Optimal Asset Allocation
Generally a diversified portfolio will give you a better overall return --a couple of factors that may address what you are looking at - 1) Correlation - The correlation between your two funds is still very high -- it's partially a function of how global economies are related and many companies are now multi-national.  It may help if you diversified into other types of products.   2) Diversification - Following up from before, you may want to also look into diversifying into some bonds, commodities, reits, etc.  They will have a much smaller correlation with a total domestic stock fund. 3) Returns - I'm not sure if by dominate you mean that it has better overall returns, but the point of diversification is to to get you the highest returns.  It's really the ability to limit the risk for the returns - this really translates to limiting the volatility.  This may mean that overall your max returns could be lower-- ie: maybe VTSAX  gives potential average returns between 3%-11%.  A diversified portfolio may give you potential average returns of 5%-9%.  A similar article debating the merits of 'smart beta ETFs' if you are curious. Hope that helps. "There are some good answers about the benefits of diversification, but I'm going to go into what is going on mathematically with what you are attempting. 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. While there does exist a minimum variance portfolio that is a combination of the two with lower vol than 100% of either individually, this portfolio is not necessarily the portfolio with highest utility under your metric.  Your metric includes returns not just volatility/variance so the different returns bias the result away from the min-vol portfolio. Using the utility function: E[x] - .5*A*sig^2 results in the highest utility of 100% VTSAX. So here the Sharpe ratio (risk adjusted return) of the U.S. portfolio is so much higher than the international portfolio over the period tracked that the loss of returns from adding more international stocks outweigh the lower risk that you would get from both just adding the lower vol international stocks and the diversification effects from having a correlation less than one. The key point in the above is ""over the period tracked"".  When you do this type of analysis you implicitly assume that the returns/risk observed in the past will be similar to the returns/risk in the future.   Certainly, if you had invested 100% in the U.S. recently you would have done better than investing in a mix of US/Intl.  However, while the risk and correlations of assets can be (somewhat) stable over time relative returns can vary wildly! This uncertainty of future returns is why most people use a diversified portfolio of assets.  What is the exact right amount is a very hard question though." "There are a couple of reasons to diversify your assets. First, since we cannot predict which of our investments will perform best, we want to ""cast our net"" broadly enough to have something invested in what's going to be performing well. Second, diversification isn't intended to provide the highest returns, but rather it is used to soften the effects of market volatility. By softening the downsides and lowering the overall volatility among our assets, returns are more consistent.  If a model does not address future downside risk it is only telling you part of the story. (Past performance does not guarantee... you get the picture)" "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."
I want to mention I've found 2 options for more powerful tools that can be used to manage asset allocation:  Advantages/Disadvantages: Vanguard Morningstar X-ray I hope this helps others struggling with asset allocation. "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:" Standard Markowitz's portfolio optimization takes trend into account, not mean reversion. Otherwise, since a portfolio is a linear combination of your individual assets, you could 1st model them separately and than establish a second-layer criteria for weighting. For the 1st layer, mean reversion (as well as trend) of returns can be captured with a ARIMA model, and for the 2nd layer, you could use the Kelly criterion, for instance. A more direct approach to mean-reversion portfolio selection is working with pairs trading. I'm not linking any materials as those topics are plentiful on the web. ...If that's still not the answer you're looking for... The problem with predicting economic cycles is that, they are long, and we hardly have a sufficient measured history to forecast anything reliable. In order to predict the mean reversion of a stock or bond market cycle, you've got to measure their long-term mean first. And there you'll have disagreements right on the start... Some researchers (see Jeremy Siegel) have tried to measure the long-term mean of returns for various asset classes. Some argue that stocks are the long-run winners and that CAPM explains that, but others say that's just questionable, since measurements go just as far as the western countries (US, UK, etc.) have thrived. Other countries have much more recent economic records. "An asset allocation formula is useful because it provides a way to manage risk. Rebalancing preserves your asset allocation. The investment risk of a well-diversified portfolio (with a few ETFs or mutual funds in there to get a wide range of stocks, bonds, and international exposure) is mostly proportional to the asset class distribution. If you started out with half-stocks and half-bonds, and stocks surged 100% over the past few years while bonds have stayed flat, then you may be left with (say) 66% stocks and 33% bonds. Your portfolio is now more vulnerable to future stock market drops (the risk associated with stocks). (Most asset allocation recommendations are a little more specific than a stock/bond split, but I'm sure you can get the idea.) Rebalancing can be profitable because it's a formulaic way to enforce you to ""buy low, sell high"". Massive recessions notwithstanding, usually not everything in your portfolio will rise and fall at the same time, and some are actually negatively correlated (that's one idea behind diversification, anyway). If your stocks have surged, chances are that bonds are cheaper. This doesn't always work (repeatedly transferring money from bonds into stocks while the market was falling in 2008-2009 could have lost you even more money). Also, if you rebalance frequently, you might incur expenses from the trading (depending on what sort of financial instrument you're holding). It may be more effective to simply channel new money into the sector that you're light on, and limit the major rebalancing of the portfolio so that it's just an occasional thing. Talk to your financial adviser. :)" "Old question I know, but I have some thoughts to share. Your title and question say two different things.  ""Better off"" should mean maximizing your ex-ante utility.  Most of your question seems to describe maximizing your expected return, as do the simulation exercises here.  Those are two different things because risk is implicitly ignored by what you call ""the pure mathematical answer.""  The expected return on your investments needs to exceed the cost of your debt because interest you pay is risk-free while your investments are risky. To solve this problem, consider the portfolio problem where paying down debt is the risk-free asset and consider the set of optimal solutions.  You will get a capital allocation line between the solution where you put everything into paying down debt and the optimal/tangent portfolio from the set of risky assets.   In order to determine where on that line someone is, you must know their utility function and risk parameters.  You also must know the parameters of the investable universe, which we don't." In answer to your last formulation, no. In a perfectly efficient market, different investors still have different risk tolerances (or utility functions). They're maximizing expected utility, not expected value.  The portfolios that maximize expected utility for different risk preferences are different, and thus generally have different expected values. (Look up mean-variance utility for a simple-ish example.)  Suppose you have log utility for money, u(x) = log(x), and your choice is to invest all of your money in either the risk-free bond or in the risky bond. In the risky bond, you have a positive probability of losing everything, achieving utility u(0) = -\infty. Your expected utility after purchase of the risky bond is:  Pr(default)*u(default) + (1-Pr(default))*u(nominalValue).  Since u(default)= -\infty, your expected utility is also negative infinity, and you would never make this investment. Instead you would purchase the risk-free bond.  But another person might have linear utility, u(x) = x, and he would be indifferent between the risk-free and risky bonds at the prices you mention above and might therefore purchase some. (In fact you probably would have bid up the price of the risk-free bond, so that the other investor strictly prefers the risky one.) So two different investors' portfolios will have different expected returns, in general, because of their different risk preferences. Risk-averse investors get lower expected value. This should be very intuitive from portfolio theory in general: stocks have higher expected returns, but more variance. Risk-tolerant people can accept more stocks and more variance, risk-averse people purchase less stocks and more bonds. The more general question about risk premia requires an equilibrium price analysis, which requires assumptions about the distribution of risk preferences among other things. Maybe John Cochrane's book would help with that---I don't know anything about financial economics. I would think that in the setup above, if you have positive quantities of these two investor types, the risk-free bond will become more expensive, so that the risky one offers a higher expected return. This is the general thing that happens in portfolio theory. Anyway. I'm not a financial economist or anything.  Here's a standard introduction to expected utility theory: http://web.stanford.edu/~jdlevin/Econ%20202/Uncertainty.pdf DCA is not 10%/day over 10 days. If I read the objective correctly, I'd suggest about a 5 year plan. It's difficult to avoid the issue of market timing. And any observation I'd make about the relative valuation of the market would be opinion. By this I mean, some are saying that PE/10 which Nobel prize winner Robert Schiller made well known, if not popular, shows we are pretty high. Others are suggesting the current PE is appropriate given the near zero rate of borrowing.  Your income puts long term gains at zero under current tax code. Short term are at your marginal rate.  I would caution not to let the tax tail wag the investing dog. The fellow that makes too many buy/sell decisions based on his taxes is likely to lag he who followed his overall allocation goals. "What you are seeking is termed ""Alpha"", the mispricing in the market. Specifically, Alpha is the price error when compared to the market return and beta of the stock. Modern portfolio theory suggests that a portfolio with good Alpha will maximize profits for a given risk tolerance. The efficient market hypotheses suggests that Alpha is always zero. The EMH also suggests that taxes, human effort and information propagation delays don't exist (i.e. it is wrong). For someone who is right, the best specific answer to your question is presented Ben Graham's book ""The Intelligent Investor"" (starting on page 280). And even still, that book is better summarized by Warren Buffet (see Berkshire Hathaway Letters to Shareholders). In a great disservice to the geniuses above it can be summarized much further: closely follow the company to estimate its true earnings potential... and ignore the prices the market is quoting. ADDENDUM: And when you have earnings potential, calculate value with: NPV = sum(each income piece/(1+cost of capital)^time) Update: See http://finance.fortune.cnn.com/2014/02/24/warren-buffett-berkshire-letter/ ""When Charlie Munger and I buy stocks..."" for these same ideas right from the horse's mouth" Over time, fees are a killer. The $65k is a lot of money, of course, but I'd like to know the fees involved. Are you doubling from 1 to 2%? if so, I'd rethink this. Diversification adds value, I agree, but 2%/yr?  