Is there any way to determine an exact level of risk when investing in a mutual fund?

for example, comparing two funds to see which is riskier.

A very simple risk measure is the fund's standard deviation, which is essentially the same thing as volatility of returns. If you're not familiar with statistics too much a simple way to compute it would be to request daily/weekly/monthly data, import your data set into an excel spreadsheet and use the stdev function to calculate it.

With the standard deviation you could also use the Sharpe Ratio, I'll attach links below that will talk about both, this ratio will essentially tell you if the returns you see on the mutual fund are by excess standard deviation (luck) or actually by skill.

Services like morningstar may give you this data, however I'm not entirely sure. For the most part though, I would just calculate it myself, because sometimes the data they provide is wrong.

EDIT:

I noticed some replies above, Beta would be a measure of systematic risk (inherent market risk). Standard Devation is a measure of individual risk.

yes..check the BETA of the fund

something like the S&P index would have a beta of "1".

If a fund has a greater beta then 1 then it is more risky then the S&P index Less then 1 is less risky.

It depends on the stocks and bond. More bonds usually means less risky but less return

Okay, so far we have heard the Beta value and the Standard Deviation. I agree with both. But just to make things more complicated, I'm kicking it up a notch.

Information Ratio.

This is not always available, but it is very handy. It basically measures the difference between risk and reward. So by looking at a fund manager's information ratio, you can determine how many units of risk you would have to "take" to get a certain number of "units" of return.

But I don't think you can look at either the beta or the standard deviations by themselves and get a good idea. If the fund does not have an appropriate benchmark, then the beta won't be worth anything.

standard deviation (square root of variance) measures risk. The variance includes a measurement of probability and therefore you cannot measure exact levels of risk.

Beta addresses anticipated market returns, not risk.