How to find an optimum linear combination of various investments?
"You're talking about modern portfolio theory. The wiki article goes into the math. Here's the gist: Modern portfolio theory (MPT) is a theory of finance that attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets. At the most basic level, you either a) pick a level of risk (standard deviation of your whole portfolio) that you're ok with and find the maximum return you can achieve while not exceeding your risk level, or b) pick a level of expected return that you want and minimize risk (again, the standard deviation of your portfolio). You don't maximize both moments at once. The techniques behind actually solving them in all but the most trivial cases (portfolios of two or three assets are trivial cases) are basically quadratic programming because to be realistic, you might have a portfolio that a) doesn't allow short sales for all instruments, and/or b) has some securities that can't be held in fractional amounts (like ETF's or bonds). Then there isn't a closed form solution and you need computational techniques like mixed integer quadratic programming Plenty of firms and people use these techniques, even in their most basic form. Also your terms are a bit strange: It has correlation table p11, p12, ... pij, pnn for i and j running from 1 to n This is usually called the covariance matrix. I want to maximize 2 variables. Namely the expected return and the additive inverse of the standard deviation of the mixed investments. Like I said above you don't maximize two moments (return and inverse of risk). I realize that you're trying to minimize risk by maximizing ""negative risk"" so to speak but since risk and return are inherently a tradeoff you can't achieve the best of both worlds. Maybe I should point out that although the above sounds nice, and, theoretically, it's sound, as one of the comments points out, it's harder to apply in practice. For example it's easy to calculate a covariance matrix between the returns of two or more assets, but in the simplest case of modern portfolio theory, the assumption is that those covariances don't change over your time horizon. Also coming up with a realistic measure of your level of risk can be tricky. For example you may be ok with a standard deviation of 20% in the positive direction but only be ok with a standard deviation of 5% in the negative direction. Basically in your head, the distribution of returns you want probably has negative skewness:  because on the whole you want more positive returns than negative returns. Like I said this can get complicated because then you start minimizing other forms of risk like value at risk, for example, and then modern portfolio theory doesn't necessarily give you closed form solutions anymore. Any actively managed fund that applies this in practice (since obviously a completely passive fund will just replicate the index and not try to minimize risk or anything like that) will probably be using something like the above, or at least something that's more complicated than the basic undergrad portfolio optimization that I talked about above. We'll quickly get beyond what I know at this rate, so maybe I should stop there."
"Probably not, though there are a few things to be said for understanding what you are doing here.  Primerica acts as an independent financial services firm and thus has various partners that specialize in various financial instruments and thus there may exist other firms that Primerica doesn't use that could offer better products.  Now, how much do you want to value your time as it could take more than a few months to go through every possible insurance firm and broker to see what rate you could get for the specific insurance you want.  There is also the question of what constitutes best here.  Is it paying the minimal premiums before getting a payout?  That would be my interpretation though this requires some amazing guesswork to know when to start paying a policy to pay out so quickly that the insurance company takes a major loss on the policy. Similarly, there are thousands of mutual funds out there and it is incredibly difficult to determine which ones would be best for your situation.  How much risk do you want to take?  How often do you plan to add to it?  What kind of accounts are you using for these investments, e.g. IRAs or just regular taxable accounts?  Do tax implications of the investments matter? Thus, I'd likely want to suggest you consider this question: How much trust do you have that this company will work well for you in handling the duty of managing your investments and insurance needs?  If you trust them, then buy what they suggest.  If you don't, then buy somewhere else but be careful about what kind of price are you prepared to pay to find the mythical ""best"" as those usually only become clear in hindsight. When it comes to trusting a company in case, there are more than a few factors I'd likely use: Questions - How well do they answer your questions or concerns from your perspective?  Do you feel that these are being treated with respect or do you get the feeling they want to say, ""What the heck are you thinking for asking that?"" in a kind of conceited perspective. Structure of meeting - Do you like to have an agenda and things all planned out or are you more of the spontaneous, ""We'll figure it out"" kind of person?  This is about how well do they know you and set things up to suit you well. Tone of talk - Do you feel valued in having these conversations and working through various exercises with the representative?  