What is “beta” for an investment or a portfolio, and how do I use it?
Beta is an indication of a Stock's risk with respect to the market.  For instance if a stock had a beta of 1 it means it is in tandem with the S&P 500. If it is more than 1, the stock is volatile.  If it is less than 1, it implies market movement doesn't affect this stock much. Tech stocks and small cap stocks have high beta, utilities have low beta. (In general, not always). Hope this helps - I've tried to explain it in very simple terms! "In addition to individual stocks, your entire portfolio will also have a beta.  It would be equal to the weighted sum of the individual asset betas  So a beta portfolio of 1 would have approximate risk equal to a market index. You would use this to construct a risk level that you were comfortable with, given the expected return of the individual assets.  You are also interested in obtaining a high level of ""alpha"" which means that your portfolio is earning more than what would be expected, given it's level of risk." I don't think either of these answers are accurate. A beta of 0 means that your stock/portfolio does not change accordingly or with the market, rather it acts independent. A beta above 0 means the stock follows what the market does. Which means if the market goes up the stock goes up, if the market goes down, the stock goes down. If the stock's beta is more than 1 the stock will go up more if the market goes up, or go down more if the market goes down. Inversely if the stock is less than 0 the stock will follow the market inversely. So if the market goes up, the stock goes down. If the market goes down, the stock goes up. Again a greater negative beta, the more this relationship will be exaggerated.
I just used the formula in below link and did some math.  I have that book too but haven't looked at it yet really.  Lots of maths to have fun with.  Let me know if this is correct or needs fixing. Source: http://wiki.fool.com/How_to_Calculate_Beta_From_Volatility_%26_Correlation Basically you'd take all the companies in a given universe (like the S&amp;P 500 or the Russell 3000) and instead of weighting them by market cap as they are currently done, you would weight by an alternative measure.  Right now, if you're invested in an index that is market cap weighted, you're effectively momentum chasing. If a stock runs up, you're going to have a higher weight in your portfolio because of it (but only after the increase).  An alternative that OppenheimerFunds has come up with is using revenue-weighting. That way you're using company fundamentals and only when the fundamentals are improving do you increase the weight in your portfolio.  I haven't yet seen any research that explores weighting by other fundamentals. I would think that revenues aren't perfect either and that you might want to weight by Net Income. Or to go several steps further, by year over year Free Cash Flow growth.   It could be a seminal paper if you are the one who empirically identifies a better weighting methodology and then have everyone else fight over the theoretical underpinnings.  This is effectively what goes into Smart Beta investing: http://www.investopedia.com/terms/s/smart-beta.asp I think I may have gotten my reasoning backwards, since beta can be thought of as just the quantification of the relationship in prices but in itself isn't the actual reason behind them.  Risk free are things such as Treasury bonds/bills. 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. Correct, long/short strategies should have zero beta with the stock market. But this is intentional, and investors in true *hedged* funds seek this *portable alpha* as a complement to their long-only sleeve in the portfolio.  My question is: if for example, you are long low P/E stocks, and a short high P/E stocks what *creates* the alpha? Your portfolio should have zero beta. I believe in the long-run this long/short P/E strategy [generates ~300 basis points of return per year (un-levered)](http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html).  Is not reasonable to assume if returns from long only investing is driven by beta (and investors use 6% to 12% discount rates in their valuation models), then an an un-levered long/short strategy should always under-perform a long-only strategy in the long-run. The purpose of long/short strategies is not to beat long-only investing, it is to create [portable alpha](https://en.wikipedia.org/wiki/Portable_alpha).  In fact, at a high level of abstraction, the *average* long/short strategy should not earn a return greater than the risk free rate in the long-run because the strategy has zero beta. I already know of this method. I was creating a peer group and found 4-5 very similar companies, however one of them is a foreign public company with a subsidiary competing directly with a company I am trying to find the beta for. I guess I have to omit this company because it's strictly foreign?   Also, what do I do if I can't find any public companies that are similar to the company I am trying to value? "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!" "Doesn't ""no rebalancing"" mean ""start with a portfolio and let it fly?""  