The Asset Allocation Paradox
Asset Allocation serves many purposes, not just mitigating risk via a diversification of asset classes, but also allowing you to take a level of risk that is appropriate for a given investor at a given time by how much is allocated to which asset classes. A younger investor with a longer timeframe, may wish to take a lot more risk, investing heavily in equities, and perhaps managed funds that are of the 'aggressive growth' variety, seeking better than market returns. Someone a little older may wish to pull back a bit, especially after a bull market has brought them substantial gains, and begin to 'take money off the table' perhaps by starting to establish some fixed income positions, or pulling back to slightly less risky index,  'value' or 'balanced' funds. An investor who is near or in retirement will generally want even less risk, going to a much more balanced approach with half or more of their investments in fixed income, and the remainder often in income producing 'blue chip' type stocks, or 'income funds'.  This allows them to protect a good amount of their wealth from potential loss at a time when they have to be able to depend on it for a majority of their income. An institution such as Yale has very different concerns, and may always be in a more aggressive 'long term' mode since 'retirement' is not a factor for them.  They are willing to invest mostly in very aggressive ways, using diversification to protect them from one of those choices 'tanking' but still overall taking a pretty high level of risk, much more so than might be appropriate for an individual who will generally need to seek safety and to preserve gains as they get older.  For example look at the PDF that @JLDugger linked, and observe the overall risk level that Yale is taking, and in addition observe the large allocations they make to things like private equity with a 27%+ risk level compared to their very small amount of fixed income with a 10% risk level.  Yale has a very long time horizon and invests in a way that is atypical of the needs and concerns of an individual investor.  They also have as you pointed out, the economy of scale (with something like #17B in assets?) to afford to hire proven experts, and their own internal PHD level experts to watch over the whole thing, all of which very few individual investors have. For either class of investor, diversification, is a means to mitigate risk by not having all your eggs in one basket.  Via having multiple different investments (such as picking multiple individual stocks, or aggressive funds with different approaches, or just an index fund to get multiple stocks) you are protected from being wiped out as might happen if a single choice might fail.  For example imagine what would have happened if you had in 2005 put all your money into a single stock with a company that had been showing record profits  such as Lehman Brothers, and left it there until 2008 when the stock tanked. or even faster collapses such as Enron, etc that all 'looked great' up until shortly after they failed utterly.   Being allocated across multiple asset classes provides some diversification all on it's own, but you can also be diversified within a class. Yale uses the diversification across several asset classes to have lower risk than being invested in a single asset class such as private equity. But their allocation places much more of their funds in high risk classes and much less of their funds in the lowest risk classes such as fixed income. "I recommend you take a look at this lecture (really, the whole series is enlightening), from Swenson. He identifies 3 sources of returns: diversification, timing and selection. He appears to discard timing and selection as impossible. A student kinda calls him out on this. Diversification reduces risk, not increase returns. It turns out they did time the market, by shorting .com's before the bubble, and real estate just before the downturn. In 1990, Yale started a ""Absolute Return"" unit and allocated like 15 percent to it, mostly by selling US equities, that specializes in these sorts of hedging moves. As for why you might employ managers for specific areas, consider that the expense ratio Wall Street charges you or me still represent a very nice salary when applied to the billions in Yale's portfolio. So they hire internally to reduce expenses, and I'm sure they're kept busy. They also need people to sell off assets to maintain ratios, and figuring out which ones to sell might take specialized knowledge. Finally, in some areas, you functionally cannot invest without management. For example, Yale has a substantial allocation in private equity, and by definition that doesn't trade on the open market. The other thing you should consider is that for all its diversification, Yale lost 25 percent of their portfolio in 2009. For a technique that's supposed to reduce volatility, they seem to have a large range of returns over the past five years."
