@quantfinancetogo: ➡️ Quant Finance from scratch part 11: diversification Step 1, a hundred assets. Every simulated asset shares the hidden market from Part 10 and gets its own push on top. Each is built to earn 8 % a year and to swing 20 %, and any two of them have a correlation of 0.30. Step 2, spread the money. All of it in one asset swings 20.0 % a year. Split evenly across ten assets, the risk drops to 12.2 %, while the return stays at about 8 % (8.3 % and 8.1 % in the run). Their own pushes partly cancel, while the market push hits all of them the same way. Step 3, the Sharpe ratio from Part 8, the return above a safe 3 % per unit of risk. One asset scores 0.26, the mix of ten scores 0.42. Less risk at no cost in expected return is why diversification is often called a free lunch. It only works this well because all these assets earn about the same; mixing in assets that earn less costs return. Step 4, the limit. 20 assets swing 11.6 %, 50 swing 11.2 % and 100 swing 11.1 %. The curve flattens toward 11.0 %, the risk of the shared market by itself. With N equal assets that each swing s and have pair correlation c, the mix swings s x sqrt(c + (1 - c) / N), which can never fall below s x sqrt(c). Textbooks call the shared part systematic or market risk, and the part that averages away idiosyncratic or firm-specific risk. How many holdings are enough is debated: Evans and Archer (Journal of Finance, 1968) found most of the effect within about ten stocks, while Statman (Journal of Financial and Quantitative Analysis, 1987) argued for at least 30 to 40. The idea that portfolio risk depends on how assets move together goes back to Harry Markowitz, "Portfolio Selection" (Journal of Finance, 1952; Nobel prize 1990) This video is for education only, and nothing in it is financial advice. #quantfinance #diversification #portfolio #risk #sharperatio

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Saturday 03 October 2026 12:38:49 GMT