Search found 323 matches

by camontgo
Wed Jun 21, 2023 9:56 am
Forum: Personal Finance (Not Investing)
Topic: How much time for the second million?
Replies: 57
Views: 13117

Re: How much time for the second million?

Lots of good replies on different Excel methods to calculate. I used the "NPER" function and created the table below. I calculated the number of years to reach $2million over a range of contribution and return assumptions. I used APY, rather than APR, as #Cruncher suggested. I think it is notable that, with a ~$1million starting balance, the portfolio is generating much more than the monthly contribution...so the monthly contribution doesn't matter as much. For example, at a 6.5% return, $500 per month gets you to the goal in 11years while $2000 per month gets you to the goal in 9.2 years. Not a huge difference for $1500 per month. Starting Balance: $950,000.00 Target Balance: $2,000,000.00 Years to Target Balance "Monthly Co...
by camontgo
Thu Jun 08, 2023 2:48 pm
Forum: Personal Consumer Issues
Topic: Learning Violin as an adult? 7 years, new recording
Replies: 350
Views: 60009

Re: Learning Violin as an adult? 6.5 Year update

Latest recording sounds great! I've enjoyed following your progress. I took violin lessons growing up, and I still enjoy playing occasionally. In addition to ensemble playing with other strings, I'd recommend keeping a look out for opportunities to play with guitar players/singers. Way back when I was young and single, I had some friends who used to play open mics and occasional paid gigs, and I joined them a few times on violin. I think we only ever tried 3 songs with violin, but we did a version of "Little Wing" based on the cover by the The Corrs that always got a great response. The violin part that Sharon Corr plays is easier than what you are currently playing, but I thought it fit the song well. These days my 8 year old son...
by camontgo
Mon Nov 28, 2022 9:00 am
Forum: Personal Consumer Issues
Topic: Chicago Region Cross Country Skiing / Trekking?
Replies: 2
Views: 298

Re: Chicago Region Cross Country Skiing / Trekking?

There is a Facebook group.... "Northern Illinois Nordic" which has good updates on trail conditions in the Chicago area. There are a several forest preserves and golf courses that have groomed XC trails...but in recent years it has been rare to have enough snow around x-mas. If there isn't sufficient snow in the Chicago area, the NIN facebook group will also have updates on the closest options to the north. Edit: In addition to the Cook County forest preserves. The DuPage county forest preserves, Arrowhead Golf Course, and Morton Arboretum are options. In my experience, Arrowhead has the best grooming. The forest preserve trails are open to hikers, bikers, and horses, so they can get pretty rough. https://www.dupageforest.org/blog...
by camontgo
Wed Jun 29, 2022 9:02 am
Forum: Personal Consumer Issues
Topic: Any Boglehead musicians out there?
Replies: 284
Views: 21812

Re: Any Boglehead musicians out there?

Sandtrap wrote: Wed Jun 29, 2022 7:10 am Wow!
Great job.
Very nice.

What kind of music do you play on the uke?

Thanks for posting the picture.
j mango :D
Thank you!

I like to try to play a little bit of everything, but I don't get to play in a group very often...and I'm not much of a singer...so I spend most of my practice time learning instrumental arrangements of songs. I enjoy the uke arrangements at ukulelehunt.com.
by camontgo
Tue Jun 28, 2022 11:29 am
Forum: Personal Consumer Issues
Topic: Any Boglehead musicians out there?
Replies: 284
Views: 21812

Re: Any Boglehead musicians out there?

Enjoying this thread...I played violin for about 10 yrs as a kid. My daughter plays now, so I still dust off my old violin to attempt a duet now and then.

These days, I'm mostly interested in building instruments. My latest is a tenor uke made from walnut, cherry, and reclaimed cedar.

Image
by camontgo
Wed Jun 13, 2018 10:44 am
Forum: Investing - Theory, News & General
Topic: Why does CAPM make sense?
Replies: 23
Views: 1885

Re: Why does CAPM make sense?

(For an arbitrarily chosen stock) Thirty years from today, assuming some fixed net profit margin, the revenue growth is going to be the major factor determining the price then. If the company grows by 10x in revenue over the next thirty years, sure the stock will do great. If it goes down by 50% in revenue, the stock probably will tank a fair bit. Does the amount of wiggling seen on the chart tell you that? Nope At a high level, there are a couple steps involved in determining a stock's price. Step1: Estimate future cash flows Step2: Determine present value of these cash flows using an appropriate discount rate (based on riskiness of the cash flows estimated in Step 1). These discounted future cash flows determine today's price for the sto...
by camontgo
Sat May 05, 2018 9:06 am
Forum: Investing - Theory, News & General
Topic: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?
Replies: 114
Views: 14500

