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.
"Wow, this analysis really surprised me. Very complete and useful, but i think my teacher request was easier. He just said: ""Try to build a diversified portfolio. Then try to add a commodity (like silver or gold) and understand how the risk vary introducing an asset like this."" So, i'm basically making a stocks portfolio and i'm calculating its expected return and risk. (for example 40%FB, 10%JNJ, 20%GS, 10%F and 20%MCD) then i'm adding GLD (so now i have something like 20%FB, 10%JNJ, 10%GS, 10%F and 20%MCD 30%GLD) and i'm actually making an excel spreadsheet where i calculate all the: -Expected returns -St Deviation -Covariance  At the end i compare the returns and the risks on the 2 different portfolios." This answer will assume you know more math than most. An ideal case: For the point of argument, first consider the following admittedly incorrect assumptions: 1)  The prices of all assets in your investment universe are continuously differentiable functions of time. 2)  Investor R (for rebalance) continuously buys and sells in order to maintain a constant proportion of each of several investments in his portfolio. 3)  Investor P (for passive) starts with the same portfolio as R, but neither buys nor sells Then under the assumptions of no taxes or trading costs, it is a mathematical theorem that investor P's portfolio return fraction will be the weighted arithmetic mean of the return fractions of all the individual investments, whereas investor R will obtain the weighted geometric mean of the return fractions of the individual investments. It's also a theorem that the weighted arithmetic mean is ALWAYS greater than or equal to the weighted geometric mean, so regardless of what happens in the market (given the above assumptions) the passive investor P does at least as well as the rebalancing investor R.  P will do even better if taxes and trading costs are factored in. The real world:  Of course prices aren't continuously differentiable or even continuous, nor can you continuously trade.  (Indeed, under such assumptions the optimal investing strategy would be to sample the prices sufficiently rapidly to capture the derivatives and then to move all your assets to the stock increasing at the highest relative rate.  This crazy momentum trading would explosively destabilize the market and cause the assumptions to break.) The point of this is not to argue for or against rebalancing, but to point out that any argument for rebalancing which continues to hold under the above ideal assumptions is bogus.  (Many such arguments do.)  If a stockbroker standing to profit from commission pushes rebalancing on you with an argument that still holds under the above assumptions then he is profiting off of BS. 1. It doesn't have an almost perfect negative correlation - its value decays very fast because of time.  In fact, something like 80% of options expire worthless.  They typically have a lifespan of 30-90 days and unless you're using them as a way to earn excess return, you'll likely just throw away your premium.  2. You're also making some assumptions about correlation and risk/reward.  You won't become wealthy by distributing risk, all you can hope for is less volatility - maybe that's what you're looking for - but you can also expect your return to be less than the market over almost any period of time.  3. Options aren't really for diversifying.  Furthermore, why diversify?  It's a myth that it adds any value.  There's around a 90% correlation for all asset classes since around 2000, so you're being sold some blue sky if someone tells you otherwise.  4. Look up prices of put options.  1-2% of your portfolio might buy you a handful of options, but again, there's a high probability you'll lose that 1-2% entirely every 30-90 days. "To be honest, I think a lot of people on this site are doing you a disservice by taking your idea as seriously as they are. Not only is this a horrible idea, but I think you have some alarming misunderstandings about what it means to save for retirement. First off, precious metals are not an ""investment""; they are store of value. The old saying that a gold coin would buy a suit 300 years ago and will still buy a suit today is pretty accurate. Buying precious metals and expecting them to ""appreciate"" in the future because they are ""undervalued"" is just flat-out speculation and really doesn't belong in a well-planned retirement account, unless it's a very small part for the purposes of diversification. So the upshot to all of this is the most likely outcome is you get zero return after inflation (maybe you'll get lucky or maybe you'll be very unlucky). Next you would say that sure, you're giving up some expected return for a reduction in risk. But, you've done away with diversification which is the most effective way to minimize risk... And I'm not sure what scenario you're imagining that the stock market or any other reasonable investment doesn't make any returns. If you invest in a market wide index fund, then the expected return is going to be roughly in proportion with productivity gains. To say that there will be no appreciation of the stock market over the next 40 years is to say that technological progress will stop and/or we will have large-scale economic disruptions that will wipe out 40 years of progress. If that happens, I would say it's highly questionable whether silver will actually be worth anything at all. I'd rather have food, property, and firearms. So, to answer your question, practically any other retirement savings plan would be better than the one that you currently outlined, but the best plan is just to put your money in a very low-cost index fund at Vanguard and let it sit until you retire. The expense ratios are so stupidly small, that it's not going to meaningfully affect your return." "If the stock market dropped 30%-40% next month, providing you with a rare opportunity to buy stocks at a deep discount, wouldn't you want to have some of your assets in investments other than stocks? If you don't otherwise have piles of new cash to throw into the market when it significantly tanks, then having some of your portfolio invested elsewhere will enable you to back up the proverbial truck and load up on more stocks while they are on sale. I'm not advocating active market timing. Rather, the way that long-term investors capitalize on such opportunities is by choosing a portfolio asset allocation that includes some percentage of safer assets (e.g. cash, short term bonds, etc.), permitting the investor to rebalance the portfolio periodically back to target allocations (e.g. 80% stocks, 20% bonds.) When rebalancing would have you buy stocks, it's usually because they are on sale. Similarly, when rebalancing would have you sell stocks, it's usually because they are overpriced. So, don't consider ""safer investments"" strictly as a way to reduce your risk. Rather, they can give you the means to take advantage of market drops, rather than just riding it out when you are already 100% invested in stocks. I could say a lot more about diversification and risk reduction, but there are plenty of other great questions on the site that you can look through instead." Chris Rea's comment captures it -- most people don't have working crystal balls. Unless you are a trader, you address risk with diversification. There are several questions on this site discussing strategies to diversify your portfolio. In many ways, the markets offer investors false choices. We have an emotional desire to react to stimuli -- but that often leads to lousy outcomes. For example, selling your NASDAQ 100 fund after its value falls is usually a bad idea. "Every investment comes with a risk. There is also a bit of speculation involved. In there is an anticipation that one expects the value to go up in normal course of events. By your definition ""If I buy this equipment, I could produce more widgets, or sell more widgets,"" as an investment. Here again there is an anticipation that the widgets you sell will give you more return. If you are investing in stock/share, you are essentially holding a small portion of value in company and to that extent you are owining some equipment that is producing some widget .... Hence when you are purchasing Stocks, it would be looked as investment if you have done your home work and have a good plan of how you want to invest along with weiging the risk involved. However if you are investing only for the purpose of making quick bucks following so called hot tips, then you are not investing but speculating." "When you invest in a single index/security, you are completely exposed to the risk of that security. Diversification means spreading the investments so the losses on one side can be compensated by the gains on the other side. What you are talking about is one thing called ""risk apettite"", more formally known as Risk Tolerance: Risk tolerance is the degree of variability in investment returns that an investor is willing to withstand. (emphasis added) This means that you are willing to accept some losses in order to get a potential bigger return. Fidelity has this graph:  As you can see in the table above, the higher the risk tolerance, the bigger the difference between the best and worst values. That is the variability. The right-most pie can be one example of an agressive diversified portfolio. But this does not mean you should go and buy exactly that security compostion. High-risk means playing with fire. Unless you are a professional stuntman, playing with fire usually leaves people burnt. In a financial context this usually means the money is gone. Recommended Reading: Investopedia; Risk and Diversification: The Risk-Reward Tradeoff Investopedia; How to construct a High Risk portfolio Fidelity: Guide to Diversification KPMG: Understanding and articulating Risk Appetite (pdf)"