How can I investigate historical effect of Rebalancing on Return and Standard Deviation?
"Do not reinvent the wheel! Historical data about stock market returns and standard deviations suffer from number of issues such as past-filling and mostly survivorship bias -- that the current answers do not consider at all. I suggest to read the paper ""A Century of Global Stock Markets"" by Philippe Jorion (UC Irvine) and William Goetzmann (Yale), here. William Bernstein comments the results here, notice that rebalancing is sometimes a good option but not always, his non-obvious finding where the low SD did not favour from rebalancing:  Look at the final page of the paper,  ""geometric returns -- represent returns to a buy-and-hold strategy"" and the ""arithmetic averages -- give equal weight to each observation interval."", where you can find your asked ""historical effect of Rebalancing on Return and Standard Deviation"". The paper nicely summarizes the results to this table:  The results in the table are from the interval 1921-1996, it is not that long-time but even longer term data has its own drawbacks. The starting year 1921 is interesting choice because it is around the times of social-economical changes and depressing moments, historical context can be realized from books such as Grapes Of Wrath (short summary here, although fiction to some extent, it has some resonance to the history). The authors have had to ignore some years because of different reasons such as political unrest and wars.  Instead of delving into marketed spam as suggested by one reply, I would look into this search here. Look at the number of references and the related papers to judge their value.  P.s. I encourage people to attack my open question here, hope we can solve it!" "Doesn't ""no rebalancing"" mean ""start with a portfolio and let it fly?""  Seems like incorporation of rebalancing is more sophisticated than not. Just ""buy"" your portfolio at the start and see where it ends up with no buying/selling, as compared with where it ends up if you do rebalance. Or is it not that simple?" "To answer your question directly..  you can investigate by using google or other means to look up research done in this area.  There's been a bunch of it Here's an example of search terms that returns a wealth of information. effect+of+periodic+rebalancing+on+portfolio+return I'd especially look for stuff that appears to be academic papers etc, and then raid the 'references' section of those.  Look for stuff published in industry journals such as ""Journal of Portfolio Management"" as an example. If you want to try out different models yourself and see what works and what doesn't, this Monte Carlo Simulator might be something you would find useful The basic theory for those that don't know is that various parts of a larger market do not usually move in perfect lockstep, but go through cycles.. one year tech might be hot, the next year it's healthcare.  Or for an international portfolio, one year korea might be doing fantastic only to slow down and have another country perform better the next year.    So the idea of re-balancing is that since these things tend to be cyclic, you can get a higher return if you sell part of a slice that is doing well (e.g. sell at the high) and invest it in one that is not (buy at the low) Because you do this based on some criteria, it helps circumvent the human tendency to 'hold on to a winner too long' (how many times have you heard someone say 'but it's doing so well, why do I want to sell now""? presuming trends will continue and they will 'lose out' on future gains, only to miss the peak and ride the thing down back into mediocrity.)  Depending on the volatility of the specific market, and the various slices, using re balancing can get you a pretty reasonable 'lift' above the market average, for relatively low risk. generally the more volatile the market, (such as say an emerging markets portfolio) the more opportunity for lift. I looked into this myself a number of years back, the concensus I came was that the most effective method was to rebalance based on 'need' rather than time.  Need is defined as one or more of the 'slices' in your portfolio being more than 8% above or below the average.  So you use that as the trigger. How you rebalance depends to some degree on if the portfolio is taxable or not.  If in a tax deferred account, you can simply sell off whatever is above baseline and use it to buy up the stuff that is below.   If you are subject to taxes and don't want to trigger any short term gains, then you may have to be more careful in terms of what you sell.  Alternatively if you are adding funds to the portfolio, you can alter how your distribute the new money coming into the portfolio in order to bring up whatever is below the baseline (which takes a bit more time, but incurs no tax hit)  The other question is how will you slice a given market?  by company size?  by 'sectors' such as tech/finance/industrial/healthcare, by geographic regions?" From Vanguard's Best practices for portfolio rebalancing:
