CME reading 16, data scaling

[AndrewWheeler87]

Can someone provide any insight into the mechanics of the adjustments to the apprasisal based volatility that are provided in the text?
How might an analyst address the biases resulting from smoothed data? To continue with the case of venture capital return data, one approach would be to rescale the reported data so that dispersion is increased but the mean is unchanged. The point is that the larger the rescaling, the larger the number of negative quarterly returns, because the frequency distribution is centered in the same place but there is more probability in the tails as dispersion is larger. For example:

• The venture returns rescaled by a factor of 1.4 provide 18 negative quarters—that is, as many as the S&P 500. The estimated standard deviation of the rescaled data is 13 percent.
• The venture returns rescaled by a factor of 4.1 provide 36 negative quarters, which is twice as many as the S&P 500. The estimated standard deviation of the rescaled data is 37 percent.
• The venture returns rescaled by a factor of 4.4 provide 38 negative quarters, 2.1 times as many as the S&P 500. The estimated standard deviation of the rescaled data is 40 percent.

Using these data in conjunction with other analyses, one might propose risks of 43 percent for early-stage venture capital, 34 percent for late-stage venture capital, 29 percent for leveraged buyouts (largely debt-financed purchases of established companies), and 20 percent for distressed debt (the debt of companies that are under financial distress or in or near bankruptcy).5
The key is to model the risks of alternative investments as if they were frequently traded, focusing not on statistical observations but on the underlying fundamental and economic drivers of returns.
How are these scaling factors being derived and do they correspond to the number of negative returns listed?
Thanks,
Andrew

 

[ink]

The reading mentions that smoothed data has a smaller variance to it, so you resclae the returns, you are esentially affecting the value of the SD of those returns. The higher SD, the more likely you are to have lower or negative returns. For instance, if mean return is 10, and SD can either be 5 or 10, then if SD is 5, you have only about 2% of having negative returns (assuming that you have a normal distribution of returns). If SD is 10, then you have 14% chance of having negative returns.
In example 7, it is mentinoned that S&P 500, had 18 negative quarters, and had an SD of 16.1. The smoothed returns from venture capital had only 6 negative quarters, and an SD 9.1. Obviously it is much more risky to invest in ventures than in an intex traking S&P, so you cant use the venture SD as a measure of risk. The question then is by how much should the return values for the smoothed venture data be scaled up in order to find an adjusted value for risk? If you rescale by 1.4, the venture SD is still smaller than S&P 500 SD, so you have to use a higher value for the rescaling factor.