Corporate bond yield change : answer makes no sense
Here we go: Schwezer notes V.3 , Hedging interest rate risk of corporate bond by shorting government bond
Two government bond: 1) 5- year ; yield 1,9% ; Effective D. 4,7 ; Price 99,96
2) 7 year ; yield 2,2% ; Effective D. 6,5 ; Price 99,56
One corporate bond: 3) 7 year ; yield 3,77% ; Effective D. 6,1 ; Price 101,5.
1) Calculate initial benchmark (G Spread) of corpo bond.
Answer: you find , by basing computation on duration, that you need to short 22,2% of government bond 1 and (1 - 22,2%) of government bond 2. Makes sense.
Benchmark yield becomes 1,64% (corpo yield - weight bond 1 x yield bond 1 - weight bond 2 x yield bond 2)
2) Estimate new price of CORPORATE BOND when yield of GOVERNMENT BOND 1, 5 years increases by 10 bp and yield of GOVERNMENT BOND 2, 7 years increases by 15 bp, while yield of CORPORATE BOND declines 3 bp
You have to use the weights computed in 1 : so 22,2% * 10 bp + (1-22,2%) * 15 bp = 13,9 bp change in the “hedge portfolio” composed of the shorted government bonds
Then, Shwezers use this in the computation applied to government bond yield change to compute the Corporate bond yield change: 13,9 bp - 3 bp = net change of 10,9 bp for Corporate bond yield.
They then apply - Duration * net change = - 6,1 * 0,00109 = -0,0066 = - 0,66%
Why on earth do they do that?
If we see the thing from the angle of the total portfolio with the short position in Gov Bond and the long position in Corpo Bond , then the net change would be [MINUS 13,9bp] - 3bp = - 16,9 bp right ?
I guess the questions is so badly asked in the book it makes the all easy stuff complicated.
Could someone help me on this? Thanks !
Ps: it is p. 367 v.3 CFA III
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