How do you compare beta and standard deviation?

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Bradleyz

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Lets say you wanted to get the unsystematic risk. You get standard deviation of .15 and beta =1.4.
I know total risk = standard deviation = beta + unsystematic risk
Obviously you would do 15-1.4 to get the unsystematic risk.
So what kind of units is beta in? Is it a percent or how can you compare it to percents?
 
Hi Bradleyz,
Standard deviation will be a measure of risk when you view an asset in isolation. Beta will be the measure of risk of an asset for a well diversified portfolio.
IMHO, it is not true that standard deviation = beta + unsystematic risk
The reason is that beta is the slope of the line of best fit when you regress asset return on an index return. Since beta is a slope, it does not have any unit, it is only a number. Beta tells you whether the asset is more or less volatile than the index and standard deviation tells you how spread out the return for the asset is.
Whenever you do any regression with only one independent variable (as will be the case for this beta computation), the distance between any single return and the line of best fit will be an error term, or in this case, unsystematic risk. Note that in order to do this linear regression you need values for both the dependent and independent variable. In order to compute a standard deviation, you need returns only for that one asset (and no index, for example).
Both standard deviation and beta are measures of risk but they cannot be added or subtracted from each other.
 
Here is the question I’m looking at. You solve for the standard deviation and beta for 2 securities. It asks you which stock has the most systematic risk, the most unsystematic risk, and the most total risk.
The beta for 1st one: 3
Standard deviation first one: 15%
Beta for 2nd one: .75
Standard deviation for 2nd one: 25%
In this case do you simply compare the betas for systematic risk and standard deviation for total risk? How would you figure out non systematic risk?
 
I would say (and I can be totally wrong):
Asset 1 has more systematic risk (higher beta), Asset 2 has more unsystematic risk as well as higher total risk. The rationale is that even though asset 2 has lower beta, it has a higher standard deviation. This means that this excess volatility around its mean must be explained by a higher level of unsystematic risk. Finally, asset 2 has higher total risk as many authors define total risk to be the level of standard deviation (and it is higher for asset 2).
If you have the answer, could you please let me know. Now I am getting curious!
 
Hockeytime, nice explanations. I am now passing through statistics and in my opinion you are totally right.
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I have the answer in front of me and it essential says the same thing you did. However, I’m still wondering if there is any way to quantify the non-systematic risk. The answer doesn’t subtract diversifiable from total risk or make any mention of giving a number to represent the unsystematic risk. So while I definitely agree that stock 1 has more systematic risk (as measured by beta), exactly how much unsystematic risk does it have?
 
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