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  • Performance of an MPT based yearly rebalanced portfolio during 2000-2011 9 comments
    Feb 7, 2012 9:06 PM | about stocks: DIA, QQQ, SPY

    In an effort to assess how asset allocation based on Modern Portfolio Theory can help an individual investor, the simplest set of assets - the three main market indices (DOW, SP500 and NASDAQ), a corporate bond fund (MUTF:FBNDX), and a long term treasury fund (MUTF:VUSTX) - was used to retrospectively construct a portfolio for each year during the period 2000-2011 on the basis of monthly returns of these assets from 1990 to the preceding year (e.g. , the MPT-based portfolio for 2005 was constructed by using the monthly returns for the period 1990-2004), and during the year the allocation was used to invest in (DIA, SPY, QQQ, FBNDX, and VUSTX). Our methodology differs slightly from the customary usage of MPT inasmuch as we base our optimization on the empirical data available at the time of the allocation, and, therefore, update the allocation every year, rather than construct a portfolio with fixed allocation on the basis of all the available data. Such a method is perhaps more rapidly responsive to changes in the statistical properties of the returns due to structural changes in the economy and the financial markets.

    Due to the frequent rumblings about MPT, one would have expected our exercise to provide convincing evidence that MPT is somewhat less than useful for the individual investor. Extremely surprisingly, the performance of this portfolio turns out to be better than that of most of the mutual funds with 5 star rating from Morningstar.

    The basic idea of MPT is very simple. It is a recipe for computing the weights of various assets in the portfolio such that the mean return for the portfolio is a specified value (the target return) while the risk of this portfolio, which the theory assumes to be the variance of the returns, is as small as possible. In other words, the method finds the weights of the various assets in the portfolio such that during the given historical period, while its mean periodic return is a specified value, a measure of the deviations of the historical periodic returns of the portfolio from the specified mean value is minimized.

    The performance of the portfolio is shown in the table below. In each column are shown the returns for the given target return for which the portfolio was updated at the beginning of every year during the period 2000-2011. It should be noted that if the target return is the same every year, the minimized risk that the MPT yields may vary from year to year. So the main caveat of the­­­­­ analysis is that this minimized risk is acceptable. Otherwise, it may be necessary to change the target return from year to year in order to design the portfolio with acceptable risk.

    1, 3, 5 and 10 Year Returns of MPT based portfolio (as of 12/30/2011)

    Target Return (%)




    1 Year Return (%)




    3 Year Return (%)




    5 Year Return (%)




    10 Year Return (%)




    The following plot depicts the growth of $1000 invested on 1/1/2000 and yearly rebalanced according to the MPT results for the target return of 10%. It is perhaps fortuitous, but there was not a single year of loss during this period. It's not really necessary to show the growth of a portfolio invested in SPY during this period as it is by now painfully well known to every investor.

    The allocation to the various indices and bonds for every year during the period is shown in the figure below. Note the ability of the method to alter the allocation to market indices during the times when the stocks did relatively better than bonds. It is also noteworthy that there was no year during which any allocation was made to SP500 (NYSEARCA:SPY).

    A search for Morningstar funds with 5 star rating and average or less than average risk whose 1, 3, 5, and 10 year returns exceed the corresponding returns of the portfolio with 10% target return yields no such funds among possibly hundreds of funds. The last five year returns of the much touted lazy portfolios also fail to improve upon this portfolio.

    What the result means in practice is that during the last twelve years an investor would have probably been better off using MPT to yearly update a portfolio of only the major market indices (of course the ETFs corresponding to the indices would have to be traded) and two bond funds rather than investing in one of the bewildering arrays of mutual funds available in the market. That is quite astonishing.

    Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

    Themes: Asset allocation, rebalancing Stocks: DIA, QQQ, SPY
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Comments (9)
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  • CostBasis
    , contributor
    Comments (11) | Send Message
    This is really good work, varan, thanks. It really calls into question a lot of traditional mutual funds / money management.


    I have some questions whose answers may shed light on ‘why’ this works well:


    1) What process does one use to decide what asset classes to use, and how much to slice things up? For example, why doesn’t this include the Russell 2000, or why wasn’t a Total Bond Market fund used instead of splitting it into FBNDX+VUSTX? My guess is that assets with significantly different correlations & volatility should be separated from each other.


    2) What happens if VUSTX is not included in the set of assets? It seems that this is not a popular investment for most portfolios unless it is part of a Total Bond Market component.


    3) What happens if a short-term bond fund is added to the set of assets?


    4) What happens if the lookback period is always 10 years instead of from 1990 to the preceding year? In other words, by keeping the start of the lookback fixed at 1990, it feels like there is a persistent preference for weighing those old years.


