NO.PZ2020010303000013
问题如下:
If the kurtosis of some returns on a small-cap stock portfolio was 6, what would the degrees of freedom parameter be if they were generated by a generalized Student’s ? What if the kurtosis was 9?
选项:
解释:
In a Student’s t, the kurtosis depends only on the degree of freedom and is k = 3(v-2)/( v-4).
This can be solved so that k(v - 4) = 3(v - 2) so that kv - 4k = 3v - 6 and kv - 3v = 4k - 6.
Finally, solving for v, v =(4k-6)/ (k-3)
Plugging in v =(24-6)/(6-3)=18/3=6 and v =(36-6)/ (9-3)= 5.
The degree of freedom is v-1.
The kurtosis falls rapidly as v grows.
For example, if v = 12 then k = 3.75, which is only slightly higher than the kurtosis of a normal (3).
plugging in 那一行里的计算是什么意思?