Fundamentals of creating a diversified portfolio based on numbers?
Good question. There are plenty of investors who think they can simply rely on intuition, and although luck is always present it is not enough to construct a proper portfolio. First of all there are two basic types of portfolio management: Passive and Active. The majority of abnormal gains are made with active portfolio management although passive managers are less likely to suffer loses.  Both types must be created with some kind of qualitative and quantitative research, but an active portfolio requires constant adjustments (Market Timing) to preserve the desired levels of risk and return.  The topic is extremely broad and every manager has his own preferred methods of quantitative analysis. I will try to list here some most common, in my opinion, ways of stock-picking and portfolio management. Roy's Criterion: The best portfolio is that with the lowest probability that the return will be below a specified level.  This is achieved by maximising the number of standard deviations between the return on the portfolio and minimum specified level: Max k = (Rp-Rl)/Sp Where (Rp) - return on portfolio, (Rl) - specified minimum return, (Sp) - standard deviation of portfolio return. Kataoka's Criterion: Maximise the minimum return (Rl) subject to constraint that the chance of a return below (Rl) is less than or equal to a specified value (a). Maximise (Rl) Subject to Prob (Rp < Rl) =< a For example, assume that the specified value is 20% - this will be met provided (Rl) is at least 0.84 standard deviations below (Rp). Therefore the best portfolio is the one that maximises (Rl) where: Rl = Rp-0.84*Sp Telser's Criterion: Maximise expected return subject to the constraint that the chance of a return below the specified minimum is less than or equal to some specified minimum (a) Maximise (Rp) subject to Prob (Rp < Rl) =< a Assuming same data as previously:  Rl =< Rp-0.84*Sp and select the portfolio with highest expected return. Security Selection Now let's look at some methods of security selection. This is important when a manager believes some shares are mispriced. The required return on security 'i' is given by: Ri = Rf+(Rm-Rf)Bi Where (Rf) - is a risk-free rate, (Rm) - return on the market, (Bi) - security's beta. The difference between the required return and the actual return expected is known as the security's alpha (Ai). Ai = Rai - Ri, where (Rai) is actual return on security 'i'. Stock Picking One way of stock-picking is to select portfolios of securities with positive alphas. Alpha of a portfolio is simply the weighted average of the alphas of the securities in the portfolio. Ap = {(n*Ai) Where ({) is sigma (sorry for such weird typing, haven't figured out yet how to type proper-looking formulas), (n) - share of 'i'th security in portfolio. So another way of stock-picking is ranking securities by their excess return to beta (ERB): ERB = (Ri - Rf)/Bi The greater the ERB the more desirable the security and the greater the proportion it will make up of the portfolio. Thus portfolios produced by this technique will have greater proportion of some securities than the market portfolio and lower proportions of other securities.  The number of securities depends on a cut-off rate (C*) for the ERB, defined so that all securities with ERB>C* are included in portfolio while if ERB  The cut-off rate for a portfolio containing the first 'j' securities is given by (i'm inserting an image cut from Word below):  Here comes the tricky part: Basically what you do is first calculate ERB for each security, then calculate Cj for each security mix (gradually adding new securities one by one and recalculating Cj each time). Then you select an optimum portfolio by comparing Cj of each mix to ERB's of it's securities. Let me show you a simple example: Say you have securities A,B,C and D you calculated ERB's: ERB(a)=6, ERB(b)=6.5, ERB(c)=5, ERB(d)=4 also you calculated: C(a)=4.1, C(ab)=4.8, C(abc)=4.9, C(abcd)=4.5. Then you check: ERB(a),ERB(b),ERB(c) are greater than C(a), but C(a) only contains security A so C(a) is not an optimum mix. ERB(a),ERB(b),ERB(c) are greater than C(ab), but C(ab) only contains securities A and B ERB(a),ERB(b),ERB(c) are greater than C(abc), and C(abc) contains A B and C so it is an optimum. ERB(d) is lower than C(abcd) so C(abcd) is not an optimum portfolio. Finally the most important part: Below is a formula to find the share of each security in the portfolio:  Here you simply plug in already obtained values for each security to find it's proportion in your portfolio. I hope this somehow answers your question, however there is a lot more than this to consider if you decide to manage your portfolio yourself. Some of the most important areas are:  Market Timing Hedging Stocks vs Bonds  Good luck with your investments! And remember, the safest portfolio is the one that replicates the Global Market.  