A very low cost S&P fund will be about .10%, others may go a bit higher. There's little magic in creating the target allocation, no two companies are going to be exactly the same, just in the general ballpark. I'd encourage you to get an idea of what makes sense, and go DIY. I agree 2% slices of some sectors don't add much, don't get carried away with this. Canadian Couch Potato has an article which is somewhat related. Ask the Spud: Can You Time the Markets? The argument roughly boils down to the following: That said, I didn't follow the advice. I inherited a sum of money, more than I had dealt with before, and I did not feel I was emotionally capable of immediately dumping it into my portfolio (Canadian stocks, US stocks, world stocks, Canadian bonds, all passive indexed mutual funds), and so I decided to add the money into my portfolio over the course of a year, twice a month. The money that I had not yet invested, I put into a money market account. That worked for me because I was purchasing mutual funds with no transaction costs. If you are buying ETFs, this strategy makes less sense. In hindsight, this was not financially prudent; I'd have been financially better off to buy all the mutual funds right at the beginning. But I was satisfied with the tradeoff, knowing that I did not have hindsight and I would have been emotionally hurt had the stock market crashed. There must be research that would prove, based on past performance, the statistically optimal time frame for dollar-cost averaging. However, I strongly suppose that the time frame is rather small, and so I would advise that you either invest the money immediately, or dollar-cost average your investment over the course of the year. This answer is not an ideal answer to your question because it is lacking such a citation. Mutual Funds are relatively evaluated and this is likely what you want.  Your answer is likely the information ratio.  If your interested, Active Portfolio Management by Grinold, Kahn is probably a good book to read.  That  being said, hedge funds will generally have absolute mandates and will be more likely to use a sharpe ratio. "You are conflating two different types of risk here.  First, you want to invest money, and presumably you're not looking at the ""lowest risk, lowest returns"" end of the spectrum. This is an inherently risky activity.  Second, you are in a principal-agent relationship with your advisor, and are exposed to the risk of your advisor not maximizing your profits. A lot has been written on principal-agent theory, and while incentive schemes exist, there is no optimal solution.  In your case, you hope that your agent will start maximizing your profits if they are 100% correlated with his profits. While this idea is true (at least according to standard economic theory, you could find exceptions in behavioral economics and in reality), it also forces the agent to participate in the first risk.  From the point of view of the agent, this does not make sense. He is looking to render services and receive income for it. An agent with integrity is certainly prepared to carry the risk of his own incompetence, just like Apple is prepared to replace your iPhone should it not start one day. But the agent is not prepared to carry additional risks such as the market risk, and should not be compelled to do so. It is your risk, a risk you personally take by deciding to play the investment gamble, and you cannot transfer it to somebody else.  Of course, what makes the situation here more difficult than the iPhone example is that market-driven losses cannot be easily distinguished from incompetent-agent losses. So, there is no setup in which you carry the market risk only and your agent carries the incompetence risk only. But as much as you want a solution in which the agent carries all risk, you probably won't find an agent willing to sign such a contract. So you have to simply accept that both the market risk and the incompetence risk are inherent to being an investor.  You can try to mitigate your own incompetence by having an advisor invest for you, but then you have to accept the risk of his incompetence. There is no way to depress the total incompetence risk to zero." I would read any and all of the John Bogle books.  Essentially:  We know the market will rise and fall.  We just don't know when specifically.   For the most part it is impossible to time the market. He would advocate an asset allocation approach to investing.  So much to bonds, tbills, S&P500 index, NASDAQ index.  In your case you could start out with 10% of your portfolio each in S&P500 and NASDAQ.  Had you done that, you would have achieved growth of 17% and 27% respectively.  The growth on either one of those funds would have probably dwarfed the growth on the entire rest of your portfolio.  BTW 2013 and 2014 were also very good years, with 2015 being mostly flat. In the past you have avoided risk in the market to achieve the detrimental effects of inflation and stagnant money.  Don't make the same mistakes going forward. Modern portfolio theory has a strong theoretical background and its conclusions on the risk/return trade-off have a lot of good supporting evidence.  However, the conclusions it draws need to be used very carefully when thinking about retirement investing.  If you were really just trying to just pick the one investment that you would guess would make you the most money in the future then yes, given no other information, the riskiest asset would be the best one.   However, for most people the goal retirement investing is to be as sure as possible to retire comfortably.  If you were to just invest in a single, very risky asset you may have the highest expected return, but the risk involved would mean there might be a good chance you money may not be there when you need it. Instead, a broad diversified basket of riskier and safer assets leaning more toward the riskier investments when younger and the safer assets when you get closer to retirement tends to be a better fit with most people's retirement goals.  This tends to give (on average) more return when you are young and can better deal with the risk, but dials back the risk later in life when your investment portfolio is a majority of your wealth and you can least afford any major swings.  This combines the lessons of MPT (diversity, risk/return trade-off) in a clearer way with common goals of retirement. Caveat:  Your retirement goals and risk-tolerance may be very different from other peoples'.  It is often good to talk to (fee-only) financial planner. It looks like there's some confusion about the purchase price and reclaiming VAT. You should pay your supplier the total amount (£10 + VAT in this scenario, so £12) - look for this figure on the invoice or receipt. The supplier doesn't normally expect you to work this out for yourself, so I'd be a little surprised if it's not on there? As Dumbcoder's said, you'd then be able to claim the VAT back from HMRC if you were VAT registered. But seeing as you're not, then you don't need to worry about claiming it. And as for selling the product without VAT, you can (and probably should) increase the unit price to cover the extra cost, otherwise you'll be operating at a loss. Hope this helps!