{"product_id":"fifty-years-of-us-equity-returns-a5","title":"Random Walks - A5","description":"\u003cp data-start=\"123\" data-end=\"182\"\u003e\u003cstrong data-start=\"123\" data-end=\"182\"\u003eWhy are short-term market movements so hard to predict?\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp data-start=\"184\" data-end=\"783\"\u003eThis visual contrasts simulated and realized equity market trajectories over one year. Each gray line represents a simulated market path generated by a geometric Brownian motion. This model, developed in early probability theory and later formalized in financial economics, describes asset prices as continuous-time processes driven by a deterministic trend and random shocks. The red line shows the realized U.S. market path in 2023. The dispersion across simulated paths illustrates that even when average return and volatility are known, short-term price movements remain dominated by randomness.\u003c\/p\u003e\n\u003cp data-start=\"785\" data-end=\"1050\"\u003e\u003cstrong data-start=\"785\" data-end=\"802\"\u003eData \u0026amp; Method\u003c\/strong\u003e\u003cbr data-start=\"802\" data-end=\"805\"\u003eOne-year geometric Brownian motion simulations (100 paths), calibrated on daily U.S. total market log returns (2023) from the Kenneth R. French Data Library. Model: dS\/S = μdt + σdW, where μ is mean return, σ volatility, and dW a Wiener process.\u003c\/p\u003e\n\u003chr data-start=\"1052\" data-end=\"1055\"\u003e\n\u003cp data-start=\"1057\" data-end=\"1083\"\u003e\u003cstrong data-start=\"1057\" data-end=\"1083\"\u003eProduct Specifications\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp data-start=\"1085\" data-end=\"1332\"\u003eFormat: A5 (148 × 210 mm)\u003cbr data-start=\"1110\" data-end=\"1113\"\u003eOrientation: Landscape\u003cbr data-start=\"1135\" data-end=\"1138\"\u003ePaper: 350 g\/m² uncoated paper\u003cbr data-start=\"1176\" data-end=\"1179\"\u003ePrinting: High-resolution digital print\u003cbr data-start=\"1218\" data-end=\"1221\"\u003eFinish: Matte\u003cbr data-start=\"1234\" data-end=\"1237\"\u003eFrame: Not included\u003cbr data-start=\"1256\" data-end=\"1259\"\u003ePackaging: Flat protective sleeve\u003cbr data-start=\"1292\" data-end=\"1295\"\u003eProduction: Printed in France (Paris)\u003c\/p\u003e","brand":"Ceteris Paribus","offers":[{"title":"Default Title","offer_id":56328057422168,"sku":null,"price":15.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0955\/0800\/5208\/files\/RANDOM.jpg?v=1769373089","url":"https:\/\/shop.ceterisparibus.art\/products\/fifty-years-of-us-equity-returns-a5","provider":"Ceteris Paribus","version":"1.0","type":"link"}