Lecture Financial modeling - Topic 11: Fixed income portfolio optimization

Financial Modeling Topic #11: Fixed Income Portfolio Optimization 1 Learning Objectives • Manage the interest rate risk of fixed income portfolios • Compute portfolio value, income, duration, convexity • Compute effective duration • Optimize liabilities funding (pension) using duration and convexity • Optimize fixed income portfolios using duration and convexity 2 Portfolio Duration and Convexity • The duration and convexity of a portfolio of assets are market-value weighted averages of all assets • One method to mitigate a firm’s net exposure to interest rate changes is to match the duration (and interest rate sensitivity) of assets and liabilities. 3 Pension Funding Copy this to PensionLiabilities Disc.Rate 4.50% Pension Year Liabilities • Suppose your organization has a defined benefit pension system and you have estimated the following pension liabilities. • Compute the present value and the duration of the pension using NPV then compute the % change in value when interest rates +/- 100 bps • Effective Duration: Average of Abs(% Value Change) for +/- 100 bps change in the NPV(Liab)rate$ 68,185 ABS(%Diff) 1 $ 10,000 2 $ 9,000 3 $ 8,100 4 $ 7,290 5 $ 6,561 6 $ 5,905 7 $ 5,314 8 $ 4,783 9 $ 4,305 10 $ 3,874 11 $ 3,487 12 $ 3,138 13 $ 2,824 14 $ 2,542 15 $ 2,288 16 $ 2,059 17 $ 1,853 18 $ 1,668 19 $ 1,501 20 $ 1,351 21 $ 1,216 22 $ 1,094 NPV(+100) NPV(-100) Eff Dur. $ 63,967 6.19% $ 72,955 7.00% 6.59% 4 23 $ 985 24 $ 886 25 $ 798 26 $ 718 27 $ 646 28 $ 581 29 $ 523 30 $ 471 Bond Functions Function moddur(cr, par, t, freq, r) Price = bondval(cr, par, t, freq, r) For i = 1 To (t * freq) moddur = moddur + ((cr * par / freq) / (1 + r / freq) ^ i) * i Next i moddur = moddur + (par / (1 + r / freq) ^ (t * freq)) * (t * freq) moddur = moddur / Price / (1 + r / freq) / freq 5 End Function ... - tailieumienphi.vn