2e:null 2f:["$","title",null,{"children":"개미투자공학 3장: 단일종목 켈리기준 | Humble Data Miner | Observable"}] 34:Tb97,chart = { replaygame; const n = 7; let series = Array.from({length: n+1}, (v,i)=>Array.from({length: n+1}, v=>0)); let means = []; for (let i = 0; i < (n+1); i++) { for (let j = i; j < (n+1); j++) series[j][i] = 2**i; means.push(d3.mean(series, d=>d[i])); } const t = Array.from({length: n+1}, (v,i)=>i); const svg = d3.create("svg") .attr("viewBox", [0, 0, width, height]); const x = d3.scaleLinear() .domain([0, d3.max(t)]) .range([margin.left, width-margin.right-75]); const y = d3.scaleLinear() .domain([0, d3.max(series, d=>d3.max(d))]) .range([height - margin.bottom, margin.top]) const line = d3.line() .defined(d => !isNaN(d)) .x((d,i) => x(t[i])) .y(d => y(d)); let paths = []; for (let seq of series) { paths.push(svg.append("g") .attr("fill", "none") .attr("stroke-width", 3) .selectAll("path") .data(seq) .join("path") .attr("visibility","hidden") .attr("stroke", "lightblue") .attr("stroke-opacity", 0.2) .style("mix-blend-mode", "multiply") .attr("d", line(seq))); } svg.append("g") .attr("transform", `translate(0,${height - margin.bottom})`) .call(d3.axisBottom(x).ticks(n+1)); svg.append("g") .attr("transform", `translate(${margin.left},0)`) .call(d3.axisLeft(y).tickFormat(x => `x${x}`)); svg.append("g") .attr("transform", `translate(${width-margin.right-75},0)`) .call(d3.axisRight(y).tickFormat(x => `x${x}`)); const arithmean = svg.append("g") .attr("visibility","hidden") .attr("transform", (d,i)=>`translate(${width-margin.right-65}, ${y(means[means.length-1])-10})`); arithmean.append("path") .attr("fill", "lightgrey") .attr("stroke", "black") .attr("stroke-width", 1) .attr("d", "M11 11 L20 20 H105 V0 H20 L11 11"); const arithmeantext = arithmean.append("text") .attr('x', 58) .attr('y', 10) .attr('font-size', 12) .attr('alignment-baseline', 'central') .attr('text-anchor', 'middle') .text("산술평균 x"+d3.format(".0f")(means[means.length-1])); const geomean = svg.append("g") .attr("visibility","hidden") .attr("transform", (d,i)=>`translate(${width-margin.right-65}, ${y(0)-10})`); geomean.append("path") .attr("fill", "lightgrey") .attr("stroke", "black") .attr("stroke-width", 1) .attr("d", "M11 11 L20 20 H105 V0 H20 L11 11"); const geomeantext = geomean.append("text") .attr('x', 58) .attr('y', 10) .attr('font-size', 12) .attr('alignment-baseline', 'central') .attr('text-anchor', 'middle') .text("기하평균 x"+d3.format(".0f")(0)); for (let i = 0; i < paths.length; i++) { paths[i].transition().delay(i*500).attr("visibility","visible"); yield svg.node(); } geomean.transition().delay((paths.length+1)*500).attr("visibility","visible"); arithmean.transition().delay(paths.length*500).attr("visibility","visible"); }35:T1211,chartkc = { replaykc; const yrs = 5; const days = 240; const n = days*yrs; const numiter = 100; const amu = mu/days; const asigma = sigma/Math.sqrt(days); const epsilon = 0.0000001; const logscale = (yscale.value == "log"); const baseseries = Array.from({length:numiter}, d=>Float64Array.from({length: n}, d=>Math.exp(d3.randomNormal(amu, asigma)())-asigma**2/2)); const fractions = [1/8,1/4,1/2,1,2,4,8]; let fseries = []; for (let i = 0; i < fractions.length; i++) { const f = fractions[i]; let series = []; for (const bseq of baseseries) { let y = [f]; for (let j = 0; j < bseq.length; j++) y.push(y[j]*bseq[j]); series.push(y.map(d => d+(1-f))); } fseries.push({ fraction:f, series:series, gmean: gmean(series, d=> Math.max(d[d.length-1],epsilon)), amean: d3.mean(series, d=> d[d.length-1]), color: d3.interpolateRdYlBu(i/(fractions.length-1)) }); } 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-margin.right]); const y = logscale? d3.scaleLog().domain([0.01, 100]).range([height - margin.bottom, margin.top]) : d3.scaleLinear().domain([-10, 100]).range([height - margin.bottom, margin.top]); const