The cut-off rate for a portfolio containing the first 'j' securities is given by (i'm inserting an image cut from Word below):  Here comes the tricky part: Basically what you do is first calculate ERB for each security, then calculate Cj for each security mix (gradually adding new securities one by one and recalculating Cj each time). Then you select an optimum portfolio by comparing Cj of each mix to ERB's of it's securities. Let me show you a simple example: Say you have securities A,B,C and D you calculated ERB's: ERB(a)=6, ERB(b)=6.5, ERB(c)=5, ERB(d)=4 also you calculated: C(a)=4.1, C(ab)=4.8, C(abc)=4.9, C(abcd)=4.5. Then you check: ERB(a),ERB(b),ERB(c) are greater than C(a), but C(a) only contains security A so C(a) is not an optimum mix. ERB(a),ERB(b),ERB(c) are greater than C(ab), but C(ab) only contains securities A and B ERB(a),ERB(b),ERB(c) are greater than C(abc), and C(abc) contains A B and C so it is an optimum. ERB(d) is lower than C(abcd) so C(abcd) is not an optimum portfolio. Finally the most important part: Below is a formula to find the share of each security in the portfolio:  Here you simply plug in already obtained values for each security to find it's proportion in your portfolio. I hope this somehow answers your question, however there is a lot more than this to consider if you decide to manage your portfolio yourself. Some of the most important areas are: Good luck with your investments! And remember, the safest portfolio is the one that replicates the Global Market. Most of the “recommendations” are just total market allocations.  Within domestic stocks, the performance rotates. Sometimes large cap outperform, sometimes small cap outperform. You can see the chart here (examine year by year):  https://www.google.com/finance?chdnp=1&chdd=1&chds=1&chdv=1&chvs=maximized&chdeh=0&chfdeh=0&chdet=1428692400000&chddm=99646&chls=IntervalBasedLine&cmpto=NYSEARCA:VO;NYSEARCA:VB&cmptdms=0;0&q=NYSEARCA:VV&ntsp=0&ei=_sIqVbHYB4HDrgGA-oGoDA Conventional wisdom is to buy the entire market. If large cap currently make up 80% of the market, you would allocate 80% of domestic stocks to large cap.  Same case with International Stocks (Developed). If Japan and UK make up the largest market internationally, then so be it.  Similar case with domestic bonds, it is usually total bond market allocation in the beginning.  Then there is the question of when you want to withdraw the money. If you are withdrawing in a couple years, you do not want to expose too much to currency risks, thus you would allocate less to international markets. If you are investing for retirement, you will get the total world market.  Then there is the question of risk tolerance. Bonds are somewhat negatively correlated with Stocks. When stock dips by 5% in a month, bonds might go up by 2%. Under normal circumstances they both go upward. Bond/Stock allocation ratio is by age I’m sure you knew that already.  Then there is the case of Modern portfolio theory. There will be slight adjustments to the ETF weights if it is found that adjusting them would give a smaller portfolio variance, while sacrificing small gains. You can try it yourself using Excel solver.  There is a strategy called Sector Rotation. Google it and you will find examples of overweighting the winners periodically. It is difficult to time the rotation, but Healthcare has somehow consistently outperformed. Nonetheless, those “recommendations” you mentioned are likely to be market allocations again.  The “Robo-advisors” list out every asset allocation in detail to make you feel overwhelmed and resort to using their service. In extreme cases, they can even break down the holdings to 2/3/4 digit Standard Industrial Classification codes, or break down the bond duration etc.  Some “Robo-advisors” would suggest you as many ETF as possible to increase trade commissions (if it isn’t commission free). For example, suggesting you to buy VB, VO, VV instead a VTI. Your question is a complex one because knowledge of the investor's beliefs about the market is required.  For almost any quantitative portfolio, one must have a good estimate of the expected return vector and covariance matrix of the assets in question.  The expected return vector, in particular, is far from estimable.  No one agrees on it and there is no way to know who is right and who is wrong. In a world satisfying the conditions of the CAPM, you can bypass this problem because the main implication of the CAPM is that the market weights are optimal.  In that case the answer to your question is that you should determine the market weights of the various assets and use those along with saving in a risk-free account or borrowing, depending on your risk tolerance.  This portfolio has the added benefit that you don't need to rebalance much...the weights in your portfolio adjust at the same rate as the market weights. Any portfolio that has something besides this also includes some notion of expected return aside from CAPM fair pricing.  The question for you, then, is whether you have such a notion.  If you do, you can mix your information with the market weights to come up with a portfolio.  This is what the Black-Litterman method does, for example: get the expected return vector implied by market weights and the covariance matrix, mix with your expected return vector, then use mean-variance optimization to come up with your final weights.
