My recommendation is to focus on improving estimates based on available data. For example, the returns of these assets classes tend to exhibit very strong serial correlations as a result of smoothing, which dampen observed volatilities. You can add a ton of value to the investment process by de-smoothing these returns and estimate risk thereafter.
I'm inclined to believe that this is more valuable than extending the returns – it's hard to gauge what kind of biases we might introduce. And if adding the extra returns doesn't change the results meaningfully (likely because we're imposing our will based on observable data), there's no value in adding them anyways.
That being said, we do extend these time series in a lot of portfolio construction research, mostly when we're studying diversification benefits (e.g., how these assets interact with others in different economic environments):
- For private equity, it's common practice to use something as simple as the returns of Russell 2000 scaled by 1.1 to 1.2, plus an in-house alpha assumption.
- Private real estate can be proxied by house prices, which already go back to the late 1800s.
- REITs behaved more like equities in the early days and can be proxied by equity benchmarks, or a blend of equities and house prices.
- Hedge fund is much more challenging. Insofar that your hedge fund portfolio is truly market neutral, the "replication" can be as simple as cash + an alpha assumption. Otherwise, you can regress either the HFRI or the CS indices against equities, bonds, credit spreads, etc. and go from there. If you're really adventurous, you can replicate some of the popular strategies (trend following, carry, etc.) and create a blend of them. Most banks also offer hedge fund replication products and they provide very detailed documentation on how they do it (mostly just simple regressions), which you can reference for ideas.