This is kind of like 1 though it would include requests they have for you. Employee turnover - How long has this person been with Primerica?  Do they generally lose people frequently?  Are you OK with your file being passed around like a hot potato?  Not that it necessarily will but just consider the possibility here. Reputation can be a factor though I'd not really use it much as some people can find those bad apples that aren't there anymore and so it isn't an issue now.  In some ways you are interviewing them as much as they are interviewing you.  There are more than a few companies that want to get a piece of what you'll invest, buy, and use when it comes to financial products so it may be a good idea to shop around a little." The study of technical analysis is generally used (sometimes successfully) to time the markets. There are many aspects to technical analysis, but the simplest form is to look for uptrends and downtrends in the charts.  Generally higher highs and higher lows is considered an uptrend.  And lower lows and lower highs is considered a downtrend.  A trend follower would go with the trend, for example see a dip to the trend-line and buy on the rebound. A simple strategy for this is shown in the chart below:  I would be buying this stock when the price hits or gets very close to the trendline and then it bounces back above it. I would then have sold this stock once it has broken through below the trendline. This may also be an appropriate time if you were looking to short this stock. Other indicators could also be used in combination for additional confirmation of what is happening to the price. Another type of trader is called a bottom fisher. A bottom fisher would wait until a break above the downtrend line (second chart) and buy after confirmation of a higher high and possibly a higher low (as this could be the start of a new uptrend). There are many more strategies dealing with the study of technical analysis, and if you are interested you would need to find and learn about ones that suit your investment styles, whether you prefer short term trading or longer term investing, and your appetite for risk. You can develop strategies using various indicators and then paper trade or backtest these strategies. You can also manually backtest a strategy in most charting packages. You can go back in time on the chart so that the right side of the chart shows a date in the past (say one year ago or 10 years ago), then you can click forward one day at a time (or one week at a time if using weekly charts). With your indicators on the chart you can do virtual trades to buy or sell whenever a signal is given as you move forward in time. This way you may be able to check years of data in a day to see if your strategy works. Whatever you do, you need to document your strategies in writing in a written trading or investment plan together with a risk management strategy. You should always follow the rules in your written plan to avoid you making decisions based on emotions. By backtesting or paper trading your strategies it will give you confidence that they will work over the long term.  There is a lot of work involved at the start, but once you have developed a documented strategy that has been thoroughly backtested, it will take you minimal time to successfully manage your investments. In my shorter term trading (positions held from a couple of days to a few weeks) I spend about half an hour per night to manage my trades and am up about 50% over the last 7 months. For my longer term investing (positions held from months to years) I spend about an hour per week and have been averaging over 25% over the last 4 years. Technical Analysis does work for those who have a documented plan, have approached it in a systematic way and use risk management to protect their existing and future capital. Most people who say that is doesn't work either have not used it themselves or have used it ad-hock without putting in the initial time and work to develop a documented and systematic approach to their trading or investing. "So my read on the question is ""How do I invest 300k such that it earns me a 'living wage' without the ongoing grind inherent in most formal employment?""  Reading the other answers to date it looks like most of them are thinking in terms of investment accounts and trying to live off of the earnings from such.  I wanted to throw out a couple of alternative choices that may be worth considering... The first is real-estate investing.  $300k should allow you to pick up 2 or 3 single family dwellings with little or no mortgage.  Turning them into rentals placed with a good property management company should easily pay their expenses and provide a consistent income with minimal effort/attention from you.  Similar story with buying into multifamily housing or commercial real-estate. Your key concern here is picking the right market in which to buy and finding a reputable manager to handle the day to day issues on your behalf. Note that you are not overly concerned with the potential resale value of the property(s), but the probable rental income they can generate, these are separate concerns that may not align with each other. Second is buying/founding a business that has a general manager other than yourself.  Franchise ownership may be a potential option for you under the circumstances.  The key concern here is picking the business, location, and manager that make you comfortable in terms of the risk involved.  