Can I get a dumbed down explanation of risk measures used for evaluating stocks?
"Standard deviation from Wikipedia : In statistics and probability theory, the standard deviation   (represented by the Greek letter sigma, σ) shows how much variation or   dispersion from the average exists.1 A low standard deviation   indicates that the data points tend to be very close to the mean (also   called expected value); a high standard deviation indicates that the   data points are spread out over a large range of values. In the case of stock returns, a lower value would indicate less volatility while a higher value would mean more volatility, which could be interpreted as high much change does the stock's price go through over time. Mean would be interpreted as if all the figures had to be the same, what would they be? So if a stock returns 10% each year for 3 years in a row, then 10% would be the mean or average return. Now, it is worth noting that there are more than a few calculations that may be done to derive a mean. First, there is the straight forward sum and division by the number of elements idea. For example, if the returns by year were 0%, 10%, and 20% then one may take the sum of 30% and divide by 3 to get a simple mean of 10%. However, some people would rather look at a Compound Annual Growth Rate which in this case would mean multiplying the returns together so 1*(1+.1)*(1+.2)=1.1*1.2=1.32 or 32% since there is some compounding here. Now, instead of dividing a cubic root is taken to get approximately 9.7% average annual return that is a bit lower yet if you compound it over 3 years it will get up to 32% as 10% compounded over 3 years would be 33.1% as (1.1)^3=1.331. Sharpe Ratio from Investopedia: A ratio developed by Nobel laureate William F. Sharpe to measure   risk-adjusted performance. The Sharpe ratio is calculated by   subtracting the risk-free rate - such as that of the 10-year U.S.   Treasury bond - from the rate of return for a portfolio and dividing   the result by the standard deviation of the portfolio returns. Thus, this is a way to think about given the volatility how much better did the portfolio do than the 10 year bond. R-squared, Alpha and Beta: These are all around the idea of ""linear regression"" modelling. The idea is to take some standard like say the ""S & P 500"" in the case of US stocks and see how well does the portfolio follow this and what if one were to use a linear model are the multipliers and addition components to it. R-squared can be thought of it as a measure as to how good is the fit on a scale of 0 to 1. An S & P 500 index fund may well have an R-squared of 1.00 or 0.99 to the index as it will track it extremely closely while other investments may not follow that well at all. Part of modern portfolio theory would be to have asset classes that move independently of each other and thus would have a lower R-squared so that the movement of the index doesn't indicate how an investment will do. Now, as for alpha and beta, do you remember the formula for a line in slope-intercept form, where y is the portfolio's return and x is the index's return: y=mx+b In this situation m is beta which is the multiple of the return, and b is the alpha or how much additional return one gets without the multiple. Going back to an index fund example, m will be near 1 and b will be near 0 and there isn't anything being done and so the portfolio's return computed based on the index's return is simply y=x. Other mutual funds may try to have a high alpha as this is seen as the risk-free return as there isn't the ups and downs of the market here. Other mutual funds may go for a high beta so that there is volatility for investors to handle."
If a market is efficient then risk/reward should be linear.  In simple markets like stocks and bonds, everyone thinks the same way and the risk/reward calculation is simple, so everyone can have an accurate idea of the risk/reward ratio, unless the company has serious undisclosed problems. But in other markets like derivatives and mortgage bonds, few people understand what they're buying so the risks remain hidden. Someone might think a company will do well, so they buy an derivative on that company. But no one understands risk/reward calculations on derivatives, so the risk/reward on the derivative could be way off the price on the derivative. Also a layman, and I didnt read the article because it did the whole 'screw you for blocking my ads' thing. But judging from the title, I'd guess someone bought a massive amount of call options for VIX, the stock that tracks volatility in the market. Whenever the market crashes or goes through difficult times, the VIX fund prospers. The 'by october' part makes me think it was call options that he purchased: basically he paid a premium for each share (a fraction of the shares cost) for the right to buy that share at today's price, from now until october. So if the share increases in value, for each call option he has, he can buy one share at todays price, and sell it at the price it is that day. Options can catapult your profit into the next dimension but if the share decreases in value or even stays the same price, he loses everything. Vicious redditors, please correct the mistakes ive made here with utmost discrimination "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!" My reaction to this is that your observation @D.W. is spot on correct: It sounds like long-term market timing: trying to do a better job than   the rest of the market at predicting, based upon a simple formula,   whether the market is over-priced or under-priced. I read the post by the founder of Valuation Informed Indexing, Rob Bennet. Glance at  the comments section. Rob clearly states that he doesn't even use his own strategy, and has not owned, nor traded, any stocks since 1996! As another commenter summarizes it, addressing Rob: This is 2011. You’ve been 100% out of stocks — including indexes —   since 1996? That’s 15 years of taking whatever the bond market, CDs or   TIPS will yield (often and currently less than 2%)... I’m curious how   you defend not following your own program even as you recommend it for   others? Rob basically says that