2e:null 2f:["$","title",null,{"children":"개미투자공학 1장: 기하브라운운동 | Humble Data Miner | Observable"}] 34:Te9d,gmbchart = { replaygbm; const niter = 3 const durdays = [1,20,80,240]; let series = []; let dots = []; let pdfs = []; let ext_y = []; for (let d = 0; d < durdays.length; d++) { const dt = durdays[d]; const amu = (mu/240)*dt; const asigma = (sigma/Math.sqrt(240))*Math.sqrt(dt); const xn = Float64Array.from({length: niter}, d3.randomNormal(amu, asigma)); const x = xn.map(x => Math.exp(x)-asigma**2/2) const px = Array.from({length: 31}, (v,i) => amu-2*asigma+i*4*asigma/30); const py = px.map(x => dt*Math.sqrt(dt)*prob_lognormal(x,amu,asigma)/100); let pathpts = [{ x: (series.length > 0 ? series[series.length-1][niter].x : 0), y: (series.length > 0 ? series[series.length-1][niter].y : 1.0)}]; for (let j = 0; j < x.length ; ++j) { pdfs.push(Array.from({length: px.length}, (v,i)=>({x:pathpts[j].x+dt-py[i],y:pathpts[j].y*(Math.exp(px[i])-asigma**2/2)}))); pathpts.push({x:pathpts[j].x+dt, y:pathpts[j].y*x[j]}); dots.push(pathpts[pathpts.length-1]); } ext_y.push([d3.min(pdfs, d=>d3.min(d,d=>d.y)),d3.max(pdfs, d=>d3.max(d,d=>d.y))]); series.push(pathpts); } const ex = [0, d3.max(series, d=>d3.max(d, d=>d.x))]; const ey = ext_y[ext_y.length-1]; const svg = d3.create("svg") .attr("viewBox", [0, 0, width, height]); const x = d3.scaleLinear() .domain(ex) .range([margin.left, width]); const zx = x.copy(); const y = d3.scaleLog() .domain(ey) .range([height - margin.bottom, margin.top]) const zy = y.copy(); const line = d3.line() .defined(d => !isNaN(d.x) && !isNaN(d.y)) .x(d => zx(d.x)) .y(d => zy(d.y)); const xAxis = (g, scale = x) => g .attr("transform", `translate(0,${height - margin.bottom})`) .call(d3.axisBottom(scale)); const yAxis = (g, scale = y) => g .attr("transform", `translate(${margin.left},0)`) .call(d3.axisLeft(scale).tickFormat(x => `x${x}`)); const path = svg.append("g") .attr("fill", "none") .attr("stroke-width", 1) .selectAll("path") .data(series) .join("path") .attr("stroke", "steelblue") .attr("d", d=>line(d)); const prob = svg.append("g") .attr("fill", "none") .attr("stroke", "black") .attr("stroke-opacity", 0.5) .attr("stroke-width", 1) .attr("stroke-dasharray", "2 2") .selectAll("path") .data(pdfs) .join("path") .attr("d", d=>line(d)); const dot = svg.append("g") .selectAll("circle") .data(dots) .join("circle") .attr("cx", d => zx(d.x)) .attr("cy", d => zy(d.y)) .attr("r", 2); const text = svg.append("g") .attr("font-size", 12) .attr('alignment-baseline', 'central') .attr('text-anchor', 'middle') .selectAll("text") .data(dots) .join("text") .attr("dx", -20) .attr("dy", -2) .attr("x", d => zx(d.x)) .attr("y", d => zy(d.y)) .text(d => "x"+d3.format(".3f")(d.y)); const gx = svg.append("g") .attr("transform", `translate(0,${height - margin.bottom})`) .call(xAxis,zx); const gy = svg.append("g") .attr("transform", `translate(${margin.left},0)`) .call(yAxis,zy); return Object.assign(svg.node(), { update(di) { const t = svg.transition().duration(750); zx.domain(di == 0 ? ex : [d3.min(series[di-1],d=>d.x), d3.max(series[di-1],d=>d.x)]); zy.domain(di == 0 ? ey : ext_y[di-1]); gx.transition(t).call(xAxis, zx); gy.transition(t).call(yAxis, zy); path.transition(t).attr("d", d=>line(d)); prob.transition(t).attr("d", d=>line(d)); dot.transition(t).attr("cx", d=>zx(d.x)).attr("cy", d=>zy(d.y)); text.transition(t).attr("x", d=>zx(d.x)).attr("y", d=>zy(d.y)); } }); }35:T1371,chart = { replaysim; const yrs = 5; const days = 250; const n = days*yrs; const numiter = 100; const items = itemindices.map(i => data[i]); const numbounds = 21; const bounds = Array.from({length: numbounds}, (v,i) => 10**(-2 + i*(4/(numbounds-1)))); let series = []; let means = []; for (let iter = 0; iter < numiter; iter++) { let seq = []; let lasts = []; for (let i = 0; i < items.length; i++) { const item = items[i]; const xn = Float64Array.from({length: n}, d3.randomNormal(item.mu, item.sigma)); const x = xn.map(x => Math.exp(x) - item.sigma**2/2) let y = [1.0]; for (let j = 0; j < x.length ; ++j) y.push(y[j] * x[j]); seq.push(y); lasts.push(y[y.length-1]); } series.push(seq); means.push(d3.mean(lasts)); } const buckets = means.map(x => d3.bisect(bounds,x)); const t = Array.from({length: n+1}, (v, i) => i/days); const svg = d3.create("svg") .attr("viewBox", [0, 0, width, height]); const x = d3.scaleLinear() .domain([0, d3.max(t)]) .range([margin.left, width*2/3]); const y = d3.scaleLog() .domain([0.01, 100]) .range([height - margin.bottom, margin.top]) const line = d3.line() .defined(d => !isNaN(d)) .x((d,i) => x(t[i])) .y(d => y(d)); let paths = []; for (let i = 0; i < series.length; i++) { const path = svg.append("g") .attr("fill", "none") .attr("stroke-width", 1) .attr("visibility","hidden") .selectAll("path") .data(series[i]) .join("path") .attr("stroke", (d,i) => items[i].color) .attr("d", d => line(d)); paths.push({elem:path, len:path.nodes().map(d=>d.getTotalLength())}); } let boxes = []; for (let i = 1; i < bounds.length; i++) { const box = svg.append("rect") .attr("fill", d3.interpolateRdBu(1-(i-1)/(bounds.length-1))) .attr("x",width*2/3+margin.right+5) .attr("y",y(bounds[i])) .attr("width",0) .attr("height",y(bounds[i-1])-y(bounds[i])); boxes.push(box); } svg.append("g") .attr("transform", `translate(0,${height - margin.bottom})`) .call(d3.axisBottom(x).ticks(yrs).tickFormat(x => `${x}Y`)); svg.append("g") .attr("transform", `translate(${margin.left},0)`) .call(d3.axisLeft(y).tickFormat(x => `x${x}`)); svg.append("g") .attr("transform", `translate(${width*2/3},0)`) .call(d3.axisRight(y).tickFormat(x => `x${x}`)); const ldim = {width: 200, height: height, itemsize: 10, itempad: 5}; const legend = svg.append("g") .attr("transform", `translate(${width - margin.right - ldim.width}, ${margin.top})`); for (let i = 0; i < items.length; i++) { legend.append('rect') .attr('fill', items[i].color) .attr('x', 0) .attr('y', i*(ldim.itemsize+ldim.itempad)) .attr('width', ldim.itemsize) .attr('height', ldim.itemsize) legend.append('text') .attr('x', ldim.itemsize + ldim.itempad) .attr('y', i*(ldim.itemsize+ldim.itempad) + ldim.itemsize) .attr('font-size', 12) .text(items[i].name); } legend.attr("visibility",showlegend?"visible":"hidden"); const arithmean = svg.append("g") .attr("visibility", "hidden"); arithmean.append("path") .attr("fill", "lightgrey") .attr("stroke", "black") .attr("stroke-width", 1) .attr("d", "M11 11 L20 20 H105 V0 H20 L11 11"); const arithmeantext = arithmean.append("text") .attr('x', 58) .attr('y', 10) .attr('font-size', 12) .attr('alignment-baseline', 'central') .attr('text-anchor', 'middle') .text("산술평균"); const animsteps = [ {show:true, showtr:0.2}, {showtr:0.4}, {showtr:0.6}, {showtr:0.8}, {showtr:1.0, showmean:true}, {boxcount:1}, {opacity:0.1, showmean:false}]; for (let tick = 0; tick < numiter*animsteps.length; ++tick) { const path = paths[Math.floor(tick/animsteps.length)]; const step = animsteps[tick%animsteps.length]; if (step.hasOwnProperty("show")) path.elem.attr("visibility", step.show ? "visible" : "hidden"); if (step.hasOwnProperty("showtr")) path.elem.attr("stroke-dasharray", (d,i)=>`${step.showtr*path.len[i]},${path.len[i]}`); if (step.hasOwnProperty("opacity")) path.elem.attr("stroke-opacity", step.opacity); if (step.hasOwnProperty("showmean")) { if (step.showmean) { const amean = means[Math.floor(tick/animsteps.length)] arithmean.attr("transform", (d,i)=>`translate(${width*2/3}, ${y(amean)-10})`); arithmeantext.text("산술평균 x"+d3.format(".2f")(amean)) } arithmean.attr("visibility", step.showmean? "visible" : "hidden") } if (step.hasOwnProperty("boxcount")) { const bucket = buckets[Math.floor(tick/animsteps.length)]; if (0 < bucket && bucket < bounds.length) { const box = boxes[bucket-1]; box.attr("width", box.node().getBBox().width+4); } } yield svg.node(); } }36:[] 32:{"id":"5f043d1af530f1f9","slug":"personal-investment-engineering-ch-1","title":"개미투자공학 1장: 기하브라운운동","thumbnail":"b451e99e00254f55cbc0acc42737900a8e021115620c3fe854b936b479ccc0cc","access_level":"public","create_time":"$D2021-10-14T18:28:01.261Z","update_time":"$D2022-10-24T12:35:49.131Z","view_time":null,"first_public_time":"$D2021-11-12T07:01:43.212Z","has_unpublished_edits":null,"fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"50faa4da52a9ff9b","login":"humble-data-miner","name":"Humble Data Miner","avatar_url":"https://avatars-next.observableusercontent.com/3046b1bea86c5e825baea7c0c403d90ad9690b5396b11b5d02b3a0839fbcb946","tier":"starter_2024"},"version":819,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"4e2fc41e06361cc3","login":"humble-data-miner","name":"Humble Data Miner","avatar_url":"https://avatars-next.observableusercontent.com/3046b1bea86c5e825baea7c0c403d90ad9690b5396b11b5d02b3a0839fbcb946","tier":null}],"members":[{"type":"individual","id":"4e2fc41e06361cc3","login":"humble-data-miner","name":"Humble Data Miner","avatar_url":"https://avatars-next.observableusercontent.com/3046b1bea86c5e825baea7c0c403d90ad9690b5396b11b5d02b3a0839fbcb946","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":true,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"8be4c7f69e492fdf","slug":"personal-investment-engineering","title":"Personal Investment Engineering","owner":{"id":"50faa4da52a9ff9b","login":"humble-data-miner","name":"Humble Data Miner"}},"type":"notebook","body":{"title":"개미투자공학 1장: 기하브라운운동","cells":[{"id":0,"value":"# 개미투자공학 1장: 기하브라운운동","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"---\n## 개미투자공학?\n
\n나 또한 한 개미인 입장에서 수리모델에 근거한 확률기반 투자전략을 생각합니다","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":25,"value":"---\n## 이 시간에 알아볼것은\n
\n1. ### **기본 전제, 기하브라운운동**\n2. 어디에 투자? 회계기반-우량후보탐색\n3. 얼마나 투자? 단일종목-켈리기준","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":545,"value":"---\n## 기하브라운운동?\n
\n- 브라운운동\n - 기체,액체내 입자의 불규칙 운동을 지칭\n - 일정시간동안의 입자의 이동이 확률적으로 발생\n- 기하브라운운동\n - 금융시장에 적용하기위해 변형된 브라운운동\n - 일정기간동안 가격의 변동배율(x1,x0.95,x1.05)이 확률적으로 발생\n - 주요 통계량\n - μ: log(변동배율)의 평균값, (+)일때 우상향 (-)일때 우하향의 경향\n - σ: log(변동배율)의 표준편차, 0일때 변동없고 큰값일수록 큰 변동성","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":593,"value":"viewof mu = Inputs.range([-0.3, 0.3], {step: 0.1, label: \"연간 μ\", value: 0.1})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":600,"value":"viewof sigma = Inputs.range([0, 0.5], {step: 0.1, label: \"연간 σ\", value: 0.1})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":605,"value":"viewof dur = Inputs.radio([...Array(5).keys()], {value:0,label:\"확대해볼 기간\", format: i => [\"전체기간\", \"1일\", \"20일(1달)\", \"80일(1분기)\", \"240일(1년)\"][i]})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":762,"value":"viewof replaygbm = html`