ERM Key Rate Durations: Measures of Interest Rate Risks. PAK Study Manual
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1 ERM Key Rate Duratons: Measures of Interest Rate Rsks
2 Related Learnng Objectve 4) Analyze fundng and portfolo management strateges to control equty and nterest rate rsk, ncludng key rate rsks. Explan the concepts of mmunzaton ncludng modern refnements and practcal lmtatons. Contrast the varous rsk measures and be able to apply these rsk measures to varous enttes Key Ponts of Ths Readng 1) Understand the advantages of key rate duratons 2) Understand how to calculate the key rate duratons 3) Understand the key rate duratons for dfferent nstruments 4) Understand how to use the key rate duratons for a portfolo
3 Effectve Duraton It measures the prce senstvty of a bond to the change n nterest rates (assume dfferent ponts n the yeld curve move n the same drecton and magntude) (parallel movement) Rate Year (Term) Change n Bond Prce = P = P D Bond Prce Eff. Dur. Change n rate
4 Key Rate Duraton It measures the prce senstvty of a bond to each key rate (KR) change Rate 1-yr rate 2-yr rate 5-yr rate 10-yr rate 30-yr rate Year (Term) Change n Bond Prce (due to a change n KR) = P = P KR
5 Key Rate Duraton D = The sum of key rate duratons s equal to the effectve duraton The total change n bond prce = = P P KR Postve Duraton A decrease n nterest rate wll ncrease the bond prce (many canddates get ths wrong)
6 Example Securty (2-yr) (16-yr) (30-yr) Effectve Duraton 2yr zero yr zero yr zero Portfolo I: $50 MV of 2-year zero coupon bonds and $50 MV of 30-year zero coupon bonds Portfolo II: $100 MV of 16-year zero coupon bonds (2-yr) (16-yr) (30-yr) Effectve Duraton Portfolo I Portfolo II
7 Example Scenaro (2-yr) (16-yr) (30-yr) 1-10bps -10bps -10bps 2 +10bps 0bps -10bps 3-10bps 0bps +10bps Calculate the changes n portfolo values n these three scenaros Portfolo 1 and Scenaro 1 P = P KR = 50 (2 0.1% %) = 1.6 Portfolo 2 and Scenaro 1 P = P KR = % = 1.6 Concluson: Same mpact
8 Example Scenaro (2-yr) (16-yr) (30-yr) 1-10bps -10bps -10bps 2 +10bps 0bps -10bps 3-10bps 0bps +10bps Calculate the changes n portfolo values n these three scenaros Portfolo 1 and Scenaro 2 P = P KR = 50 (2 0.1% %) = 1.4 Portfolo 2 and Scenaro 2 P = P KR = % = 0 Concluson: No mpact on portfolo 2
9 Example Scenaro (2-yr) (16-yr) (30-yr) 1-10bps -10bps -10bps 2 +10bps 0bps -10bps 3-10bps 0bps +10bps Calculate the changes n portfolo values n these three scenaros Portfolo 1 and Scenaro 3 P = P KR = 50 (2 0.1% %) = 1.4 Portfolo 2 and Scenaro 3 P = P KR = % = 0 Concluson: No mpact on portfolo 2
10 Yeld Curve Movements Level Movement Steepness Rate Rate Year (Term) Curvature Rate Year (Term) Year (Term)
11 Key Rate Duraton Profle 20 Zero-Coupon Bond (ZCB)(20-Year) Coupon Bond (CB)(30-Year, 9%) Key Rate Term 20 Term Callable Corporate Bond (9% vs. 8% 30-Year) Callable Bond Wth Snkng Fund Term Term
12 Key Rate Duraton Profle 10-Year European Call/PutOpton (on a 30-Year Bond) Embedded Opton n a Callable Bond (30-Year, 9%) Put Call Term 30-yr Term 10-yr 30-yr GNMA Pass-Through (30-Year Fxed Rate) Interest-Only (IO) and Prncpal-Only (PO) IO Term 30-yr Term PO 10-yr 30-yr
13 Use to Identfy Interest Rate Bets Term Total Number of KRs = 11 Average = 4.59 / 11 = Term Rato Rato(0.25) = 0.02 / = 0.05 Rato(1) = 0.19 / = 0.46 Rato(30) = 0.16 / = 0.38 Rato() > 1.0 That means the ndex s more senstve to that
14 Use to Create a Hedge Portfolo Calculate the weght: W = T The sum of the weghts s equal to 1: 1 = W The value of the hedge portfolo: V W = V T Invest VW 0 n cash Invest n = 1 VW n zero-coupon bond
15 Use to Create a Hedge Portfolo Term Total Suppose we have ths profle of a portfolo and want to create a hedge portfolo to hedge ts nterest rate exposure VW V T $ = = = $19 1 VW1 = V = = T $ VW2 = V = = T 2 2 Invest $8.0 n three-month blls Invest $19.0 n 1-year ZCB Invest $17.5 n 2-year ZCB VW(1) VW(2) VW(3) VW(4) VW(5) VW(6) VW(7) VW(8) VW(9) VW(10) VW(11) Total Investment V W = VW + VW = = VW VW = 1.5 n Borrow $1.5 n cash
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