At its simplest level it's an application of basic statistics/probability: Suppose you have n independent and identically distributed assets with the return on asset i denoted R_i which has mean m and variance s^2 (same for all assets). You can easily weaken these assumptions but I make them to simplify the exposition  [Square brackets show a numerical example with n=20, m=8%, s=2%] if you invest in one of these assets you expect to get a return of m [8%] with standard deviation s [2%] (so you expect with probability 95% (approx) to get a return between m-2*s and m+2*s.  [between 4% and 12%] Now suppose you split your money equally among the n-assets.  Your return is now R = (1/n)\Sum{i=1}^n R_i your expected return is  E(R) = (1/n)\Sum{i=1}^n E(R_i) = (1/n)\Sum{i=1}^n m = m   [8%] the variance of your return is  Var(R) = Var( (1/n)\Sum{i=1}^n R_i )       = (1/n^2)\Sum{i=1}^n Var(R_i) = n * s^2 / n^2) = s^2/n    So, the standard deviation is SD(R) = Sqrt(V(R)) = s/Sqrt(n) [2%/Sqrt(20) = 0.44%] Now, with 95% probability we get a return between E(R)-2*SD(R) and E(R)+2*SD(R) [between 7.12% and 8.88%].  This interval is smaller than when we invested in the single asset, so in effect with this portfolio we are achieving the same return m [8%] but with lower variance (risk) [0.44% instead of 2%].  This is the result of diversification.     You can assume the assets are not independent (and most book expositions of this topic do indeed do that). In that case the calculation is modified because the variance of the portfolio now depends on the correlation between returns, as does the reduction in variance caused by the diversification.  If assets are negatively correlated the result of the diversification will be more reduction in risk and vice versa.   You can also assume the assets are not identically distributed and the above analysis does not change too much.   You might look for some references on CAPM (Capital Asset Pricing Model) or portfolio theory but broadly these are based on what I have described above - finding the portfolio with minimum variance for a given return by investing proportionally in treasury bonds and risky assets. You can't have it both ways. Either in average blacks are stupider than whites or IQ is a poor measure of intelligence. There's no middle ground.  A standard deviation us enough to matter statistically. That's what a standard deviation means. If IQ measures intelligence, then blacks are statistically less intelligent than whites. Individual variation is accounted for within the model.  I don't believe blacks are stupider than whites, but that's because I believe that IQ is a shitty measure of intelligence and that it doesn't cross cultural barriers well.  You on the other hand think it's perfect so face up to your racism and own it. "Volume is really only valuable when compared to some other volume, either from a historical value, or from some other stock.  The article you linked to doesn't provide specific numbers for you to evaluate whether volume is high or low. Many people simply look at the charts and use a gut feel for whether a day's volume is ""high"" or ""low"" in their estimation. Typically, if a day's volume is not significantly taller than the usual volume, you wouldn't call it high. The same goes for low volume. If you want a more quantitative approach, a simple approach would be to use the normal distribution statistics: Calculate the mean volume and the standard deviation. Anything outside of 1.5 to 2.0 standard deviations (either high or low) could be significant in your analysis. You'll need to pick your own numbers (1.5 or 2.0 are just numbers I pulled out of thin air.) It's hard to read anything specific into volume, since for every seller, there's a buyer, and each has their reasons for doing so. The article you link to has some good examples of using volume as a basis for strengthening conclusions drawn using other factors." "The portfolio described in that post has a blend of small slices of Vanguard sector funds, such as Vanguard Pacific Stock Index (VPACX).  And the theory is that rebalancing across them will give you a good risk-return tradeoff.  (Caveat: I haven't read the book, only the post you link to.) Similar ETFs are available from Vanguard, iShares, and State Street.  If you want to replicate the GFP exactly, pick from them.  (If you have questions about how to match specific funds in Australia, just ask another question.)  So I think you could match it fairly exactly if you wanted to. However, I think trying to exactly replicate the Gone Fishin Portfolio in Australia would not be a good move for most people, for a few reasons: Brokerage and management fees are generally higher in Australia (smaller market), so dividing your investment across ten different securities, and rebalancing, is going to be somewhat more expensive. If you have a ""middle-class-sized"" portfolio of somewhere in the tens of thousands to low millions of dollars, you're cutting it into fairly small slices to manually allocate 5% to various sectors.  