Seems like incorporation of rebalancing is more sophisticated than not. Just ""buy"" your portfolio at the start and see where it ends up with no buying/selling, as compared with where it ends up if you do rebalance. Or is it not that simple?" You should use the Gordon Growth model, but you are using the wrong rate.  required return = rf + market premium x Beta  rm = 0,12, premium = 0,08 --&gt; rf = 0,04 thus rr = 0.04 + 0.08 * 1.5 = 0.16  then you get $15/(0.16-0.05) = $136,36 There is none, whatever sector you invest in will be subject to cyclical market difficulties, however alpha can be generated from two sources: Timing and selection.  Its much easier to get the timing done over a long period of time. "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." "As other people have posted starting with ""fictional money"" is the best way to test a strategy, learn about the platform you are using, etc. That being said I would about how Fundamental Analysis works . Fundamental Analysis is the very basis of learning about an assets true value is priced. However in my humble opinion, I personally just stick with Index funds. In layman's terms Index Funds are essentially computer programs that buy or sell the underlying assets based on the Index they are associated with in the portion of the underlying index. Therefore you will usually be doing as good or as bad as the market. I personally have the background, education, and skillsets to build very complex models to do fundamental analysis but even I invest primarily in index funds because a well made and well researched stock model could take 8 hours or more and Modern Portfolio Theory would suggest that most investors will inevitably have a regression to the mean and have gains equal to the market rate or return over time. Which is what an index fund already does but without the hours of work and transaction cost." "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:" "A diversified portfolio (such as a 60% stocks / 40% bonds balanced fund) is much more predictable and reliable than an all-stocks portfolio, and the returns are perfectly adequate. The extra returns on 100% stocks vs. 60% are 1.2% per year (historically) according to https://personal.vanguard.com/us/insights/saving-investing/model-portfolio-allocations To get those average higher stock returns, you need to be thinking 20-30 years (even 10 years is too short-term). Over the 20-30 years, you must never panic and go to cash, or you will destroy the higher returns. You must never get discouraged and stop saving, or you will destroy the higher returns. You have to avoid the panic and discouragement despite the likelihood that some 10-year period in your 20-30 years the stock market will go nowhere. You also must never have an emergency or other reason to withdraw money early. If you look at ""dry periods"" in stocks, like 2000 to 2011, a 60/40 portfolio made significant money and stocks went nowhere. A diversified portfolio means that price volatility makes you money (due to rebalancing) while a 100% stocks portfolio means that price volatility is just a lot of stress with no benefit. It's somewhat possible, probably, to predict dry periods in stocks; if I remember the statistics, about 50% of the variability in the market price 10 years out can be explained by normalized market valuation (normalized = adjusted for business cycle and abnormal profit margins). Some funds such as http://hussmanfunds.com/ are completely based on this, though a lot of money managers consider it. With a balanced portfolio and rebalancing, though, you don't have to worry about it very much. In my view, the proper goal is not to beat the market, nor match the market, nor is it to earn the absolute highest possible returns. Instead, the goal is to have the highest chance of financing your non-financial goals (such as retirement, or buying a house). To maximize your chances of supporting your life goals with your financial decisions, predictability is more important than maximized returns. Your results are primarily determined by your savings rate - which realistic investment returns will never compensate for if it's too low. You can certainly make a 40-year projection in which 1.2% difference in returns makes a big difference. But you have to remember that a projection in which value steadily and predictably compounds is not the same as real life, where you could have emergency or emotional factors, where the market will move erratically and might have a big plunge at just the wrong time (end of the 40 years), and so on. If your plan ""relies"" on the extra 1.2% returns then it's not a reasonable plan anyhow, in my opinion, since you can't count on them. So why suffer the stress and extra risk created by an all-stocks portfolio?" You're correct. Amazon literally doesn't give a shit if they don't make profits for a while on this business. Hell it's potentially possible that their 1P business is still in the red and just used for the platform. Amazon isn't looking at whole foods for profit in the short term or even on a 5 year time horizon. They're looking to expand their presence into the fresh market, give people a local touch point to pick up online orders, and get more people into their platform.   It's completely likely you'll see some form of price decline.   Edit: just wanted to add, this is far from new.