{"id":6565,"date":"2012-03-26T09:54:43","date_gmt":"2012-03-26T08:54:43","guid":{"rendered":"https:\/\/www.portfolioprobe.com\/?p=6565"},"modified":"2012-03-26T09:54:43","modified_gmt":"2012-03-26T08:54:43","slug":"beta-is-not-volatility","status":"publish","type":"post","link":"https:\/\/www.portfolioprobe.com\/2012\/03\/26\/beta-is-not-volatility\/","title":{"rendered":"Beta is not volatility"},"content":{"rendered":"

The missing link between beta and volatility is correlation.<\/p>\n

Previously<\/h2>\n

“4 and a half myths about beta in finance”<\/a> attempted to dislodge several myths about beta, including that beta is about volatility.<\/p>\n

“Low (and high) volatility strategy effects”<\/a> showed a plot of beta versus volatility for stocks in the S&P 500 for estimates from 2006.\u00a0 This post looks at the same thing at the other end of the time frame used in that post.<\/p>\n

Data<\/h2>\n

Betas and volatilities of almost all the stocks in the S&P 500 are estimated on the 250 trading days from 2011 March 01 to 2012 February 24.\u00a0 This should be thought of as a random — not data-snooped — window.\u00a0 Shorthand for this time period is the “final” window.<\/p>\n

Pictures<\/h2>\n

Figure 1 shows beta versus volatility for the stocks.\u00a0 Like the similar graph in “Low (and high) volatility strategy effects”<\/a> there is an outlier with high volatility but moderate beta.\u00a0 But it is a different stock.<\/p>\n

Figure 1: The volatility versus beta estimates from the “final” window. \"\"<\/a><\/p>\n

Figure 2: Returns for the S&P 500 and NFLX in the “final” window. \"\"<\/a>The beta of NFLX is small relative to its volatility because its correlation with the index is small.\u00a0 The smallest, actually.\u00a0 Figure 3 shows the distribution of the correlations.<\/p>\n

Figure 3: Density of correlation of stocks to the S&P 500 during the “final” period — the vertical blue line is NFLX correlation. \"\"<\/a>NFLX is clearly an outlier in terms of correlation with the index.<\/p>\n

Figure 4 is an indication of the dynamics of the beta-volatility relationship.<\/p>\n

Figure 4: Beta versus volatility from 2006 to the “final” period (blue points). \"\"<\/a>Figure 5 shows that the straight line in Figure 4 for NFLX was in actuality far from straight.\u00a0 But the beta estimate never went negative.<\/p>\n

Figure 5: The beta-volatility dynamics of NFLX using a 250 trading day window. \"\"<\/a>For the eagle-eyed and suspicious: The volatility estimate in Figure 5 is the usual unweighted standard deviation, but the volatilities in the other plots are time-weighted<\/a>.\u00a0 Hence the numbers are not exactly the same for the same timepoints.<\/p>\n

Summary<\/h2>\n

The correlation of a stock to the index is a determinant of the stock’s beta along with its volatility.<\/p>\n

Beta is not constant.<\/p>\n

Appendix R<\/h2>\n

segment plot<\/h4>\n

The code to produce Figure 4 is:<\/p>\n

plot(sp5.volfin, sp5.betafin, xlab=\"Volatility\",\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ylab=\"Beta\", col=\"steelblue\",\r\n        xlim=range(sp5.vol06, sp5.volfin),\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0ylim=range(sp5.beta06, sp5.betafin))\r\nsegments(sp5.volfin, sp5.betafin, sp5.vol06, sp5.beta06,\r\n        col=\"gold\")\r\npoints(sp5.volfin, sp5.betafin, col=\"steelblue\")<\/pre>\n
beta-volatility dynamics<\/h4>\n
Two functions were written to create Figure 5 — one to do the computing, and one to do the actual plotting.\u00a0 They are pp.rollbetavol<\/code><\/a> and pp.timeline<\/code>.<\/a>\u00a0 The second of these fails to say it in the function definition, but they are both in the public domain — you can do whatever you like with them.<\/p>\n
Subscribe to the Portfolio Probe blog by Email<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
The missing link between beta and volatility is correlation. Previously “4 and a half myths about beta in finance” attempted to dislodge several myths about beta, including that beta is about volatility. “Low (and high) volatility strategy effects” showed a plot of beta versus volatility for stocks in the S&P 500 for estimates from 2006.\u00a0 … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11,6],"tags":[111,234,144],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/posts\/6565"}],"collection":[{"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/comments?post=6565"}],"version-history":[{"count":0,"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/posts\/6565\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/media?parent=6565"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/categories?post=6565"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.portfolioprobe.com\/wp-json\/wp\/v2\/tags?post=6565"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}