To keep brokerage costs low you probably want to buy each ETF only once every one-two years or so.  You also need to keep track of the tax consequences of each of them. If you are earning and spending Australian dollars, and looking at the portfolio in Australian dollars, a lot of those assets are going to move together as the Australian dollar moves, regardless of changes in the underlying assets.  So there is effectively less diversification than you would have in the US. The post doesn't mention the GFP's approach to tax.  I expect they do consider it, but it's not going to be directly applicable to Australia. If you are more interested in implementing the general approach of GFP rather than the specific details, what I would recommend is: The Vanguard and superannuation diversified funds have a very similar internal split to the GFP with a mix of local, first-world and emerging market shares, bonds, and property trusts.  This is pretty much fire-and-forget: contribute every month and they will take care of rebalancing, spreading across asset classes, and tax calculations.  By my calculations the cost is very similar, the diversification is very similar, and it's much easier. The only thing they don't generally cover is a precious metals allocation, and if you want that, just put 5% of your money into the ASX:GOLD ETF, or something similar." There has been a lot of research on the effects of stock splits. Some studies have concluded that: However note that (i) these are averages over large samples and does not say it will work on every split and (ii) most of the research is a bit dated and more recent papers have often struggled to find any significant performance impact after 1990, possibly because the effect has been well documented and the arbitrage no longer exists. This document summarises the existing research on the subject although it seems to miss some of the more recent papers. More practically, if you pay a commission per share, you will pay more commissions after the split than before. Bottom line: don't overthink it and focus on other criteria to decide when/whether to invest. The answer would depend on the equities held. Some can weather inflation better than others (such as companies that have solid dividend growth) and even outpace inflation. Some industries are also safer against inflation than others, such as consumer staples and utilities since people usually have to purchase these regardless of how much $ they have. In looking over the data comparing S&P 500 returns, dividends, and inflation, the results are all over the map. In the 50's the total return was 19.3% with inflation at 2.2%. Then in the 70's returns were 5.8% with inflation at 7.4 percent, leading one to think that inflation diminished returns. But then in the 80's inflation was 5.1%, yet the return on the S&P was up to 17.3% Either way, aside from the 70's every other decade since 1950 has outpaced inflation (as long as you are including dividends; hence my first paragraph). S&P 500: Total and Inflation-Adjusted Historical Returns Also, the 7% average stock appreciation you mention is just that, an average. You are comparing a year-over-year number (7% inflation) with an aggregated one (stock performance over x number of years) and that is a misrepresentation and is not being weighted for the difference in what those numbers mean. Finally, there are thousands of things that have an effect on the stock market and stocks. Some are controllable and others are not. The idea that any one of them, such as inflation, has any sort of long-term, everlasting effect on prices that they cannot outmaneuver is improbable. This is where researching your stocks comes in...and if done prudently, who cares what the inflation rate is? Asset prices are inversely related to interest rates. If you're valuing a business or a bond, if you use a lower interest rate you get a higher valuation.  Historic equity returns benefit from a falling interest rate environment which won't be repeated as interest rates can only go so low.  edit: typo Smaller markets can actually be more volatile so it's not a good idea to lower Graham's criteria for them. The only real adjustment possible is inflation adjustment. $100 million in 1973 United States works out to $500 million today based on the difference in CPI/Inflation from 1973. This number will be different for other markets where the rate of inflation since 1973 has been different. So the real question to ask is - what is to $100 million in the United States in 1973 worth today in your market? Source: http://www.serenitystocks.com/how-build-complete-benjamin-graham-portfolio