It is very simple: invest the same amount of money in each of the N assets considered by the investor.Why do you think this policy works so well in practice?Here is some evidence. From the information in the MSCI Equal Weighted Indices, and over a 10-years period, the world 1/N policy obtained an annual return of 10.9%, versus the 5.7% return of the corresponding world index. That is, it almost doubles the market return. The volatility of the 1/N policy is worse, but only a bit: 14% versus 13.4% for the world index.In other words, the Sharpe ratio (SR) of the 1/N policy was 0.78 and the SR of the world index was 0.42.The same results are obtained for other asset compositions: Europe, USA, Japan, etc.I would like to know your opinions.

Intuitively one would assume that market cap-weighted indices are going to have performance highly skewed by the giants and you are pretty much just capturing the returns for those stocks. Price weighted is most likely worse in this aspect (Apple is what 20% of Nasdaq 100 now?). With equal weighting you are more in a position to capture the returns for the whole market instead of limiting your scope. This leads to a more diversified portfolio where losses are more easily offset by upward movements.The question of why price weighted and market cap weighted indices aren't quick enough to capture the change in returns I can't answer but one can guess that it's because they've become so highly skewed that the lower price/cap ones just don't matter at all and even if a top 10 constituent gets high negative returns it may still remain in the top 10 but perhaps a bit lower ranked.

eckhardt platen has done quite a bit of work on this Approximating the Numeraire Portfolio by Naive Diversification At least from his point of view, the idea is that you cannot estimate the mean, so best to minimise the variance by diversifying as much as possiblethe problem (which he doesn't deal with) as I understand it is that it doesn't scale:for reasonable sized portfolios you end up with a sizeable portion of the whole share capital of small companies ( which obviously distorts the share prices)

QuoteOriginally posted by: jnogalesIt is very simple: invest the same amount of money in each of the N assets considered by the investor.Why do you think this policy works so well in practice?You really haven't given any evidence for that. Why don't you go collect and post some 20+ year records of mutual fundsthat practice the 1/N policy in US stocks and compare them vs the lowest cost S&P500 funds (say Vanguard). Then, we'll have some real evidence one way or the other.

In the MSCI Equal Weighted Indices, you can also find similar results for US stocks.For instance, and over a 10-years period (no more data is available), the SR of the US equal weighted index was 0.48, whereas the SR of the cap-weighted index was 0.24, much worse.To confirm these findings, I have run my own experiments with the stocks composing the S&P 500.The back-test is as follows: at a given week from 2006 up to now, I consider the 1/N policy, and a week later I compute the corresponding portfolio return, net of transaction costs (of 40 bps) respect to the last portfolio composition. For the S&P 500 index, I consider the corresponding weekly return, but net of any transaction costs. I rebalance the 1/N policy every four weeks and repeat the previous procedure for every week in the last five years. The results are the following:The 1/N strategy attained a volatility of 24% (versus 21% of the S&P 500), a 14% worse. But this is more than compensated by the return performance. The annualized mean return of the 1/N policy (after proportional transaction costs of 40 bps were discounted) was 12% versus the 3.7% return of the S&P 500, more than three times better!For the 1/N policy, this corresponds to an annualized SR of 0.49. On the other hand, the SR of the S&P 500 was 0.17, almost three times worse. As a conclusion, there exists clear evidence that the 1/N policy dominates the corresponding market indexes, showing it attains consistently better risk-adjusted returns.

QuoteOriginally posted by: jnogalesIt is very simple: invest the same amount of money in each of the N assets considered by the investor.Why do you think this policy works so well in practice?Here is some evidence. From the information in the MSCI Equal Weighted Indices, and over a 10-years period, the world 1/N policy obtained an annual return of 10.9%, versus the 5.7% return of the corresponding world index. That is, it almost doubles the market return. The volatility of the 1/N policy is worse, but only a bit: 14% versus 13.4% for the world index.In other words, the Sharpe ratio (SR) of the 1/N policy was 0.78 and the SR of the world index was 0.42.The same results are obtained for other asset compositions: Europe, USA, Japan, etc.I would like to know your opinions.Dealing with a large number of financial instruments of the same type like stock market , options, cds' people like to characterize its market condition by one word say example good or better or volatile or not. Index 1/N should probably emphasize that they are about equal in a particular sense. Other type weighted index should probably highlight difference in weigh in another sense. Index is developed for one-word statement of a particular sortWhen I first time learned about DJI it was confusing that it calculated by using open interest. It seemed to me that the date t value of DJI more related to market prices of its components at t. Now It seems that more complete characteristic of a stock market are 3 other different indexes which can be used instead of one benchmark DJI. But it always to possible to present argument in favor of an existing one that seems worst. It is just historical tradition the way that people feel better to measure something. Arithmetic actions are simpler for decimal system while many people like ponds and inches.