    You may be wondering why no Morningstar funds have returns (or strategies) like this. Here’s my guess:


    Mutual funds seem to be all about convincing investors to buy a product. It’s probably harder to convince an investor to pay high fees for a simpler strategy (with fewer asset classes). Investors probably feel better with more years in the lookback, even if that is detrimental to performance. Many lazy portfolios have no trading which enables managers to tell investors “just don’t touch things and keep holding & hoping” whereas with trading strategies, there is the risk (to the manager) that the investor will be ‘mad’ that a recent trade ‘went bad’ and they’ll leave the fund.
    16 Jan 2012, 10:56 PM Reply Like
  • varan
    , contributor
    Comments (4680) | Send Message
    Author’s reply » 1. I just wanted to use the simplest classes of assets. Market indices and bonds seem to be such. In some sense if you use Total Bond you are letting someone else decide the allocation to the two types. Why not let the MPT decide?


    2. It may not be advisable to leave out VUSTX as it is quite distinct in style from FBNDX. TLT or FLBIX may be used for trading instead of VUSTX, but VUSTX has the historical data for the longer time.


    3. I will have to look for one.


    4. This leads to (1, 3, 5, and 10) years returns of (6%, 11%, 11% and 8.6%) that still beat all 5 star funds except three government bond funds.
    17 Jan 2012, 12:01 AM Reply Like
  • CostBasis
    , contributor
    Comments (11) | Send Message
    Thanks for the fast reply.


    1. I was just curious what your rationale was. For instance, similarly, why not let MPT decide the allocation of sectors within the cap-weighted stock indices?


    2. Right, my expectation is that the removal of VUSTX/TLT will hurt the performance, but I'm wondering how much. i.e. once VUSTX/TLT is removed, does it start performing as bad as typical funds?


    4. Thanks for investigating this so fast. I guess the question for a strategy like this is, how do we convince ourselves what time frame to use for the lookback?


    Thanks again.
    17 Jan 2012, 12:12 AM Reply Like
  • stevesauto
    , contributor
    Comments (5) | Send Message
    is there a software program available that will do the calculations for weighting the assets as you described?
    16 Feb 2012, 09:05 PM Reply Like
  • varan
    , contributor
    Comments (4680) | Send Message
    Author’s reply » @setvesauto


    I am sure lots of software is available but I have not done any search as I use my own homegrown version. Perhaps I will make a web site some day where you can do these calculations online.


    16 Feb 2012, 10:22 PM Reply Like
  • Reader101
    , contributor
    Comments (58) | Send Message
    Thanks for the interesting post.


    I ask myself the following questions:


    What would happen if you add gold as another, highly uncorrelated, asset?


    Is it possible to give the performance for older years, starting from say1972?
    The simba-backtest spreadsheat has all annual data starting from that year.


    2 Jul 2012, 05:28 PM Reply Like
  • MrBobDobalina
    , contributor
    Comments (70) | Send Message
    Varan - I have to admit. I am not even sure what goes into an MPT calculation. Do you have a google docs spreadsheet you could share to illustrate what you have done? Or maybe a link or a brief description of how to do the calculations?


    I am not a big MPT believer, but I find this interesting. There are always unique ways of looking at things. This might be an interesting way to allocate a "lazy" 1/2 of my 401k - or even better to use with my son's 529 plan since you can only make allocation changes once per year and typically quarterly switching (or what have you) won't work for 529 plans.


    26 Dec 2012, 03:36 PM Reply Like
  • mpd3892
    , contributor
    Comments (19) | Send Message
    Hi Varan,
    First, I'm an avid follower of your work and am very appreciative of your efforts. Thank you for your work and willingness to share with others. In a sea of financial BS I find your articles and comments on SA to be educational and informative. I look forward to future contributions.


    I am most interested in using your finding in the above cited article to manage my own investments. I am wondering if you have any updates since you published the article? While I think there is real value in MPT, I do not think that a static portfolio is the best way to maximize returns. Your work proves that.


    Perhaps you might be persuaded to write a follow up article that updates your findings as well as provides guidance on how ordinary investors might implement this method. I must admit that I am somewhat lost as to how to implement your rebalancing method into a real world portfolio.


    Any guidance will be greatly appreciated. Again, thank you very much for your contributions and efforts to educate the individual investor.


    9 Jun 2013, 05:19 AM Reply Like
  • varan
    , contributor
    Comments (4680) | Send Message
    Author’s reply » Thanks.


    YTD returns for the MPT based portfolio have been dismal (-.86%), due to heavier weighting of treasury fund (VUSTX 72% QQQ 28%). Overall, however, the basic premise that this simple MPT based strategy has done much better than the market during the last ten years still stands.
    11 Jun 2013, 11:28 AM Reply Like
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