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Camontgo, is the upper line of the V (hyperbola-through-the-cone-focus) in your second chart, the tangent line to the curve in your first chart? I don't think so. I think I'd need to add an additional asset with near zero SD to the Markowitz framework, rather than moving one of the original assets, in order for the hyperbola-through-cone-focus frontier to converge to the same tangent line you drew on the first frontier. Although in this example it does seem to converge. So, maybe I'm missing something. :? The original asset had defined mean, SD, and covariance with the other assets. I could have changed the shape of the Markowitz frontier in the first chart by just changing the covariances for that asset while keeping the mean and SD const...
by camontgo
Fri May 04, 2018 10:03 am
Forum: Investing - Theory, News & General
Topic: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?
Replies: 114
Views: 14500

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

I am trying (and not succeeding) to visualize what happens in three-space if you have a surface representing the efficient frontier for three risky assets, and you move one of the assets so that it becomes less and less risky and finally becomes riskless. I think the tangent-line diagram is just a way of expressing this special case without requiring three dimensions, but I can't see it in my mind yet. Why do you need more dimensions for more assets? This plot is the efficient frontier for 4 assets (each of which is shown by a "*"...none of them are on the efficient frontier). http://www.calculatinginvestor.com/wp-content/uploads/2018/05/cov_nonzero.png If I take the lowest standard deviation asset, and move it to near zero stand...
by camontgo
Tue Oct 10, 2017 4:33 pm
Forum: Personal Consumer Issues
Topic: Best weight loss resources?
Replies: 54
Views: 5938

Re: Best weight loss resources?

I lost over 80lbs in 2014, and I've kept it off since. I watched my diet very carefully (tracked all food and exercise in the myfitnesspal app) while losing the weight. I've also become a bit of a triathlon fanatic over the past few years, and that has helped with maintaining my weight. I read quite a few books on weight loss, but the one I liked best was "The Diet Fix" by Yoni Freedhoff. I'd already lost a lot of weight when I found this book, so I can't say it was instrumental in my own weight loss...but it was a great summary of what I learned through the whole experience. I've recommended it to several friends and family members who have found it helpful. I found the book based on this review in Runner's World: https://www.run...
by camontgo
Fri Jan 06, 2017 5:03 pm
Forum: Investing - Theory, News & General
Topic: Research Paper Request: Active Manager Performance
Replies: 8
Views: 999

Re: Research Paper Request: Active Manager Performance

A very clearly written paper is Bogle's "Selecting Equity Mutual Funds" from the Journal of Portfolio Management (1992). Unfortunately, I can't find a link to an un-gated link to this paper...but here are some of my notes. Bogle uses the annual Honor Roll published by Forbes as the basis for mutual fund selection (funds selected based on long term track record and other sensible screening criteria). Forbes has published the Honor Roll each year since 1973 (nearly 20 years of data at the time of Bogle’s study). Bogle finds that an investor who carefully forms and adjust his portfolio based on Forbes Honor Roll does slightly outperform the average mutual fund (before accounting for fees). However, Bogle finds that after accounting f...
by camontgo
Tue Nov 22, 2016 5:26 pm
Forum: Investing - Theory, News & General
Topic: Fama-French factors, "financials," and DFA funds
Replies: 6
Views: 1946

Re: Fama-French factors, "financials," and DFA funds

This is a good question. I don't know the answer, but I don't think it is inconsistent that the best process for constructing a "small" or "value" investment portfolio may be different from the process of constructing the FF factors (HML and SMB). Fama and French sort stocks using characteristics (large/small, growth/value) when constructing the factor portfolios. They exclude financials and utilities in these sorts because of leverage and regulation. They then use these factor portfolios to run regressions and determine the factor loading of various stocks and funds. They find that an additional risk premium (beyond the market premium) is associated with a loading on the SMB or HML factors. There was a series of papers ...
by camontgo
Fri Oct 21, 2016 9:18 am
Forum: Investing - Theory, News & General
Topic: Humble Giants - Interview with Vanguard's Gerry O'Reilly and Jim Rowley
Replies: 3
Views: 1034

Humble Giants - Interview with Vanguard's Gerry O'Reilly and Jim Rowley

Excellent podcast interview with Vanguard Index Portfolio managers.

http://investorfieldguide.com/vanguard/

Some very interesting discussion on variety of topics frequently discussed on this forum such as: liquidity in smaller stocks, index construction, market structure, high frequency trading, Vanguard culture, and running a 4 minute mile.
by camontgo
Thu Oct 13, 2016 9:19 pm
Forum: Investing - Theory, News & General
Topic: Cliff Asness - Turning Over Accepted Wisdom with Turnover
Replies: 29
Views: 4961

Re: Cliff Asness - Turning Over Accepted Wisdom with Turnover

My take-aways: 1. In Sharpe's analysis, passive investors don't rely on active investors for indexing to work well. 2. In Pedersen's analysis, some trading is always necessary for a cap weighted index of the "the market". The cost of this trading may be quite small if there is a large pool of active traders who establish "fair" prices for any newly issued securities an index purchases and provide sufficient liquidity for the index to buy/sell as needed. So, indexing may work great, but if the amount of active investing/trading was substantially lower it might not work as well. 3. Active investors don't provide price discovery/liquidity for free. There are costs to the indexer which are small but not trivial. These costs ...
by camontgo
Wed Apr 01, 2015 11:23 am
Forum: Personal Consumer Issues
Topic: Pull-ups and Push-ups
Replies: 678
Views: 182159

Re: Pull-ups and Push-ups

I've managed to go from zero pull-ups to 4 pull-ups in about a month after being inspired by some of the earlier discussions on this thread.

