Diversification reduces risk, but does this base on the assumption that expected return of each asset is always in proportion to its risk?
Diversifying your portfolio between asset A and asset B only reduces the portfolio risk if asset A and asset B are not correlated. If they have either a low correlation or a negative correlation to each other, then you benefit from combining them in a portfolio in terms of risk reduction. The standard deviation of returns will be lower in a portfolio of low or uncorrelated assets. If on the other hand you combine two correlated assets into a portfolio you are doubling down on the same assumption, which means you are not reducing your risk. You are also wasting capital because now you have allocated capital to 2 separate trades / investments yet they have shown a high tendency of moving together. Here is an article that discusses this further: Why Diversify your Stock Portfolio if I have a asset A with expected return of 100% and risk(measured by standard deviation) 1%, and asset B with expected return of 1% and risk 100%, would it be rational to put asset B into the portfolio ? No, because Modern Portfolio Theory would say that if there is another asset (B2) with the same (or higher) return but less risk (which you already have in asset A), you should invest in that. If those are the only two assets you can choose from, you would invest completely in Asset A. The point of diversification is that, so long as two assets aren't perfectly positively correlated (meaning that if one moves up the other always moves up), then losses in one asset will sometimes be offset by gains in another, reducing the overall risk. If you have 100% of your money in one security that is inherently more risky than splitting your money 50/50 between two securities, regardless of the purported riskiness of the two securities. The calculations people use to justify their particular breed of diversification may carry some assumptions related risk/reward calculations.  But these particular justifications don't change the fact that spreading your money across different assets protects your money from value variances of the individual assets.  Splitting your $100 between Apple and Microsoft stock is probably less valuable (less well diversified) than splitting your money between Apple and Whole Foods stock but either way you're carrying less risk than putting all $100 in to Apple stock regardless of the assumed rates of return for any of these companies stock specifically. Edit: I'm sure the downvotes are because I didn't make a big deal about correlation and measuring correlation and standard deviations of returns and detailed portfolio theory.  Measuring efficacy and justifying your particular allocations (that generally uses data from the past to project the future) is all well and good.  Fact of the matter is, if you have 100% of your money in stock that's more stock risk than 25% in cash, 25% in bonds and 50% in stock would be because now you're in different asset classes.  You can measure to your hearts delight the effects of splitting your money between different specific companies, or different industries, or different market capitalizations, or different countries or different fund managers or different whatever-metrics and doing any of those things will reduce your exposure to those specific allocations.   It may be worth pointing out that currently the hot recommendation is a plain vanilla market tracking S&P 500 index fund (that just buys some of each of the 500 largest US companies without any consideration given to risk correlation) over standard deviation calculating actively managed funds.  If you ask me that speaks volumes of the true efficacy of hyper analyzing the purported correlations of various securities. If you are diversifying just for diversification purposes then all you are doing is averaging down your returns. You shouldn't just buy two securities because you think it is safer than putting all your money into one. A better method is to use money management and position sizing to limit your risk and exposure in any one security. You should know what your maximum risk is before you buy any security and know when it is time to get out of it. There are better ways to manage your risk. Don't put all your eggs in the one basket - yes, but don't diversify just for diversification purposes. if I have a asset A with expected return of 100% and risk(measured by standard deviation) 1%, and asset B with expected return of 1% and risk 100%, would it be rational to put asset B into the portfolio ? In the capital asset pricing model (CAPM), investors are rational and have access to perfect information. Asset A sounds like an excellent investment,  B like a lousy one -- B is probably very far from the efficient frontier. Investors know this, so A's market capitalization will be high, B's low. According to the CAPM, you should then do the same rational thing everyone else is doing, which is to buy a lot of A and very little of B (each in proportion to its market capitalization). Of course the CAPM is just a model, and like any model it is only as good as its assumptions. However, I think this particular application of the model gives a pretty reasonable common-sense answer to the question.
