Actually, I think you're wrong on both counts:
It doesn't tell anything about the rate of growth
Sure it does - you just take your periodic rate of return and adjust it to an annual rate of return using the following formula:
Say over 6 months your account has grown 5%, meaning your account is worth 105% of it's original value. Your annual rate of return would assume that you earn another 5% over the next 6 month, so your account will be worth another 105% , os at the end of one year your value will be
(1.05 * 1.05) = 1.1025, which means you have a 10.25% annual return.
More generally, you can convert your return
R over any time period
T (as a number of years) to an annual return
r using the formula
r = (1 + R)^(1/T)
It is very susceptible to day to day market noise
No, the day-to-day noise evens out. Sure if you have a good or bad day then it will skew the return a bit for that day, but if your rate of return over the past 6 months is 5%, then your annualized rate of return will be calculated using the same formula above. Over the effect of day-to-day changes will be miniscule.
What kind of metrics do you look at, while analyzing the health of your stock market investments?
I compare it to a benchmark that represents my risk tolerance. For me, since I'm heavy in equities, the S&P 500 is a decent benchmark to compare myself against.
A second measure would be to compare your risk (variability of daily changes) to the same benchmark. That's more complicated since it involves calculating the daily return of your portfolio and the benchmark, but my brokerage site does that for me. If you have a less risky portfolio, you can expect lower returns, and if you want more returns you can go with slightly riskier investments. The worst case is a risky portfolio with below-average returns over the long run.