Financial advisers like to ask lots of questions and get nitty-gritty about investment objectives, but for the most part this is not well-founded in financial theory.  Investment objectives really boils down to one big question and an addendum.  The big question is how much risk you are willing to tolerate.  This determines your expected return and most characteristics of your portfolio. The addendum is what assets you already have (background risk).  Your portfolio should contain things that hedge that risk and not load up on it.  If you expect to have a fixed income, some extra inflation protection is warranted.  If you have a lot of real estate investing, your portfolio should avoid real estate.  If you work for Google, you should avoid it in your portfolio or perhaps even short it. Given risk tolerance and background risk, financial theory suggests that there is a single best portfolio for you, which is diversified across all available assets in a market-cap-weighted fashion. "When you have multiple assets available and a risk-free asset (cash or borrowing) you will always end up blending them if you have a reasonable objective function.  However, you seem to have constrained yourself to 100% investment.  Combine that with the fact that you are considering only two assets and you can easily have a solution where only one asset is desired in the portfolio.  The fact that you describe the US fund as ""dominating"" the forign fund indicates that this may be the case for you.  Ordinarily diversification benefits the overall portfolio even if one asset ""dominates"" another but it may not in your special case. Notice that these funds are both already highly diversified, so all you are getting is cross-border diversification by getting more than one.  That may be why you are getting the solution you are.  I've seen a lot of suggested allocations that have weights similar to what you are using. Finding an optimal portfolio given a vector of expected returns and a covariance matrix is very easy, with some reliable results.  Fancy models get pretty much the same kinds of answers as simple ones.  However, getting a good covariance matrix is hard and getting a good expected return vector is all but impossible.  Unfortunately portfolio results are very sensitive to these inputs.  For that reason, most of us use portfolio theory to guide our intuition, but seldom do the math for our own portfolio.  In any model you use, your weak link is the expected return and covariance.  More sophisticated models don't usually help produce a more reasonable result. For that reason, your original strategy (80-20) sounds pretty good to me.  Not sure why you are not diversifying outside of equities, but I suppose you have your reasons." "John Bensin's answer covers the math, but I like the plain-English examples of the theory from William Bernstein's fine book, The Intelligent Asset Allocator.  At the author's web site, you can find the complete chapter 1 and chapter 2, though not chapter 3, which is the one with the ""multiple coin toss"" portfolio example I want to highlight. I'll summarize Bernstein's multiple coin toss example here with some excerpts from the book.  (Another top user, @JoeTaxpayer, has also written about the coin flip on his blog, also mentioning Bernstein's book.) Bernstein begins Chapter 1 by describing an offer from a fictitious ""Uncle Fred"": Imagine that you work for your rich but eccentric Uncle Fred. [...] he   decides to let you in on the company pension plan. [...] you must pick   ahead of time one of two investment choices for the duration of your   employment: Certificates of deposit with a 3% annualized rate of return, or, A most peculiar option: At the end of each year Uncle Fred flips a coin. Heads you receive a 30% investment return for that year, tails a   minus 10% (loss) for the year. This will be hereafter referred to as   ""Uncle Fred’s coin toss,"" or simply, the ""coin toss."" In effect, choosing option 2 results in a higher expected return than option 1, but it is certainly riskier, having a high standard deviation and being especially prone to a series of bad tosses.  Chapters 1 and 2 continue to expand on the idea of risk, and take a look at various assets/markets over time.  Chapter 3 then begins by introducing the multiple coin toss example: Time passes. You have spent several more years in the employ of your   Uncle Fred, and have truly grown to dread the annual coin-toss   sessions. [...] He makes you another offer. At the end of each year,   he will divide your pension account into two equal parts and conduct a   separate coin toss for each half [...] there are four possible   outcomes [...]: [...]   Being handy with numbers, you calculate that your annualized return   for this two-coin-toss sequence is 9.08%, which is nearly a full   percentage point higher than your previous expected return of 8.17%   with only one coin toss. Even more amazingly, you realize that your   risk has been reduced — with the addition of two returns at the   mean of 10%, your calculated standard deviation is now only 14.14%, as   opposed to 20% for the single coin toss. [...] Dividing your portfolio between assets with uncorrelated results increases return while decreasing risk. [...]   If the second coin toss were perfectly inversely correlated   with the first and always gave the opposite result [hence, outcomes   1 and 4 above never occurring], then our return would always be 10%.   In this case, we would have a 10% annualized long-term return with zero risk! I hope that summarizes the example well.  