zhan chen

A buyback can lift earnings per share without improving the business. Calculate timing, funding costs and net dilution, then test whether the price paid helps remaining shareholders.

A quoted yield is not a guaranteed annual gain. Work through coupon cash flows, reinvestment, early-sale prices and call provisions to calculate the return that fits your holding horizon.

Three worked paths show when rebalancing helps or hurts. Calculate 60/40 allocation drift, cash-flow corrections, trading costs and the difference between percentage-point and relative bands.

A $110 strike does not cap a $120 stock's loss at $10. Reconcile the premium, gap execution, cost basis and expiry before treating a position as protected.

Calculate home-currency returns, dividend conversion and a fixed-principal hedge. A 10% asset gain can become a 3.2% loss—and trading currency is not a hedge.

Reprice a 100,000 bond position, compare duration with convexity, and see why zero net DV01 can still lose money when the yield curve twists.

A five-stock index gains 0.8% even as four constituents fall. Rebuild the contributions, compare equal weighting and breadth, and avoid confusing closing weights with capital flows.

A balance chart can show a 10% drawdown while investment performance falls 32.5%. Rebuild the unit-value path, handle cash-flow timing and calculate recovery and remaining risk room.

A flat benchmark can leave a daily 2× ETF down 1.1852%. Worked examples separate compounding, fund NAV and account returns, including premiums, execution costs and break-even levels.