stocks haven't shown the right signals for buying since 1996, so he's stuck with bonds, CD's and fixed-income instead. This is a VERY long-term horizon point of view (a bit of sarcasm edges in from me). Answering your more general question, what do I think of this particular Price/ Earnings based ratio as a way to signal asset allocation change i.e. Valuation Informed Investing? I don't like it much. I think by definition there aren't, generally speaking, any indicators (as in chart indicators, I assume you mean)  for fundamental analysis. Off the top of my head I can't think of one chart indicator that I wouldn't call 'technical', even though a couple could possibly go either way and I'm sure someone will help prove me wrong. But the point I want to make is that to do fundamental analysis, it is most certainly more time consuming. Depending on what instrument you're investing in, you need to have a micro perspective (company specific details) and a macro perspective (about the industry it's in). If you're investing in sector ETFs or the like, you'd be more reliant on the macro analysis. If you're investing in commodities, you'll need to consider macro analysis in multiple countries who are big producers/consumers of the item. There's no cut and dried way to do it, however I personally opt for a macro analysis of sector ETFs and then use technical analysis to determine my entry and/or exit. "With every caveat that Rick said plus many many more lets have some fun.  One common way to measure risk is volatility of returns roughly how much the value of your asset jumps around.  Interestingly, the following ordering is fairly similar for many other common measures of risk. The first three on the list would be mostly interchangeable.  Generally, putting your money in ""cash"" investments has no real day-to-day price variability and the main risk is that the bank won't give you your money back at the end.  Money market funds are last as they can ""Break the buck"". To get a feel for the next few on the list I'm using previous 360 day volatility numbers for representative broad indices (asof 2014-10-27).  While these volatility values can move around quite a bit, the order is actually remarkably stable. Hedge funds might seem out of place here, but remember that hedge funds can hold be long and short at the same time and this can cancel out daily variation.  However, Hedge funds do have plenty of risks that may not be well accounted for by this measure.   For derivatives I'll refer to back to Rick's answer. This is a measure for broad investment in these categories your particular investment in Long-term Capital Management or Argentine Bonds may vary. It is important to note that your return on your investment generally grows as you go toward more risky investments down this list as people generally expect to be rewarded  in the long term for risky investments." "Beta is the correct answer.  It is THE measure of the risk relationship of a stock with the broad market. R squared is incorrect unless you mean something very odd by ""co-efficiency.""  A stock that goes up each time the market goes down has very low co-efficiency (negative risk as you have defined it) but very high R squared.  A stock that goes the same direction as the market but twice as far (with a lot of noise) has a very low R squared but contains a lot of market risk.  A stock that always goes in the same direction as the market but only a 100th as far is very safe but has a very high R squared. You can calculate beta using ""slope"" in excel or doing a regression, but the easiest thing is just to look up the beta in yahoo finance or elsewhere.  You don't need to calculate it for yourself normally." James Roth provides a partial solution good for stock picking but let's speed up process a bit, already calculated historical standard deviations: Ibbotson, very good collection of research papers here, examples below Books The value of a share depends on the value of the company, which involves a lot more than the value of its assets -- it requires making decisions about what you think will happen to the company in the future. That's inherently not something that can be reduced to a single formula, at least not unless you can figure out how to represent your guesses and your confidence in them in the formula ... and even if you could do all that it would only say what you think the stock is worth; others will be using different numbers and legitimately get different results. Disagreement over value is what the stock market is all about, I'm afraid. "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:" "Here's a dump from what I use. Some are a bit more expensive than those that you posted. The second column is the expense ratio. The third column is the category I've assigned in my spreadsheet -- it's how I manage my rebalancing among different classes. ""US-LC"" is large cap, MC is mid cap, SC is small cap. ""Intl-Dev"" is international stocks from developed economies, ""Emer"" is emerging economies. These have some overlap. I don't have a specific way to handle this, I just keep an eye on the overall picture. (E.g. I don't overdo it on, say, BRIC + Brazil or SPY + S&P500 Growth.) The main reason for each selection is that they provide exposure to a certain batch of securities that I was looking for. In each type, I was also aiming for cheap and/or liquid like you. If there are substitutes I should be looking at for any of these that are cheaper and/or more liquid, a comment would be great. High Volume: Mid Volume (<1mil shares/day): Low Volume (<50k shares/day): These provide enough variety to cover the target allocation below. That allocation is just for retirement accounts; I don't consider any other savings when I rebalance against this allocation. When it's time to rebalance (i.e. a couple of times a year when I realize that I haven't done it in several months), I update quotes, look at the percentages assigned to each category, and if anything is off the target by more than 1% point I will buy/sell to adjust. (I.e. if US-LC is 23%, I sell enough to get back to 20%, then use the cash to buy more of something else that is under the target. But if US-MC is 7.2% I don't worry about it.) The 1% threshold prevents unnecessary trading costs; sometimes if everything is just over 1% off I'll let it slide. I generally try to stay away from timing, but I do use some of that extra cash when there's a panic (after Jan-Feb '09 I had very little cash in the retirement accounts). I don't have the source for this allocation any more, but it is the result of combining a half dozen or so sample allocations that I saw and tailoring it for my goals." "Specifically, what does my broker mean when they say an asset or investment strategy is high risk?  