QuoteOriginally posted by: jnogalesIn the MSCI Equal Weighted Indices, you can also find similar results for US stocks.For instance, and over a 10-years period (no more data is available), the SR of the US equal weighted index was 0.48, whereas the SR of the cap-weighted index was 0.24, much worse.To confirm these findings, I have run my own experiments with the stocks composing the S&P 500.The back-test is as follows: at a given week from 2006 up to now, I consider the 1/N policy, and a week later I compute the corresponding portfolio return, net of transaction costs (of 40 bps) respect to the last portfolio composition. For the S&P 500 index, I consider the corresponding weekly return, but net of any transaction costs. I rebalance the 1/N policy every four weeks and repeat the previous procedure for every week in the last five years. The results are the following:The 1/N strategy attained a volatility of 24% (versus 21% of the S&P 500), a 14% worse. But this is more than compensated by the return performance. The annualized mean return of the 1/N policy (after proportional transaction costs of 40 bps were discounted) was 12% versus the 3.7% return of the S&P 500, more than three times better!For the 1/N policy, this corresponds to an annualized SR of 0.49. On the other hand, the SR of the S&P 500 was 0.17, almost three times worse. As a conclusion, there exists clear evidence that the 1/N policy dominates the corresponding market indexes, showing it attains consistently better risk-adjusted returns.Quote And so, in July 1971, the first index fund was born, with a $6 million contribution from the Samsonite pension fund.The basic design and software were developed by McQuowen's Management Sciences group, but Vertin saw to theday-to-day management of the fund and asked Fouse to manage the strategy. The scheme was tohold an equal dollar amount (emphasis, and below, alan's) of each of the 1,500 or so stocks listed on the New York Stock Exchange, which seemed the most appropriate replication of "the market".The diea was fine. The Department of Finance at the University of Chicago could only approve. The the execution of the ideaturned out to be a nightmare. Some stocks moved more widely than others, and a few moved in the oppositie directionfrom the pack, so that the equal weighting would just not stand still. Heavy transaction costs were incurred for theconstant re-weighting back to the original eqal dollar increments.Although Vertin complained about the "cumbersome record-keeping and the bean-counting", he recognized that newquantitative investment services were in the making. In 1973, his set up a comingled fund open to any and all trustaccounts. The fund would track the performance of the 500 stocks of Standard & Poor's Composite Index, which thenaccounted for about 65 percent of the total marketable equity market in the United States.The first two contributions to the fund were Wells Fargo's own pension fund, with $5 million, and the pension fund ofIllinois Bell, with a like amount. ... From that point forward, the S&P500 index fund has held the 500 stocks in proportion totheir relative market values. In 1976, Samsonite folded its equal-weighted New York Stock Exchange fund into the S&P500 index fund. That fund has been the model for index funds ever since ... from Peter L. Bernstein's 'Capital Ideas'

JnogalesFor my education, could you justify the transaction cost calc? Do you pay 40 bps for all stocks in S&P 500? What size notional is required?

@AlanI have found more evidence in favor of the equal weight strategy than against. I agree it is possible to outperform the equal weight strategy, although it is difficult. But my message is the following: I do not know a simpler strategy that outperforms a cap-weight index in terms of risk and return.Regarding the transaction costs, the equal weight policy has a monthly turnover around 10%. But taking into account the transaction costs, the 1/N policy is still more profitable than the market index.@spv205I compute the transaction costs in a standard way. Say at this moment we have 1000$ in a given company but we want to increase this position by 200$. Hence I compute the cost of this update as 200*40bps = 0.8$.Next I compute this cost for all the N available stocks, and discount the total cost from the current 1/N portfolio return.As I said, this is a standard way of computing transaction costs. But I want to notice this way does not take into account fixed costs, only proportional ones. For a large investor, fixed costs are negligible but not for a small investor.

