zhan chen

A stock with beta of 0.4 can still have 40% annual volatility. Reproduce a four-period regression and separate market exposure, residual risk and genuine evidence of added value.

A reproducible six-month example reverses the ranking of two strategies. See how the return target, downside-deviation denominator, annualization and negative ratios change the conclusion.

A 60/40 capital split can produce a 90/10 split of volatility risk. Work through covariance, component contributions, equal risk and joint stress tests before judging diversification.

Reprice a call as the stock rises, time passes and implied volatility falls. A worked model separates those effects from executable bid ask losses and the expiry breakeven.

A plunge from 90 to 32 can be a gain after a three-for-one split. Reconcile share units, portfolio value, chart data, fractional shares and adjusted option deliverables before judging the move.

An ETF can have zero tracking error and still steadily trail its index. Recalculate a four-quarter example and a trade ledger to separate replication risk, return shortfall and investor costs.

Collecting $200 is not the same as earning $200. Reconcile a covered call through expiry payoffs, interim marks and a roll ledger before treating option premiums as income.

A portfolio gains 8% while its investor loses 820. Reconcile the cash ledger, compound the returns and calculate the annual IRR to see what each performance measure actually answers.

A quote of 98 can mean paying 99. Reconcile clean prices, accrued interest and coupon cash across two holding scenarios, then check settlement dates and entitlement before calculating profit.