.05) (1.05)2(1.05)3 (1.05)3 1136.16 3127.31 D 三 2.75 years 1136.16 行贺影小号

Measuring duration Measuring duration † If YTM = 5% 1000 face value, 10% coupon, 3 year, 5% YTM 1136.16 (1.05) 1000 * 3 + (1.05) 100 * 3 + (1.05) 100 * 2 + (1.05) 100 * 1 D 1 2 3 3 = = 2.75 years 1136.16 3127.31 D =

Measuring duration ▣If YTM=20O 1000 face value,10%coupon,3 year,20%YTM 2131.95 D 三 2.68 years 789.35 猫f的贺6号

Measuring duration Measuring duration † If YTM = 20% 1000 face value, 10% coupon, 3 yea r, 20% YTM = 2.68 years 789.35 2131.95 D =

Measuring duration If YTM 12%and Coupon =0 1000 face value,0%coupon,3 year,12%YTM 1000 1000×3 D 三 (1.12)3 3(by definition 1000 (1.12 猫1的對香+手

Measuring duration Measuring duration † If YTM = 12% and Coupon = 0 1000 face value, 0% coupon, 3 yea r, 12% YTM 1000 |-------|-------|-------| 0 1 2 3 3 (by definition (1.12) 1000 (1.12) 1000 3 D 3 3 = × =