You need the place to make enough money to pay for itself and the salary of everyone working there, with enough left over for you to live on.  Sounds easy enough, but not so much in practice.  Generally you can expect at least a few years of being hands on and watching things very closely to make sure it is going the way you want it to.  Finding a mentor who has done this type of transition before to walk you through it would be strongly advised.  So would preparing yourself for a failure or two before you work out the exact combination of factors that work for you." There are a great number of briquetting plant manufacturer or supplier that happen to be involved in the manufacturing of briquetting equipment. These manufacturers are generally experienced in and possessing the professional expertise in developing qualitative briquetting equipment design and style to offer their potential customers optimum performance and consistent in giving the desire output also with the Guranteed results. I'd recommend looking at fundamental analysis as well -- technical analysis seems to be good for buy and sell points, but not for picking what to buy.  You can get better outperformance by buying the right stuff, and it can be surprisingly easy to create a formula that works.  I'd check out Morningstar, AAII, or Equities Lab (fairly complicated but it lets you do technical and fundamental analysis together).  Also read Benjamin Graham, and/or Ken Fisher (they are wildly different, which is why I recommend them both). "I would just buy one ETF (index-fund) on the market you think will perform better. It will take care to buy the 5 most solid stock in this market and many other more to reduce the risk to the bear minimum. You will also spend only few bucks in comissions, definitely less than what you would spend buying multiple stocks (even just 5). It's hard enough to forecast which market will perform better, it's even harder to do stock picking unless you have the time and the knowledge to read into companies' balance sheets/economic incomes/budgets/market visions etc. And even if you are great in reading into companies balance sheets/economic incomes/budgets, the stock market usually behaves like a cows' drove, therefor even if you choosed the most valuable solid stocks, be prepared to see them run down even a 50% when all the market runs down a 50%. During the 2008 crisis the Europe market has lost a 70%, and even the most solid sectors/stocks like ""Healthcare"" and ""Food & Beverage"" lost a painful 40% to 50% (true that now these sectors recovered greatly compared to the rest of the market, but they still run down like cows during the crisis, and if you holded them you would have suffered a huge pain/stress). But obviously there's always some profet/wizard which will later tell you he was able to select the only 5 stocks among thousands that performed well." Any time you are optimizing a portfolio, the right horizon to use for computing the statistics you will use for optimization (expected return, covariance, etc.) will be the same as your rebalance/trading frequency.  If you expect your trading strategy to trade once a day, you should use daily data for optimization.  Ditto for monthly or quarterly.  If at all possible you should use statistics across the board that are computed at the same frequency as your trading. Regarding currency pricing, I see no reason you can't take the reported prices and convert them to whatever currency you want using that day's foriegn exchange rate.  Foreign exchange rates are available for free at the Fed and elsewhere.  Converting prices from one currency to another is not rocket science. Since you are contemplating putting actual money behind this, note that using data to compute statistics is less reliable for lower statistical moments.  The mean (expected return) is the first moment, so using historical returns is extremely unreliable at predicting future returns.  The variances and covariances are second moments, they are better.  Skewness and kurtosis, yet better.  The fact that the expected return can't reliably be estimated from past returns is the major downfall of the Markowitz method (resulting portfolios are often very crazy and will depend critically on the data period you use to set them up).   There are approaches to fixing this, such as Black-Litterman's (1992) method, but they get complicated fast. "JoeTaxpayer nailed it.  Here's another way to look at it: Generally, we invest in something, then might leave it there for a few years, then take it out, but don't touch it in between.  In that case, to get the final amount X(N), we need to take the initial amount, then multiply by growth in the first year, then multiply by growth in the second year, etc. So, for three years, we have: X(3) = X(0) * G(1) * G(2) * G(3) = X(0) * ""average annual growth"" ^ 3 So, here, we see that we want the average annual growth to the power three equal to the product of the annual growth rates, thus, geometric mean: geometric mean = (G(1) * G(2) * G(3)) ^ (1/3) On the other hand, consider a situation where I have three investments X,Y,Z over one year. Now I have, after one year: X(1)+Y(1)+Z(1) = X(0)*G(1,X) + Y(0)*G(1,Y) + Z(0)*G(1,Z) = ( X(0)+Y(0)+Z(0) ) * ""average annual growth"" Now, in this case, if we assume X(0) = Y(0) = Z(0) = 1, i.e. I put equal amounts in each, we see that the average annual growth rate we want in this case is the arithmetic mean: arithmetic mean = (G(1,X) + G(1,Y) + G(1,Z)) / 3 (if we had unequal amounts at the beginning, it would be a weighted average). TL;DR:"