Of course, in the real world, one of the tricks to building a good portfolio is finding assets that aren't well-correlated, and if you're interested in more on the subject I suggest you check out his books (including The Four Pillars of Investing) and read more about Modern Portfolio Theory (MPT)." "I have a similar situation -- five different accounts between me and my wife. Just as you and @Alex B describe, I maintain my asset allocation across the combination of all accounts. I also maintain a spreadsheet to track the targets, deviations from the targets, amounts required to get back in balance, and overall performance. I (mostly) don't use mutual funds. I have selected, for each category, 1 or 2 ETFs. Choosing index ETFs with low expense ratios and a brokerage with cheap or free trades keeps expenses low. (My broker offers free ETF trades if you buy off their list as long as you aren't short-term trading; this is great for rebalancing for free 2 or 3 times a year.) Using ETFs also solves the minimum balance problem -- but watch out for commissions. If you pay $10 to buy $500 worth of an ETF, that's an immediate 2% loss; trade a couple of times a year and that ETF has to gain 5% just to break even. One issue that comes up is managing cash and avoiding transaction fees. Say your IRA has all the growth stock funds and your Roth has the bonds. Stocks do well and bonds do poorly, so you sell off some stocks, which creates a bunch of cash in your IRA. Now you want to buy some bonds but you don't have enough cash in your Roth, so you buy the bonds in your IRA. Not a problem at first but if you don't manage it you can end up with small amounts of various funds spread across all of your accounts. If you're not careful you can end up paying two commissions (in two different accounts) to sell off / purchase enough of a category to get back to your targets. Another problem I had is that only one account (401k) is receiving deposits on a regular basis, and that's all going into an S&P 500 index fund. This makes it so that my allocation is off by a fair amount every quarter or so -- too much in large cap equities, not enough of everything else. My solution to this going forward is to ""over-rebalance"" a couple of times a year: sell enough SPY from my other accounts so that I'm under-allocated in large caps by the amount I expect to add to my 401k over the next 3 months. (So that in six months at my next rebalancing I'm only 3 months over-allocated to large caps -- plus or minus whatever gains/losses there are.)" "Yes, the ""based on"" claim appears to be true – but the Nobel laureate did not personally design that specific investment portfolio ;-) It looks like the Gone Fishin' Portfolio is made up of a selection of low-fee stock and bond index funds, diversified by geography and market-capitalization, and regularly rebalanced.  Excerpt from another article, dated 2003: The Gone Fishin’ Portfolio  [circa 2003] Vanguard Total Stock Market Index (VTSMX) – 15%   Vanguard Small-Cap Index (NAESX) – 15%   Vanguard European Stock Index (VEURX) – 10%   Vanguard Pacific Stock Index (VPACX) – 10%   Vanguard Emerging Markets Index (VEIEX) – 10%   Vanguard Short-term Bond Index (VFSTX) – 10%   Vanguard High-Yield Corporates Fund (VWEHX) – 10%   Vanguard Inflation-Protected Securities Fund (VIPSX) – 10%   Vanguard REIT Index (VGSIX) – 5%   Vanguard Precious Metals Fund (VGPMX) – 5%   That does appear to me to be an example of a portfolio based on Modern Portfolio Theory (MPT), ""which tries to maximize portfolio expected return for a given amount of portfolio risk"" (per Wikipedia).  MPT was introduced by Harry Markowitz, who did go on to share the 1990 Nobel Memorial Prize in Economic Sciences.  (Note: That is the economics equivalent of the original Nobel Prize.) You'll find more information at NobelPrize.org - The Prize in Economics 1990 - Press Release. Finally, for what it's worth, it isn't rocket science to build a similar portfolio.  While I don't want to knock the Gone Fishin' Portfolio (I like most of its parts), there are many similar portfolios out there based on the same concepts.  For instance, I'm reminded of a similar (though simpler) portfolio called the Couch Potato Portfolio, made popular by MoneySense magazine up here in Canada. p.s. This other question about asset allocation is related and informative." "The argument you are making here is similar to the problem I have with the stronger forms of the efficient market hypothesis.  That is if the market already has incorporated all of the information about the correct prices, then there's no reason to question any prices and then the prices never change.  However, the mechanism through which the market incorporates this information is via the actors buying an selling based on what they see as the market being incorrect. The most basic concept of this problem (I think) starts with the idea that every investor is passive and they simply buy the market as one basket.  So every paycheck, the index fund buys some more stock in the market in a completely static way.  This means the demand for each stock is the same.  No one is paying attention to the actual companies' performance so a poor performer's stock price never moves.  The same for the high performer.  The only thing moving prices is demand but that's always up at a more or less constant rate. This is a topic that has a lot of discussion lately in financial circles.  Here are two articles about this topic but I'm not convinced the author is completely serious hence the ""worst-case scenario"" title. These are interesting reads but again, take this with a grain of salt.  