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𝙐𝙎𝙀 𝙃𝙀𝘼𝘿𝙋𝙃𝙊𝙉𝙀𝙎 🎧 𝙁𝙊𝙍 𝘼 𝘽𝙀𝙏𝙏𝙀𝙍 𝙀𝙓𝙋𝙀𝙍𝙄𝙀𝙉𝘾𝙀 ♫ ♥️𝙎𝙇𝙊𝙒𝙀𝘿 + 𝙍𝙀𝙑𝙀𝙍𝘽 ✦ | 𝙏𝙐𝙍𝙉 𝙐𝙋 𝙏𝙃𝙀 𝙑𝙊𝙇𝙐𝙈𝙀. 𝙇𝙊𝙎𝙀 𝙔𝙊𝙐𝙍𝙎𝙀𝙇𝙁🔥🚩#fyp #SMW #viral #justiceforsidhumosewala #nayab_7

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The best ✨🔥 #edit #hansohee #jiwoo #myname #kdrama

A motorbike rider was knocked to the ground after a car suddenly veered into his bike in a dramatic moment caught on CCTV. The collision sent the motorcycle crashing forward into another man sitting nearby outside a tea shop in Tamil Nadu, India. The man was taken to the hospital but reportedly escaped serious injury. #india #cctv #car #driving #news

A motorbike rider was knocked to the ground after a car suddenly veered into his bike in a dramatic moment caught on CCTV. The collision sent the motorcycle crashing forward into another man sitting nearby outside a tea shop in Tamil Nadu, India. The man was taken to the hospital but reportedly escaped serious injury. #india #cctv #car #driving #news

➡️ Quant Finance from scratch Part 13: the efficient frontier Step 1, three simulated assets with assumed numbers, not forecasts: A, like bonds, earns 4 % a year at 6 % risk (volatility), B, like stocks, 7 % at 18 %, and C, like a riskier stock, 11 % at 25 %. A moves on its own, while B and C have a correlation of 0.5. For real assets these inputs have to be estimated from data. Step 2, every mix is a dot. The program mixes the three assets in 5,000 random ways (weights from 0 to 100 %, adding up to 100 %) and puts every mix on a map with risk across and expected return up. The risk of a mix depends on how its assets move together, which is why mixing can lower it (Parts 10 and 11). Step 3, the upper edge. At every level of risk, the mixes on the upper edge of the cloud earn the most. The program sorts the mixes by risk and keeps a mix only if it earns more than every mix with less risk, and 825 of the 5,000 pass. The mix with the lowest risk in this simulation swings 5.7 % (return 4.4 %), a little less than A alone. Asset B alone sits below the edge: at the same 18 % risk the edge earns 9.1 % instead of 7.0 %, so its Sharpe ratio (Part 8, safe rate 3 %) is 0.34 instead of 0.22. Along the edge, more return always costs more risk, and which point fits depends on how much risk someone wants to take. More mixes bring the edge closer to the exact frontier, which Markowitz showed in 1956 can be computed directly by quadratic programming. The idea goes back to Harry Markowitz,

➡️ Quant Finance from scratch Part 13: the efficient frontier Step 1, three simulated assets with assumed numbers, not forecasts: A, like bonds, earns 4 % a year at 6 % risk (volatility), B, like stocks, 7 % at 18 %, and C, like a riskier stock, 11 % at 25 %. A moves on its own, while B and C have a correlation of 0.5. For real assets these inputs have to be estimated from data. Step 2, every mix is a dot. The program mixes the three assets in 5,000 random ways (weights from 0 to 100 %, adding up to 100 %) and puts every mix on a map with risk across and expected return up. The risk of a mix depends on how its assets move together, which is why mixing can lower it (Parts 10 and 11). Step 3, the upper edge. At every level of risk, the mixes on the upper edge of the cloud earn the most. The program sorts the mixes by risk and keeps a mix only if it earns more than every mix with less risk, and 825 of the 5,000 pass. The mix with the lowest risk in this simulation swings 5.7 % (return 4.4 %), a little less than A alone. Asset B alone sits below the edge: at the same 18 % risk the edge earns 9.1 % instead of 7.0 %, so its Sharpe ratio (Part 8, safe rate 3 %) is 0.34 instead of 0.22. Along the edge, more return always costs more risk, and which point fits depends on how much risk someone wants to take. More mixes bring the edge closer to the exact frontier, which Markowitz showed in 1956 can be computed directly by quadratic programming. The idea goes back to Harry Markowitz, "Portfolio Selection" (Journal of Finance, 1952). He shared the 1990 Nobel prize in economics with Merton Miller and William Sharpe, and his part was awarded for having developed the theory of portfolio choice, whose core picture is this curve. Everything is simulated with a fixed seed, nothing was downloaded, and every number comes from a real run of the code. This video is for education only, and nothing in it is financial advice. #quantfinance #portfoliotheory #efficientfrontier #markowitz #python

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