"Some of the other answers recommended peer-to-peer lending and property markets. I would not invest in either of these. Firstly, peer-to-peer lending is not a traditional investment and we may not have enough historical data for the risk-to-return ratio. Secondly, property investments have a great risk unless you diversify, which requires a huge portfolio. Crowd-funding for one property is not a traditional investment, and may have drawbacks. For example, what if you disagree with other crowd-funders about the required repairs for the property? If you invest in the property market, I recommend a well-diversified fund that owns many properties. Beware of high debt leverage used to enhance returns (and, at the same time, risk) and high fees when selecting a fund. However, traditionally it has been a better choice to invest in stocks than to invest in property market. Beware of anyone who says that the property market is ""too good to not get into"" without specifying which part of the world is meant. Note also that many companies invest in properties, so if you invest only in a well-diversified stock index fund, you may already have property investments in your portfolio! However, in your case I would keep the money in risk-free assets, i.e. bank savings or a genuine low-cost money market fund (i.e. one that doesn't invest in corporate debt or in variable-rate loans which have short duration but long maturity). The reason is that you're going to be unemployed soon, and thus, you may need the money soon. If you have an investment horizon of, say, 10 years, then I would throw stocks into the mix, and if you're saving for retirement, then I would go all in to stocks. In the part of the world where I live in, money market funds generally have better return than bank savings, and better diversification too. However, your 2.8% interest sounds rather high (the money market fund I have in the past invested in currently yields at 0.02%, but then again I live in the eurozone), so be sure to get estimates for the yields of different risk-free assets. So, my advice for investing is simple: risk-free assets for short time horizon, a mixture of stocks and risk-free assets for medium time horizon, and only stocks for long time horizon. In any case, you need a small emergency fund, too, which you should consider a thing separate from your investments. My emergency fund is 20 000 EUR. Your 50 000 AUD is bit more than 30 000 EUR, so you don't really have that much money to invest, only a bit more than a reasonably sized emergency fund. But then again, I live in rental property, so my expenses are probably higher than yours. If you can foresee a very long time horizon for part of your investment, you could perhaps invest 50% of your money to stocks (preference being a geographically diversified index fund or a number of index funds), but I wouldn't invest more because of the need for an emergency fund." Your initial premise (mid-cap and small-cap company stocks have outperformed the market) is partially correct - they have, over many 40 yr periods, provided higher returns than large caps (or bond funds). The important thing to consider here is that risk adjusted, the returns from a diversified portfolio are far more robust - with proper asset allocation you and expect high returns and reduce your risk simultaneously.  Imagine this scenario - you decide to stick to small / mid caps for 10 - 15 yrs and move into a more diversified portfolio then. Had you made that decision during a sustained period of poor small cap performance (late 80s or the 40's) you would have lost a boatload of return, as those were periods were small / mids underperformed the market as a whole, and large caps in particular. As an example, from 1946 to 1958 large caps outperformed small every single year. If 2016 were to be the first year of a similar trend, you've done yourself a major disservice.  Since the dot com crash small /mids have outperformed for sure, pretty much every year - but that doesn't mean that they will continue to do so. The reason asset allocation exists is precisely this - over a 40 yr period, no single asset class outperforms a diversified portfolio.  If you attempt to time the market, even if you do so with a multi-decade time horizon in mind, there a good chance that you will do more poorly. It's important to realize that any portfolio, if sufficiently diversified should track overall GDP growth, and anything growing via a percentage per annum is going to double eventually. (A good corner-of-napkin estimate is 70/the percentage = years to double). Just looking at your numbers, if you initially put in the full $7000, an increase to $17000 after 10 years represents a return of ~9.3% per annum (to check my math $7000*1.09279^10 ≈ $17000). Since you've been putting in the $7000 over 10 years the return is going to be a bit more than that, but it's not possible to calculate based on the information given.  A return of 9.3% is not bad (some rules of thumb: inflation is about 2-4% so if you are making less than that you're losing money, and 6-10% per annum is generally what you should expect if your portfolio is tracking the market)... I wouldn't consider that rate of return to be particularly amazing, but it's not bad either, as you've done better than you would have if you had invested in an ETF tracking the market. The stock market being what it is, you can't rule out the possibility that you got lucky with your stock picks. If your portfolio was low-risk, a return of 9%ish could be considered amazing, but given that it's about 5-6 different stocks what I'd consider amazing would be a return of 15%+ (to give you something to shoot for!) Either way, for your amount of savings you're probably better off going with a mutual fund or an ETF. The return might be slightly lower, but the risk profile is also lower than you picking your stocks, since the fund/ETF will be more diversified. (and it's less work!) 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. it's kind of like a circular loop:  i think he would suggest identifying strategies/portfolio managers who have demonstrated outperformance in a persistent manner.  Thing is, that's also really hard to do.  I think empirically, MPT suffers when the market does. By diversifying, you'll only be down less. He's suggesting shooting for absolute returns -- no matter what the market does, he wants to see positive gains.  (a lot) easier said than done "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 would recommend using growth/value/income/bond based asset allocation because your goal is to find asset classes that have different performance trends (when 1 is up, the other is down and vice-versa).    If you chose Domestic, US stocks and diversified between Med Cap and Large Cap stocks, they would not exactly mirror each other, but they would roughly rise and fall at the same time, preventing you from taking full advantage of diversification, increasing risk and lowering returns. ChrisW's comment may appear flippant, but it illustrates (albeit too briefly) an important fact - there are aspects of investing that begin to look exactly like gambling. In fact, there are expressions which overlap - Game Theory, often used to describe investing behavior, Monte Carlo Simulation, a way of convincing ourselves we can produce a set of possible outcomes for future returns, etc.  You should first invest time. 100 hours reading is a good start. 1000 pounds, Euros, or dollars is a small sum to invest in individual stocks. A round lot is considered 100 shares, so you'd either need to find a stock trading less than 10 pounds, or buy fewer shares. There are a number of reasons a new investor should be steered toward index funds, in the States, ETFs (exchange traded funds) reflect the value of an entire index of stocks. If you feel compelled to get into the market this is the way to go, whether a market near you of a foreign fund, US, or other.