An approach to determining the desired allocation to the alternative asset classes is to make the initial asset allocation decision using only the broad, liquid asset classes and do a second iteration of the asset allocation exercise incorporating alternative assets.

There are three primary approaches that investors use to approach this second iteration.

- Monte Carlo simulation.
- Mean-variance optimization.
- Risk factor based optimization.

Modeling the risk and return properties of alternative investments is challenging. Because asset valuations for many alternative investments are based on appraisals, returns data are likely to be artificially smoothed and are often stale. As a result, using these data without adjustment would underestimate risk. Testing returns data for serial correlation is a suggested method for detecting this smoothing effect. If serial correlation is present, statistical techniques exist that can be used to unsmooth the data.

The distribution of returns is also known to be non-normal, exhibiting skew and excess kurtosis to a greater extent than traditional asset classes. Here, too, the data can be adjusted with statistical methods (such as stochastic volatility, regime switching, or extreme value theory) or by using observed returns instead of an assumed normal distribution of returns. A further limitation is the relatively short history of alternative investments, which may result in small-sample and time-period biases.

One method for modeling a distribution with fat tails (positive excess kurtosis) is to define risk and return properties for two or more distinct market environments, for example, a normal period and a high-volatility period. Returns for each of these can be described with a normal distribution with its own assumed mean and variance. Combining the distributions, using an assumed probability of each environment occurring, results in a non-normal distribution.

**Monte Carlo simulation **can be a very useful tool in asset allocation to alternative investments.

- Decide between asset class returns or risk factors as the variables to be simulated.
- Define how the model should behave statistically, for example by accounting for properties like mean reversion, fat-tailed distributions, or unstable correlations.
- If the model is based on risk factors, translate them to asset class returns.
- Use the resulting asset class return scenarios to develop meaningful outputs, such as the probability of a shortfall to a portfolio’s required or target rate of return.

When using **mean-variance optimization** with alternative investments, the results may produce an excessive allocation to this asset class, particularly to illiquid investments such as private equity, especially when the data are not properly adjusted for smoothed returns. An optimization model may be designed to constrain the allocation to alternative investments (or any asset class) to be within a minimum and maximum percentage, or to limit overall volatility or downside risk.

Investors should consider the asset allocations suggested by an optimization model to be a guideline rather than a prescription. They must consider the allocation in the context of their objectives and constraints, such as their liquidity requirements. They must also be aware of the limitations of mean-variance optimization. For example, small changes in the inputs may generate significant changes in optimal asset allocations.

**Risk factor based optimization** is similar to MVO, but instead of modeling asset classes by their return and risk characteristics, the investor models risk factors and factor return expectations. Exposures to risk factors are optimized with respect to an overall risk budget. As with mean-variance optimization, constraints can be included in the model. In this case, the constraints are limits on specific risk factor exposures.

A risk factor based approach requires the additional step of translating the optimized risk exposures to an asset allocation. For example, both public and private equity provide exposure to economic growth risk, but the allocation to each depends on the desired exposure to liquidity risk.

One of the limitations of this approach is that asset classes’ return sensitivity to some risk factor exposures might not be stable over time. Another is that correlations among risk factors may behave like correlations among asset class returns and increase during periods of financial stress.