Diversification is spreading your investments around so that one point of risk doesn't sink your whole portfolio. The effect of having a diversified portfolio is that you've always got something that's going up (though, the corollary is that you've also always got something going down... winning overall comes by picking investments worth investing in (not to state the obvious or anything :-) ))
It's worth looking at the different types of risk you can mitigate with diversification:
This is the risk that the company you bought actually sucks. For instance, you thought gold was going to go up, and so you bought a gold miner. Say there are only two -- ABC and XYZ. You buy XYZ. Then the CEO reveals their gold mine is played out, and the stock goes splat. You're wiped out. But gold does go up, and ABC does gangbusters, especially now they've got no competition. If you'd bought both XYZ and ABC, you would have diversified your company risk, and you would have been much better off. Say you invested $10K, $5K in each. XYZ goes to zero, and you lose that $5K. ABC goes up 120%, and is now worth $11K. So despite XYZ bankrupting, you're up 10% on your overall position.
You can categorize stocks by what "sector" they're in. We've already talked about one: gold miners. But there are many more, like utilities, bio-tech, transportation, banks, etc. Stocks in a sector will tend to move together, so you can be right about the company, but if the sector is out of favor, it's going to have a hard time going up.
Lets extend the above example. What if you were wrong about gold going up? Then XYZ would still be bankrupt, and ABC would be making less money so they went down as well; say, 20%. At that point, you've only got $4K left. But say that besides gold, you also thought that banks were cheap. So, you split your investment between the gold miners and a couple of banks -- lets call them LMN and OP -- for $2500 each in XYZ, ABC, LMN, and OP. Say you were wrong about gold, but right about banks; LMN goes up 15%, and OP goes up 40%.
At that point, your portfolio looks like this:
XYZ start $2500 -100% end $0
ABC start $2500 +120% end $5500
LMN start $2500 +15% end $2875
OP start $2500 +40% end $3500
For a portfolio total of: $11,875, or a total gain of 18.75%.
See how that works?
So, now what if everything's been going up in the USA, and everything seems so overpriced? Well, odds are, some area of the world is not over-bought. Like Brazil or England. So, you can buy some Brazilian or English companies, and diversify away from the USA. That way, if the market tanks here, those foreign companies aren't caught in it, and could still go up. This is the same idea as the sector risk, except it's location based, instead of business type based.
There is an additional twist to this -- currencies. The Brits use the pound, and the Brazilians use the real. Most small investors don't think about this much, but the value of currencies, including our dollar, fluctuates. If the dollar has been strong, and the pound weak (as it has been, lately), then what happens if that changes? Say you own a British bank, and the dollar weakens and the pound strengthens. Even if that bank doesn't move at all, you would still make a gain.
You buy British bank BBB for 40 pounds a share, when each pound costs $1.20. Say after a while, BBB is still 40 pounds/share, but the dollar weakened and the pound strengthened, such that each pound is now worth $1.50. You could sell BBB, and because of the currency exchange once you've got it converted back to dollars you'd have a 25% gain.
Market cap risk
Sometimes big companies do well, sometimes it's small companies. The small caps are riskier but higher returning. When you think about it, small and mid cap stocks have much more "room to run" than large caps do. It's much easier to double a company worth $1 billion than it is to double a company worth $100 billion.
Stocks aren't the only thing you can invest in. There's also bonds, convertible bonds, CDs, preferred stocks, options and futures. It can get pretty complicated, especially the last two. But each of these investment behaves differently; and again the idea is to have something going up all the time.
The classical mix is stocks and bonds. The idea here is that when times are good, the stocks go up; when times are bad, the bonds go up (because they're safer, so more people want them), but mostly they're there to providing steady income and help keep your portfolio from cratering along with the stocks. Currently, this may not work out so well; stocks and bonds have been moving in sync for several years, and with interest rates so low they don't provide much income.
So what does this mean to you?
I'm going make some assumptions here based on your post. You said single index, self-managed, and don't lower overall risk (and return). I'm going to assume you're a small investor, young, you invest in ETFs, and the single index is the S&P 500 index ETF -- SPY.
S&P 500 is, roughly, the 500 biggest companies in the USA. Further, it's weighted -- how much of each stock is in the index -- such that the bigger the company is, the bigger a percentage of the index it is. If slickcharts is right, the top 5 companies combined are already 11% of the index! (Apple, Microsoft, Exxon, Amazon, and Johnson & Johnson). The smallest, News Corp, is a measly 0.008% of the index.
In other words, if all you're invested in is SPY, you're invested in a handfull of giant american companies, and a little bit of other stuff besides.
Company risk and sector risk aren't really relevant to you, since you want broad market ETFs; they've already got that covered. The first thing I would do is add some smaller companies -- get some ETFs for mid cap, and small cap value (not small cap growth; it sucks for structural reasons). Examples are IWR for mid-cap and VBR for small-cap value.
After you've done that, and are comfortable with what you have, it may be time to branch out internationally. You can get ETFs for regions (such as the EU - check out IEV), or countries (like Japan - see EWJ). But you'd probably want to start with one that's "all major countries that aren't the USA" - check out EFA.
In any case, don't go too crazy with it. As index investing goes, the S&P 500 is not a bad way to go. Feed in anything else a little bit at a time, and take the time to really understand what it is you're investing in.
So for example, using the ETFs I mentioned, add in 10% each IWR and VBR. Then after you're comfortable, maybe add 10% EFA, and raise IWR to 20%. What the ultimate percentages are, of course, is something you have to decide for yourself.
Or, you could just chuck it all and buy a single Target Date Retirement fund from, say, Vanguard or T. Rowe Price and just not worry about it.