How do you quantify investment risk?
"The question is: how do you quantify investment risk? As Michael S says, one approach is to treat investment returns as a random variable. Bill Goetzmann (Yale finance professor) told me that if you accept that markets are efficient or that the price of an asset reflects it's underlying value, then changes in price represent changes in value, so standard deviation naturally becomes the appropriate measure for riskiness of an asset. Essentially, the more volatile an asset, the riskier it is. There is another school of thought that comes from Ben Graham and Warren Buffett, which says that volatility is not inherently risky. Rather, risk should be defined as the permanent loss of capital, so the riskiness of an asset is the probability of a permanent loss of capital invested.  This is easy to do in casino games, based on basic probability such as   roulette or slots. But what has been done with the various kinds of   investment risks? My point is saying that certain bonds are ""low risk""   isn't good enough; I'd like some numbers--or at least a range of   numbers--and therefore one could calculate expected payoff (in the   statistics sense). Or can it not be done--and if not, why not? Investing is more art than science. In theory, a Triple-A bond rating means the asset is riskless or nearly riskless, but we saw that this was obviously wrong since several of the AAA mortgage backed securities (MBS) went under prior to the recent US recession. More recently, the current threat of default suggests that bond ratings are not entirely accurate, since US Treasuries are considered riskless assets.  Investors often use bond ratings to evaluate investments - a bond is considered investment grade if it's BBB- or higher. To adequately price bonds and evaluate risk, there are too many factors to simply refer to a chart because things like the issuer, credit quality, liquidity risk, systematic risk, and unsystematic risk all play a factor.  Another factor you have to consider is the overall portfolio. Markowitz showed that adding a riskier asset can actually lower the overall risk of a portfolio because of diversification. This is all under the assumption that risk = variance, which I think is bunk.  I'm aware that Wall Street is nothing like roulette, but then again   there must be some math and heavy economics behind calculating risk   for individual investors. This is, after all, what ""quants"" are paid   to do, in part. Is it all voodoo? I suspect some of it is, but not all   of it. Quants are often involved in high frequency trading as well, but that's another note. There are complicated risk management products, such as the Aladdin system by BlackRock, which incorporate modern portfolio theory (Markowitz, Fama, Sharpe, Samuelson, etc) and financial formulas to manage risk.  Crouhy's Risk Management covers some of the concepts applied.  I also tend to think that when people point to the last x number of   years of stock market performance, that is of less value than they   expect. Even going back to 1900 provides ""only"" 110 years of data, and   in my view, complex systems need more data than those 40,500 data   points. 10,000 years' worth of data, ok, but not 110. Any books or articles that address these issues, or your own informed   views, would be helfpul. I fully agree with you here. A lot of work is done in the Santa Fe Institute to study ""complex adaptive systems,"" and we don't have any big, clear theory as of yet. Conventional risk management is based on the ideas of modern portfolio theory, but a lot of that is seen to be wrong. Behavioral finance is introducing new ideas on how investors behave and why the old models are wrong, which is why I cannot suggest you study risk management and risk models because I and many skilled investors consider them to be largely wrong. There are many good books on investing, the best of which is Benjamin Graham's The Intelligent Investor. Although not a book on risk solely, it provides a different viewpoint on how to invest and covers how to protect investments via a ""Margin of Safety."" Lastly, I'd recommend Against the Gods by Peter Bernstein, which covers the history of risk and risk analysis. It's not solely a finance book but rather a fascinating historical view of risk, and it helps but many things in context. Hope it helps!" "Another approach would be more personalized, which is to measure the risk of missing your goals, rather than measuring the risk of an investment in some abstract sense. Financial planners do this for example with Monte Carlo simulation software (see http://en.wikipedia.org/wiki/Monte_Carlo_method). They would put in a goal such as not running out of money before you die, with assumptions such as the longest you might live and how much you'll withdraw every year. You'd also assume an asset allocation. The Monte Carlo simulation then generates random market movements over the time period, considering historical behavior of your asset allocation, and each run of the simulation would either succeed (you are able to support yourself until death) or fail (you run out of money). The risk measure is the percentage of simulation runs that fail. You can do this to plan saving for retirement in addition to planning withdrawals; then your goal would be to have X amount of money in real after-inflation dollars, perhaps, and success is if you end