Less risk, more reward

Private equity investors have a vast universe of investment opportunities ranging from angel financing of tiny start-up companies to leveraged buyouts of large international corporations. Additionally, investors nowadays also have the freedom to invest into primary funds, to buy secondary interests in existing funds or to invest directly into companies. Investors can build up global private equity programs or they can focus on certain regions. As the universe of investment opportunities is highly diverse, the asset allocation has a profound impact both on the risk and the return of a private equity portfolio.

More than 50 years ago, Harry Markowitz, Nobel Prize co-recipient for Modern Portfolio Theory and the Capital Asset Pricing Model, proposed the mean-variance framework for portfolio optimization, which is considered to be a major milestone of modern finance theory. In this model, the optimal portfolio maximizes the expected return for a given risk measured through volatility. While providing the first quantitative asset allocation framework, the resulting optimal portfolios are subject to the following drawbacks:

They are generally concentrated in a small number of assets.

The optimal solution is highly sensitive to changes of the input parameters.

For private equity, there is an additional shortcoming: it does not allow for rebalancing the portfolio in a cheap and simple way. Therefore, the asset allocation process that optimizes the portfolio has to be stable over time in the sense that two successive optimal allocations should not differ drastically. This property is often referred to as robustness…

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