2e:null 2f:["$","title",null,{"children":"개미투자공학 번외편:첨도(Kurtosis)로 살펴본 국장의 극단성 | Humble Data Miner | Observable"}] 34:T24b1,date_stats_chart = { const hh = 400; // height of histogram area const hp = 400; // height of plot area const height = hh+hp; const margin = {top: 0, right: 30, bottom: 30, left: 30}; const svg = d3.create("svg").attr("viewBox", [0, 0, width, height]); const eh = [Math.log(0.7), -Math.log(0.7)]; const xh = d3.scaleLinear().domain(eh).range([margin.left, width-margin.right]); // x-axis of histogram const xp = d3.scaleTime().domain(d3.extent(dates)).range([margin.left, width-margin.right]); // x-axis of plot const ye = [d3.min(stats,d=>d.kosuni)-20, d3.max(stats,d=>d.kosuni)+40]; const yp = d3.scaleLinear().domain(ye).range([height-margin.bottom,hh+margin.top]); const maxd = Math.max(d3.max(stats,d=>d.ktssp), d3.max(stats,d=>d.ktssn)); const yd = d3.scaleLinear().domain([-maxd,maxd]).range([height-margin.bottom,hh+margin.top]); svg.append("g").attr("transform",`translate(0,${hh-margin.bottom})`).call(d3.axisBottom(xh).tickFormat(d=>`${d}(${((Math.exp(d)-1.0)*100).toFixed(0)}%)`)); svg.append("g").attr("transform",`translate(0,${height-margin.bottom})`).call(d3.axisBottom(xp)); svg.append("g").attr("transform",`translate(${margin.left},0)`).call(d3.axisLeft(yp)); svg.append("g").attr("transform",`translate(${width-margin.right},0)`).call(d3.axisRight(yd).tickFormat(d=>d<0?-d:d)); const line_kosuni = d3.line().x((d,i)=>xp(dates[i])).y(d=>yp(d)); const mw = 2; // marker-width const lp = d3.line().x(d=>xp(d.x)).y(d=>yp(d.y)); const ld = d3.line().x(d=>xp(d.x)).y(d=>yd(d.y)); const series = []; console.log(); series.push({op:1.0,color:d3.schemeCategory10[1],line:lp,values:stats.map((d,i)=>({x:dates[i],y:d.kosuni}))}); series.push({op:0.5,color:d3.color(d3.schemeCategory10[3]).brighter(),line:ld,values:stats.map((d,i)=>({x:dates[i],y:d.ktssp}))}); series.push({op:1.0,color:d3.color(d3.schemeCategory10[3]).darker(),line:ld, values:stats.map((d,i)=>({x:dates[i],y:d3.mean(stats.slice(i-19,i+1),_=>_.ktssp)})).filter(d=>d.y)}); series.push({op:0.5,color:d3.color(d3.schemeCategory10[0]).brighter(),line:ld,values:stats.map((d,i)=>({x:dates[i],y:-d.ktssn}))}); series.push({op:1.0,color:d3.color(d3.schemeCategory10[0]).darker(),line:ld, values:stats.map((d,i)=>({x:dates[i],y:d3.mean(stats.slice(i-19,i+1),_=>-_.ktssn)})).filter(d=>d.y)}); //console.log(line(series[0])); svg.append("g").selectAll("path") .data(series) .join("path") .attr("d",d=>d.line(d.values)) .attr("fill","none") .attr("stroke",d=>d.color) .attr("opacity",d=>d.op); const hdots = svg.append("g"); svg.append("g").append("path").attr("fill","none").attr("stroke","gray").attr("opacity",0.4) .attr("d",`M ${margin.left} ${hh-8} v ${4} H ${width-margin.right} v${-4}`); var tri = d3.symbol().type(d3.symbolTriangle).size(40); const cross = svg.append("g"); const ctri = cross.append("path").attr("fill","gray").attr("stroke","none").attr("opacity",0.4).attr("d",tri()); const cline = cross.append("path").attr("fill","none").attr("stroke","gray").attr("opacity",0.4); const