Workplace reviews and discussion: 凱基證券股份有限公司

It happens regularly every day! The results from the previous batch of experiments still haven’t come out, and the daily optical-disc deliveries have turned my hair gray. Every day I try to find people, but no one can be found. Only this problem seems to be meaningful.

“Determining the Extreme Value of the Cross-Period Net Economic Utility at Year-End Settlement Including Cookie Consumption”

An investor conducted a Year-End Settlement in 2024 and adopted the following criteria as the evaluation standard:

Year-End Settlement objective function =

Financial book profit and loss

Foreign-exchange effects

− Present-value expenses of life events

− Monetary equivalent of utility losses

± Marginal-utility adjustment for cookie consumption

I. Financial Positions (Complete Calculation Required)

(1) Futures

The investor holds 2 long Taiwan Stock Index futures contracts

Contract multiplier: 200

Entry index: 15,750

Year-end settlement index: 16,180

Margin as a percentage of notional value: 12%

Annualized funding cost: 3.5%

The opportunity cost of margin is calculated using continuous compounding

(2) Warrants (Underlying Asset Without Dividends)

European call warrant

Current underlying price: 102

Strike price: 100

Time to expiration: 1 year

No dividends

Risk-free interest rate: 2% (continuously compounded)

Volatility: 28%

Recognized at year-end using the Black–Scholes theoretical value

The number of warrants is configured so that Delta is not 0 (not Delta-neutral)

(3) Currency Position

At the beginning of the year, 120,000 USD was purchased at 29.8 TWD/USD

Year-end exchange rate: 31.4

No interest accrued throughout the year

Foreign-exchange gains and losses must be adjusted for an inflation rate of 1.5%

II. Life Events (Included in the Year-End Settlement After Discounting)

(1) Marriage

Married mid-year

One-time expense: 1,350,000 TWD

Psychological discount rate: 3%

(2) Having a Child

Child born at year-end

Expected expense period: 22 years

Annual real expenditure: 320,000 TWD

Expenditure growth rate: 1%

Discount rate: 2%

(3) Loss of Life Utility

Caused by investment and work-related stress:

Insufficient sleep, utility loss equivalent to 90,000 TWD

Fewer trips to the cinema, utility loss of 45,000 TWD

Fewer visits to all-you-can-eat restaurants, utility loss of 35,000 TWD

III. Cookies (Core Difficulty)

The investor consumed a total of 480 cookies during the year

Price per cookie: 35 TWD

Cookies are immediate-gratification consumption

The marginal utility function of cookies is:

Marginal utility = 1200 / square root of n

where n is the cumulative number of cookies consumed

When marginal utility is less than 35, that portion of consumption is considered overconsumption

The utility corresponding to overconsumption must be included

The utility loss multiplied by a penalty coefficient of 0.6 is used as the year-end settlement adjustment item

IV. Question

After fully incorporating all financial gains and losses, foreign-exchange adjustments, the present value of life events, utility losses, and the marginal-utility adjustment for cookies, which of the following is closest to the investor’s “adjusted net economic effect after the 2024 Year-End Settlement”?

Options (only one correct)

A. Positive 2,800,000 TWD

Financial operations were highly successful, and cookie consumption remained within the range of rational consumption

B. Positive 1,050,000 TWD

Financial gains were significant, but having a child and cookie consumption substantially eroded the results

C. Negative 650,000 TWD

There was a book profit, but the year-end settlement resulted in a substantial real loss

D. Negative 2,300,000 TWD

Highly leveraged financial operations, long-term life expenses, and excessive cookie consumption caused the overall economic situation to deteriorate