Workplace reviews and discussion: 合作金庫金融控股股份有限公司

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“Determining the Extremum of the Cross-Period Net Economic Utility at Year-End Settlement, Including Biscuit Consumption”

During the year-end settlement in 2024, an investor used the following criteria for evaluation:

Year-end settlement objective function =

Financial book profit and loss

Foreign-exchange effects

− Present value of life-event expenses

− Monetary equivalent of utility loss

± Marginal utility adjustment for biscuit consumption

I. Financial Positions (Full Calculations 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 at its 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 were exchanged at 29.8 TWD/USD

Year-end exchange rate: 31.4

No interest earned 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 midyear

One-time expense: 1,350,000 TWD

Psychological discount rate: 3%

(2) Having a Child

Child born at year-end

Expected expenditure 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. Biscuits (Core Difficulty)

The investor consumed a total of 480 biscuits during the year

Price per biscuit: 35 TWD

Biscuits are a form of immediate-pleasure consumption

The marginal utility function of biscuits is:

Marginal utility = 1200 / square root of n

where n is the cumulative number of biscuits already consumed

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

The utility corresponding to overconsumption must be included

The utility loss is multiplied by a penalty coefficient of 0.6 as a 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 biscuit consumption, which of the following is closest to the investor’s “adjusted net economic effect after year-end settlement” for 2024?

Options (Only one is correct)

A. Positive 2,800,000 TWD

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

B. Positive 1,050,000 TWD

Financial profits were substantial, but having a child and biscuit consumption significantly eroded the gains

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 biscuit consumption caused the overall economic situation to deteriorate