Asset Liability Management (ALM) Using Duration and Convexity Matching Example 3 3 and 3 4 in Chapter 3 of Phelims Boyles textbook An insurance company has a liability of paying out an annuity, $163 per year for the next fifteen years The duration of this liability is calculated to be 6 2789 years at 10 YTM Solve for the convexity of the liability at 5 , 10 , 15 and 20 rate of interest (last column of Table 3 6) Show your calculations in EXCEL (Note that Example 3 3 provides the duration of bonds, the EXCEL lecture for Week 9 computes the duration of the liability and you have already solved for the convexity of different bonds in Assignment 7 ) Now consider ALM using duration and convexity matching of assets and liability The three bond portfolio of assets that you are going to employ are Bond paying 10 coupons for 5 years Bond paying 10 coupons for 10 years Bond paying 10 coupons for 15 years Assume a flat term structure of 10 (YTM) That means all bonds are trading at par What is quantity of each bond you shall have in your portfolio to match the duration and convexity of the asset portfolio with that of the liability Assume fractionalization of bonds is possible (Hint Watch the last six minutes of the EXCEL lecture for this week) Once you have solved for the quantities of the three bonds in b above, hold that portfolio fixed Chapter three of P Boyles book (posted material) calls it portfolio AP3 in Table 3 7 (page 13 of 13 of the pdf file) Now vary the rates of interest from 8 to 12 in increments of 0 5 (first column of Table 3 7), and fill out columns 2, 3 and 4 of Table 3 7 using your own calculations Show the work in EXCEL (groups not showing the work lose points)

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Aug 26, 2024

Asset Liability Management (ALM) Using Duration and Convexity Matching: Example 3.3 and 3.4 in Chapter 3 of Phelims Boyles textbook An insurance company has a

Asset Liability Management (ALM) Using Duration and Convexity Matching: Example 3.3 and 3.4 in Chapter 3 of Phelims Boyles textbook

An insurance company has a liability of paying out an annuity, $163 per year for the next fifteen years. The duration of this liability is calculated to be 6.2789 years at 10% YTM. Solve for the convexity of the liability at 5%, 10%, 15% and 20% rate of interest (last column of Table 3.6). Show your calculations in EXCEL (Note that Example 3.3 provides the duration of bonds, the EXCEL lecture for Week 9 computes the duration of the liability and you have already solved for the convexity of different bonds in Assignment 7!)
Now consider ALM using duration and convexity matching of assets and liability. The three-bond portfolio of assets that you are going to employ are:
1. Bond paying 10% coupons for 5 years
2. Bond paying 10% coupons for 10 years
3. Bond paying 10% coupons for 15 years

Assume a flat term structure of 10% (YTM). That means all bonds are trading at par.

What is quantity of each bond you shall have in your portfolio to match the duration and convexity of the asset portfolio with that of the liability? Assume fractionalization of bonds is possible (Hint: Watch the last six minutes of the EXCEL lecture for this week)

Once you have solved for the quantities of the three bonds in b. above, hold that portfolio fixed. Chapter three of P Boyles book (posted material) calls it portfolio AP3 in Table 3.7 (page 13 of 13 of the pdf file). Now vary the rates of interest from 8% to 12% in increments of 0.5% (first column of Table 3.7), and fill out columns 2, 3 and 4 of Table 3.7 using your own calculations. Show the work in EXCEL (groups not showing the work lose points).