up with it, and failure is if you don't. The great thing about this risk measure is that it's relevant and personal; ""10% chance of being impoverished at age 85,"" ""20% chance of having to work an extra decade because you don't have enough at 65,"" these kinds of answers. Which is a lot easier to act on than ""the variance is 10"" or ""the beta is 1.5"" - would you rather know your plan has a 90% chance of success, or know that you have a variance of 10? Both numbers are probably just guesses, but at least the ""chance of success"" measure is actionable and relevant. Some tangential thoughts FWIW:" "The standard measure of risk is the variance of the asset. The return on investment of the asset is understood as a random variable with a particular distribution. One can make inferences about the underlying distribution using historical data. As you say, this is what the quants do. There are other, more sophisticated measures of risk that allow for such things as skewed distributions and Markov switching. If you are interested in learning more, I suggest starting with the foundations of Modern Portfolio Theory: ""Portfolio Selection"" by Harry Markowitz and ""Capital Asset Prices"" by William Sharpe." "For a retail investor who isn't a Physics or Math major, the ""Beta"" of the stock is probably the best way to quantify risk.  Examples: A Beta of 1 means that a stock moves in line with the market. Over 1 means that you would expect the stock to move up or down faster than the market as a whole. Under 1 means that you would expect the stock to move slower than the market as a whole." I use two measures to define investment risk: What's the longest period of time over which this investment has had negative returns? What's the worst-case fall in the value of this investment (peak to trough)? I find that the former works best for long-term investments, like retirement. As a concrete example, I have most of my retirement money in equity, since the Sensex has had zero returns over as long as a decade. Since my investment time-frame is longer, equity is risk-free, by this measure. For short-term investments, like money put aside to buy a car next year, the second measure works better. For this purpose, I might choose a debt fund that isn't the safest, and has had a worst-case 8% loss over the past decade. I can afford that loss, putting in more money from my pocket to buy the car, if needed. So, I might choose this fund for this purpose, taking a slight risk to earn higher return. In any case, how much money I need for a car can only be a rough guess, so having 8% less than originally planned may turn out to be enough. Or it may turn out that the entire amount originally planned for is insufficient, in which case a further 8% shortfall may not be a big deal. These two measures I've defined are simple to explain and understand, unlike academic stuff like beta, standard deviation, information ratio or other mumbo-jumbo. And they are simple to apply to a practical problem, as I've illustrated with the two examples above. On the other hand, if someone tells me that the standard deviation of a mutual fund is 15%, I'll have no idea what that means, or how to apply that to my financial situation. All this suffers from the problem of being limited to historical data, and the future may not be like the past. But that affects any risk statistic, and you can't do better unless you have a time machine.
Whether it's wise or not depends on what you think and what you should consider are the risks both ways. What are the risks? For Let's say that the company produces great value and its current price and initial price are well below what it's worth.  By investing some of your money in the company, you can take advantage of this value and capitalize off of it if the market recognizes this value too, or when the market does (if it's a successful company it will be a matter of when). Other reasons to be for it are that the tech industry is considered a solid industry and a lot of money is flowing into it.  Therefore, if this assumption is correct, you may assume that your job is safe even if your investment doesn't pay off (meaning, you don't lose income, but your investment may not be a great move). Against Let's say that you dump a lot of money into your company and invest in the stock.  You're being paid by the company, you're taking some of that money and investing it in the company, meaning that, depending on how much you make outside the company, you are increasing your risk of loss if something negative happens to the company (ie: it fails). Other reasons to be against it are just the opposite as above: due to the NSA, some analysts (like Mish, ZeroHedge, and others) think that the world will cut back on doing IT business with the United States, thus the tech industry will take a major hit over the next decade.  In addition to that, Jesse Colombo (@TheBubbleBubble) on Twitter is predicting that there's another tech bubble and it will make a mess when it pops (to be fair to Colombo, he was one of analysts who predicted the housing bubble and his predictions on trading are often right). Finally, there is a risk of lost money and there is also a risk of lost opportunity.  Looking at your past investments, which generally hurt more?  That might give you a clue what to do. Investing in the stock market early is a good thing.  