I read an example on L1 where they calculated the I/Y of a semi-annual bond and then to get to the annualized YTM they simply double the I/Y.
However, I would think it is more correct to square (compounding) the I/Y instead of just doubling it.
I mean that the effective yield should be a better measure of return. Do you agree?
Look at Quant: there are all sorts of measures of return:
Is any one of those a better measure of return than all of the others? Not necessarily. It depends on what you plan to do with the measure you calculate.
Your specific question is asking if EAY is a better measure of return than BEY. No, it isn’t necessarily better, nor is it necessarily worse. It’s simply different.
I understand your point.
But, let me clarify what I meant.
The curriculum teaches us that we should generally “compound” i.e. that the return of 10% for 5 years is not 50%, but it is instead 1.1^5 - 1 = 61%.
So I don’t see why it kind of detracts from this general guideline and not mention that it would be more “appropriate” to compound the semi-annual return to get to the annual return vs. simply doubling the semi-annual return. I haven’t seen it do that. Would you agree with that? Obviously there are many different measures of return but I thought the above calculation more closely followed the “compounding” principle.
How do you define “appropriate”?
Everyone in the bond world quotes yields as BEY. Therefore, it’s “appropriate” to teach candidates how to understand what bond managers are saying, and to be able to talk their language.
Everyone also knows that BEY isn’t an effective yield, and that if you want to know how much your portfolio will be worth in 5 years you need to use an effective yield. But talking about EAY when everyone else in the room is talking about BEY will be harmful, and can lead to stupid, costly errors.
(1+ semi-annual result)2 - 1 = effective annual rate
semi-annual result * 2 = nominal rate compounded semi-annually
As long as the rates are used in a consistent manner, PV and FV will be the same under either rate. 
The question is for BEY specifically and not the EAY calculation.
As prompted by the question, BEY is not EAY basis.
BEY is simply a convention (using 365 days and a periodicity of 2) as discussed in down-to-earth explanation of @S2000magician s2000magician.
@breadmaker: what you labeled as “nominal rate compounded semiannually” should simply be annualised semiannual rate as
(1) there is no compounding in semiannual x 2 and
(2) the other formula (1+semiannual)^2 is also nominal.
With all due respect, this is an effective rate (assuming that by “semiannual” you mean the semiannual effective rate).
Technically, it’s a nominal rate compounded annually (once per year), but nobody would ever refer to it as a nominal rate.
Nominal is contrasted with real (nominal = real rate + inflation) and that is the only usage in finance, which I meant.
“Technically, it’s a nominal rate compounded annually (once per year)”
What is it in “it’s”? The term nominal?
If you mean nominal as the rate with periodicity of 1 then as you said no one refers to it as such.
There is no such thing or usage as semiannual effective rate (unless you
convert periodicity to 2 from a lower compounding frequency say monthly or daily) so I don’t mean it this way.
In (1+semiannual)^2, semiannual is the rate per period in BEY (annual rate with periodicity = 2). There is no other technical distinction or refinement.
Plus there are some people who adamantly leave P/Y=C/Y=1 on their BAIIs. They have to use 2 * semi-annual rate to get to the BEY for bond questions. 
Again, with all due respect, that is not the only usage in finance.
Nominal (sometimes called stated) is also contrasted with effective. An effective interest rate includes the effects of compounding; a nominal (stated) interested rate does not.
If you invest $100 for one year at an effective (annual) rate of 6%, at the end of the year you will have $106 in your account.
If you invest $100 for one year at a nominal (annual) rate of 6% compounded semiannually, at the end of the year you will have $106.09 in your account.
Of course there is. You can have an effective rate for any length of time. If you can compound it, it’s an effective rate.
In my second example, above, the semiannual effective rate is 3% (= 6% Ă· 2).