Wrote up a long response to a forum post on portfolio construction and thought I would share.

It was in response to a Monte Carlo testing whether portfolio diversification actually improves returns or just smooths the ride.

Basic Setup: 25-year horizon, $1M starting balance, $100k/year in contributions.

Two scenarios:

1. 100% SPY vs.

2. 50% SPY / 25% Diversifier A / 25% Diversifier B

Assumptions: identical expected returns (10%) and vol (15%) across all three asset classes.

- SPY/Diversifier A correlation 0.5.

- SPY/Diversifier B correlation 0.

New contributions used for rebalancing (no forced sales since the diversifiers they used were illiquid privates). 1,000 simulations.

Results:

- Mean ending value: virtually identical (~$25M)

- Median: $23.1M diversified vs $21.5M SPY-only

- Worst case: $8.1M vs $4.0M

- Diversified portfolio outperformed in ~75% of scenarios

This is exactly what diversification should produce: a tighter distribution. Same mean, higher median, much better downside. That's the rebalancing premium working as advertised.

If you ran a naive optimization on these inputs, it would push more into the diversifiers (e.g. 33/33/33), not less. More rebalancing would also help quite a bit, as would more asset classes. So, if anything, the model is understating the case for diversification.

I have probably had some version of this conversation a few hundred times with investors and the two most common concerns are:

1. Tracking Error - You achieve similar performance in the long run but on a year-to-year basis you would expect material tracking error. This can be hard to explain to 'stakeholders' (AKA spouses, etc) and can also cause people to give up at the worst possible time.

2. Lower Returns - Some version of "I hate sacrificing even 1%/year on a 40 year horizon in the name of reduced volatility."

The tracking error is unavoidable and one of the reasons diversified strategies just aren't popular among most investors.

The solution to lower returns is to hold a more diversified portfolio — 33/33/33 (or even more aggressive on the diversifiers) and modestly lever it to equity-like volatility. If you ran 20 or 30% leverage on this scenario and allowed for full rebalancing, I suspect it would get materially better.

Practically, the problem is that most low-correlation strategies have lower volatility than equities so a diversified portfolio is under-risked relative to equities (hence the performance drag).

If you're picking one alternative to model in more depth, I'd use trend following. It's got the longest track record of being genuinely diversifying to equities and it's liquid, cheap to implement with a deep literature. Add trend following to the mix, lever it to historical equity volatility, and I am almost sure the distribution looks much better.

This is where the conversation usually dies, because people hear "leverage" and pattern-match to 3x MicroStrategy or LTCM.

In my opinion, there's a real difference between:

- Levering an undiversified high-vol portfolio (AKA gambling, WSB, etc.)

- Modestly levering a broadly diversified portfolio — global equities, broad fixed income, broad commodities, and some diversifying alts.

There's a decent number of institutions that get this and risk parity, all-weather, and similar strategies are more popular there than at the retail level.

Ultimately, when talking to people I recommend either:

1. If it's worth it to them, get into the history and math of diversification and historical asset returns enough to be comfortable doing something with modest leverage and holding through multi-year periods of underperformance relative to SPY. Expected Returns by Antti Ilmanen (amazon.com/Expected-Ret…) is a nice (albeit dense) starting point that surveys a lot of the literature and return histories of various asset classes.

2. Just do globally diversified equity beta (or SPY if they insist on US only) as that makes sense as the default for highest expected return from a single asset class. A modest private allocation alongside is fine if you have access to good managers (along with all the basic sequencing risk considerations around retirement and other flows).

I think many privates like litigation finance are interesting and worth inclusion in modest allocations, but the historical data is thin and the persistence assumption is doing a lot of work. The current trend towards seeking higher returns via illiquid privates seems to me like it increases the risk of a worst-of-all-worlds scenario with lower returns / higher drawdowns / less liquidity.

I personally need quite a bit of juice to give up daily liquidity and decades of return data, and am more apt to look at lower-returning but more diversifying alternatives (Carry, Trend, etc.) where the persistence seems more likely. (This is not to mention tax efficiency concerns, which are also material in many high-return privates.)

If you start from the perspective of maximizing what I like to call "returns you can eat" long-term, risk-adjusted, after-tax, real return, then it is hard to not end up somewhere in the universe of a broadly diversified and modestly leveraged portfolio of stocks, bonds, commodities, and some diversifying alts like trend and carry. There are many different and consequential implementation details within that realm, but those are the broad strokes.

Other approaches reflect investors' beliefs about their ability to successfully engage in market timing or generate alpha (which is possible but much harder than most believe IMO!). Or, they reflect preferences for other characteristics, with the most common being preferences for cash flow over total return, leverage aversion, and discounting inflation/tax implications.

These are all perfectly fine preferences to have, but are deviations from "returns you can eat."