Systematic/Unsystematic Risk

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sparty419

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Rachel Stephens, CFA, examines data for two computer stocks, AAA and BBB, and derives the following results:
Standard deviation for AAA is 0.50
Standard deviation for BBB is 0.50
Standard deviation for the S&P500 is 0.20
Correlation between AAA and the S&P500 is 0.60
Beta for BBB is 1.00
Stephens is asked to identify the stock that has the highest systematic risk and the stock that has the highest unsystematic risk. Stephens should draw the following conclusions:
Highest Systematic Risk Highest Unsystematic Risk
A) Stock AAA Stock AAA
B) Stock BBB Stock BBB
C) Stock BBB Stock AAA
D) Stock AAA Stock BBB
Your answer: D was correct!
First, compare the betas for the two stocks.
AAA has larger beta [Using the formula Correlation(Mi)*SD(M)/SD(i)] and greater systematic risk than stock BBB which has a beta equal to 1. To assess the unsystematic risk, note that total risk is measured by the standard deviation. Note that the standard deviations for AAA and BBB are identical. Therefore, AAA and BBB have identical total risk. Moreover, note that:
total risk = systematic risk + unsystematic risk.
We have already concluded that both stocks have identical total risk and that AAA has greater systematic risk. Therefore, BBB must have higher unsystematic risk.
My question is that, if Total risk = Systematic+unsystematic, then for AAA 0.5 = 1.5+(-1) and for BBB 0.5 = 1+(-0.5) which means AAA will also have greater unsystematic risk wouldn’t it becuz -.15>0.5 in absolute values. This is what I am not getting. Or maybe I am not understanding something here. Any help will be appreciated. Thanks
 
beta(AAA) = 0.5*0.6/0.2=1.5
beta(BBB) = 1
therefore, AAA’s systematic risk is higher
since stdev(AAA) = stdev(BBB) = 0.5 (total risk is the same) -> unsystematic risk of AAA is lower.
 
sparty419 Wrote:
——————————————————-
> Rachel Stephens, CFA, examines data for two
> computer stocks, AAA and BBB, and derives the
> following results:
>
> Standard deviation for AAA is 0.50
> Standard deviation for BBB is 0.50
> Standard deviation for the S&P500 is 0.20
> Correlation between AAA and the S&P500 is 0.60
> Beta for BBB is 1.00
> Stephens is asked to identify the stock that has
> the highest systematic risk and the stock that has
> the highest unsystematic risk. Stephens should
> draw the following conclusions:
>
> Highest Systematic Risk Highest Unsystematic Risk
>
>
> A) Stock AAA Stock AAA
>
> B) Stock BBB Stock BBB
>
> C) Stock BBB Stock AAA
>
> D) Stock AAA Stock BBB
>
>
> Your answer: D was correct!
>
> First, compare the betas for the two stocks.
>
> AAA has larger beta and greater systematic risk
> than stock BBB which has a beta equal to 1. To
> assess the unsystematic risk, note that total risk
> is measured by the standard deviation. Note that
> the standard deviations for AAA and BBB are
> identical. Therefore, AAA and BBB have identical
> total risk. Moreover, note that:
>
> total risk = systematic risk + unsystematic risk.
>
> We have already concluded that both stocks have
> identical total risk and that AAA has greater
> systematic risk. Therefore, BBB must have higher
> unsystematic risk.
>
>
>
> My question is that, if Total risk =
> Systematic+unsystematic, then for AAA 0.5 =
> 1.5+(-1) and for BBB 0.5 = 1+(-0.5) which means
> AAA will also have greater unsystematic risk
> wouldn’t it becuz -.15>0.5 in absolute values.
> This is what I am not getting. Or maybe I am not
> understanding something here. Any help will be
> appreciated. Thanks
Unsystematic risk cannot be negative as it is measured in terms of stddev, which is always positive.
 
Risk measured as variance is always positive. But when we convert variance into stdev then it can be + or - as stdev = sqrt(variance).
Normally stdev is quoted as + ve.
Black Swan,
Are you talking about my post or about the question?
 
Black Swan Wrote:
——————————————————-
> The question.
it was covered in Level I (CAPM model)
 
I know CAPM, but the formula Beta = Correlation (Mi) *SD(M)/SDi is either new to me or I really really forgot it.
 
Black Swan,
you’ve probably seen Beta(X) = Cov(X,Market)/Var(Market) either in CAPM or Linear Regression section.
Cov(X,Market) = Cor*StDev(X)*StDev(Market)
Var(Market) = StDev(Market)^2
Therefore, Beta(X) = Cor*StDev(X)/StDev(Market)
 
I guess the definition (Systematic+Unsystematic Risk) and the calculation (Standard deviation) of TOTAL RISK are different, just like degree of leverage(DOL).
 
cfafrank Wrote:
——————————————————-
> I guess the definition (Systematic+Unsystematic
> Risk) and the calculation (Standard deviation) of
> TOTAL RISK are different, just like degree of
> leverage(DOL).
I can’t tell if I just got ripped on. Anyhow, overall this was a good thread, reminded me to touch up my stats and risk background (I’m in book 6 of CFAI right now and book one just seems like ages ago).
 
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