Concentration by itself doesn't work. I have been using concentration + momentum + best risk/reward funds + being in the right wide-range categories.
Since I started in 1995, there have been three long term cycles
1995-2000 + 2010-2020 = US Large cap tilting growth
2000-2010 = US Value, some small cap and some international
BTW, I changed the number of funds from 5 (2000-2018) to only 2-3 since retirement in 2018 because I can only find very limited great ideas.
You can read how I did it (here).

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I based my system loosely on 3 Buffet’s rules but adapted it to funds: Rule No. 1: Never Lose Money. Rule No. 2: Never Forget Rule No. 1 and Rule 3: Diversification is a protection against ignorance. I added a fourth rule: momentum. I also liked Bogles' ideas of owning just 2-3 funds but changed it to 5 funds.
I used the above until 2018 and changed. I realized I only have 2-3 great ideas (funds) at any moment.
It doesn't matter if you have 2 or 10 accounts, 100 funds to select from, or 10K+. You are in control of how many funds you own.

I think that most investors would generate similar to better results over time by using up to 5-7 funds, mostly indexes, hardly trade, and rebalance...all based on their goals, style and risk tolerance.
I never believed in any of the above, which is why I became a trader in 2000, when the stock market started to go down. It worked really well for me, using wide range categories
Another observation: markets have long cycles where 1-3 categories are above the rest, so why rebalance?
I started investing in 1995 based on the following:.
1995-2000: US LC tilting growth.
2000-2010: US Value+SC, and international. SPY+QQQ lost money for 10 years.
2010-2024: US LC tilting growth. Since 2018, I'm mostly in bond OEFs.

Thanks @Charles. ISTM that at one time (maybe late 90s) Jack Bogle recommended that investors wanting just 1 fund use VTSAX (total stock market index fund) rather than an S&P 500 fund.
Not to praise or promote James Stack’s InvesTech Research. Folks can do their own research as to its worth. But as a current subscriber I decided to do a count of his fund recommendations. I found that his currently posted ”Model Portfolio” includes a cash position plus 9 funds. Unlike my 10/10 portfolio, Stack’s picks are not equally weighted. An interesting coincidence nonetheless.

"Morningstar's John Rekenthaler starts with a simple but unusual observation that if 2 assets have the same long-term (LT) TR, then rebalancing will definitely benefit the TR."
In all other cases, rebalancing hurts TR, but does control risk

That's the inverse of the JR wrote, and inverses are often not true. (See The Fallacy of the Inverse, and Example 41 here.)
JR: If two assets have same LT TR, rebalancing helps portfolio TR.
Inverse: If two assets do not have same LT TR, rebalancing does not help (hurts) portfolio TR.
JR's statement can be understood intuitively. If asset 1 has a good year (relative to asset 2) and the assets have the same long term returns, then in the other years (on average) asset 1 must do worse. Since it will do worse, one would be better off moving some money from asset 1 to asset 2, i.e. rebalancing.
But even if asset 2 has poorer long term returns than asset 1, it could have better returns in the right years so that rebalancing still improves performance.
Suppose we have stocks (asset 1) and bonds (asset 2), and they return 10% and 8% respectively in odd years, and 8% and 9% respectively in even years. On average (long term), stocks return just under 9.0% (10% and 8% compounded), while bonds return just under 8.5% (8% and 9%).
In odd years, stocks do better (10% vs 8%) and rebalancing moves money from stocks to bonds. The next (even) year, bonds do better (9% vs. 8%). So moving money from stocks to bonds (rebalancing) turns out to be the right move. Likewise, in even years, bonds do better; rebalancing moves money from bonds to stocks which then do better the next year. Again, the right move.
The world isn't that neat, and often rebalancing won't improve portfolio performance. But arithmetically, one can't say that rebalancing must hurt total return.

I have the answer @hank. I just checked my Roth, 401k and T IRA accounts, which I try to manage as one portfolio, and the answer to your question is 15. 16 if you add cash that I group as treasuries, CDs and MM. No more, no less should be used! / I'm being facetious. That just happens to be where I'm at. As you know it is totally up to the individual’s comfort level …

@MikeM is right where I was up until about 12-15 months ago. Try as I might, I couldn’t seem to bring the total number of holdings (TOD, Roth & Traditional IRAs) below the 15-17 number. Each held a unique “spot” inside a diversified portfolio. So when a “spark inside my brain” led me to the 10/10 idea, it seemed like a giant leap forward. Now, however, it has been suggested that only 4 holdings might achieve similar benefits!
Wonder of wonders. I am still processing this revelation!

@yogibearbull, I started a parallel discussion referencing the same article after your post here.
My apologies to yogi and readers.
Here's a link to that discussion/reader comments:
https://mutualfundobserver.com/discuss/discussion/62524/when-rebalancing-creates-higher-returns-and-when-it-doesn-t#latest

@Mona, even within categories, active manager styles vary, so it's OK to hold 1-2 active funds in the categories you hold. This isn't an issue with index funds.
I would be comfortable holding 25-75% in a fund.
Diversified Funds https://ybbpersonalfinance.proboards.com/thread/307/diversified-nondiversified-funds

Often recommended limit of 5% applies to individual stocks to reduce company specific risks. So, people holding only stocks (i.e. no funds) should have a portfolio of 20+ stocks.
Must funds are diversified, so they can be held at much higher levels. May be limit the sector funds to 5-10%.

