Finding Uncorrelated Assets
Have a look at: Diversify Portfolio. The site provides various tools all focused on correlation, diversification and portfolio construction. You can scan through every stock and ETF listed on the NASDAQ and NYSE to find any kind of correlation you're looking for. You can also create a portfolio and then analyze all the correlations within it, or search for specific stocks that can be added to the portfolio based on correlation and various other factors.
One approach would be to create Journal Entries that debit asset accounts that are associated with these items and credit an Open Balance Equity account. The value of these contributions would have to be worked out with an accountant, as it depends on the lesser of the adjusted basis vs. the fair market value, as you then depreciate the amounts over time to take the depreciation as a business expense, and it adjusts your basis in the company (to calculate capital gains/losses when you sell). If there were multiple partners, or your accountant wants it this way, you could then debit open balance equity and credit the owner's contribution to a capital account in your name that represents your basis when you sell. From a pure accounting perspective, if the Open Balance Equity account would zero out, you could just skip it and directly credit the capital accounts, but I prefer the Open Balance Equity as it helps know the percentages of initial equity which may influence partner ownership percentages and identify anyone who needs to contribute more to the partnership. Google 'information ratio'. It is better suited to what you want than the Sharpe or Sortino ratios because it only evaluates the *excess* return you get from your investment, ie. return from your investment minus the return from a benchmark investment. The benchmark here could be an index like the S&amp;P500. "An ""asset"" is something which you own that has a monetary value. Some examples would be your car, your house, the money in your wallet, and yes the pile of gold in your garage. Assets also include intangible things such as money owed to you for instance; although these are calculated somewhat differently. ""liabilities"" are what you owe. For instance, your car loan, your mortgage, and your student loan. Liabilities can also include future debts which you may not be paying at the moment." "The fact that some asset (in this case corporate bonds) has positive correlation with some other asset (equity) doesn't mean buying both isn't a good idea.  Unless they are perfectly correlated, the best risk/reward portfolio will include both assets as they will sometimes move in opposite directions and cancel out each other's risk.  So yes, you should buy corporate bonds.  Short-term government bonds are essentially the risk-free asset.  You will want to include that as well if you are very risk averse, otherwise you may not.  Long-term government bonds may be default free but they are not risk free.  They will make money if interest rates fall and lose if interest rates rise.  Because of that risk, they also pay you a premium, albeit a small one, and should be in your portfolio. So yes, a passive portfolio (actually, any reasonable portfolio) should strive to reduce risk by diversifying into all assets that it reasonably can.  If you believe the capital asset pricing model, the weights on portfolio assets should correspond to market weights (more money in bonds than stocks).  Otherwise you will need to choose your weights.  Unfortunately we are not able to estimate the true expected returns of risky assets, so no one can really agree on what the true optimal weights should be.  That's why there are so many rules of thumb and so much disagreement on the subject.  But there is little or no disagreement on the fact that the optimal portfolio does include risky bonds including long-term treasuries. To answer your follow-up question about an ""anchor,"" if by that you mean a risk-free asset then the answer is not really.  Any risk-free asset is paying approximately zero right now.  Some assets with very little risk will earn a very little bit more than short term treasuries, but overall there's nowhere to hide--the time value of money is extremely low at short horizons.  You want expected returns, you must take risk." "There may well be several such graphs, I expect googling will turn them up; but the definition of risk is actually quite important here. My definition of risk might not be quite the same as yours, so the relative risk factors would be different. For example: in general, stocks are more risky than bonds.  But owning common shares in a blue-chip company might well be less risky than owning bonds from a company teetering on the edge of bankruptcy, and no single risk number can really capture that. Another example: while I can put all my money in short-term deposits, and it is pretty ""safe"", if it grows at 1% so that my investment portfolio cannot fund my retirement, then I have a risk that I will run out of money before I shuffle off this mortal coil.  How to capture that ""risk"" in a single number? So you will need to better define your parameters before you can prepare a visual aid. Good Luck" "@farnsy has provided a good answer. I'm only addressing my comment about the data quality. The portfolio optimization technique you employed is very sensitive to the inputs. In particular, it relies entirely on the mean and (co)variance assumptions (i.e. the first two moments) and the results could change drastically with very small amount of change in the inputs. To see that, you can make up some inputs for the solver you have, and try adjusting the inputs a little bit and see the results. Therefore if you decide to take this approach, data quality is very crucial. EDIT: What I meant by ""data quality"" I have no experience with this website but this should be easy to spot check. The answer is usually ""yes"" for liquid assets. Illiquid assets can often be priced at a level with no volume, and the bid-ask spread could be huge.  