The Mathematics of Financial Modelingand Investment Management

2-Financial Markets Page 42 Wednesday, February 4, 2004 1:15 PM

42 The Mathematics of Financial Modeling and Investment Management

pension plans are governed by the Employee Retirement Income Secu-

rity Act of 1974 (ERISA). Pension funds are exempt from taxation.

There are two basic and widely used types of pension plans: defined

contribution plans and defined benefit plans. In a defined contribution

plan, the plan sponsor is responsible only for making specified contribu-

tions into the plan on behalf of qualifying participants. The payments

that will be made to qualifying participants upon retirement will depend

on the growth of the plan assets; that is, payment is determined by the

investment performance of the assets in which the pension fund is

invested. Therefore, in a defined contribution plan, the employee bears

all the investment risk. In a defined benefit plan, the plan sponsor agrees

to make specified dollar payments to qualifying employees at retirement

(and some payments to beneficiaries in case of death before retirement).

The retirement payments are determined by a formula that usually takes

into account both the length of service and the earnings of the

employee. The pension obligations are effectively the liability of the

plan sponsor, who assumes the risk of having insufficient funds in the

plan to satisfy the contractual payments that must be made to retired

employees. Thus, unlike a defined contribution plan, in a defined benefit

plan, all the investment risks are borne by the plan sponsor.

Investment Companies

Investment companies sell shares to the public and invest the proceeds

in a diversified portfolio of securities. Each share they sell represents a

proportionate interest in a portfolio of securities. The securities pur-

chased could be restricted to specific types of assets such as common

stock, government bonds, corporate bonds, or money market instru-

ments. The investment strategies followed by investment companies

range from high-risk active portfolio strategies to low-risk passive port-

folio strategies.

There are two types of managed investment companies: open-end

funds and closed-end funds. An open-end fund, more popularly referred

to as a mutual fund, continually stands ready to sell new shares to the

public and to redeem its outstanding shares on demand at a price equal

to an appropriate share of the value of its portfolio, which is computed

daily at the close of the market. A mutual fund’s share price is based on

its net asset value (NAV) per share, which is found by subtracting from

the market value of the portfolio the mutual fund’s liabilities and then

dividing by the number of mutual fund shares outstanding.

In contrast to mutual funds, closed-end funds sell shares like any

other corporation and usually do not redeem their shares. Shares of

closed-end funds sell on either an organized exchange, such as the New