Well, my message is that it is a silly mechanical rule that doesn't have the nice properties of the market cap rule.First, paper studies are unconvincing. Second, there is a logical flaw. Let's suppose your thesis is correct: the 1/N policy consistently beats the cap-weightedindex. If that was true, eventually everybody will realize that jnogales was right. Now what happens? The only stable result is that there ismassive selling of the large caps and massive buying of the small caps until every stock has a 1/N market weight.Basically, you are saying, once a stock enters an index, it deserves to have the same capitalization asthe maket leaders. This is silly. Here is another message: "beating the market" is much harder than you apparently realize.

jnogalesI didn't express myself well. My question is whether its really true that you would pay 40 bps for a large cap and a small cap?On the one hand the transaction cost should get lower as you do larger trades, however large trades on a small cap will move the market, no?I think it would be worth identifying the proportion of share capital/liquidity of these shares:ie what notional do you need to get 40 bps transaction cost, what proportion of the share capital is that?This is one critique: equal weighted index critique

@AlanI partially agree with you. It is true that if the markets were completely efficient, the best choice would be to invest in the market index. This is why it is difficult to beat the market. But I think the market is not perfectly efficient all the time. For instance, there are well-known anomalies in the financial markets: small stocks tend to outperform big stocks, value stocks tend to outperform growth ones, momentum effect, stocks that do not always exhibit positive correlation between risk and return, etc. This is not true always, but most of the time in the recent history.In this line, and over the long run, I have found evidence that equal weight indices tend to outperform cap-weighted ones. Of course, past performance does not assure the same future performance. But this is the current evidence.I agree that if all people would invest in a rational and efficient way, these anomalies would disappear. Hence, I?m not saying the 1/N policy has a theoretical justification. Just it tends to outperform (not always) market indices.This is why I started this post: to ask for some reasons of this anomaly.@spv205I?m sorry for the misunderstanding. I agree that the assumption of 40bps transaction costs is perhaps too simplistic. As you say, it depends on factors like liquidity, etc. I?ve supposed that proportional costs to focus on the statistical performance of several investment strategies. I?ve checked the performance is robust against similar transaction costs.Thanks for the reference. As I said, I?ve found more evidence in favor of equal weight indices than against. But of course, in finance, the evidence is not always sure?

QuoteOriginally posted by: jnogales@AlanI partially agree with you. It is true that if the markets were completely efficient, the best choice would be to invest in the market index. This is why it is difficult to beat the market. But I think the market is not perfectly efficient all the time. For instance, there are well-known anomalies in the financial markets: small stocks tend to outperform big stocks, value stocks tend to outperform growth ones, momentum effect, stocks that do not always exhibit positive correlation between risk and return, etc. This is not true always, but most of the time in the recent history.In this line, and over the long run, I have found evidence that equal weight indices tend to outperform cap-weighted ones. Of course, past performance does not assure the same future performance. But this is the current evidence.I agree that if all people would invest in a rational and efficient way, these anomalies would disappear. Hence, I?m not saying the 1/N policy has a theoretical justification. Just it tends to outperform (not always) market indices.This is why I started this post: to ask for some reasons of this anomaly.@spv205I?m sorry for the misunderstanding. I agree that the assumption of 40bps transaction costs is perhaps too simplistic. As you say, it depends on factors like liquidity, etc. I?ve supposed that proportional costs to focus on the statistical performance of several investment strategies. I?ve checked the performance is robust against similar transaction costs.Thanks for the reference. As I said, I?ve found more evidence in favor of equal weight indices than against. But of course, in finance, the evidence is not always sure?Well, I have to say I see you talking out of both sides of your mouth, becausein the trading forum, you make similar recommendations and say"As a summary, the low-volatility strategy dominates the market index (always, and over the last year), showing it attains consistently better risk-adjusted returns". So, really, my conclusion is that your goal is not really to discuss the merits/problems of this (silly, IMO)mechanical rule. Instead you are simply a money manager that is "spamming" the forum to attract assets.

@AlanI think you have misunderstood me, I?m sorry if I have explained myself bad.My objective is indeed to discuss some anomalies in the financial markets and see if we can exploit them. For instance, in the trading forum, I try to discuss about the ?low-volatility? anomaly. That is, low-volatility portfolios tend to outperform the market index in terms of risk and return.And in this post I try to discuss the 1/N anomaly. But these two anomalies are totally complementary, this is why I recommend both.I?m not a money manager, simply an academic. So, I have no reason to spam. But I?m sorry again if you have misunderstood me.

Fair enough -- I retract my complaint.