Please see the case study below and find question at the bottom.

Scenario Background

Cascadia is a small country undergoing big changes. A decade ago, Cascadia enacted

legislation to modernize its workforce. Among other things, the legislation established the

Cascadia Department of Education Foundation (CDEF), a fund to support higher education

costs for eligible Cascadian youth.

About the Cascadian school system

Most Cascadians send their children to public primary and secondary schools, which run from

grade 1 to grade 10. Currently, all Cascadian colleges are publicly funded, and all charge the

same tuition.

About the CDEF

The CDEF is separate from all other government funds. An independent body is tasked to

manage the fund according to the risk guidelines given in the legislation. To fund the CDEF, a

special payroll tax is assessed annually against each employed person. The amount of the tax

was fixed at 1,050 Cascadian dollars (CAS) when the fund was established; legislative action is

required to change the payroll tax assessment amount. The fund is available to pay up to four

years of college1 tuition on behalf of eligible college students. The fund is very popular and

recent legislation extended its lifetime to provide payments for any eligible student entering

college within the next 30 years.

CDEF funding is available to students who graduate from a Cascadian public high school and

enroll full-time and immediately at a Cascadian college. Students must maintain a 65% grade

average to receive funding for each subsequent year. Funding covers the full cost of tuition and

is available for four consecutive college years.

An Investment Statement consisting of

Statement of Investment Objectives

Policies

Return Expectations Risk Management

was established to document the key investment objectives, policies, standards and procedures

approved by the Board of Directors of the CDEF Investment Board for the assets of the CDEF,

in accordance with the CDEF Investment Board Act and CDEF Investment Board Regulations.

The Investment Statement is intended to govern the day-to-day management of the CDEF,

including decision authorities, risk management policies and standards, performance

measurement standards and reporting protocols.

The investment policy has not changed since the CDEF was established and recommends the

following target asset mix:

Asset Class Target Mix (%) Portfolio Allocation

Treasuries 15 0% - 30%

Bonds 75 40% - 90%

Equities 10 0% - 30%

The CDEF Investment Board Act had the following objectives:

Assist the CDEF in meeting its obligations to beneficiaries and their contributors.

Manage the assets in the best interest of the CDEF beneficiaries and their contributors.

Invest assets to achieve a maximum rate of return without undue risk of loss.

Ensures the CDEF meets its financial obligations on any given business day.

Recent changes

Following a contentious election, the newly elected government has enacted a program to

determine the true financial health of the Cascadian government. This has prompted a fresh

review of all governments and quasi-government agencies, including the CDEF. A team of

auditors, lawyers, actuaries and forensic business analysts ("ALAF") were tasked with reporting

findings on best and worst practices.

Summary of ALAF's findings related to the CDEF

The current portfolio composition is as follows:

a. 20% of the portfolio is invested in the Build Large Inc. construction company.

b. 15% of the portfolio is invested in the National Oil Company ("NOC") of the

neighboring country Vashnie. NOC is the largest global oil and gas company with a

consistent return of more than 25% over the last 10 years.

c. 15% of the portfolio is invested in Cabbage Incorporated ("CI") a cutting-edge

biopharmaceutical company located outside of Cascadia. CI is developing a

technology to harvest electricity from plants and root vegetables. Their reputation

came from a specialized gene-therapy treatment for cancer which combined Nanotechnology

and DNA-based medicine. In addition to CI's local government, CDEF is

the sole foreign investor in CI.

d. The remaining portfolio of CDEF is invested in traditional assets such as equity, fixed

income and cash in the following proportion: 25% equity, 15% bond and 10% cash.

The Board claims that the investment policy strategy was too restrictive and that it is

there for uninitiated investors only. Furthermore, performance generated for CDEF is a

true testimony to that vision and approach. In fact, the CDEF balance has doubled under

their watch. Last year alone the fund returned 30%.

The Board was also considering as part of their next investment an acquisition of an IT

service company based outside of Cascadia. A discussion has been initiated in

valuations and pricing to pay for the acquisition. There is no paperwork of any prior

discussions other than a thank you email from the president and owner of the IT service

company.

Your Role

You are an actuary working for Fixham Harbor Consulting. Fixham was originally retained by

ALAF to assist in the review of several government agencies, and now the Cascadian Minister

of Finance has asked Fixham to offer recommendations regarding the financial and operational

health of CDEF.

TASK

Fixham has been asked to examine the CDEF investment strategy and portfolio composition. As

part of that larger effort, you have specifically been asked to construct a bond-only portfolio

option. You are provided with the cash flow generated based on the current students' population

which represents the future payments from the CDEF for the foreseeable future. Using the yield

curve provided in the data below, please perform the following:

Calculate the reserve for the CDEF.

Determine the single equivalent rate that would produce the same reserve.

Calculate the modified duration of the reserves.

Recommend an investment strategy which matches the CDEF obligation based on your

answer above; given that in Cascadia there are 3 types of bonds portfolio:

o Short Duration: 9.8

Medium Duration: 13.9

Long Duration 18.2

Summarize and present work in a memo contrasting the

current investment strategy with your recommended strategy.

Data:

Variable: Benefit Payments for Total Liability

Year "Agg Yield

Results" Curve Payment

0 4,623,445,920 1.30% 4,623,445,920

1 4,774,041,344 1.69% 4,774,041,344

2 4,951,737,213 2.04% 4,951,737,213

3 5,151,774,176 2.37% 5,151,774,176

4 5,359,919,338 2.67% 5,359,919,338

5 5,576,438,572 2.94% 5,576,438,572

6 5,801,727,349 3.18% 5,801,727,349

7 6,036,138,306 3.41% 6,036,138,306

8 6,280,020,174 3.61% 6,280,020,174

9 6,533,722,355 3.79% 6,533,722,355

10 6,797,683,311 3.96% 6,797,683,311

11 7,072,312,870 4.10% 7,072,312,870

12 7,358,028,404 4.23% 7,358,028,404

13 7,655,287,705 4.35% 7,655,287,705

14 7,964,532,505 4.46% 7,964,532,505

15 8,286,284,164 4.55% 8,286,284,164

16 8,621,080,300 4.63% 8,621,080,300

17 8,969,399,971 4.70% 8,969,399,971

18 9,331,764,391 4.76% 9,331,764,391

19 9,708,754,247 4.81% 9,708,754,247

20 10,100,987,231 4.85% 10,100,987,231

21 10,509,107,355 4.88% 10,509,107,355

22 10,933,661,648 4.91% 10,933,661,648

23 11,375,367,547 4.93% 11,375,367,547

24 11,834,942,473 4.95% 11,834,942,473

25 12,313,079,989 4.96% 12,313,079,989

26 12,810,527,197 4.97% 12,810,527,197

27 13,328,082,191 4.97% 13,328,082,191

28 13,866,516,677 4.97% 13,866,516,677

29 14,426,709,880 4.96% 14,426,709,880

30 9,465,578,993 4.96% 9,465,578,993

31 5,889,616,805 4.96% 5,889,616,805

32 2,493,773,730 4.96% 2,493,773,730