ctitle = cross.append("text").attr("class","txtitle").attr("y",hh+7) .attr("font-size", 12).attr("font-weight","bold").attr("dominant-baseline","hanging").attr("text-anchor","middle") .text("로그수익률 히스토그램"); const cdate = cross.append("text").attr("class","txdate").attr("y",hh+20) .attr("font-size", 12).attr("font-weight","bold").attr("dominant-baseline","hanging").attr("text-anchor","middle"); const legend = svg.append("g"); const append_text = (g,db,ta,x,y,size,txt,dx=0,dy=0) => g.append("text").attr("dominant-baseline",db).attr("text-anchor",ta).attr("dx",dx).attr("dy",dy).attr("x",x).attr("y",y).attr("font-size",size).text(txt); append_text(legend,"hanging","start",margin.left,hh,12,"KOSUNI",2,4); append_text(legend,"hanging","end",width-margin.right,hh,12,"첨도(+)",-2,4); append_text(legend,"auto","end",width-margin.right,height-margin.bottom,12,"첨도(-)",-2,-4); append_text(legend,"auto","end",width-margin.right,hh-margin.bottom,12,"로그수익률(수익률%)",-2,-4); const labels = [ {color:d3.schemeCategory10[1],txt:"KOSUNI"}, {color:d3.color(d3.schemeCategory10[3]).brighter(),txt:"첨도(+)"}, {color:d3.color(d3.schemeCategory10[3]).darker(),txt:"20일평균 첨도(+)"}, {color:d3.color(d3.schemeCategory10[0]).brighter(),txt:"첨도(-)"}, {color:d3.color(d3.schemeCategory10[0]).darker(),txt:"20일평균 첨도(-)"}, ]; const center = margin.left + (width-margin.left-margin.right)/2; const lw = 150; // label-width const lx = center - lw*(labels.length/2); for(let i=0; i < labels.length; i++) { legend.append("path").attr("d",`M ${lx+i*lw} ${height-margin.bottom-8} h ${10}`) .attr("stroke",labels[i].color).attr("stroke-width",4); append_text(legend,"auto","start",lx+i*lw+10,height-margin.bottom-4, 12, labels[i].txt,2,0); } const guides = svg.append("g"); svg.append("g").append("rect").attr("x",margin.left).attr("y",0).attr("width",width).attr("height",20) .attr("fill","white").attr("stroke","none").attr("opacity",0.8); // background pad const line_mu = guides.append("path").attr("stroke","black").attr("stroke-dasharray","2 2"); const line_sigmap = guides.append("path").attr("stroke","black").attr("stroke-dasharray","2 2"); const line_sigman = guides.append("path").attr("stroke","black").attr("stroke-dasharray","2 2"); const line_ub = guides.append("path").attr("stroke","red").attr("stroke-dasharray","2 2").attr("d",`M ${xh(Math.log(1.3))} ${margin.top} V ${hh-margin.bottom}`); const line_lb = guides.append("path").attr("stroke","blue").attr("stroke-dasharray","2 2").attr("d",`M ${xh(Math.log(0.7))} ${margin.top} V ${hh-margin.bottom}`); const stat_vals = svg.append("g"); const text_mu = append_text(stat_vals,"hanging","middle",0,0,14,"",0,4); const text_sigmap = append_text(stat_vals,"hanging","start",0,0,14,"",2,4); const text_sigman = append_text(stat_vals,"hanging","end",0,0,14,"",-2,4); const text_ub = append_text(stat_vals,"hanging","middle",xh(Math.log(1.3)),0,14,"일변동 상한(+30%) = 0.262",0,4).attr("fill","red"); const text_lb = append_text(stat_vals,"hanging","start",xh(Math.log(0.7)),0,14,"일변동 하한(-30%) = -0.357",0,4).attr("fill","blue"); const text_ktssp = append_text(stat_vals,"auto","middle",0,hh/2,20,"",0,0).attr("fill","red").attr("font-weight","bold"); const text_ktssp_val = append_text(stat_vals,"auto","middle",0,hh/2+20,20,"",0,0).attr("fill","red").attr("font-weight","bold"); const text_ktssn = append_text(stat_vals,"auto","middle",0,hh/2,20,"",0,0).attr("fill","blue").attr("font-weight","bold"); const text_ktssn_val = append_text(stat_vals,"auto","middle",0,hh/2+20,20,"",0,0).attr("fill","blue").attr("font-weight","bold"); update(Math.floor(dates.length/2)); function update(new_ci) { const d = dates[new_ci]; const s = stats[new_ci]; const cb = [eh[0]**4,eh[1]**4]; // color-bound ctri.attr("transform",`translate(${xp(d)},${hh})`); cline.attr("d",`M ${xp(d)} ${hh} V ${height-margin.bottom}`); ctitle.attr("x",xp(d)); cdate.attr("x",xp(d)).text(d.toISOString().split('T')[0]); const radius = 1.5; const dodge = dodger(radius*2+1); hdots.selectAll("circle") .data(flucs[new_ci]) .join("circle") .attr("fill",d=>{ const z = (d-s.mu)/s.sigma; const cb = [(eh[0]-s.mu)/s.sigma,(eh[1]-s.mu)/s.sigma]; // color-bound return z>1?d3.interpolateReds(z/cb[1]):z<-1?d3.interpolateBlues(z/cb[0]):"white"; }) .attr("stroke","black").attr("stroke-opacity",0.4) .attr("cx",d=>xh(d)).attr("cy",d=>hh-margin.bottom-dodge(xh(d))-radius-1).attr("r",radius); line_mu.attr("d",`M ${xh(s.mu)} ${margin.top} V ${hh-margin.bottom}`); text_mu.attr("x",xh(s.mu)).text(`μ=${s.mu.toFixed(3)}`); line_sigmap.attr("d",`M ${xh(s.mu+s.sigma)} ${margin.top} V ${hh-margin.bottom}`); text_sigmap.attr("x",xh(s.mu+s.sigma)).text(`μ+σ=${(s.mu+s.sigma).toFixed(3)}`); line_sigman.attr("d",`M ${xh(s.mu-s.sigma)} ${margin.top} V ${hh-margin.bottom}`); text_sigman.attr("x",xh(s.mu-s.sigma)).text(`${(s.mu-s.sigma).toFixed(3)}=μ-σ`); text_ktssp.attr("x",(xh(Math.log(1.3))+xh(s.mu+s.sigma))/2).attr("fill",d3.interpolateReds(Math.max(s.ktssp/40,0.3))) .text(`첨도(+)=${s.ktssp.toFixed(2)}`); text_ktssp_val.attr("x",(xh(Math.log(1.3))+xh(s.mu+s.sigma))/2).attr("fill",d3.interpolateReds(Math.max(s.ktssp/40,0.3))) .text(`=${(s.ktssp*s.len).toFixed(0)}/${s.len}`); text_ktssn.attr("x",(xh(Math.log(0.7))+xh(s.mu-s.sigma))/2).attr("fill",d3.interpolateBlues(Math.max(s.ktssn/40,0.3))) .text(`첨도(-)=${s.ktssn.toFixed(2)}`); text_ktssn_val.attr("x",(xh(Math.log(0.7))+xh(s.mu-s.sigma))/2).attr("fill",d3.interpolateBlues(Math.max(s.ktssn/40,0.3))) .text(`=${(s.ktssn*s.len).toFixed(0)}/${s.len}`); } function drag(e) { if(e.type == "start" || e.type == "drag") { const newci = Math.max(Math.min(d3.bisectLeft(dates,xp.invert(e.x)), dates.length-1),0) update(newci); } } svg.call(d3.drag().on('drag', drag).on('start', drag).on('end', drag)); return Object.assign(svg.node(), { set_preset(d) { update(dates.findIndex(x=>x.getTime() == d.getTime())); }, }); }35:T464,viewof preset_chosen = { const tbl_preset = Inputs.table(stats, { maxWidth:890, multiple:false, columns:["date","ktssp","ktssn","mu","pos","neg", "odds", "logit", "kosuni"], rows:5, width: { date: 70, ktssp: 50, ktssn: 50, pos: 120, neg: 120, odds: 60, logit: 90, }, format:{ date:x=>x.toISOString().split('T')[0], ktssp:x=>x.toFixed(2), ktssn:x=>x.toFixed(2), mu:x=>`${x>0?"+":""}${((Math.exp(x)-1)*100).toFixed(2)}%`, pos:(x,i)=>`${x} (${(x/stats[i].len*100).toFixed(1)}%)`, neg:(x,i)=>`${x} (${(x/stats[i].len*100).toFixed(1)}%)`, odds:x=>x.toFixed(2), logit:x=>x.toFixed(2), kosuni:x=>x.toFixed(2), }, header:{ date:"일자", ktssp:"첨도(+)", ktssn:"첨도(-)", mu:"평균수익률(%)", pos:"평균이상종목수(A)", neg:"평균이하종목수(B)", odds:"오즈(A/B)", logit:"로짓(log(A/B))", kosuni:"KOSUNI", } }); 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첨도(Kurtosis)로 살펴본 국장의 극단성\n\n* 최근들어 국장의 매매경향이 **도박장**같다는 느낌적인 느낌...\n * 극소수의 종목들만 크게 급등 → 표면적 상승장\n * 극소수의 종목들을 제외한 다른종목들은 미미한 등락\n * 극단적인 단일종목투자 상황예시\n * 오늘하루 1000종목중 10개 종목만 급등하고 나머진 보합일때\n * 분명 시장은 상승장인듯한데 내 종목은 지지부진하다면\n * 급등할 10종목중 하나를 운에 의존하지 않고 고르는게 가능할까?","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":49,"value":"---\n## 첨도(Kurtosis)?\n\n* 위키백과상의 서술적 정의\n> 첨도(尖度, 영어: kurtosis 커토시스[*])는 확률분포의 꼬리가 두꺼운 정도를 나타내는 척도이다.\n> 극단적인 편차 또는 이상치가 많을 수록 큰 값을 나타낸다.\n> 첨도값(K)이 3에 가까우면 산포도가 정규분포에 가깝다.\n\n* 수학적 정의\n\n>> ${tex`{\\displaystyle \\operatorname {Kurt} [X]=\\operatorname {E} \\left[\\left({\\frac {X-\\mu }{\\sigma }}\\right)^{4}\\right]=\\frac{\\left({\\frac {x_{1}-\\mu }{\\sigma }}\\right)^{4}+\\left({\\frac {x_{2}-\\mu }{\\sigma }}\\right)^{4}+...+\\left({\\frac {x_{n}-\\mu }{\\sigma }}\\right)^{4}}{N}}`}\n\n* 첨도를 평균(${tex`\\mu`})을 기준으로 이등분한 부분첨도의 도입\n * 첨도 = 첨도(+) ${tex`{+}`} 첨도(-)\n * 첨도(+) = 평균을 기준으로 우측에 위치한 값(${tex`x>\\mu`})들의 첨도 부분합\n * 첨도(-) = 평균을 기준으로 좌측에 위치한 값(${tex`x<\\mu`})들의 첨도 부분합\n\n* 높은 첨도를 갖는 수익률분포의 특성\n * 평균(${tex`\\mu`})에서 크게 벗어난 값→소수의 이상치가 존재(소수종목의 급등락)\n * 낮은 표준편차(${tex`\\sigma`})→다수가 평균치 근처에 분포(다수종목의 미미한등락)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":52,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":212,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":747,"value":"
\n## 결과 해석\n* 첨도(+) 한정 (평균대비 상승종목의 경우)\n * 지속적으로 다소 높은 첨도 유지(>15) → 극소수의 상승종목만 급등\n * 거의 대부분의 기간동안 상한가 종목이 존재\n * 매우높은 첨도값(>20)이 특정기간에 몰려서 발생 → 인위적인 발생?\n * 최근 2023-05-22 에서 2023-05-26 사이에 연속으로 30이상의 첨도 발생\n* 첨도(-) 한정 (평균대비 하락종목의 경우)\n * 일반적으로 낮은 첨도(<10)를 보인다 → 하락종목의 하락률이 고르게 발생\n * 매우높은 첨도값(>20)은 가끔씩 떨어져 발생 → 자연스러운 발생?\n* (2020년 3월~2020년 12월) 코로나바이러스 시기에 안정적인 첨도값\n * 등락이 고르고 넓게 분포 → 자본시장의 옥석가리기가 잠시 제대로 동작?\n * 개인투자자들이 국장에서 수익을 내던 시기와 일치([호기심해결 in 주식시장: 투자주체별 수익현황](https://observablehq.com/@humble-data-miner/myth-buster-in-finance-gain-and-loss-of-krx-investor-groups-2022) 참고)\n\n## 개인적인 의견\n* 뭔가 단단히 잘못되어가고 있는 도박장같은 국장\n * 매일매일 급변하는 급등하는 종목들의 그럴듯한 이유조차 찾기 어렵고\n * 소수 특정주에 자본이 몰리면 그에 비례에서 경제가치를 창출할것도 아니고\n * 실적이랑 관계없이 지수만 오르면 시장이 강하다 추켜세우는 상황에서\n* 첨도가 높은 이런상황이 지속된다고 할때 우리의 대응책은?\n * (부분적으로라도)국장 투자자금 회수\n * (부분적으로라도)국장 종목투자 중단 → 1000개중 10개 뽑기 거부\n * (굳이 투자한다면)국장 인덱스펀드 매수 → 1000개중 1000개 뽑기","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":834,"value":"---\n## 참고사항\n* 데이터셋\n * 2015-01-02~2023-06-23 사이의 KOSPI,KOSDAQ 종목별 일가격변동\n* 주식시장 하한가/상한가\n * 2015년 6월부터 ±15% → ±30%로 조정됨\n * 거래정지후 거래재개시 ±30%가 넘는 가격하락이 가능\n * 여기서 사용한 데이터셋에서는 이런 이상치들을 ±30% 상하한으로 조정\n* 3단 차트에 대한 부연설명\n * 상단: 지정된 일자의 2000여종목의 하루 가격변동 히스토그램\n * 중단: KOSUNI(KOSPI,KOSDAQ 통합지수)값과 일별 첨도(+,-) 표시\n * 하단: 테이블에서 선택한 일자를 상단,중단 차트에 반영\n* KOSUNI\n * 한국거래소(KOSDAQ,KOSPI)에 상장된 종목들을 균일하게 평균한 지수\n * 자세한 내용은 [개미투자공학 5장](https://observablehq.com/@humble-data-miner/personal-investment-engineering-ch-5) 참고\n* 로그수익률\n * 수익률(-30%,+30%)이 아닌 수익배율(x0.7,x1.3)에 로그함수를 취한 결과\n * (-),(+) 수익률의 산술계산 결과 왜곡을 바로잡기 위해 일반적으로 사용\n * 자세한 내용은 [개미투자공학 6장](https://observablehq.com/@humble-data-miner/personal-investment-engineering-ch-6) 참고\n\n## Reference\n* [위키백과 - 첨도](https://ko.wikipedia.org/wiki/%EC%B2%A8%EB%8F%84) / [Wikipedia - Kurtosis](https://en.wikipedia.org/wiki/Kurtosis)\n* [KRX | 정보데이터시스템](http://data.krx.co.kr/contents/MDC/MAIN/main/index.cmd)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":859,"value":"---\n## 부연설명 동영상\n\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":43,"value":"---\n## Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":13,"value":"zipfile = FileAttachment(\"daily_price_stats@5.zip\").zip()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"adates = zipfile.file('dates.csv').csv({array:true,typed:true})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"dates = adates.map(d=>d[0])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"flucs = zipfile.file('date_flucs.csv').csv({array:true,typed:true})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"stats = zipfile.file('date_stats.csv').csv({typed:true})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":205,"value":"high_ktss_dates = stats.map((x,i)=>({date:dates[i],ktss:x.ktssp+x.ktssn,ktssp:x.ktssp,ktssn:x.ktssn})).toSorted((a, b) => b.ktssp-a.ktssp).slice(0,50)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":167,"value":"dodger = radius => {\n const radius2 = radius ** 2;\n const bisect = d3.bisector(d => d.x);\n const circles = [];\n return x => {\n const l = bisect.left(circles, x - radius);\n const r = bisect.right(circles, x + radius, l);\n let y = 0;\n for (let i = l; i < r; ++i) {\n const { x: xi, y: yi } = circles[i];\n const x2 = (xi - x) ** 2;\n const y2 = (yi - y) ** 2;\n if (radius2 > x2 + y2) {\n y = yi + Math.sqrt(radius2 - x2) + 1e-6;\n i = l - 1;\n continue;\n }\n }\n circles.splice(bisect.left(circles, x, l, r), 0, { x, y });\n return y;\n };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":46,"value":"html`\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":227,"value":"{\n if(preset_chosen)\n date_stats_chart.set_preset(preset_chosen.date);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":281,"value":"{\n stats.forEach((x,i)=>{ stats[i][\"date\"] = dates[i]; stats[i][\"odds\"] = stats[i].pos/stats[i].neg; stats[i][\"logit\"]=Math.log(stats[i][\"odds\"]); });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":362,"value":"d3_slider= require(\"d3-simple-slider\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W36","stdlib":"1","titling":"auto"}} 33:"$32:body"