tag:blogger.com,1999:blog-7391239709117021140.post5637651955427536761..comments2011-12-13T03:59:34.691-08:00Comments on Hedge Fund Quant Blog: Calculating Average Returns - Arithmetic vs. Geometric Averageaacchttp://www.blogger.com/profile/16231375899940908730noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-7391239709117021140.post-34817988471171621462011-12-13T03:59:34.691-08:002011-12-13T03:59:34.691-08:00Dear Mr.Aaron Wormus,
The basic Calculation is ex...Dear Mr.Aaron Wormus,<br /><br />The basic Calculation is expalined in very simple & Understandable.<br /><br />Thank you very much for your inoformation on this website.<br /><br />Regards,<br /><br />Natesh,INDIANateshhttps://www.blogger.com/profile/01489485363353309085noreply@blogger.comtag:blogger.com,1999:blog-7391239709117021140.post-31197229750041881422011-03-25T09:46:26.679-07:002011-03-25T09:46:26.679-07:00Aaron, thanks for the concise explanation of the d...Aaron, thanks for the concise explanation of the difference between the two calculations. I have a follow up question (or questions) for you. I recently calculated my investment returns versus the S&P 500. I used two methodologies for measuring the compounded annual return of the S&P 500 – first, I simply took the dividend/split adjusted S&P 500 level from the first day I invested (August 2005) and the most recent closing date (March 24, 2011) and compared that return to my split/dividend adjusted returns (using an XIRR formula). Second, I attempted to recreate a “time-adjusted” S&P 500 return. I began investing in August 2005 and made subsequent investments in different stocks across that period. It struck me as a little misleading to compare my returns to the S&P 500 returns by taking the first and last day without considering that I had invested at many more periods along the way (basically, if I were reviewing my own returns, I would want to know if I did better than the S&P simply because many of my investments were made during low points across the measured period). So, I created a mechanism by which at any point I invested in stocks (actual investments used in my own return calculation), a corresponding “investment” in a share of the S&P 500 was made (I did this by multiplying the dollar amount invested by the S&P 500 close on that day, making the assumption that I bought “shares” in the S&P 500 equal to the amount theoretically invested). Then, I took the implied number of S&P 500 “shares” purchased since August 2005 and multiplied that amount by the March 25, 2011 S&P 500 adjusted close and used an XIRR formula to calculate the return. <br /><br />Long story to get to my questions but hopefully that gave you some context. First, is either of these ways the “correct” or generally accepted way to compare returns to the S&P 500. Second, if I try to use the geometric average (which it sounds like a hedge fund would use in this situation) to compare returns, do I need to account for timing differences – if so, what is the best way to do that, if not, could you elaborate on the theoretical reasons why it is either already factored into the calculation or why this isn’t a theoretical concern when analyzing return comparisons? Thanks in advance!Unknownhttps://www.blogger.com/profile/15212422046951630719noreply@blogger.comtag:blogger.com,1999:blog-7391239709117021140.post-66941351588777015242011-01-13T11:47:32.076-08:002011-01-13T11:47:32.076-08:00Thanks for the comment Cameron. I've added you...Thanks for the comment Cameron. I've added your blog to my blogroll. I hope to be able to provide more statistically focused blog entries in the upcoming weeks.aacchttps://www.blogger.com/profile/16231375899940908730noreply@blogger.comtag:blogger.com,1999:blog-7391239709117021140.post-25999408623523288592011-01-13T11:03:30.022-08:002011-01-13T11:03:30.022-08:00Great point Aaron because this is an important dis...Great point Aaron because this is an important distinction. This is a critical consideration in portfolio management because a drawdown has a disproportionate impact on returns. For instance, if a $100M fund goes up 50% in one year and down 50% the next, the fund only has $75M left. This dynamic highlights the importance of downside estimation in portfolio construction: http://blog.alphatheory.com/2010/12/which-way-is-up-why-six-of-one-is-not-always-worth-a-half-dozen-of-another.html.Cameron Hight, CFAhttps://www.blogger.com/profile/01053537804584527466noreply@blogger.com