Still an embarrassingly low number, but things are moving in the right direction. I think I'm still in the stage where gains come relatively easy!

My fitness goals for this year are 10 pull-ups and a sub-20 minute 5k. I could do both throughout my late teens and early 20s, but I haven't been in shape to do either for at least 10 years. Getting close on the 5k, so hopefully the pull-ups will continue to improve.
by camontgo
Mon Jan 26, 2015 9:52 pm
Forum: Investing - Theory, News & General
Topic: Effect of 0.79 correlation: fantasy vs. reality
Replies: 58
Views: 7686

Re: Effect of 0.79 correlation: fantasy vs. reality

For those who are skilled at this sort of thing, would it be possible/practical to create something along the lines of an efficient frontier time-lapse video (or gif)? Or is that the sort of thing that would take a huge amount of time? If not, I think it'd be super neat as a way to get across the message that efficient frontiers are not especially stable. Here is a first try at it...still needs some work: http://www.calculatinginvestor.com/wp-content/uploads/2015/01/meanvar_video.mp4 The video shows the mean variance frontier using rolling 60 month returns for the 3 Fama-French factors (RMRF, HML, SMB)...the frontier is plotted at each one month step. I didn't annualize the returns and standard deviations, so everything is monthly. I also ...
by camontgo
Mon Jan 26, 2015 2:38 pm
Forum: Investing - Theory, News & General
Topic: Effect of 0.79 correlation: fantasy vs. reality
Replies: 58
Views: 7686

Re: Effect of 0.79 correlation: fantasy vs. reality

Beliavsky wrote:
camontgo wrote:Actually, in theory, alpha can be less than 1, but then you'd need to short the fund to increase your Sharpe Ratio.
I think "alpha can be less than 0" was meant.
Yes, thanks, fixed it.
by camontgo
Mon Dec 22, 2014 11:33 am
Forum: Investing - Theory, News & General
Topic: Asness response to value redundancy
Replies: 47
Views: 9072

Re: Asness response to value redundancy

Very interesting read and nice to see that value isn't dead and that there are sort of investment products that capture all 5 of those metrics. (mkt, smb, hml, rmw, umd). In a recent interview, Gene Fama said the following... "...once you get beyond two dimensions of expected returns, the third adds very little. No matter how you stack them, it doesn't matter where you start. So, if you start with size and add value, say, and you add profitability, you don't get much. If you start with profitability and value, size doesn't get much. The problem is that these thing tend to be correlated. For example, momentum and value - well, value stocks tend to be negative momentum stocks. So, if you want to get momentum, you have to give up a lot o...
by camontgo
Sat Dec 20, 2014 12:50 pm
Forum: Investing - Theory, News & General
Topic: Effect of 0.79 correlation: fantasy vs. reality
Replies: 58
Views: 7686

Re: Effect of 0.79 correlation: fantasy vs. reality

People are apt to say "well, the lower the better, but anything that isn't 1.0 is still helpful ." I think that if the goal is maximizing Sharpe Ratio, any fund added needs to have a positive alpha (relative to the benchmark) to be "helpful"....not just a correlation less than 1.0. Actually, in theory, you can get a benefit when alpha is less than 0, but then you'd need to short the fund to increase your Sharpe Ratio. For example, run a CAPM style regression: http://www.calculatinginvestor.com/wp-content/uploads/2012/07/capmeq.gif If alpha is positive, then the investment can be combined with the benchmark to increase the Sharpe ratio. If alpha is negative, we can't (unless we allow shorting). If you want to calculate h...
by camontgo
Thu Aug 14, 2014 11:38 am
Forum: Personal Investments
Topic: Good Harbor and F-Squared
Replies: 17
Views: 2722

Re: Good Harbor and F-Squared

There are some earlier discussion on Good Harbor:

My thoughts are included in this one : http://www.bogleheads.org/forum/viewtop ... 1&t=115155

There was also some discussion around a WSJ article suggesting that traders were front running GH's trades...

http://www.bogleheads.org/forum/viewtop ... 1&t=132218

I'm not familiar with F-Squared
by camontgo
Tue Jul 01, 2014 11:02 am
Forum: Personal Consumer Issues
Topic: burning 1 lb is how many calories?
Replies: 69
Views: 9030

Re: burning 1 lb is how many calories?