line = d3.line() .defined(d => !isNaN(d)) .x((d,i) => x(t[i])) .y(d => y(logscale ? Math.max(d,epsilon) : d)); let paths = []; for (let i = 0; i < fseries.length; i++) { const color = fseries[i].color; const opacity = 0.1; const path = svg.append("g") .attr("fill", "none") .attr("stroke-width", 1) .selectAll("path") .data(fseries[i].series) .join("path") .attr("stroke", color) .attr("stroke-opacity", opacity) .attr("d", d => line(d)); paths.push({elem:path, len:path.nodes().map(d=>d.getTotalLength())}); } const scaleformatter = x => (logscale ? "x":"") + x; 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 => `${scaleformatter(x)}`)); svg.append("g") .attr("transform", `translate(${width*2/3-margin.right},0)`) .call(d3.axisRight(y).tickFormat(x => `${scaleformatter(x)}`)); const fx = d3.scaleLog().domain([d3.min(fractions), d3.max(fractions)]).range([width*2/3+margin.left, width-margin.right]); const fy = d3.scaleLinear().domain([0,30]).range([height-margin.bottom, margin.top]); svg.append("g").attr("transform", `translate(0,${height-margin.bottom})`).call(d3.axisBottom(fx).tickValues(fractions).tickFormat(x=>x)); svg.append("g").attr("transform", `translate(${width*2/3+margin.left},0)`).call(d3.axisLeft(fy)); svg.append("text").attr("font-size", 11).attr("text-anchor", "middle").attr("x", width*5/6).attr("y", height - 5).text("투자비율"); const flinegm = d3.line().curve(d3.curveNatural).x(d=>fx(d.fraction)).y(d=>fy(d.gmean)); const flineam = d3.line().curve(d3.curveNatural).x(d=>fx(d.fraction)).y(d=>fy(d.amean)); // geometric mean svg.append("g").append("path").attr("fill","none").attr("stroke", "black").attr("stroke-width",1).attr("d",flinegm(fseries)); svg.append("g").selectAll("circle").data(fseries).join("circle") .attr("cx", d => fx(d.fraction)).attr("cy", d => fy(d.gmean)).attr("r", 3).attr("fill", d=>d.color).attr("stroke","black"); svg.append("g").attr("font-size", 11).attr('text-anchor', "middle") .selectAll("text").data(fseries).join("text") .attr("dx",-2).attr("dy", 15).attr("x", d => fx(d.fraction)).attr("y", d => fy(d.gmean)) .text((d,i) => (i == fseries.length-1 ? "기하평균: ":"") + d3.format(".2f")(d.gmean)); // arithmentic mean svg.append("g").append("path").attr("fill","none").attr("stroke", "black").attr("stroke-width",1).attr("d",flineam(fseries)); svg.append("g").selectAll("circle").data(fseries).join("circle") .attr("cx", d => fx(d.fraction)).attr("cy", d => fy(d.amean)).attr("r", 3).attr("fill", d=>d.color).attr("stroke","black"); svg.append("g").attr("font-size", 11).attr('text-anchor', "middle") .selectAll("text").data(fseries).join("text") .attr("dx", -2).attr("dy", -10).attr("x", d => fx(d.fraction)).attr("y", d => fy(d.amean)) .text((d,i) => (i == fseries.length-1 ? "산술평균: ":"") + d3.format(".2f")(d.amean)); return svg.node(); }36:[] 32:{"id":"7ad664096531fa38","slug":"personal-investment-engineering-ch-3","title":"개미투자공학 3장: 단일종목 켈리기준","thumbnail":"532e14f4bb19ba67e1f030b26bb2306d57173a9b0d7eced332ee69bc587a4f5e","access_level":"public","create_time":"$D2021-11-08T18:17:29.003Z","update_time":"$D2022-10-24T12:38:05.526Z","view_time":null,"first_public_time":"$D2021-11-12T07:09:04.842Z","has_unpublished_edits":null,"fork":false,"stars":0,"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":460,"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 3장: 단일종목 켈리기준","cells":[{"id":0,"value":"# 개미투자공학 3장: 단일종목 켈리기준","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"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":21,"value":"---\n## 변형된 상트페테르부르크 게임\n
\n앞면-뒷면이 나올 확률이 동일한 동전던지기 게임을 한다. 매 시행마다\n- 앞면이 나오면 건돈의 두배를 받고 다시 게임을 할수 있고\n- 뒷면이 나오면 모두 잃고 게임이 끝난다\n\n당신은 이 게임에 돈을 걸겠는가?\n- 즉각적으로 떠오르는 답은?\n- 아래 산술평균(기대값)을 확인해보고 선택한 답은?\n\n과연 기대값에 근거한 투자는 안정적인 수익률로 이어질까?","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":142,"value":"viewof replaygame = html`