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Lecture Financial modeling - Topic 11: Fixed income portfolio optimization
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Topic 11 - Fixed income portfolio optimization. After completing this topic, you should be able to: 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. | Financial Modeling Topic #11: Fixed Income Portfolio Optimization L. Gattis 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 3 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. Pension Funding 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 discount rate 4 Copy this to Excel 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 End Function Function convexity(cr, par, t, freq, r) Price = bondval(cr, par, t, freq, r) For i = 1 To (t * freq) convexity = convexity + (cr * par / freq) * (1 + r / freq) ^ -i * i * (1 + i) Next i convexity = convexity + par * (1 + r / freq) ^ -(t * freq) * (t * freq) * (1 + t * freq) convexity = convexity / (Price * (1 + r / freq) ^ 2) * freq ^ (-2) End Function Function bondval(cr, par, t, freq, r) n = t * freq 'number of pmts For i = 1 To n bondval = bondval + (cr * par / freq) / (1 + r / freq) ^ i Next i bondval = bondval + par / (1 + r / freq) ^ n End Function 5 How to Invest the Pension Assets? Find mix of the following bonds that maximizes | Financial Modeling Topic #11: Fixed Income Portfolio Optimization L. Gattis 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 3 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. Pension Funding 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 .