I've lost 50lbs+ over the past 7 months through exercise and counting calories with a fitness app. Back at my high school weight now :happy Calorie tracking involves a lot of estimating and there are many complicating factors, but I've nevertheless found the rule that a 3500 calorie deficit equals 1 lb of weight loss to be in the ballpark. Regardless, for me, it was easy to dial-in a consistent weekly weight loss once I started tracking everything. I haven't completely eliminated any of my favorite foods. I just need to fit what I eat in the calorie budget. However, I have found that healthy eating (avoiding processed foods, lots of veggies, moderate amount protein, easy on the fat) makes it much easier to stay within my calorie budget with...
by camontgo
Tue Apr 22, 2014 10:55 am
Forum: Investing - Theory, News & General
Topic: Is 1800s stock market data even relevant?
Replies: 63
Views: 7745

Re: Is 1800s stock market data even relevant?

The current situation is never an especially close match with any historical time. As we go back further, the differences are greater, and the data accuracy is more suspect. The 1800s data may be irrelevant for calculating a "Siegel Constant" or running a PE10 expected return regression. Although, if you are doing this type of calculation, I think it is interesting to start with all available data and then compare the results to a more recent dataset. If you do this comparison, you might conclude that average risk premiums have been different across different economic eras, and this might temper your enthusiasm for giving much weight to the 1800s data when estimating tomorrow's expected return. Some of the comments in the discussi...
by camontgo
Wed Apr 09, 2014 1:15 pm
Forum: Investing - Theory, News & General
Topic: BH Greatest Hits: PE10 predictive power
Replies: 39
Views: 7562

Re: BH Greatest Hits: PE10 predicitive power

I believe this maps to my interpretation of DeLong in http://www.bogleheads.org/forum/viewtopic.php?p=2023098#p2023098 Do you disagree with that post? Following the link: He's (DeLong) saying the only possible choices are (1) p/e predicts returns, (2) p/e predicts earnings/dividend growth, (3) the price of risk changes over time, and implies these are mutually exclusive. He picks (1) as an empirical matter, rejects (3) as an empirical matter and therefore rejects (2) as a matter of logic. Cochrane appears to regard (1) and (2) as the only possible choices and assumes they are mutually exclusive. He rejects (2) as an empirical matter and therefore picks (1). He ignore (3). I think over the long term, it is between the first 2: (1) p/e predi...
by camontgo
Wed Apr 09, 2014 11:31 am
Forum: Investing - Theory, News & General
Topic: BH Greatest Hits: PE10 predictive power
Replies: 39
Views: 7562

Re: BH Greatest Hits: PE10 predicitive power

If we combine the two adjustments of 1 for the lower dividend payout and 4 for the FSB 142 change, the current CAPE 10 at 24.9 which looks way above the mean, doesn’t look so overvalued at a now 19.9. In fact, that’s right about in line with it’s average since 1960. Which begs the questions: a) Are stocks really overvalued or just highly valued (meaning returns are likely to be lower than historical levels, but that there is no reason to expect a major correction due to RTM)? b) To what mean should the CAPE ratio revert: The 16.5 mean of the past 113 years, or the 19.6 mean since 1960? These three points — that over time it’s logical to believe that the equity risk premium for U.S. stocks might have fallen, the accounting change regarding ...
by camontgo
Wed Apr 09, 2014 10:49 am
Forum: Investing - Theory, News & General
Topic: BH Greatest Hits: PE10 predictive power
Replies: 39
Views: 7562

Re: BH Greatest Hits: PE10 predicitive power

One major difference between the two cases is that in the first instance we had a constant underlying distribution while in the later case the underlying distribution could change over time. Yes, it will change over time. It could be that the market is more risky at some times than others, and this drives changes in valuation. I don't think that is inconsistent with Cochrane's argument. If the risk is changing, it would mean that market participants shouldn't be overly excited by low or high valuations. However, it is still true that if there is no correlation between valuation and the average level of growth then there will be a correlation between valuation and average return. Bogle uses this equation for expected returns: Return = Yield...
by camontgo
Wed Apr 09, 2014 9:31 am
Forum: Investing - Theory, News & General
Topic: BH Greatest Hits: PE10 predictive power
Replies: 39
Views: 7562

Re: BH Greatest Hits: PE10 predicitive power

How does one prove dividend growth has not been forecastable by the market? Perhaps the price of risk has changed? Assuming dividend growth is not forecastable, does that necessarily mean that returns are forecastable? Why? Example: Suppose I purchase the opportunity to draw a "payoff" from some distribution of possible outcomes. You purchase a similar opportunity to independently draw a "payoff" from the same distribution, but you pay a higher price for the opportunity. Is my expected return not higher? Of course, in any particular instance your realized return might be higher...but not over many trials. Now, it could be that the market pays a higher price for shares at some times because the market has some limited ab...
by camontgo
Fri Apr 04, 2014 11:39 am
Forum: Investing - Theory, News & General
Topic: Gordon equation-stock buybacks
Replies: 11
Views: 1636

