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Portfolio Weights, Short Selling, and Leverage: The Math

Your home mortgage is a leveraged portfolio — you just haven't seen it that way yet. This video breaks down the foundational concept of portfolio weights: how every investment position is defined not by dollar amounts or share counts, but by proportions of total wealth. From there, we build up to short selling (negative weights) and leverage (weights exceeding 100%), showing exactly how a 5:1 leveraged mortgage turns a 2% housing decline into a 10% equity loss. Key concepts covered: • Portfolio weight vectors and the formula for calculating individual weights • The constraint that weights must always sum to 100% — and why this is a mathematical identity, not a rule • Short selling as negative portfolio weights, with a worked two-asset example • Leverage through borrowing: how investing twice your capital creates 2:1 exposure • Home mortgage as a leveraged portfolio: a full numerical walkthrough at 5:1 leverage • The 130-30 institutional portfolio structure and its variants • Leveraged S&P 500 returns (1x, 2x, 3x) from 2019–2024 and the cost of amplified drawdowns • Portfolio weight drift: why not rebalancing is itself an active decision • Zero-investment portfolios as the foundation of arbitrage strategies — ORIGINAL SOURCE This video distills concepts from the following lecture:    • Ses 13: Risk and Return II & Portfolio The...   Full credit to the original author and lecturer. — About Ludium Learn. Play. Discover. Ludium distills long lectures into focused concept videos, making rigorous ideas accessible without sacrificing depth. GitHub: https://github.com/Augustinus12835/au... #PortfolioTheory #Leverage #ShortSelling #PortfolioWeights #InvestingMath #FinancialEducation #RiskManagement #Ludium