@yogibearbull what higher levels do you have in mind for diversified mutual funds?

I posted on it a few days ago and highlighted,
"Morningstar's John Rekenthaler starts with a simple but unusual observation that if 2 assets have the same long-term (LT) TR, then rebalancing will definitely benefit the TR."
In all other cases, rebalancing hurts TR, but does control risk.
https://www.mutualfundobserver.com/discuss/discussion/62512/m-jr-on-rebalancing#latest"

Often recommended limit of 5% applies to individual stocks to reduce company specific risks. So, people holding only stocks (i.e. no funds) should have a portfolio of 20+ stocks.
Must funds are diversified, so they can be held at much higher levels. May be limit the sector funds to 5-10%.

Excellent @msf. Thank you. And @MikeM - “I approve of this message.” :)
The 4 fund portfolio @msf outlines seems workable. With the current 10% cash and 10% short-term bond positions, I’m already close to the hypothetical 25% cash his model suggests. I oversimplified the long bond position. It’s actually a corporate BBB grade CEF with 25% leverage. A bit of a “hot dog” that could possibly help offset a severe decline in equities (if accompanied by falling rates).
My commitment to the 2 bond funds is the weakest of the lot. If the CEF does well near term I’d move that into a more stable OEF or ETF of similar duration. I’d sell all / part of the short-term bond fund to add to equities in the event of a market sell-off. Don’t like to speculate on return, but the inherent risks in the portfolio wouldn’t be worth taking if it couldn’t best nominal cash returns by an average of 2 or 3 percentage points longer term.
Thanks for the P/V link. I haven’t played with it yet but surely will.

I put ten funds through Portfolio Visualizer to see how it would optimize such a portfolio.
Some of your categories are easy to understand. Others are not so well defined (and Lipper and M* can differ as well). I took my best shot and picked some suitable (or not so suitable) representatives:
Long/Short: Hull Tactical US HTUS and AQR Long/Short QLENX.
Arbitrage Income: JPMorgan Equity Premium Income JEPAX.
M* calls this "derivative income". Lipper call it "options arbitrage". I don't know whether covered calls were what you had in mind with arbitrage income. Perhaps you were thinking of merger arbitrage, e.g. MERFX. These are "event driven" funds according to both Lipper and M*.
The easy stuff (index funds where possible):
Cash: Blackrock Ultra Short ICSH - Portfolio Visualizer doesn't like to optimize with true cash
Balanced (domestic): Vanguard Balanced Index VBIAX
Balanced (global) : Vanguard Lifestrategy Moderate Growth VSMGX - a fund of index funds, 60/40 domestic/foreign, overlayed on a traditional 60/40 stock/bond allocation
Global Infrastructure: Lazard Global Listed Infrastructure GLIFX
IG Bond (5+ yr): Vanguard Total Bond Index VBTLX
IG Bond (1-3 yr): Vanguard Short-Term Bond Index VBIRX
Risk Premia: Permanent Portfolio PRPFX
I optimized by asking for the greatest annual return that would still allow max drawdown to be kept under 10%.
Anything with bonds drops out. Arbitrage income (at least as I've used it) and infrastructure also drop out. Cash serves as ballast - the lower the desired volatility, the greater the cash allocation. When shooting for a 10% drawdown, cash also drops out - that ballast isn't needed.
In short, with these ten funds as your potential universe, only four funds are needed - the two long/short funds, PRPFX, and cash if ballast is required.
With such a simple portfolio, it's not hard to read the efficient frontier graph in the Portfolio Visualizer output.

• Until you get up to an 11% std dev (i.e. if you want less volatile portfolios), little HTUS is used. Allow more volatility, and the amount of HTUS shoots up quickly.
• The optimal portfolio starts with 100% cash for 0% volatility, and cash decreases along a straight line until the allowed volatility reaches 11%. At that point, the cash allocation is down to zero.
• The other two funds, QLENX and PRPFX together make up the remainder of the portfolio.

Here's the PV link. You can play with it yourself to swap out funds, adjust objectives, etc.
If one wants to maximize Sharpe ratio, one gets a lower return than optimizing for 10% max drawdown. But that comes with much reduced volatility. To achieve this low volatility result, one has to use cash for nearly half the portfolio.

John Rekenthaler articles makes a few important points:

while value and growth stocks might seem the unlikeliest rebalancing opportunity, as they are subsegments of the same investment universe, their fortunes have substantially diverged. In 2022, the Morningstar US Growth Index shed 36.7% of its value, while the US Value index lost less than 1.0%. That was the opportunity that rebalancing seized

At present, do we all have a favorite LCV Fund that we can reallocate LCG outsized gains?

in this universe, as opposed to the alternative world of hypothetical studies, assets don’t regularly record the same long-term returns. Which begs the question: Over that same 9.5-year period, using the same portfolio assumptions, what was the actual benefit of rebalancing?
Not much, as it turns out.