Re: Gordon equation-stock buybacks

I would be interested to hear how Bernstein and others think buybacks factor into the expected return on stocks under the Gordon equation. Bernstein wrote a paper with Robert Arnott in 2003 that had a very good discussion on the net effect of buybacks and dilution. http://portfolioconstruction.com.au/obj/articles/Real%20long%20term%20earnings%20growth.pdf Most of the analysis I've seen show that the net effect over long periods is a fairly small (though perhaps not negligible). For example, see the paper "A Supply Model of the Equity Risk Premium" which is available in the collection of papers here: http://www.cfainstitute.org/learning/products/publications/contributed/Pages/rethinking_the_equity_risk_premium.aspx The authors app...
by camontgo
Mon Jan 06, 2014 10:26 am
Forum: Investing - Theory, News & General
Topic: Expected Future Market Returns
Replies: 32
Views: 4402

Re: Expected Future Market Returns

According to a Vanguard study, PE and Shiller's 10 year PE are the best forecasts of future market returns. Vanguard says they have done equally well, but only explain about 40%. In other words, they are the best methods but are not very good. I've run the regressions myself, and, as Vanguard's results show, the Shiller PE is only a bit better than regular PE at the 10-year horizon...but Shiller PE has been a lot better at the 20 year horizon. For example, over the full Shiller dataset (more return history than Vanguard used), the R^2 is less than 0.35 for both Shiller PE and standard PE for 10 year return regressions...but for 20 year regressions PE10 R^2 goes to 0.61 and for PE is only 0.33. The "speculative" component of retur...
by camontgo
Mon Jan 06, 2014 9:29 am
Forum: Investing - Theory, News & General
Topic: Expected Future Market Returns
Replies: 32
Views: 4402

Re: Expected Future Market Returns

Here is a free collection of papers discussing the equity risk premium. Includes papers from prominent academics and practitioners. It is a couple years old now, but still an interesting read:

http://www.cfainstitute.org/learning/pr ... emium.aspx
by camontgo
Sun Dec 22, 2013 8:36 pm
Forum: Investing - Theory, News & General
Topic: The Single Greatest Predictor of Future Stock Market Returns
Replies: 158
Views: 39033

Re: The Single Greatest Predictor of Future Stock Market Ret

The author has now posted a new post which includes a critique of his earlier post...another interesting read :happy

http://philosophicaleconomics.wordpress ... e-fitting/
by camontgo
Sun Dec 22, 2013 2:33 pm
Forum: Investing - Theory, News & General
Topic: Interesting article about CAPE/ PE10
Replies: 16
Views: 3627

Re: Interesting article about CAPE/ PE10

Wow--that was perhaps the most interesting finance article I've read all year. A purely mathematical way of thinking about what returns one can reasonably expect apart from any judgement as to what level the market "should" trade at. I'd like to use the numbers he was using from FRED and tinker with them a bit. An r-squared over 90 feels like an overfit to me--wonder what it would be like if you looked prospectively at 5 years or 15. I agree it seems overfit. I tried to reproduce the regression results. I "only" got an R^2 of 0.81...but, I used 10 year CAGR of TSM as the dependent variable. I think these regressions are usually done with an arithmetic average annual return as the dependent variable. Also, the author use...
by camontgo
Sat Dec 21, 2013 11:14 am
Forum: Investing - Theory, News & General
Topic: Interesting article about CAPE/ PE10
Replies: 16
Views: 3627

Re: Interesting article about CAPE/ PE10

This is a very interesting blog. The Shiller PE post is excellent, but the newest post is even more thought provoking. It presents a new indicator of "future returns" that I had not seen before, and it has a very interesting (and extremely long) explanation of why it works. http://philosophicaleconomics.wordpress.com/2013/12/20/the-single-greatest-predictor-of-future-stock-market-returns/ Ultimately, the price of equity is determined in the same way that the price of everything is determined–via the forces of supply and demand. For any given stock (or for the space of stocks in aggregate), price is always and everywhere produced by the coming together of those that don’t own the stock and want to allocate their wealth into it, and...
by camontgo
Tue Dec 17, 2013 1:21 pm
Forum: Personal Consumer Issues
Topic: Mega Millions jackpot to $636 million
Replies: 82
Views: 7068

Re: Mega Millions jackpot to $636 million

According to this analysis, the expected value of a ticket actually goes down when the jackpot is at record levels....because the number of tickets sold grows super-linearly vs. jackpot size so the probability of ties increases more rapidly than the expected payout. http://www.circlemud.org/jelson/megamillions/ I tried to estimate the value of a ticket for the current jackpot using the method from the blog post....the big unknown is the number of tickets in play, but I get an expected value of about $0.46 per ticket using a conservative estimate of total sales.....so, it's not worth investing a dollar :happy Here's my calculation: https://docs.google.com/spreadsheet/ccc?key=0Am2C19KBrGAIdDc1X2l4NGtBdHJ3VWVybG5HNVBTMVE&usp=drive_web#gid=0
by camontgo
Sun Dec 08, 2013 5:11 pm
Forum: Investing - Theory, News & General
Topic: Math q's about "rotated" eff. front. charts like Rick's
Replies: 2
Views: 594

