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    Optimal Investment Allocation

    Something I've recently gotten into is asset allocation optimization and using AI (Extended Kalman Filter) & statistics in this area. Anyway, I was ready to move 100% into stocks so I put 80% into VTSAX (Vanguard Total Market Admiral) & 20% into VGTSAX (Vanguard Total Intl Stock)...

    Anyway, using an excel document I put together with different weights for different portfolios I'm getting results that are telling me that a portfolio of 100% VTSAX dominates the portfolio that I have now.

    I was always under the assumption that as long as two securities are less than perfectly correlated (i.e. 1), that the standard deviation/risk would be less than if I had put 100% into either of the securities.

    VTSAX & VGTSX have a correlation coefficient of .889 meaning that they move together, but not perfectly. Does it even makes sense for me to put into VGTSX or international stocks if I have a portfolio of 100% domestic stocks that dominates any combination involving international stocks.

    Using the utility function: E[x] - .5*A*sig^2 results in the highest utility of 100% VTSAX.

    Any thoughts or recommendations about moving 100% into VTSAX? I'm just curious if anyone else tracks their portfolios this way.

    #2
    Originally posted by keelerjr12 View Post
    Something I've recently gotten into is asset allocation optimization and using AI (Extended Kalman Filter) & statistics in this area. Anyway, I was ready to move 100% into stocks so I put 80% into VTSAX (Vanguard Total Market Admiral) & 20% into VGTSAX (Vanguard Total Intl Stock)...

    Anyway, using an excel document I put together with different weights for different portfolios I'm getting results that are telling me that a portfolio of 100% VTSAX dominates the portfolio that I have now.

    I was always under the assumption that as long as two securities are less than perfectly correlated (i.e. 1), that the standard deviation/risk would be less than if I had put 100% into either of the securities.

    VTSAX & VGTSX have a correlation coefficient of .889 meaning that they move together, but not perfectly. Does it even makes sense for me to put into VGTSX or international stocks if I have a portfolio of 100% domestic stocks that dominates any combination involving international stocks.

    Using the utility function: E[x] - .5*A*sig^2 results in the highest utility of 100% VTSAX.

    Any thoughts or recommendations about moving 100% into VTSAX? I'm just curious if anyone else tracks their portfolios this way.
    I don't think there is such a thing as an optimal AA. It's a question of risk tolerance, not a mathematical formula.

    I suggest you read this page: http://www.bogleheads.org/wiki/Bogle...g_start-up_kit
    seek knowledge, not answers
    personal finance

    Comment


      #3
      Originally posted by feh View Post
      I don't think there is such a thing as an optimal AA. It's a question of risk tolerance, not a mathematical formula.

      I suggest you read this page: http://www.bogleheads.org/wiki/Bogle...g_start-up_kit
      Ehh not really the case. I will admit that past performance is not a predictor of future performance but there are optimal portfolios that lie on the efficient frontier... There are portfolios that truly dominate other portfolios such that E[r_a] > E[r_b] and Sig_a < Sig_b... Thanks though!

      Comment


        #4
        Originally posted by keelerjr12 View Post
        Ehh not really the case. I will admit that past performance is not a predictor of future performance but there are optimal portfolios that lie on the efficient frontier... There are portfolios that truly dominate other portfolios such that E[r_a] > E[r_b] and Sig_a < Sig_b... Thanks though!
        If you're so sure of your formula, then why not use leverage to double, triple, quadruple your returns?

        Good luck with whatever you decide.
        seek knowledge, not answers
        personal finance

        Comment


          #5
          Originally posted by feh View Post
          If you're so sure of your formula, then why not use leverage to double, triple, quadruple your returns?

          Good luck with whatever you decide.
          This has little to do with buying on margin or shorting. Especially when I set constraints for that. This has to do with Modern Portfolio Theory...

          http://en.m.wikipedia.org/wiki/Modern_portfolio_theory

          Comment


            #6
            The best performing portfolio will always be the one with 100% the best performing security.

            If you look at this link
            http://www.fortreess.com/resources/annual-returns/

            You can clearly see the best performer one year is not the best performer two straight years, most of the time. The purpose of asset allocation is to minimize volatility, not maximize returns.

