# CFAI V3: Pg 17 (Example 8)

Need some help here!! What is meant by rescaling in this example? If I am looking at historical data it implies that I have the data. I am not generating data based on probability distribution. How did the quarters with negative returns increased to 18 from 6 (in Example 7) after rescaling by a factor of 1.4? My understanding was that these were quarterly returns based on change over previous quarters. Are these negative returns based on quarterly return average over the 19 year period i.e. the returns were lower than the average in the 19 yr period? I suppose I am lost. Any help is appreciated. Thanks in advance!!

Any responses?

Can’t answer the question w/out the books. Need more details.

Gags Wrote: ------------------------------------------------------- > Need some help here!! > > What is meant by rescaling in this example? If I > am looking at historical data it implies that I > have the data. I am not generating data based on > probability distribution. Rescaling means that historical data is rescaled(what the word means) so that dispersion is increased but keeping the mans the same. Fat tails. You are not generating the data, you have the data, just modifying it. > > How did the quarters with negative returns > increased to 18 from 6 (in Example 7) after > rescaling by a factor of 1.4? My understanding was > that these were quarterly returns based on change > over previous quarters. Are these negative returns > based on quarterly return average over the 19 year > period i.e. the returns were lower than the > average in the 19 yr period? I suppose I am lost. > Any help is appreciated. Thanks in advance!! All you have to know here is that smoothed data has lower standard deviation.

Checked the forum after a long long time. Thanks for the response derswap07. However, if I have to implement this in real life then how does it work. If I scale all the values by a factor of 1.4 my mean would change. So if I have to keep mean the same but just rescale the overall data by 1.4, individual return values will have to be modified differently. Is there some kind of methodology or simulation that needs to be carried out and if it is result of a random process will this always lead to 18 instances of negative returns or is this just the number CFAI got? Thanks!!

the goal is do un-do the smoothing effect. trying to increase variance while maintaining the other statistical properties of the data. if i remember correctly, by looking at quarterly (or was it annual) return data for private equity it’s statistical properties make it appear to be less risky than public equities (using more frequent data) soley because of a smoothing effect. I believe scaling by 1.4 made its st. dev. characteristics similar to or slightly higher than public equities… which we would believe to be the case.

Gags, So, your questions are : Why rescale by 1.4 and how the negative returns increased to 18 from 6 (in Example 7) ? These are really confusing ! Maybe you shall ask CFAI. Sometime, the statements in the readings are vague and some statements even can be misleading.