Re: Math q's about "rotated" eff. front. charts like Rick's

I think the arithmetic mean to geometric mean change results in something more complex than a simple rotation of the standard efficient frontier. In my approximation of Rick's curve in the previous thread, I subtracted 0.5*sigma^2 from each return...which is subtracting a parabola shape. The 0.5*sigma^2 is only an approximation of the true arithmean to geomean conversion, but a more accurate conversion will bend the plot similarly. Markowitz has a good description of the difference between the two means and the approximation calculation in Chapter 6 of his 1959 book (available as a free PDF here: http://cowles.econ.yale.edu/P/cm/m16/)....though in a quick scan I didn't find an explicit discussion of the reasons for using arithmetic means in...
by camontgo
Fri Dec 06, 2013 3:24 pm
Forum: Investing - Theory, News & General
Topic: Math question about Rick Ferri's efficient frontier curve
Replies: 45
Views: 6032

Re: Math question about Rick Ferri's efficient frontier curv

By the way, in your chart, to my eyeball it looks as if there is just the tiniest bit of actual decline in return at the 100%-US end? That is, the return for 85% U.S. 15% foreign is higher, not just in risk-adjusted return (tangent line), but in just plain old return? Yes, there is a small decline in the geometric mean...it is about 0.01%. If I continued the plot (which would require shorting international to be greater than 100% U.S.) the geometric mean would fall even more. Here are the Markowitz model inputs I used. I added back the 0.5*sigma^2, so my return values are higher than what you would read directly from Rick's plot. I do get about 15% min variance (not 14%), but it is hard to see on my plot because the x-axis labels are screw...
by camontgo
Fri Dec 06, 2013 2:04 pm
Forum: Investing - Theory, News & General
Topic: Math question about Rick Ferri's efficient frontier curve
Replies: 45
Views: 6032

Re: Math question about Rick Ferri's efficient frontier curv

That's basically correct. The total rate of return is calculated by using an IRR on the ending value of each $10,000 portfolio over the Jan 1970 - October 2013 period. The standard deviation is annualized using monthly returns for each portfolio over the same period. Rick Ferri So, the IRR is giving the geometric mean. In the standard Markowitz model, the expected return is equivalent to the arithmetic mean. I think Rick's version is probably more accurate for what he's trying to communicate, but it is not technically a Markowitz efficient frontier. The tangency portfolio, capital allocation line, etc..would be off when using the geometric means...but, the geomeans are a better representation of the actual returns earned by investors. I us...
by camontgo
Wed Dec 04, 2013 2:47 pm
Forum: Investing - Theory, News & General
Topic: Math question about Rick Ferri's efficient frontier curve
Replies: 45
Views: 6032

Re: Math question about Rick Ferri's efficient frontier curv

The textbook Markowitz efficient frontier is a single period model which uses arithmetic mean returns. It is symmetric about a horizontal line through the minimum variance portfolio. It is true that the single period analysis can be misleading if not interpreted carefully (for example, the high variance portfolios have low median outcomes when compounded over multiple periods..even though expected return is high), and it is also true that the Markowitz model isn't very practical because it is very sensitive to inputs which are hard to estimate with precision. However, the idea is that you can draw a capital allocation line and find a combination of risky assets which maximizes the Sharpe ratio, and you can combine this "tangency" ...
by camontgo
Wed Dec 04, 2013 11:01 am
Forum: Investing - Theory, News & General
Topic: Math question about Rick Ferri's efficient frontier curve
Replies: 45
Views: 6032

Re: Math question about Rick Ferri's efficient frontier curv

If calculated by the textbook method, the efficient frontier plot should be symmetric about a horizontal line going with the minimum variance portfolio. Bill Sharpe has the equations posted for two risky assets here: http://www.stanford.edu/~wfsharpe/mia/rr/mia_rr5.htm The expected return (y-values) are given by: ep = e1 + x2*(e2-e1) Where e1 and e2 are the expected return of each asset, and x2 is the weight in asset 2. The variance (x-values) is given by (usually you would plot the standard deviation, so take the square root of this): vp = v1 + 2*x2*(c12-v1) + (x2^2)*(v1-2*c12+v2) This looks exactly like what I am doing. I'd quote my spreadsheet expression but it's too confusing turning cell references back into variable names... Note tha...
by camontgo
Wed Dec 04, 2013 9:58 am
Forum: Investing - Theory, News & General
Topic: Math question about Rick Ferri's efficient frontier curve
Replies: 45
Views: 6032

Re: Math question about Rick Ferri's efficient frontier curv

If calculated by the textbook method, the efficient frontier plot should be symmetric about a horizontal line going with the minimum variance portfolio.