You should follow the links in the articles because they give a more nuanced understanding of each potential issue.  One thing that's important is that the reality is nothing like what I outline above. One of the links in these articles that is interesting is the one that talks about how we now have more indexes than stocks on the US markets.  The writer points to this as a problem in the first article, but think for a moment why that is.  There are many different types of strategies that active managers follow in how they determine what goes in a fund based on different stock metrics.  If a stocks P/E ratio drops below a critical level, for example, a number of indexes are going to sell it.  Some might buy it.  It's up to the investors (you and me) to pick which of these strategies we believe in. Another thing to consider is that active managers are losing their clients to the passive funds.  They have a vested interest in attacking passive management." "The reason that UltraLong funds and the like are bad isn't because of the leverage ratio. It's because they're compounded daily, and the product of all the doubled daily returns is not mathematically equivalent to the double the long-term return. I'd consider providing big fancy equations using uppercase pi as the 'product of elements in a sequence' operator and other calculus fanciness, but that would be overkill, I don't think I can do TeX here, and I don't know the relevant TeX anyway. Anyway. From the economics theory perspective, the ideal leverage ratio is 1X - that is, unlevered, straight investment. Consider: Using leverage costs money. You know that, surely. If someone could borrow money at N% and invest at an expected N+X%, where X > 0, then they would. They would borrow all the money they could and buy all the S&P500 they could. But when they bought all that S&P500, they'd eventually run out of people who were willing to sell it for that cheap. That would mean the excess return would be smaller. Eventually you'd get to a point where the excess return is... zero? .... well, no, empirically, we can see that it's definitely not zero, and that in the real world that stocks do return more than bonds. Why?  Because stocks are riskier than bonds. The difference in expected return between an index like the S&P500 and a US Treasury bond is due to the relative riskiness of the S&P500, which isn't guaranteed by the US Government to return your principal. Any money that you make off of leverage comes from assuming some sort of a risk. Now, assuming risk can be a profitable thing to do, but there are also a lot of people out there with higher risk tolerance than you, like insurance companies and billionaires, so the market isn't exactly short of people willing to take risks, and you shouldn't expect the returns of ""assuming risk"" in the general case to be qualitatively awesome. Now, it's true that investing in an unlevered fashion is risky also. But that's not an excuse to go leveraged anyway; it's a reason to hold back. In fact, regular stocks are sufficiently risky that most people probably shouldn't be holding a 100% stock portfolio. They should be tempering that risk with bonds, instead, and increasing the size of their bond holdings over time. The appropriate time to use leverage is when you have information which limits your risk. You have done research, and have reason to believe that you understand the future of an individual stock/index better than the rest of the stock market does. You calculate that the potential for achieving returns with leverage outweighs the risks. Then you dump your money into the leveraged position. (In exchange for this, the market receives information about anticipated future returns of this instrument, because of the price movement which occurs as a result of someone putting his money where his mouth is.) If you're just looking to dump money into broad market indicies in a leveraged fashion, you're doing it wrong. There is no free money. (Ed. Which is not to say there's not money. There's lots of money. But if you go looking for the free kind, you won't find it, and may end up with money that you thought was free but was actually quite expensive.) Edit. Okay, so you don't like my answer. I'm not surprised. I'm giving you a real answer instead of a ""make free money"" answer. Okay. Here's your ""how to make free money"" answer. Assume you are using a constant leverage ratio over the length of time you've invested your money, and you don't get to just jump into and out of the market (that's market-timing, not leverage) so you have to stay invested. You're going to have a scenario which falls into one of these categories: The S&P500 historically rises over time. The average rate of return probably exceeds the average interest rate. So the ideal leverage ratio is infinite. Of course, this is a stupid answer in real life because you can't pull that off. Your risk tolerance is too low and you will have trouble finding a lender willing to lend you unsecured money, and you'll probably lose all your money in a crash sooner or later. Ultimately it's a stupid answer because you're asking the wrong question. You should probably ask a better question: ""when I use leverage to gain additional exposure to risk, am I being properly compensated for assuming that risk?""" The quant aspect '''''. This is the kind of math I was wondering if it existed, but now it sounds like it is much more  complex in reality then optimizing by evaluating different cost of capital. Thank you for sharing "In economics, there is a notion called the Sunk Cost Fallacy.  