In this context, it is a statement based on past events and probability. It is based on how confident s/he is that the investment will perform to certain benchmarks. This is a math question, primarily (with some opinion mixed in, granted). This is where the Sharpe ratio and others fit well. How am I supposed to answer a question like ""rate your risk tolerance from low to high""? This is the hard question, as you have seen. In this context, risk tolerance is derived from your current position and future plans (goals). This is a planning, goal setting, and strategy question, primarily (with some math mixed in, granted). How vulnerable is your current position and future plans to an under-performing investment? If you answer ""very"", then you choose investments that have a lower probability of under-performing.  The Sharpe ratio has little to do with answering this question. It is a tool to find investments that better match your answer to this question." Efficient Frontier has an article from years ago about the small-cap and value premiums out there that would be worth noting here using the Fama and French data. Eugene Fama and Kenneth French (F/F) have shown that one can explain   almost all of the returns of equity portfolios based on only three   factors: market exposure, market capitalization (size), and   price-to-book (value). Wikipedia link to the factor model which was the result of the F/F research. That's exactly what immunofort is saying, and it lines up with established financial theory (well, some of it).  The general argument is that stocks are priced according to what risks they're exposed to.  Several (although not all) of the major financial economics theories propose (and find empirical evidence for this) that the market as whole is a risk factor, so individual stocks would be priced in part based on how correlated they are with the market.  Strictly speaking, the risk free rate is purely theoretical and can't be directly observed, but the US T-bill yield is usually considered to be a pretty good proxy for it. Since you seem determined to consider this, I'd like to break down for you why I believe it is an incredibly risky proposition: 1) In general, picking individual stocks is risky. Individual stocks are by their nature not diversified assets, and a single company-wide calamity (a la Volkswagen emissions, etc.) can create huge distress to your investments. The way to mitigate this risk is of course to diversify (invest in other types of assets, such as other stocks, index funds, bonds, etc.). However, you must accept that this first step does have risks.  2) Picking stocks on the basis of financial information (called 'fundamental analysis') requires a very large amount of research and time dedication. It is one of the two main schools of thought in equity investing (as opposed to 'technical analysis', which pulls information directly from stock markets, such as price volatility). This is something that professional investors do for a living - and that means that they have an edge you do not have, unless you dedicate similar resources to this task. That information imbalance between you and professional traders creates additional risk where you make determinations 'against the grain'.  3) Any specific piece of public information (and this is public information, regardless of how esoteric it is) may be considered to be already 'factored into' public stock prices. I am a believer in market efficiency first and foremost. That means I believe that anything publically known related to a corporation ['OPEC just lowered their oil production! Exxon will be able to increase their prices!'] has already been considered by the professional traders currently buying and selling in the market. For your 'new' information to be valuable, it would need to have the ability to forecast earnings in a way not already considered by others. 4) I doubt you will be able to find the true nature of the commercial impact of a particular event, simply by knowing ship locations. So what if you know Alcoa is shipping Aluminium to Cuba - is this one of 5 shipments already known to the public? Is this replacement supplies that are covering a loss due to damaged goods previously sent? Is the boat only 1/3 full? Where this information gets valuable, is when it gets to the level of corporate espionage. Yes, if you had ship manifests showing tons of aluminum being sold, and if this was a massive 'secret' shipment about to be announced at the next shareholders' meeting, you could (illegally) profit from that information. 5) The more massive the company, the less important any single transaction is. That means the super freighters you may see transporting raw commodities could have dozens of such ships out at any given time, not to mention news of new mine openings and closures, price changes, volume reports, etc. etc. So the most valuable information would be smaller companies, where a single shipment might cover a month of revenue - but such a small company is (a) less likely to be public [meaning you couldn't buy shares in the company and profit off of the information]; and (b) less likely to be found by you in the giant sea of ship information. In summary, while you may have found some information that provides insight into a company's operations, you have not shown that this information is significant and also unknown to the market. Not to mention the risks associated with picking individual stocks in the first place. In this case, it is my opinion that you are taking on additional risk not adequately compensated by additional reward.