"Diversification is extremely important and the one true ""Free Lunch"" of investing, meaning it can provide both greater returns and less risk than a portfolio that is not diversified. The reason people say otherwise is because they are talking about ""true"" portfolio diversification, which cannot be achieved by simply spreading money across stocks. To truly diversify a portfolio it must be diversified across multiple, unrelated ""Return Drivers."" I describe this throughout my best-selling book and am pleased to provide complimentary links to the following two chapters, where I discuss the lack of diversification from spreading money solely across stocks (including correlation tables), as well as the benefits of true portfolio diversification: Jackass Investing - Myth #8: Trading is Gambling – Investing is Safer Jackass Investing - Myth #20: There is No Free Lunch" Asset Allocation serves many purposes, not just mitigating risk via a diversification of asset classes, but also allowing you to take a level of risk that is appropriate for a given investor at a given time by how much is allocated to which asset classes. A younger investor with a longer timeframe, may wish to take a lot more risk, investing heavily in equities, and perhaps managed funds that are of the 'aggressive growth' variety, seeking better than market returns. Someone a little older may wish to pull back a bit, especially after a bull market has brought them substantial gains, and begin to 'take money off the table' perhaps by starting to establish some fixed income positions, or pulling back to slightly less risky index,  'value' or 'balanced' funds. An investor who is near or in retirement will generally want even less risk, going to a much more balanced approach with half or more of their investments in fixed income, and the remainder often in income producing 'blue chip' type stocks, or 'income funds'.  This allows them to protect a good amount of their wealth from potential loss at a time when they have to be able to depend on it for a majority of their income. An institution such as Yale has very different concerns, and may always be in a more aggressive 'long term' mode since 'retirement' is not a factor for them.  They are willing to invest mostly in very aggressive ways, using diversification to protect them from one of those choices 'tanking' but still overall taking a pretty high level of risk, much more so than might be appropriate for an individual who will generally need to seek safety and to preserve gains as they get older.  For example look at the PDF that @JLDugger linked, and observe the overall risk level that Yale is taking, and in addition observe the large allocations they make to things like private equity with a 27%+ risk level compared to their very small amount of fixed income with a 10% risk level.  Yale has a very long time horizon and invests in a way that is atypical of the needs and concerns of an individual investor.  They also have as you pointed out, the economy of scale (with something like #17B in assets?) to afford to hire proven experts, and their own internal PHD level experts to watch over the whole thing, all of which very few individual investors have. For either class of investor, diversification, is a means to mitigate risk by not having all your eggs in one basket.  Via having multiple different investments (such as picking multiple individual stocks, or aggressive funds with different approaches, or just an index fund to get multiple stocks) you are protected from being wiped out as might happen if a single choice might fail.  For example imagine what would have happened if you had in 2005 put all your money into a single stock with a company that had been showing record profits  such as Lehman Brothers, and left it there until 2008 when the stock tanked. or even faster collapses such as Enron, etc that all 'looked great' up until shortly after they failed utterly.   Being allocated across multiple asset classes provides some diversification all on it's own, but you can also be diversified within a class. Yale uses the diversification across several asset classes to have lower risk than being invested in a single asset class such as private equity. But their allocation places much more of their funds in high risk classes and much less of their funds in the lowest risk classes such as fixed income. "While it's definitely possible (and likely?) that a diversified portfolio generates higher returns than the S&P 500, that's not the main reason why you diversify. Diversification reduces risk.  Modern portfolio theory suggests that you should maximize return while reducing risk, instead of blindly chasing the highest returns. Think about it this way--say the average return is 11% for large cap US stocks (the S&P 500), and it's 10% for a diversified portfolio (say, 6-8 asset classes). The large cap only portfolio has a 10% chance of losing 30% in a given year, while the diversified portfolio has a 1% chance of losing 30% in a year. For the vast majority of investors, it's worth the 1% annual gap in expected return to greatly reduce their risk exposure. Of course, I just made those numbers up. Read what finance professors have written for the ""data and proof"". But modern portfolio theory is believed by a lot of investors and other finance experts. There are a ton of studies (and therefore data) on MPT--including many that contradict it." "The calculation and theory are explained in the other answers, but it should be pointed out that the video is the equivalent of watching a magic trick.  