I try to discipline myself to "milk" the cow when I am blessed with a 20% + gain (YTD) in my portfolio...where to put it is the more difficult question.

Swapping between growth and value stocks remained helpful. Otherwise, though, rebalancing reduced the portfolios’ returns.

The rebalanced portfolio may forgo some gains, but it will not surrender its relative safety. Consequently, the risk/return trade-off remains intact. That said, there may, in fact, be a trade-off, rather than an unambiguous benefit. Rebalancing can provide a free lunch—but, as this column has shown, it does not always do so.

when-rebalancing-creates-higher-returns-and-when-it-doesnt?

I have the answer @hank. I just checked my Roth, 401k and T IRA accounts, which I try to manage as one portfolio, and the answer to your question is 15. 16 if you add cash that I group as treasuries, CDs and MM. No more, no less should be used!
I'm being facetious. That just happens to be where I'm at. As you know it is totally up to the individuals comfort level. I try to follow a rule though that says less than 5%, why bother... which I regularly break. But that's just me.

I turn 70 this month, but have heirs in mind. I suppose I'm more aggressive than others would be at my age. Wife is almost 20 years younger. One grown son.
I don't want to add any more positions. Including "cash," I'm already at 11. Market right now is overbought, so I'm growing cash.
I want my funds to give me diversification. More and more, dividends matter to me. I want at least a 3% yield. Some of my stuff offers quite a bit higher yield. My single stocks (there are 4) give me sector exposure:
1) Regional bank. 5.4% of total.
2) Telecom, media. 1.59% of total.
3) oil/gas midstream. 5.49% of total.
4) oil/gas pipe manufacturer. 1.06% of total.
...So, the single stocks are at about 13% of total.
"K.I.S.S." it. After transferring out of BRUFX, we put my wife's IRA $$$ into a conservative allocation fund: WBALX.
In my own IRA, there are 4 funds. Two are junk bonds. I do keep a sharp eye on how they behave, but they both are the most un-volatile holdings I own right now.
There is a tiny amount in the Fallen Angels ETF. FALN.
Cash 4
Domestic stocks 47
Foreign stocks 6
Bonds 40
"other" 3

“To each his own, it’s all unknown.” Bob Dylan. 1970. Hank. You are an experienced investor and your allocation is what’s right for you at this stage of your life. I advise my affluent youngest daughter with her allocation and I always have to remind myself that asset allocation is so different for a 33 year old compared to a 75 year old. she has four funds and so do I but the mix is wildly different. Age matters.

This has been tossed around & debated before. But it’s Sunday and the board is a bit slow. We all learn / evolve as investors. In addition, aging may affect our approach. My approach today is different than 5, 10, 20 years ago. Yours probably is too. About a year ago I simplified things by moving to a 10 fund equally weighted portfolio (with regular rebalancing). I expect it to be diversified enough to experience down years no greater than 7-10% or bear market losses no greater than 20%. It hasn’t yet been tested. I add / reduce risk as desired by swapping out funds. When using individual stocks, 3 combined typically count as one 10% weighting. Right now I’m underweight equities at 37% of portfolio. A more normal weighting would be 40-45%.
- 10% Cash / cash alts
- 10% Balanced (domestic)
- 10% Balanced (global)
- 10% Long-short (fund A)
- 10% Long-short (fund B)
-10% Global infrastructure
- 10% Arbitrage income
- 10% Investment grade bond (5+ year duration)
- 10% Investment grade bond (1-3 year duration)
- 10% Risk premia (PRPFX)
That comes to 10 positions. I can add / reduce risk by exiting one position and substituting a more aggressive or conservative one. The advantage of 10 as I see it is simplicity. I’ve considered cutting back to 8 or even 5. If 8 positions, each would count 12.5%. If 5, each would equal 20%.
PS - Feel free to criticize this. It won’t deter me, but might be enlightening or even amusing. Has anyone tried something similar?

Yes, as a Long/Short Equity Product, VELIX is worth considering. It's a 3.8 year-old fund with only $67M in AUM. Its LT APR is 15.6%. It does well on the downside (202201-202209) beating the SP 500 by 10.4%; however, Immediately afterward (202210-202406), it lagged by -10.8. Versus the SP 500, its 3/yr. performance is -2.1%; its 1/yr is -7.8% ((Source MFO Premium). It's not a GO, which as you may know, has a high bar.) When I wrote the profile, the fund was 80% Long. I'm waiting for a response from the co-manager if that's still accurate. Typically it is long. Attached is the fund's 2Q commentary from Ric Dillon, CIO and CEO. Let me know if you have further questions or concerns.
https://funddocs.filepoint.com/vela/?file=VELA-LargeCap-Commentary.pdf