# sol9 - ACTSC 445 Asset-Liability Management Fall 2008...

This preview shows pages 1–2. Sign up to view the full content.

ACTSC 445: Asset-Liability Management – Fall 2008 Department of Statistics and Actuarial Science, University of Waterloo Solutions for Unit 9 Exercises 1. We have that the variance of the overall return on the portfolio, σ 2 V , is equal to 6 . 5 × 10 - 5 . Therefore VaR 0 . 99 , 5 = 5 × 200 000 × 6 . 5 × 10 - 5 × 2 . 33 = 8400 . 93. The sum of the VaR of the two portfolios is 2( 5 × 100 , 000 × 0 . 01) × 2 . 33 = 10420 . 08, so diversification reduces VaR by 2019.14. 2. Can write dV = ∂V ∂f 1 f 1 + ∂V ∂f 2 f 2 where f 1 and f 2 are not correlated since they come from a principal components analysis. The in- formation in the problem tells us that dV = 6 f 1 - 4 f 2 with a variance of 20 2 and 8 2 for f 1 and f 2 , respectively. Therefore, Var( dV ) = σ 2 V = (6 × 20) 2 + (4 × 8) 2 , and so σ V = 124 . 19. Therefore, VaR 0 . 90 , 5 = 5 × 124 . 19 × 1 . 282 = 356 . 02. 3. We have that L = V 0 - V = V 0 - V 0 (1 + R ) = - RV 0 . Therefore CTE = E( - RV 0 | - RV 0 > σV 0 z α ) = E( - RV 0 | - R > σz α ) = - V 0 1 P ( - R > σz α ) - σz α -∞ r e - r 2 / 2 σ 2 2 πσ dr = V 0 σ 2 π (1 - α ) - σz α -∞ - r σ 2 e - r 2 / 2 σ 2 dr = V 0 σ 2 π (1 - α ) e - z 2 α / 2 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern