2e:null 2f:["$","title",null,{"children":"Stock Investment in a Greenhouse Part3 | Humble Data Miner | Observable"}] 34:T1b58,function draw_covariance_comparison_chart(dt, years, items, yscale, margin, height, strokewidthposcov, strokewidthnegcov) { const n = years*dt; const xnormal = Float64Array.from({length: n}, d3.randomNormal(0,1)); let seriesposcov = []; for (let i = 0; i < items.length; i++) { const item = items[i]; const xposcov = xnormal.map(x => Math.exp(x*item.sigma + item.mu - item.sigma**2/2)); seriesposcov.push(cumulative_product(1, xposcov)); } let meanposcov = []; for (let i = 0; i <= n; i++) { let values = []; for (let j = 0; j < seriesposcov.length; j++) values.push(seriesposcov[j][i]); meanposcov.push(d3.mean(values)); d3.min } let seriesnegcov = Array.from({length:items.length}).map(x => [ 1.0 ]); for (let i = 0; i < xnormal.length; i++) { const x = xnormal[i]; for (let j = 0; j < items.length; j++) { const item = items[j]; const multiplier = Math.exp(x*(j%2==0?1:-1)*item.sigma + item.mu - item.sigma**2/2); seriesnegcov[j].push(seriesnegcov[j][i]*multiplier); } } let meannegcov = []; for (let i = 0; i <= n; i++) { let values = []; for (let j = 0; j < seriesnegcov.length; j++) values.push(seriesnegcov[j][i]); meannegcov.push(d3.mean(values)); } let t = []; for (let i = 0; i <= n; i++) t.push(i/dt); const xp = d3.scaleLinear() .domain(d3.extent(t)) .range([margin.left, width/2 - margin.right]); const xn = d3.scaleLinear() .domain(d3.extent(t)) .range([width/2 + margin.left, width - margin.right]); const y = (yscale == "log" ? d3.scaleLog() : d3.scaleLinear()) .domain([ d3.min([d3.min(seriesposcov, d => d3.min(d)), d3.min(seriesnegcov, d => d3.min(d))]), d3.max([d3.max(seriesposcov, d => d3.max(d)), d3.max(seriesnegcov, d => d3.max(d))])]) .range([height - margin.bottom, margin.top]); const lineposcov = d3.line() .defined(d => !isNaN(d)) .x((d, i) => xp(t[i])) .y(d => y(d)); const linenegcov = d3.line() .defined(d => !isNaN(d)) .x((d, i) => xn(t[i])) .y(d => y(d)); const svg = d3.create("svg") .attr("viewBox", [0, 0, width, height]) .style("overflow", "visible"); svg.append("g") .attr("transform", `translate(0,${height - margin.bottom})`) .call(d3.axisBottom(xp).ticks(years).tickFormat(x => `${x}Y`)); svg.append("g") .attr("transform", `translate(0,${height - margin.bottom})`) .call(d3.axisBottom(xn).ticks(years).tickFormat(x => `${x}Y`)); svg.append("g") .attr("transform", `translate(${margin.left},0)`) .call(d3.axisLeft(y).tickFormat(x => `x${yscale=="log"?logratio_formatter(x):linearscale_formatter(x)}`)) svg.append("g") .attr("transform", `translate(${width/2 - margin.right},0)`) .call(d3.axisRight(y).tickFormat(x => `x${yscale=="log"?logratio_formatter(x):linearscale_formatter(x)}`)) svg.append("g") .attr("transform", `translate(${width/2 + margin.left},0)`) .call(d3.axisLeft(y).tickFormat(x => "")) svg.append("g") .attr("transform", `translate(${width - margin.right},0)`) .call(d3.axisRight(y).tickFormat(x => `x${yscale=="log"?logratio_formatter(x):linearscale_formatter(x)}`)) // positive covariance svg.append("g") .attr("fill", "none") .attr("stroke-width", strokewidthposcov) .selectAll("path") .data(seriesposcov) .join("path") .style("mix-blend-mode", "multiply") .attr("stroke", (d,i) => items[i].color) .attr("d", d => lineposcov(d)); const gp = svg.append("g") .attr("transform", `translate(${xp(t[t.length-1])}, ${y(meanposcov[meanposcov.length-1])})`); const labeloffset = 25; gp.append("line") .attr("x1", 0) .attr("y1", 0) .attr("x2", labeloffset) .attr("y2", 0) .attr("stroke", "black") .attr("stroke-width", 1) .attr("stroke-dasharray", "2,2"); gp.append("rect") .attr("x", labeloffset) .attr("y", -20/2) .attr("width", 60) .attr("height", 20) .attr("fill", "yellow") .attr("stroke", "black") .attr("stroke-width", 1); gp.append('text') .attr('x', labeloffset + 60/2) .attr('y', 0) .attr('font-size', 12) .attr('alignment-baseline', 'central') .attr('text-anchor', 'middle') .text("Mean x"+d3.format(".2f")(meanposcov[meanposcov.length-1])); svg.append("path") .datum(meanposcov) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", 2) .attr("d", d => lineposcov(meanposcov)); svg.append("path") .datum(meanposcov) .attr("fill", "none") .attr("stroke", "yellow") .attr("stroke-width", 1) .attr("d", d => lineposcov(meanposcov)); svg.append("line") .attr("x1", xp(t[0])) .attr("x2", xp(t[t.length-1])) .attr("y1", y(1)) .attr("y2", y(1)) .attr("stroke", "white") .attr("stroke-width", 1); svg.append("line") .attr("x1", xp(t[0])) .attr("x2", xp(t[t.length-1])) .attr("y1", y(1)) .attr("y2", y(1)) .attr("stroke", "black") .attr("stroke-width", 1) .attr("stroke-dasharray", "2,2"); // negative-covariance svg.append("g") .attr("fill", "none") .attr("stroke-width", strokewidthnegcov) .selectAll("path") .data(seriesnegcov) .join("path") .style("mix-blend-mode", "multiply") .attr("stroke", (d,i) => items[i].color) .attr("d", d => linenegcov(d)); const gn = svg.append("g") .attr("transform", `translate(${xn(t[t.length-1])}, ${y(meannegcov[meannegcov.length-1])})`); gn.append("line") .attr("x1", 0) .attr("y1", 0) .attr("x2", labeloffset) .attr("y2", 0) .attr("stroke", "black") .attr("stroke-width", 1) .attr("stroke-dasharray", "2,2"); gn.append("rect") .attr("x", labeloffset) .attr("y", -20/2) .attr("width", 60) .attr("height", 20) .attr("fill", "yellow") .attr("stroke", "black") .attr("stroke-width", 1); gn.append('text') .attr('x', labeloffset + 60/2) .attr('y', 0) .attr('font-size', 12) .attr('alignment-baseline', 'central') .attr('text-anchor', 'middle') .text("Mean x"+d3.format(".2f")(meannegcov[meannegcov.length-1])); svg.append("path") .datum(meannegcov) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", 2) .attr("d", d => linenegcov(meannegcov)); svg.append("path") .datum(meannegcov) .attr("fill", "none") .attr("stroke", "yellow") .attr("stroke-width", 1) .attr("d", d => linenegcov(meannegcov)); svg.append("line") .attr("x1", xn(t[0])) .attr("x2", xn(t[t.length-1])) .attr("y1", y(1)) .attr("y2", y(1)) .attr("stroke", "white") .attr("stroke-width", 1); svg.append("line") .attr("x1", xn(t[0])) .attr("x2", xn(t[t.length-1])) .attr("y1", y(1)) .attr("y2", y(1)) .attr("stroke", "black") .attr("stroke-width", 1) .attr("stroke-dasharray", "2,2"); return svg.node(); }35:[] 32:{"id":"33cbf3b64e63d517","slug":"stock-investment-in-a-greenhouse-part3","title":"Stock Investment in a Greenhouse Part3","thumbnail":"d4c616737588c1ead8013f63e0a9c56a1b2eaf28033ed6dbe3e1eac7d0227e9d","access_level":"public","create_time":"$D2021-07-15T18:25:53.737Z","update_time":"$D2021-07-15T19:51:21.184Z","view_time":null,"first_public_time":"$D2021-07-15T19:45:52.139Z","has_unpublished_edits":null,"fork":{"id":"db691a336b5d20bd","slug":"stock-investment-in-a-greenhouse-part3-korean","title":"Stock Investment in a Greenhouse Part3 (Korean)","owner":{"id":"50faa4da52a9ff9b","login":"humble-data-miner","name":"Humble Data Miner"}},"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":291,"publish_version":291,"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":"693a1556761fc3fc","slug":"stock-investment-in-a-greenhouse","title":"Stock Investment in a Greenhouse","owner":{"id":"50faa4da52a9ff9b","login":"humble-data-miner","name":"Humble Data Miner"}},"type":"notebook","body":{"title":"Stock Investment in a Greenhouse Part3","cells":[{"id":0,"value":"md`# Stock Investment in a Greenhouse Part3`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"md`\n
\n## Part3: Stocks with positive or negative covariance\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"md`\n
\n### Only ${data.length} stocks left in the world\n
\nThe volatility characteristics of those stocks is represented as 1-year probability distriution of gross return. Refer to the Part1 if you want to remind what this is\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"draw_lognormal_pdf(data, 100, 240, margin, width*2/3, 250)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"md`\n
\n### Single asset simulation with (+) and (-) covariance\n\n* \\\\# of stocks in portfolio: 2 (doubled 1 stock)\n* [**Left**] (+) covariance: A tendency that one increases the other increases, one decreases the other decreases\n* [**Right**] (-) covariance: A tendency that one icreases the other decreases, one decreases the other increases\n* Simulation duration: 5 years\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":63,"value":"viewof assetindex = Inputs.select([...Array(data.length).keys()], {label: \"stock to simulate?\", format: i => data[i].name});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":67,"value":"viewof yscale_multiverse = Inputs.radio(scales, {label: \"Y-axis scale\", value: scales[0], format: x => x.name}) ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":182,"value":"viewof replay_multiverse = button({value: \"Replay single asset simulation\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":172,"value":"{\n replay_multiverse;\n const asset = data[assetindex];\n const items = [\n {mu:asset.mu, sigma:asset.sigma, color:d3.schemeCategory10[assetindex]},\n {mu:asset.mu, sigma:asset.sigma, color:d3.schemeCategory10[assetindex]}\n ];\n return draw_covariance_comparison_chart(dt, years, items, yscale_multiverse.value, margin, height, 4, 2);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":190,"value":"md`\n
\n#### As a result of single asset simulation with (+) and (-) covariance\n\n* Where covariance is +1 (Perfect Positive), mean variance is same as the variance of the single stock\n* Where covariance is -1 (Perfect Negative), mean variance is maintained at a low level and close to its own inclination (also known as hedging risk)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":194,"value":"md`\n
\n### Multiple stocks simulation with (+) and (-) covariance\n\n* \\\\# of stocks in portfolio: 20 (doubled 10 stocks)\n* [**Left**] (+) covariance: A tendency that one increases the other increases, one decreases the other decreases\n* [**Right**] (-) covariance: A tendency that one icreases the other decreases, one decreases the other increases\n* Simulation duration: 5 years\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":197,"value":"viewof yscale_present = Inputs.radio(scales, {label: \"Y-axis scale\", value: scales[0], format: x => x.name}) ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":200,"value":"viewof replay_present = button({value: \"Replay multi-stock simulation\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":203,"value":"{\n replay_present;\n let items = [];\n for(let i = 0; i < data.length; i++)\n {\n let x = data[i];\n items.push({mu:x.mu, sigma:x.sigma, color:d3.schemeCategory10[i]});\n items.push({mu:x.mu, sigma:x.sigma, color:d3.schemeCategory10[i]});\n }\n return draw_covariance_comparison_chart(dt, years, items, yscale_present.value, margin, height, 1, 1);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":214,"value":"md`\n
\n#### As a result of multi-stock simulation with (+) and (-) covariance\n\n* Any diversified investment doesn't work when all the stocks have +1 covariance each other\n* If there's a way to take -1 covarance for each stock, diversified investment work perfect with a low mean variance\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":218,"value":"md`\n
\n### Closing Part3, the last\n\n* In the real world, positive covariance seems somehow usual called as bull or bear market. Some stocks in a specific category occasionally moves in the same direction\n* On the other hand, it is difficult to find two stocks their covariance is negative. Instead, those authorized could order a short selling in order to take an effect of negative covariance.\n* If we can accept that some stocks moves together, it's recommended not to put those eggs into one basket because of high mean variance\n* Last but not least, hope your investment sustainable and successful\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"md`---\n## Appendix\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"data = {\n var d = stocks10;\n for (let i = 0; i < d.length; i++)\n d[i]['name'] = \"stock #\" + (i+1) + \" \" + label_mu_sigma(d[i].mu*dt, d[i].sigma*Math.sqrt(dt));\n return d;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"dt = 240","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":59,"value":"years = 5","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":54,"value":"height = 400","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":69,"value":"scales = [ {name:\"linear\", value: \"linear\"}, {name:\"log\", value:\"log\"}];","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"margin = ({top: 10, right: 70, bottom: 10, left: 25})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":80,"value":"function cumulative_product (init, values) {\n let product = init;\n let result = [product];\n for (let i = 0; i < values.length; i++)\n result.push(product*=values[i]);\n return result;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":122,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"import {stocks10, draw_lognormal_pdf, draw_gbm_chart, logratio_formatter, linearscale_formatter, label_mu_sigma} from \"@humble-data-miner/finance-library\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":184,"value":"import {button} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W35","stdlib":"1","titling":"auto"}} 33:"$32:body"