{"id":2088013,"date":"2018-10-02T12:26:24","date_gmt":"2018-10-02T06:56:24","guid":{"rendered":"http:\/\/stockviz.biz\/index.php\/?p=2088013"},"modified":"2018-10-02T15:53:21","modified_gmt":"2018-10-02T10:23:21","slug":"lumpsum-vs-sip-thinking-in-probabilities","status":"publish","type":"post","link":"https:\/\/stockviz.biz\/index.php\/2018\/10\/02\/lumpsum-vs-sip-thinking-in-probabilities\/","title":{"rendered":"Lumpsum vs. SIP: Thinking in Probabilities"},"content":{"rendered":"

This is a continuation of Lumpsum vs. Dollar Cost Averaging (SIP)<\/a> that modeled different return series and concluded that a prudent investor would be better off with a SIP because of a smaller probability of incurring a large loss. However, we stopped short of comparing different indexes to see if the conclusion held.<\/p>\n

The ‘average’ return<\/h3>\n

What happens if we take the average weekly return of an index and create a synthetic index that just gives those average returns without any variance? We end up with a parabolic looking cumulative return profile below:
\n\"cumulative<\/a>
\nThe small cap index was chosen on purpose to illustrate how ‘average’ returns relate to real returns on an extremely volatile index.<\/p>\n

The average return series is, of course, a fantasy. What we are interested in is in the probability of getting those returns.<\/p>\n

Probabilities<\/h3>\n

Just like our first post, we start by modeling the returns of the NIFTY 50, MIDCAP and SMLCAP indexes as a Generalised Lambda Distribution and running a 10,000 path simulation to obtain a series of DCA vs lumpsum investment returns. We then feed that into a empirical cumulative distribution function so that we can query it for probabilities under different thresholds. To put that in a picture:
\n\"lumpsum<\/a><\/p>\n

The vertical lines mark the different thresholds we are interested in. <\/p>\n