Bill Sharpe has the equations posted for two risky assets here:

http://www.stanford.edu/~wfsharpe/mia/rr/mia_rr5.htm

The expected return (y-values) are given by:

ep = e1 + x2*(e2-e1)

Where e1 and e2 are the expected return of each asset, and x2 is the weight in asset 2.

The variance (x-values) is given by (usually you would plot the standard deviation, so take the square root of this):

vp = v1 + 2*x2*(c12-v1) + (x2^2)*(v1-2*c12+v2)
by camontgo
Tue Nov 26, 2013 12:56 pm
Forum: Investing - Theory, News & General
Topic: Due diligence on RAFI Pure Small Value
Replies: 189
Views: 28678

Re: Due diligence on RAFI Pure Small Value

Robert T,

Thanks for the additional analysis! Looks like the fund is worth watching as a potential SCV option.
by camontgo
Tue Nov 26, 2013 11:19 am
Forum: Investing - Theory, News & General
Topic: Due diligence on RAFI Pure Small Value
Replies: 189
Views: 28678

Re: Due diligence on RAFI Pure Small Value

The factor loadings and positive alpha look attractive, but there has been a lot written about other RAFI funds benefiting from the fortuitous timing of their index reconstitution in 2009.

Based on the table in the original post, 2009 looks extreme for this index as well. It would be interesting to look at time series of the FF3F residuals. How much is 2009 affecting the results? Just curious to know if the relative outperformance of this index can be attributed to a single home run or if it is the result of consistent base hits.
by camontgo
Thu Nov 21, 2013 1:34 pm
Forum: Personal Investments
Topic: what is the formula?
Replies: 12
Views: 1552

Re: what is the formula?

jbh42 wrote:Grt2bOutdoors, thanks for the answer.

But is there a formula where similar numbers can be plugged in while using a basic
handheld calculator?

If you want to calculate with a handheld calculator, you can use the equation here:

http://www.financeformulas.net/Number-o ... Value.html

Just need an "ln" key.
by camontgo
Thu Nov 14, 2013 11:07 am
Forum: Investing - Theory, News & General
Topic: "There is a rebalancing bonus ... false"
Replies: 188
Views: 25076

Re: "There is a rebalancing bonus ... false"

Akiva wrote:
Which isn't much different in the two cases with 20% sd because most of the benefit is captured just from having the starting 50/50 balance.
The median looks significantly higher to me. As does the CAGR. And both of those are what matter in terms of making a real world decision.
The CAGR is 0.1% higher for the 20% sd case (I fixed the labeling problem). If I invested in only 1 asset, as opposed to rebalancing between 2, the difference would be 1% as your earlier calculation shows. So, 90% of the benefit is captured by starting at 50/50 even if I never rebalance.

I'd prefer to have that extra 0.1%...but there may be other costs associated with rebalancing.
by camontgo
Thu Nov 14, 2013 10:38 am
Forum: Investing - Theory, News & General
Topic: "There is a rebalancing bonus ... false"
Replies: 188
Views: 25076

Re: "There is a rebalancing bonus ... false"

I'm still concerned about your median outcome being higher while your mean isn't. For a normal distribution, that shouldn't happen. The returns are drawn from a normal distribution. The final wealth is based on the compounding of these random returns over multiple periods, it isn't normal, it's right skewed. The log of final wealth outcomes would be normally distributed. So you *are* using a log-normal distribution. That's a problem because it means you can't use the mean since that only works for a normal distribution or something very close to it. Your "mean" figures above are basically garbage numbers and should be ignored. The median is the right figure here. And it *does* show that your returns are higher with rebalancing (a...
by camontgo
Thu Nov 14, 2013 10:21 am
Forum: Investing - Theory, News & General
Topic: "There is a rebalancing bonus ... false"
Replies: 188
Views: 25076

Re: "There is a rebalancing bonus ... false"

Akiva wrote: I'm still concerned about your median outcome being higher while your mean isn't. For a normal distribution, that shouldn't happen.
The returns are drawn from a normal distribution. The final wealth is based on the compounding of these random returns over multiple periods, it isn't normal, it's right skewed. The log of final wealth outcomes would be normally distributed.

(u+e)^n and (u-e)^n aren't equidistant from u^n. That's the whole reason the mean and median are different.