Should I close my eyes on the fact that these cryptocurencies aren't perfectly priced in my currency and use another one (such as the dollar) You seem to have concern about data quality in at least the price quoted in your currency and are thinking about using data quoted in USD, but would it be any better? The law of one price tells us that there shouldn't be any discrepancy between prices in different currencies (otherwise there would be arbitrage). In addition, (when compared to traditional assets) cryptocurrency price data has a shorter data history, and with lower liquidity in the market. The short history means you have less data to infer the characteristics of the price behavior. Low liquidity means the volatility may well be underestimated. So we have an input-sensitive technique combined with not-so-perfect data. I wouldn't allocate my money solely based on the result of this exercise. EDIT: I have quite some reservation about doing portfolio optimization for cryptocurrency. Personally I'm not a fan of the technique as is. The optimization has an underlying assumption that returns follow a certain distribution, and correlation is fixed. I don't know if you can make such assumption for cryptocurrencies. From what I read about BTC for example, it seems to have a high risk exposure concerning Chinese monetary policy. For that kind of assets perhaps a fundamental analysis approach is a better one.  Also if you would like to learn more about portfolio optimization, try quant.SE" "I'm no accountant, but I think the way I'd want to approach this kind of thing in Gnucash would be to track it as an Asset, since it is. It sounds like your actual concern is that your tracked asset value isn't reflecting its current ""market"" value. Presumably because it's risky it's also illiquid, so you're not sure how much value it should have on your books. Your approach suggested here of having it as just as expense gives it a 0 value as an asset, but without tracking that there's something that you own. The two main approaches to tracking an investment in Gnucash are: Of course, both of these approaches do assume that you have some notion of your investment's ""current value"", which is what you're tracking. As the section on Estimating Valuation of the concepts guide says of valuing illiquid assets, ""There is no hard rule on this, and in fact different accountants may prefer to do this differently."" If you really think that the investment isn't worth anything at the moment, then I suppose you should track it at 0, but presumably you think it's worth something or you wouldn't have bought it, right? Even if it's just for your personal records, part of a regular (maybe annual?) review of your investments should include coming up with what you currently value that investment at (perhaps your best guess of what you could sell it for, assuming that you could find a willing buyer), and updating your records accordingly. Of course, if you need a valuation for a bank or for tax purposes or the like, they have more specific rules about how they are tracking what things are worth, but presumably you're trying to track your personal assets for your own reasons to get a handle on what you currently own. So, do that! Take the time to get a handle on the worth of what you currently own. And don't worry about getting the value wrong, just take your best guess, since you can always update it later when you learn new information about what your investment is worth." The other example I'd offer is the case for diversification. If one buys 10 well chosen stocks, i.e. stocks spread across different industries so their correlation to one another is low, they will have lower risk than each of the 10 folk who own one of those stocks per person. Same stocks, but lower risk when combined. "All of these frameworks, Markowitz, Mean/CVaR, CARA, etc  sit inside a more general framework which is that ""returns are good"" and ""risk/lack of certainty in the returns is bad"", and there's a tradeoff between the two encoded as some kind of risk aversion number.  You can measure ""lack of certainty in returns"" by vol, CVaR, weighted sum of higher moments, but even sector/region concentration.  Similarly do I want more ""returns"" or ""log returns"" or ""sqrt returns"" in the context of this tradeoff?  You don't need any formal notion of utility at that point - and I don't know what formal ideas of utility beyond ""I want more returns and less risk"" really buys you. The Sharpe ratio only really gets its meaning because you've got some formal asset-pricing notion of utility.   In my view the moment that you're putting constraints on the portfolio (e.g. long only, max weights, don't deviate too much from the benchmark ...) - really you're operating in this more general framework anyway and you're not in ""utility-land"" anymore." The portfolio manager at Value Research Online does this very nicely. It tracks the underlying holdings of each fund, yielding correct calculations for funds that invest across the board. Take a look at the screenshot from my account:  If you have direct equity holdings (e.g., not through a mutual fund), that too gets integrated. Per stock details are also visible. "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." Annualize quarterly returns:      AR = (1+QR)^4  Where *QR* is a decimal return, e.g. 0.05.  Standard deviations are similar:      Annual SD = SD * sqrt(T)  If you have quarterly deviations, *T=4*, if you have daily, *T=252*, etc.  As an aside, for work with money riding on it, it is *not* okay to aggregate standard deviations if there's autocorrelation amongst observations at a smaller time scale. Volatility is often quoted this way and that's fine, but it is dangerous to do any sort of risk management with this and you'll require more due diligence. It's a good enough approximation for napkin math, though. "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. :)" If you have access, factset and bloomberg have this.  However, these aren't standardized due to non-existent reporting regulations, therefore each company may choose to categorize regions differently.  This makes it difficult to work with a large universe, and you'll probably end up doing a large portion manually anyways. you can check google scholar for some research reports on it.  depends how complex you want to get...  it is obviously a function of the size of the portfolio of each type of asset. do you have a full breakdown of securities held? you can get historical average volumes during different economic periods, categorized by interest rates for example, and then calculate the days required to liquidate the position, applying a discount on each subsequent day.