In a nutshell, the sunk cost fallacy says that human beings tend to prefer to ""throw good money after bad"" because of a strong loss aversion.  That, coupled with how we frame an issue, makes it very tempting to say, ""if I just add these funds, I'll recoup my loss plus..."" In reality, the best best is to ignore sunk costs.  (I know, far easier said than done, but bear with me a second.)  How much you've invested is really irrelevant.  The only question worth asking is this: ""Would I invest this money in the asset today?"" Put it this way - any money you spend on ""rescuing"" this upside mortgage is an investment that trades ready funds for a little more equity.  Knowing that the mortgage is $100K in excess of the value, why buy that asset?  If you could do a HARP, different story - but as you say, you can't. As such, buying into that investment is not the best use of your funds. You are throwing good money after bad.  Invest your money where it will earn the best rate of return - not where your heart lead you." From Vanguard's Best practices for portfolio rebalancing: I don't see a contrast. It's really hard to predict which mutual funds will do well in the future. Predicting that ones which have done well recently will continue to do well works slightly better than chance. The WSJ article and Morningstar agree on all the objective facts, they just spin them differently. Funds can't limit themselves to a small number of stocks without also limiting themselves to a small amount of total investment. I think 25 companies is too small to be practical from their point of view. "Modern portfolio theory dramatically underestimates the risk of the recommended assets.  This is because so few underlying assets are in the recommended part of the curve.  As investors identify such assets, large amounts of money are invested in them.  This temporarily reduces measured risk, and temporarily increases measured return.  Sooner or later, ""the trade"" becomes ""crowded"".  Eventually, large amounts of money try to ""exit the trade"" (into cash or the next discovered asset).  And so the measurable risk suddenly rises, and the measured return drops. In other words, modern portfolio theory causes bubbles, and causes those bubbles to pop. Some other strategies to consider:" The commenters who referred you to the prisoner's dilemma are exactly correct, but I wanted to give a more detailed explanation because I find game theory quite interesting.  The prisoner's dilemma is a classic scenario in game theory where even though it's in the best interests of two or more players to cooperate, they fail to do so. Wikipedia has a simple example using prisoners, but I'll use a simple example using Fidel and Charles, who are fund managers at Fidelity and Charles Schwab, respectively.  To make the table shorter, I abbreviated a bit: INC = increase fees, KEEP=keep fees the same, DEC=decrease fees. Here is the dilemma itself, in the table that shows the resulting market shares if each fund manager follows the course of action in question.  While this example isn't mathematically rigorous because I completely fabricated the numbers, it makes a good example. The most profitable course of action would be both fund managers agreeing to increase their fees, which would keep their market shares the same but increase their profits as they earn more fees. However, this won't happen for several reasons.  Because economies of scale exist in the market for investment funds, it's reasonable to assume in a simple example that as funds grow larger, their costs decrease, so even though a fund manager decreases his fees (betraying the other players), this decrease won't be enough to reduce their profits. In fact, the increased market share resulting from such a decrease may well dominate the decreased fees and lead to higher profits. The prisoner's dilemma is highly applicable to markets such as these because they exist as oligopolies, i.e. markets where a relatively small number of established sellers possess considerable market power. If you actually wanted to model the market for donor-advised funds using game theory, you need to take a few more things into account. Obviously there are more than two firms. It's probably a valid assumption that the market is an oligopoly with significant economies of scale, but I haven't researched this extensively.  There is more than one time period, so some form of the iterated prisoner's dilemma is needed. The market for donor-advised funds is also complicated by the fact that these are philanthropic funds. This may introduce tax implications or the problem of goodwill and institutional opinion of these funds. Although both funds increasing their fees may increase their profits in theory, institutional investors may look on this as a pure profit-seeking and take their funds elsewhere. For example, they may choose to invest in smaller funds with higher fees but better reputations. While reputation is important for any company, it might make more of a difference when the fund/investment vehicle is philanthropic in nature.  I am by no means an expert on game theory, so I'm sure there are other nuances to the situation that I'm unaware of. absolutely $SPY ETF is the way to go if your point of comparison is the S&P and you want to do low maintenance.