Читать книгу Alternative Investments - Black Keith H. - Страница 32

As noted, mean-variance optimizers can be error maximizers. Therefore, erroneous forecasts of the mean, variance, and covariance can result in extreme portfolio weights, with a resulting portfolio concentration in a few assets with estimated high means and estimated low volatilities. Most institutions view such concentrated positions as unacceptable speculation on the validity of the forecasted mean and volatility.

Although higher frequency of observed data can improve the accuracy of the estimated variance and covariance, for most alternative assets, high-frequency data is not available. More important, the assets whose prices cannot be observed with high frequency tend to be illiquid, and the reported quarterly returns are based on appraisals such as those used in real estate and private equity. These prices tend to be smoothed and therefore can substantially understate the variance and covariance of returns. Because volatility and covariance are key inputs in the optimization process, asset classes with low estimated correlation and volatility receive relatively large weights in the optimal portfolio. If smoothing has caused the reported volatility and correlation of an asset to substantially underestimate the true volatility, then a traditional mean-variance optimizer would overweight the asset. In this case, and to prevent extremely large allocations to assets with smoothed returns, the time series of returns may be unsmoothed, as discussed in Chapter 15, before being added to the optimization routine. But unsmoothing is imperfect, and other issues with accurately forecasting volatility and correlation remain.