Systematic Variance v/s Systematic risk

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Ankit Sharma

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I have a question which confused me.
1. The sum of an asset’s systematic variance and its nonsystematic variance of returns is equal to the asset’s
  • beta.
  • total risk.
  • total variance.
I have given answer as total risk, but the solution says that it is total variance. Dont we use the word varience and Risk interchangebly , If there is any diference can you please point me out .
2. The other doubt is in one of the question we have used Negative Beta , how can a negative beta be possible, It is the measure of systematic risk, how can risk be negative. The last possible value is 0 for risk free asset, but the Ciriculum claims that insurance companies can have negative beta, Is that so?
 
Total risk is associated with standard deviation in this conext.
Additionally, variances are additive while standard deviations aren’t. (Therefore, total risk (standard deviation) can’t be the answer).
Negative beta implies that the asset’s returns tend to move in opposite directions of the chosen index’s return (on average)– the correlation of the two returns is negative. This is entirely possible. The systematic risk is judged by the magnitude of beta, not necessarily the direction.
 
leocfahelper wrote:
Ankit,
I have made a video that explains how to derive variance from CAPM and what the curriculum means when it says insurance companies can have negative beta. Hope it helps.
https://youtu.be/5aun06wZrxQ
Click to expand...
Leo, awesome video! I do have some (hopefully) constructive criticisms, though. You may want to adjust some of the terminology used in your video. For example, ei isn’t variance– it’s a random error. the E(ei)=0 means that the expected error is zero, not that the variance is zero. I also think you’re using the market model, rather than the CAPM. The CAPM employs the market risk premium (as its slope) instead of the market return (employed in market model as the independent variable).
I think there is a quicker shortcut to deriving the variance than the shortcut you offered— just use the variance operator both sides and apply basic rules of variances:
Yi = ai + bi*Rm + ei where ai is the intercept (constant) in the model, bi is the slope, Rm is a random variable, and ei is a random error (variable)
Var (Yi) = Var (ai + bi*Rm + ei) = Var (0) + Var(bi*Rm) + Var(ei) = (bi^2)*Var(Rm) + Var (ei)
Var(ei) is idiosyncratic (non-systematic, firm-specific) variance
and the remaining term on the LHS is the systematic variance
I should also clarify that the variances are only additive if the variables are independent– in other words, if the error term is some how correlated with the independent variable(Rm, in this case), you should account for the covariance between the variables.
Overall, I think it’s a helpful video, and it’s good to see more free content popping up!
 
Ankit Sharma wrote:
1. The sum of an asset’s systematic variance and its nonsystematic variance of returns is equal to the asset’s
  • beta.
  • total risk.
  • total variance.
have given answer as total risk, but the solution says that it is total variance. Dont we use the word varience and Risk interchangebly , If there is any diference can you please point me out .
Click to expand...
Put another way…all flimjams are either systematic or nonsystematic. Therefore, the sum of all systematic flimjam and all nonsystematic flimjams are….wait for it….TOTAL FLIMJAMS. (This is true by definition.)
It is safe to assume that all variance falls into one of two categories–either systematic, or not systematic. Therefore, the total of all systematic variance + all nonsystematic variance must equal….total variance–by definition.
This is where common sense and a logic come to mind. You don’t need to be trained in finance to understand the question and come up with the correct answer.
 
Greenman72 wrote:
Ankit Sharma wrote:
1. The sum of an asset’s systematic variance and its nonsystematic variance of returns is equal to the asset’s
  • beta.
  • total risk.
  • total variance.
have given answer as total risk, but the solution says that it is total variance. Dont we use the word varience and Risk interchangebly , If there is any diference can you please point me out .
Click to expand...
Put another way…all flimjams are either systematic or nonsystematic. Therefore, the sum of all systematic flimjam and all nonsystematic flimjams are….wait for it….TOTAL FLIMJAMS. (This is true by definition.)
It is safe to assume that all variance falls into one of two categories–either systematic, or not systematic. Therefore, the total of all systematic variance + all nonsystematic variance must equal….total variance–by definition.
This is where common sense and a logic come to mind. You don’t need to be trained in finance to understand the question and come up with the correct answer.
Click to expand...
This is the point I was getting at by mentioning the additive nature of variances for variables that are independent of one another. You don’t need a finance background to understand it (although statistics or mathematics would probably help). The question stem asks about the sum of variances, which would equal another variance (without further manipulation).
Your point furthers the demonstration that logical thought could get one to the correct answer (even without understanding some of the rules regarding variances).
 
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