A portfolio with ten ETFs does not necessarily contain ten independent bets. Several sector funds may rise and fall with the same equity-market shock. A collection of bond ETFs may share much of it...

A high-volatility state estimated from historical returns can help describe market risk. Turning that state into an option price requires another ingredient: the price investors assign to future re...

In the realm of financial planning, incorporating risk into investment decisions is paramount. This post explores a stochastic programming model aimed at optimizing investment strategies over a giv...

This post is about methodologies to measure private investment return (python code included). Reference for this post can be found in INSEAD case studies. Full python code can be found in my GitHub...

Two regressions can explain almost the same sector returns while assigning quite different importance to value, profitability, and investment. When those factor returns overlap, the data may identi...

Technology and Utilities are both equity sectors, but their responses to common return patterns differ. Factor analysis makes those differences visible. The harder question is whether an exposure e...

A credit default swap exchanges a running premium for protection against specified credit events. A useful implementation must connect the quoted spreads to survival probabilities and then explain ...

A cross-currency swap combines two interest-rate exposures with an exchange-rate exposure. Before choosing a curve engine, it helps to write the actual currency ledger, including principal exchange...

An interest rate swap becomes easier to reason about when “pay fixed” and “receive floating” are written as signed cash flows. Its initial fair coupon is a consequence of those flows, their schedul...

A floating-rate coupon needs a forecast of its index fixing and a discount factor for its payment date. Those are different modeling jobs. A desk implementation should make that distinction explici...