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Private Equity and Mean-Variance Optimizaiton

Mar 27, 2013 Marc Odo

Occasionally we will get questions at Zephyr Associates about the viability of including private equity and/or venture capital (PE/VC) into a mean-variance optimization (MVO).  Ultimately it will be up to you whether or not you think it makes sense, but I am of the opinion that a simple, “naïve” allocation is a better approach than trying to optimize PE/VC into the efficient frontier.

Much of this has to do with the nature of the asset class itself.  Data for private equity is hard to come by, and what you cannot measure you cannot model.

1. Many private equity partnerships have no reason or obligation to report their numbers to anyone, making the creation of indices or category averages quite difficult.

2. Returns in PE/VC are typically calculated on an internal rate-of-return (IRR) basis, whereas other asset classes calculate on a time-weighted return (TWR) basis.  The two methods are not very compatible.

3. Numbers that are reported for PE/VC are often subject to revision, so a year or two later the indices could still be changing.

4. Private equity returns are often impacted by pricing lags or subjective valuations.  The ripple effect of this is that standard deviations are dampened and correlations lower than if PE was priced in real-time.  Seeing as how standard deviation and correlations are two of the three inputs required in a mean-variance optimization, it follows that PE will be overly favored unless adjustments are made to the inputs.

All of these caveats are valid, but are a bit technical in nature.  The main reason why I believe PE/VC should be excluded from MVO is more top-down and macro.

Let’s step back and ask ourselves, “What is the point of MVO?”  The idea of MVO is build a set of optimal portfolios along the risk-return horizon and then compare your existing portfolio with the alternatives.  Is your current portfolio on pace to reach your goals?  Are there better portfolios out there?  Do we need to make some marginal changes?

The problem with handing over a chuck of money to a private equity or venture capital fund is that once those assets are committed, they are locked-up.  One can’t easily revisit their asset allocation once a quarter and make allocation shifts in or out of PE/VC based on changing expectations.  I’ll concede that marginal asset allocation changes can be made with re-investing of PE/VC dollars, but by and large it’s difficult to actually implement reallocations to PE/VC once that money has been committed.

Therefore I find myself in the camp of those who recommend a “naïve” allocation to PE/VC.  One should simply set aside a portion of their assets for PE/VC and not try to model it within Markowitz’s efficient frontier.  Of course if one has the money it makes sense to diversify along the J-curve by investing in different vintage years, but that discussion is outside of the scope of this post.  More information can be found in Thomas Meyer and Pierre-Yves Mathonet’s book “Beyond The J-Curve”.

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