PEG ratio - does not factor into account risk

The text says the PEG ratio (as does the P/E ratio). Since the P/E ratio is one component of the PEG ration, shouldn’t the PEG ratio already incorporate risk into its valuation of assets since it already incorporates the P/E ratio (in the numerator of the PEG ratio)?

I am confused at this point. Here is my explanation

P/E takes risk into account by considering required rate of return. And P/E is widely accepted.

In English, " account for " means give a satisfactory explanation.

PEG ratio certainly explains a part of the risk when P/E is calculated.

But by using G as denominator, we emphasize more on the aspect of growth, relative=ly overlooked the Risk.

Here is the thing. CFAI thinks that Growth and Risk are two different things. (For example, Higher Growth leads to Higher P/E, but Higher Risk leads to Lower P/E, of course, ceteris paribus.) So the PEG ratio considers Growth, but not Risk. The Curriculum also says this.

As per my understanding, while making investment decisions we use the P/E ratio of one company in comparison to the P/E of another company or industry. if a company has a lower P/E in comparison to its benchmark, it is not always necessary that the company is undervalued, its P/E could be low because the subject company might have a higher risk and lower growth. The growth-related issue is incorporated in the PEG ratio, the risk-related issues will still be there and we really have to compare the subject company’s risk with other peer companies.