# Immunized rate and cushion spread (Reading 27 Fixed-income portfolio Management-part I Page 346 to 347)

The following example is illustrated in CFA reading 27 For example, if a firm has a 3-year investment horizon over which it must earn 3% and it can immunize its asset portfolio at 4.75%. If the manager started with a \$500 million portfolio, after three years the portfolio needs to grow to =500*(1+0.03/2)2*3 =546.72 At time 0, the portfolio can be immunized at 4.75%, which implies that the required initial portfolio amount, where dollar amounts are in millions, is Required terminal value/(1+immunized rate/2)2T = 546.72/(1+0.0475/2) 2*3=474.9 If the manager invests the entire 500 million in 4.75%, 10-year notes at par and the YTM immediately changes, what will happen to the dollar safety margin? If the YTM suddenly drops to 3.75%, the value of the portfolio will be \$541.36 million. But I got \$519.21 below, not \$541.36 above Step 1 Terminal value of 10-year note at time 0 =500*(1+0.03/2) 2*10 =673.42 Step 2 The value of portfolio after the three years =673.42/(1+0.0375/2) 2*7=519.21 Any help? Thanks!

This is nothing but a simple bond calculation. PMT=11875000 (500M * 0.02375) 4.75/100/2===0.02375 FV=500M N=20 (10*2) I/Y=1.875% (3.75/2) solve for PV PV=541.36M

546.72/(1+0.0375/2) 2*3 = 489.056 - value of liabilities FV = 500,000,000 Coupon = 11,875,000 I = 1.875 N = 20 PV = 541.36 Here we go

ws beat me!

Only because of a faster computer.