The secret is: ""Stock A and B are perfectly negatively correlated.""  The video glasses over that fact that without that fact the risk doesn't drop to zero. The rule is that true diversification does decrease risk. That is why you are advised to spread year investments across small-cap, large-cap, bonds, international, commodities, real estate. Getting two S&P 500 indexes isn't diversification.  Your mix of investments will still have risk, because return and risk are backward calculations, not a guarantee of future performance. Changes that were not anticipated will change future performance. What kind of changes: technology, outsourcing, currency, political, scandal." "Diversification tends to protect you from big losses. But it also tends to ""protect"" you from big gains. In any industry, some companies provide good products and services and prosper while others have problems and fail. (Or maybe the winners are just lucky or they paid off the right politicians, whatever, not the point here.) If you put all your money in one stock and they do well, you could make a bundle. But if you pick a loser, you could lose your entire investment. If you buy a little stock in each of many companies, then some will go up and some will go down, and your returns will be an average of how everyone in the industry is doing. Suppose I offered to bet you a large sum of money that if I roll a die, it will come up 6. You might be reluctant to take that bet, because you can't predict what number will come up on one roll of a die. But suppose I offered to bet you a large sum of money that a die will come up 6, 100 times in a row. You might well take that bet, because the chance that it will turn up 6 time after time after time is very low. You reduce risk by spreading your bets. Anyone who's bought stock has surely had times when he said, ""Oh man! If only I'd bought X ten years ago I'd be a millionaire now!"" But quite a few have also said, ""If only I'd sold X ten years ago I wouldn't have lost all this money!""  I recently bought a stock a stock that within a few months rose to 10 times what I paid for it ... and then a few months later the company went bankrupt and the stock was worth nothing. I knew the company was on a roller coaster when I bought the stock, I was gambling that they'd pull through and I'd make money. I guessed wrong. Fortunately I gambled an amount that I was willing to lose." "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." Diversification is used by many to hopefully reduce the risk when bad investments are made. Diversification does not help you make more profits but instead averages down your profits. There is no way one can tell whether a stock or portfolio of stocks will go up or down once they are purchased. In order to try to provide some protection against total loss of the portfolio, a lazy so called long term investor will use diversification as a way of risk management. But the best outcome for them will be an averaging down of their profits. A better method is to let the market tell you when your purchased investment is a bad one and get out of that investment early and thus limiting your losses, whilst letting your good investments (as determined by the market) run and make larger profits. "In an ""efficient"" investment market the amount of risk premium would EXACTLY offset the likelihood of loss, such that over long time frames the expected return on investment would be equal for all investment options.  In practice, we usually see that riskier investments yield a higher long-term return because the risk premium is larger than that ""efficient"" amount. This is because many investors don't have a long-term time horizon, and the pain of loss is greater than the reward of gain (""asymmetric preferences""). It's also important to think about the risk-reward interaction as being PERCEIVED risk to EXPECTED reward.  If I'm lending money to somebody who is likely not to pay me back, I'd want a better deal than if I were lending to somebody who is certain to pay. I think that addresses your confusion, but if I misinterpreted what's puzzling you, please let me know and I" I think to answer this question it is best for you to learn more about why people diversify through asset allocation. Look at related questions involving Asset Allocation here.   I've asked a couple questions about asset allocation - I think you'll find the top rated answer on this post useful. In answer to your last formulation, no. In a perfectly efficient market, different investors still have different risk tolerances (or utility functions). They're maximizing expected utility, not expected value.  