Practice Problems for Reading 26, Q 10

[B_C]

Refer to CFAI L3 textbook Vol 3, Practice Problems for Reading 26, Q 10. P.334
The book suggests that efficient frontier reflecting the true return parameters must be superior to (lie above) conventional efficient frontier and resampled efficient frontier because the latter two has estimation errors.
I don’t understand why estimation errors would make conventional efficient frontier and resampled efficient frontier inferior to efficient frontier without estimation errors?
Could someone please explain this ?

 

[elcfa]

One of the reasons is that sampled frontier will always overestimate standard deviation of the TRUE frontier, thus also lie to the right of the true frontier (thus under it).
Remember from level I, when you don’t know the real population standard deviation and have to estimate it from sampled data.
The distribution of sampled data will take on t-distribution shape which is fatter (wider than true distribution which is normal distribution). As n approaching infinity, the sampled distribution resembles more and more normal distribution and the stddev of sampled data tightens (i.e., stddev lowers).
For the same reason, the sampled stddev is higher than real stddev for each of the portfolio and thus for the whole frontier, so the sample frontier will also be to the right of the true frontier (or below it)

 

[B_C]

Thanks elcfa!