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banner/background for a TIkTok profile, you know? A profile banner in TikTok is a static image that appears at the top of a user’s page, right behind the avatar and short bio. Unlike the avatar, which is circular, the banner occupies a rectangular area and serves as the background element of the profile. Its main function is to visually identify the account, convey the theme of the content, and create the first impression for visitors before they look at the posts. From a technical standpoint, the banner is uploaded through the profile settings in the mobile app or the web version of the service. The recommended image size is 1080 by 540 pixels with a 2:1 aspect ratio. JPEG and PNG formats are supported, with the maximum file size limited to a few megabytes. After uploading, the image is automatically scaled to different screen resolutions, so important elements of the composition should be placed closer to the center so they don’t get cut off on devices with different display proportions. Part of the banner may overlap with the avatar and interface elements such as the follow button or analytics counters, which should be taken into account when choosing a design. New profile banners come as sets of ready-made images created with consideration of the platform’s current visual trends. Such sets are usually classified by style: minimalism with an emphasis on solid backgrounds and simple geometric shapes, gradient transitions with smooth color blending, neon and cyberpunk aesthetics with bright, contrasting lines, pastel and nature-inspired motifs, as well as themed options for gaming, music, educational, and commercial content. A separate category is personalized banners that include the account owner’s nickname, logo, or slogan. Using a high-quality banner is considered an element of personal branding on the social network. A unified visual style of the profile, including an avatar, banner, and post design in a coordinated color palette, increases the account’s recognizability and can positively affect retention rates for new visitors. Banner sets are distributed through specialized websites, channels in messaging apps, and directly inside TikTok via posts with download links. Many creators provide such materials for free, using them as a way to attract an audience to their main platforms. #баннер #фон #профиль #оформление #тикток @курьер водолаза
banner/background for a TIkTok profile, you know? A profile banner in TikTok is a static image that appears at the top of a user’s page, right behind the avatar and short bio. Unlike the avatar, which is circular, the banner occupies a rectangular area and serves as the background element of the profile. Its main function is to visually identify the account, convey the theme of the content, and create the first impression for visitors before they look at the posts. From a technical standpoint, the banner is uploaded through the profile settings in the mobile app or the web version of the service. The recommended image size is 1080 by 540 pixels with a 2:1 aspect ratio. JPEG and PNG formats are supported, with the maximum file size limited to a few megabytes. After uploading, the image is automatically scaled to different screen resolutions, so important elements of the composition should be placed closer to the center so they don’t get cut off on devices with different display proportions. Part of the banner may overlap with the avatar and interface elements such as the follow button or analytics counters, which should be taken into account when choosing a design. New profile banners come as sets of ready-made images created with consideration of the platform’s current visual trends. Such sets are usually classified by style: minimalism with an emphasis on solid backgrounds and simple geometric shapes, gradient transitions with smooth color blending, neon and cyberpunk aesthetics with bright, contrasting lines, pastel and nature-inspired motifs, as well as themed options for gaming, music, educational, and commercial content. A separate category is personalized banners that include the account owner’s nickname, logo, or slogan. Using a high-quality banner is considered an element of personal branding on the social network. A unified visual style of the profile, including an avatar, banner, and post design in a coordinated color palette, increases the account’s recognizability and can positively affect retention rates for new visitors. Banner sets are distributed through specialized websites, channels in messaging apps, and directly inside TikTok via posts with download links. Many creators provide such materials for free, using them as a way to attract an audience to their main platforms. #баннер #фон #профиль #оформление #тикток @курьер водолаза
➡️ 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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