The portfolios that maximize expected utility for different risk preferences are different, and thus generally have different expected values. (Look up mean-variance utility for a simple-ish example.)  Suppose you have log utility for money, u(x) = log(x), and your choice is to invest all of your money in either the risk-free bond or in the risky bond. In the risky bond, you have a positive probability of losing everything, achieving utility u(0) = -\infty. Your expected utility after purchase of the risky bond is:  Pr(default)*u(default) + (1-Pr(default))*u(nominalValue).  Since u(default)= -\infty, your expected utility is also negative infinity, and you would never make this investment. Instead you would purchase the risk-free bond.  But another person might have linear utility, u(x) = x, and he would be indifferent between the risk-free and risky bonds at the prices you mention above and might therefore purchase some. (In fact you probably would have bid up the price of the risk-free bond, so that the other investor strictly prefers the risky one.) So two different investors' portfolios will have different expected returns, in general, because of their different risk preferences. Risk-averse investors get lower expected value. This should be very intuitive from portfolio theory in general: stocks have higher expected returns, but more variance. Risk-tolerant people can accept more stocks and more variance, risk-averse people purchase less stocks and more bonds. The more general question about risk premia requires an equilibrium price analysis, which requires assumptions about the distribution of risk preferences among other things. Maybe John Cochrane's book would help with that---I don't know anything about financial economics. I would think that in the setup above, if you have positive quantities of these two investor types, the risk-free bond will become more expensive, so that the risky one offers a higher expected return. This is the general thing that happens in portfolio theory. Anyway. I'm not a financial economist or anything.  Here's a standard introduction to expected utility theory: http://web.stanford.edu/~jdlevin/Econ%20202/Uncertainty.pdf Any portfolio, even one composed of risk-free assets is subject to risk. That said, to short an equity without margin risk, puts can provide.  To replicate a short without excess margin, an at the money put should be used.  To take on less leverage, a deep in the money put can be used.  Puts are not available on equities deemed illiquid by regulation. A long/short portfolio can help mitigate variance risk, but then the problem becomes the risk of a lack of volatility since options decline in value over time and without a beneficial change in the underlying. "Years ago I wrote an article Risk, Reward, Coin Flipping which explains from a 'game theory' perspective how diversifying works to minimize standard deviation in one's returns.  It's long and tedious, not easy to summarize, but it holds up well, I'm pleased with how the analogy does its job.  Update - the above is too ""link-only"", written over 5 years ago. The article I wrote offers a mathematical approach via an understandable example of coin flipping. With just 2 options, a 'head' is a 10% loss, while a 'tail' is a 30% gain. This actually represents the market fairly well as it results in a 10% average gain and 28% standard deviation for just 2 flips. The article shows how by 'diversifying', choosing to make multiple smaller bets, the average 10% stays the same, but the standard deviation is brought down dramatically, 7.6% when we use a sample experiment with 7 coins." I researched quite a bit around this topic, and it seems that this is indeed false. Long ter asset growth does not converge to the compound interest rate of expected return. While it is true that standard deviations of annualized return decrease over time, because the asset value itself changes over time, the standard deviations of the total return actually increases.      Thus, it is wrong to say that you can take increased risk because you have a longer time horizon.  Source "So it's not always what degree of risk you want be exposed to, but what *type* of risk. So let's say you were happy with the S&amp;P 500 ETF but you wanted to avoid oil stocks, so you combine that ETF with some derivatives that profit if oil goes down and you will outperform the S&amp;P 500 on a net basis.  Hedge funds can be very crafty with what exposure they want. They include a LOT of different strategies, so it's kind of incorrect to group them into one ""asset class"" per se.  As for the question if hedge funds are worth it? Well if the market tanks, you might find your hedge fund's performance to be very positive (ex: Kyle Bass made big money with the crisis)." I would suggest the use of a management company to handle a rental property.  They will take care of things like collecting rent, coordinating repairs and all the little things that come up when dealing with a renters.    They typically charge a percentage of the rent or a flat fee, so make sure you include that in your rent calculation.  You take a little bit of a financial hit, but save a lot of head aches - especially if you decide to acquire multiple properties in the future.