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I am looking for intuition here. I understand that diversification decreases the variance of the portfolio. However, what I am confused is that it also effectively decreases the return.

Assume I have perfectly negatively correlated assets — one goes up, another one goes down. Net I am 0 with 0 volatility. So, what's the point? I have a basket, half are up and half are down because I diversified well. But then so as my return will be 0? As soon as combine opposites I also decrease my return? Only if all assets grow and negatively correlated I do get positive return which is some average between the holdings. But I think I should strive for mostly negatively correlated assets and thus my return will always be the difference between the two? I am just confused how diversification affects the investing goal of maximizing a return!

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  • You might find this explanation helpful: risk theory. (Note the related Java applet is now unsupported.) Jun 8, 2023 at 19:58
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    The figure of merit is not the return, but the return per unit of risk Jun 10, 2023 at 11:35

4 Answers 4

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You're right that diversification isn't the way to maximize your return irrespective of risk. If you want the highest return possible, you need to select investments that can give you that return - but your risk will be very high.

The goal of diversification is to maximize your risk-adjusted return by being on the efficient frontier (at least according to modern portfolio theory). Essentially, it's minimizing risk for a given rate of return (or conversely, maximizing your return given an allowable risk level).

You could use a combination of one asset class (e.g. U.S. equities) and cash to build a portfolio with a certain target return or risk, but it likely won't be on the efficient frontier. Maybe you could squeeze a little more return with the same amount of risk if you used some bonds instead of cash, or maybe you could get the same return with less risk by adding international equities into the mix - both of these would get you closer to the efficient frontier. (Purely an example, NOT investment advice.)

Correlation has to do with the directionality of returns, not the magnitude. So two assets with a correlation of -1 could have returns of 10% and -1%, while another pair of assets with a correlation of -1 could have returns of 5% and -5%.

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You are assuming that assets go up and down equally. But if such assets exist, then there's no point in investing in them, as you will make no money in the long term.

Most investments go up, on average. A balanced portfolio should go up broadly in line with that average. If instead you bought only one investment, then it might go up a lot, or it might go down a lot. So a balanced portfolio reduces your risk.

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  • If they do go up on average, wouldn't I want to get into leveraged etf for whatever sector I am investing? I ha e the same diversification yet higher return overall? What additional risk I am taking?
    – Medan
    Jun 12, 2023 at 15:25
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    @Medan anything leverated increases your risk. If you leverage 10:1 and the thing you're buying goes down 10%, then you lose all your money.
    – Simon B
    Jun 12, 2023 at 19:08
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The goal is not to perfectly diversify such that you get zero risk (and hence return, the goal is to decide on a risk level that you're comfortable with and design your portfolio accordingly so that you maximize return for a given level of risk. Most people do not know what actual measure of risk they can tolerate, so they use broad guidelines like having X% in bonds and 100-x% in stocks, maybe with some alternate investments like real estate mixed in to diversify further. It's rarely very scientific for individuals. Only institutional investors have the data and resources needed to make more quantitative decisions.

Even with a high risk tolerance, investing diversely in many high-risk assets with some correlation less than 1 will reduce risk without reducing expected return significantly.

Diversification also reduces the risk of extreme losses (e.g. betting on a single stock that goes bankrupt) but also reduces the risk of extreme gains. In return, you get a "narrower" range of returns near your expected return. Some may go up, some may go down, but the extremes will tend to cancel each other out.

It's a bit like betting all of your money on one number at the roulette wheel versus betting a smaller amount on several numbers or combinations. Obviously you wouldn't just bet on Red and Black as they would completely offset (not a perfect analogy since the expected return at the roulette wheel is negative, but hopefully illustrates the point). You have less risk of "hitting it big" then you would betting on a single stock, but you have a greater chance of getting near your expected return.

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I would add that diversification usually offers a way to minimize variance at no (or very little) cost to the expected return. (And the expected return on all stocks you consider is of course positive. Otherwise you should not be investing.) Very simply let's say there are two stocks you are considering buying. Say you have equal expectations for their expected return. This is quite common since you probably have no better guess than the market, i.e. your best guess is trusting the efficiency of the market. Then you can either invest in one of them or in both. This choice does not affect the expected value of your return. However, it does reduce the variance.

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    Exactly. If I think Coke and Pepsi are likely to do equally well, I can buy just one of those stocks or I can buy both. If I'm right about the market for fizzy sugarwater, I make the same returns either way. But if Coke or Pepsi has some unforeseen company-specific event, good or bad, the impact of that event on me is halved if I split my portfolio. Jun 9, 2023 at 18:49

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