However, it does have a learning curve, and that curve can, and eventually will, cost you. One basic rule in investing is that risk and reward are proportional.  The greater the reward, the higher the risk that you either (a) won't get the reward, or (b) lose your money instead.  Given that, don't invest money you can't afford to lose (you mentioned you're on a student budget). If you want to start with short but sercure investments, try finding a high-interest savings account or CD.  For example, the bank I use has an offer where the first $500 in your account gets ~6% interest - certainly not bad if you only put $500 in the account.  Unfortunately, most banks are offering a pittance for savings rates or CDs. If you're willing to take more risk, you could certainly put money into the stock market.  Before you do, I would recommend spending some time learning about how the stock market works, it's flows and ebbs, and how stock valuations work.  Don't buy a stock because you hear about it a lot; understand why that stock is being valued as such.  Also consider buying index funds (such as SPY) which is like a stock but tracks an entire index.  That way if a specific company suddenly drops, you won't be nearly as affected.  On the flip side, if only 1 company goes up, but the market goes down, you'll miss out.  But consider the odds of having picked that 1 company. The smaller and more quantifiable and consistent risks will probably result (obviously in addition to smaller premiums) in a smaller spread in favor of the insurance company since there is a lot more leverage for companies like Tesla to negotiate with to drive down prices. It may reduce costs for Geico but it sure as hell will reduce profits too. How can I calculate my currency risk exposure?  You own securities that are priced in dollars, so your currency risk is the amount (all else being equal) that your portfolio drops if the dollar depreciates relative to the Euro between now and the time that you plan to cash out your investments. Not all stocks, though, have a high correlation relative to the dollar.  Many US companies (e.g. Apple) do a lot of business in foreign countries and do not necessarily move in line with the Dollar.  Calculate the correlation (using Excel or other statistical programs) between the returns of your portfolio and the change in FX rate between the Dollar and Euro to see how well your portfolio correlated with that FX rate.  That would tell you how much risk you need to mitigate. how can I hedge against it?  There are various Currency ETFs that will track the USD/EUR exchange rate, so one option could be to buy some of those to offset your currency risk calculated above.  Note that ETFs do have fees associated with them, although they should be fairly small (one I looked at had a 0.4% fee, which isn't terrible but isn't nothing). Also note that there are ETFs that employ currency risk mitigation internally - including one on the Nasdaq 100 .   Note that this is NOT a recommendation for this ETF - just letting you know about alternative products that MIGHT meet your needs. 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. Are there any frameworks to deal with the following situation: assume you're invested in an asset which has gained 10x, there is a chance for the asset to gain another 10x (100x in total) and go to zero. The probabilities of the various outcomes are unknown. You can evaluate portfolio raw returns or risk adjusted returns. To evaluate raw returns, I would personally compute the total returns over the time period in question for both portfolios.  To compute total returns, split the time into a bunch of subperiods by the dates at which you contributed money.  Compute each subperiod return by dividing the value of the portfolio at the end of the subperiod (but before adding additional cash on that day) by the value at the beginning of the subperiod (after adding cash on that day).  Then multiply all these returns together.  Finally, subtract 1.  That's your total return. For the portfolio where you didn't add any money it's easy: just divide the end value by the beginning and subtract 1. Whichever has a higher return performed better. To compute risk adjusted returns, get the portfolio returns from both portfolios (daily or monthly) and use OLS to regress on a benchmark portfolio return (something like the S&P500).  The intercept of the regression is a measure of the risk-adjusted peformance of your portfolio.  Higher the better.  More sophisticated models will do multiple regression using a few benchmark portfolios at the same time. The software you provided as an example won't teach you much about investing. The most important things of investing are: These are the only free lunches in investing. Allocation tells you how much expected return (and also how much risk) your portfolio has. Diversification is the only way to reduce risk without reducing return; however, just note that there is market risk that cannot be eliminated with diversification. Every penny you save on costs and taxes is important, as it's guaranteed return. If you were to develop e.g. software that calculates the expected return of a portfolio when given allocation as an input, it could teach you something about investing. Similarly, software that calculates the average costs of your mutual fund portfolio would teach you something about investing. But sadly, these kinds of software are uncommon.