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College teachers showed that diversification is free lunch for getting rid of part of the risk, but does this argument based on the assumption that expected return of each asset is always in proportion to its risk? The teacher illustrate this by using a portfolio where the one with higher return always have higher risk. But, I wondered, for example, 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 ?

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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

  • -1. Very confusing answer. "Diversifying your portfolio... only reduces the portfolio risk if asset A and asset B are not correlated" is simply incorrect. (Expected) standard deviation of returns decreases as correlation decreases. – xiaomy Mar 24 '17 at 17:27
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    It may help your confusion to read through the question again, so that the answer is seen in context: "if I have a asset A with expected return of 100% and risk(measured by standard deviation) 1%". Your comment and the answer are saying the same thing,...reduce correlation and expected standard deviation of returns reduces (which is what the OP is using as a measure of risk) – darkpool Mar 25 '17 at 8:42
  • Your use of the term is confusing me. By "not correlated" what do you mean? 0 correlation? or -1? – xiaomy Mar 25 '17 at 13:17
  • Oh ok, I see the confusion. When I say not correlated, I mean not +1. As the assets become less and less positively correlated towards zero and then towards -1, you benefit from a lower expected standard deviation of returns. However if you add two assets that are highly positively correlated, there is no benefit (with respect to standard deviation of returns which is what the OP referenced as his measure of risk) – darkpool Mar 25 '17 at 15:16
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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.

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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.

  • Investment horizon matters. 100% stock makes more sense if your horizon is counted in years and decades (as opposed to weeks or months). That is why all these 401K strategies recommend allocating all stock for young people. It's the shortfall risk that should matter. – xiaomy Mar 24 '17 at 18:38
  • And the point of that 100% allocation is to expose your assets to the risk. The point of rolling that in to less risky asset classes as you age is to ease off the risk. But your stock holdings should be diversified to some extent, no one is advocating a 100% 401(k) allocation into a single company stock. Additionally, you should think in terms of all of your assets, cash, short/longer term savings, retirement, etc. For example, your emergency savings should not be exposed to the market no matter your age because you have an unknown time horizon and would need the liquidity in an emergency. – quid Mar 24 '17 at 18:45
  • I wouldn't say the point is to expose yourself to the risk, but rather to the much higher expected return. The market risk is simply less relevant when the horizon is long. As people age, risk becomes more relevant and thus they roll back. – xiaomy Mar 24 '17 at 19:09
  • Risk isn't bad, it's not a four-letter-word. You expose your money to the risk to get the return. As people age liquidity becomes more relevant (you'll need to spend your assets) so you roll off the risk to avoid a forced sale at an inopportune time. This is why you need to think of your asset allocations holistically. You want to avoid forced asset sales. – quid Mar 24 '17 at 19:19
  • I think we are saying the same thing - you want return, you get it by bearing risks. But it's important to note that not all risks are equal. There are risks that reward you for taking them, and there are those that don't. The whole idea of diversification is to remove the latter (unsystematic risks). – xiaomy Mar 24 '17 at 19:53
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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.

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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.

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