            I would look up efficient frontier- that will tell you that an 80-20 portfolio actually gives higher risk adjusted returns than a 100% stock portfolio.

            Comment


              #7
              Originally posted by jIM_Ohio View Post
              The best performing portfolio will always be the one with 100% the best performing security.

              If you look at this link
              http://www.fortreess.com/resources/annual-returns/

              You can clearly see the best performer one year is not the best performer two straight years, most of the time. The purpose of asset allocation is to minimize volatility, not maximize returns.

              I would look up efficient frontier- that will tell you that an 80-20 portfolio actually gives higher risk adjusted returns than a 100% stock portfolio.
              Thank you for this. However, I read that and I've seen articles regarding that, but when I gather the data myself of these two indexes and use 15-20 years worth of data I get that 100% VTSAX has a better risk adjusted return.

              For example the greatest Sharpe ratio is found with the profile with 100% VTSAX and 0% VGTSX. Here is a sample of my findings:

              https://drive.google.com/file/d/0B0h...ew?usp=sharing

              The first graph is showing Expected Return vs Standard Deviation which implies that the greatest return is given with the lowest risk (std dev). You can see this in the last graph which is weight of VTSAX vs Sharpe Ratio. Looking at the data to the left side, the highest sharpe ratio is the one with a weight of VTSAX equal to 1 telling me that this is the most efficient portfolio for these two funds.

              I'm just trying to understand how this is the case. But no matter how I slice and dice the data I'm always getting high correlations between international and domestic stocks for these two funds telling me there's no point in keeping anything in VGTSX.
              Last edited by keelerjr12; 01-13-2015, 09:56 AM.

              Comment


                #8
                You are assuming that the only measure of risk is standard deviation. There are a lot of other types of risk that you can protect yourself from with more diversification.

                You are also looking at a relatively narrow timeline in which US securities had vastly better returns. They may have high correlation, but they aren't exact, so there will likely be a period where International equities enjoy a growth spurt while us equities don't.

                I recently adjusted my asset allocation more towards international equities, because I'm also searching for the optimal asset allocation.

                Comment


                  #9
                  Originally posted by autoxer View Post
                  You are assuming that the only measure of risk is standard deviation. There are a lot of other types of risk that you can protect yourself from with more diversification.

                  You are also looking at a relatively narrow timeline in which US securities had vastly better returns. They may have high correlation, but they aren't exact, so there will likely be a period where International equities enjoy a growth spurt while us equities don't.

                  I recently adjusted my asset allocation more towards international equities, because I'm also searching for the optimal asset allocation.
                  Foreign stocks will do good with a WEAK DOLLAR.
                  Weak dollar means imports are expensive (think $4/gallon for gas)

                  Domestic stocks will do well with a STRONG DOLLAR
                  Strong dollar means imports are cheap (think $2/gallon gas prices)

                  The fed can lower interest rates and create a weak dollar
                  The fed can raise interest rates and create a strong dollar

                  This will impact spending (as in price of gas) and how investments perform.
                  Buying foreign stocks now is a good idea (buying LOW). They key is to realize even if the companies are doing well, the strong dollar could hold returns back. Keeping the holdings until interest rates go lower again will be a profitable move.

                  My main thought is no more than 30-40% of my asset allocation is foreign (2 stock funds, 10% each and one bond fund at 10%). Some of my other holdings might drift and hold foreign securities, but if I see 40% on an x-ray, that would be an alarm.

                  Comment


                    #10
                    Thanks guys, exactly what I was looking for. I ran everything again but assumed a falling correlation at different rates and it seemed that anywhere from 20-35% in international stocks worked best.

                    I realize 15 years of international data isn't much to go by, but it's very hard finding monthly or even annual returns for a global benchmark.

                    Although with such high correlations, 100% in domestic equities proves to offer the greatest returns for the lowest risk; as with most things in economics, I do believe this is cyclical and when correlations do fall it will be good to have at least some level of international exposure.

                    Thanks again!

                    Comment


                      #11
                      As for VTSAX vs. having both VTSAX and VTIAX maybe you could back test your portfolio in some manner. you said you are having 100% domestic stocks that dominates any combination involving international stocks, then it is OK.

                      Comment

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