Rebalancing reduces skew...but not that much when comparing starting 50/50 vs. 50/50 with rebalancing.
by camontgo
Thu Nov 14, 2013 7:18 am
Forum: Investing - Theory, News & General
Topic: "There is a rebalancing bonus ... false"
Replies: 188
Views: 25076

Re: "There is a rebalancing bonus ... false"

Yes, the variance in outcomes is higher with no rebalancing than it is with rebalancing. It isn't a very big difference for the parameters I'm using, but the difference grows as I increase volatility. I've already noted that I agree rebalancing reduces risk and it improves the median outcome. Both of these things are desirable benefits. It also improves the average Sharpe ratio...which is related to the other two. However, for examples of the type I've shown (i.e. two uncorrelated assets with same expected return which follow a random walk) rebalancing does not change the expected wealth outcome (which only depends on the arithmetic mean). I've also tried to demonstrate that the expected wealth only depends on arithmetic mean using the coin...
by camontgo
Wed Nov 13, 2013 3:41 pm
Forum: Investing - Theory, News & General
Topic: "There is a rebalancing bonus ... false"
Replies: 188
Views: 25076

Re: "There is a rebalancing bonus ... false"

The point is that volatility hurts and that arithmetic averages are meaningless to multi-period investing. You seem to have gotten the later point, but missed the former. This a key point where we disagree. I agree with you that, when looking at specific sequence of returns, the geometric mean of the sequence tells us the final wealth outcome. The arithmetic mean of the sequence by itself tells us nothing. However, when looking at the distribution of multi-period outcomes for a random walk process, which is important when thinking about rebalancing as a strategy, the arithmetic mean of the process is meaningful. The arithmetic mean tells us the average value of final wealth across all outcomes, and the geometric mean tells us the median va...
by camontgo
Wed Nov 13, 2013 1:11 pm
Forum: Investing - Theory, News & General
Topic: "There is a rebalancing bonus ... false"
Replies: 188
Views: 25076

Re: "There is a rebalancing bonus ... false"

Akiva wrote:
camontgo wrote:
Akiva wrote:That's not true. And the coin-flipping example above illustrates this.
Here is my analysis of a coin flip example:

Example:

We flip a coin with a 100% return for heads, and a -50% return for tails. We make 100 flips with an initial bet of $1 and parlay the winnings. Compare rebalancing between two coins, with no rebalancing.

No rebalancing:
This isn't the example that was discussed earlier in the thread.
It is similar to an example posted by rmelvey, and I already had the spreadsheet for it. Where does it go wrong?

The point I'm making is that even in this extreme example there is no change in expected wealth with rebalancing. This example isn't based on simulation...I use the properties of the distributions of returns.
by camontgo
Wed Nov 13, 2013 1:04 pm
Forum: Investing - Theory, News & General
Topic: "There is a rebalancing bonus ... false"
Replies: 188
Views: 25076

Re: "There is a rebalancing bonus ... false"

That's not true. And the coin-flipping example above illustrates this. Here is my analysis of a coin flip example: Example: We flip a coin with a 100% return for heads, and a -50% return for tails. We make 100 flips with an initial bet of $1 and parlay the winnings. Compare rebalancing between two coins, with no rebalancing. No rebalancing: The arithmetic average return is 25%. The geometric average return is 25% - 0.5(75%)^2 = -3.125% (approx) The expected value of 100 flips with winnings parlayed ($1 starting bet) is related to the arithmetic average: 1 * 1.25^100 = $4,909,093,465 The median return of 100 flips ($1 starting bet) is related to the geometric mean return: 1 * 0.96875^2 = $0.04 The key point is that the expected value is rel...
by camontgo
Wed Nov 13, 2013 11:29 am
Forum: Investing - Theory, News & General
Topic: "There is a rebalancing bonus ... false"
Replies: 188
Views: 25076

Re: "There is a rebalancing bonus ... false"

It would be luck if the rebalancing strategy sometimes had better asset allocation and sometimes had worse asset allocation. However, if the returns of the two assets aren't identical, then the rebalancing strategy always has the inferior allocation (its never better).... That's not true. And the coin-flipping example above illustrates this. Similarly, stocks have higher returns than bonds, but having a small bond allocation and rebalancing between stocks and bonds still does better than stocks alone. (And if you want to talk about *risk-adjusted* returns, then you are better off with a much larger bond allocation because adding additional stock increases risk by more than returns.) In a random walk, the two assets are never going to end u...
by camontgo
Wed Nov 13, 2013 11:10 am
Forum: Investing - Theory, News & General
Topic: "There is a rebalancing bonus ... false"
Replies: 188
Views: 25076

Re: "There is a rebalancing bonus ... false"

I don't disagree with that. However, a practical rebalancing strategy loses an offsetting amount (on average) by holding an inferior (ex-post) asset allocation in all instances where the asset returns diverge over full the holding period. It only loses due to dumb luck. And you can't retire on luck. What is the variance of the terminal returns for the rebalancing case vs. the non-rebalancing case? The rebalanced returns should be much more tightly clustered because they are minimizing the effects of luck whereas the non-rebalanced ones are just letting things run their course. It would be luck if the rebalancing strategy sometimes had better asset allocation and sometimes had worse asset allocation relative to the no rebalancing strategy. ...