Company Specific Risk

[archived_user]

We are given the following and asked how much of RBC stock’s excess return variation can be attributed to company specific risk.
Regression Statistics
Multiple R = 0.7131
R-squared = 0.5086
Standard error of estimate = 0.0269
Observations= 60
This is the solution:
The R2 in this regression is 0.5086. This result suggests that about 51 percent of the total variation in the excess return to RBC stock (the return to RBC above the risk-free rate) can be explained by excess return to the market portfolio. The remaining 49 percent of RBC stock’s excess return variation is the nonsystematic component, which can be attributed to company-specific risk.
Why not use the Standard Error of Estimate to find the SSE which is related to the errors of the regression?

 

[archived_user]

Onda wrote: Why not use the Standard Error of Estimate to find the SSE which is related to the errors of the regression?

Because it takes a lot more work to arrive at the same answer.
When flying from New York to Los Angeles, why go through Atlanta, Dallas, Seattle, and Phoenix when you can take a nonstop?

 

[archived_user]

so technically my way of thinking is not wrong?
I tried using the formula of SEE to find SEE and I get 4.27% which is not the same answer as the one above.
my calculation- 0.0269 = squared root of SEE over 59 and 4.27%

 

[archived_user]

Your way of thinking is OK, but I don’t understand your calculation.
How many independent variables are there? You need to know that to follow your approach.

 

[archived_user]

There is 1 one independent variable. So what I did is used the below formula:
SEE=(SSE/n-2)0.5

 

[archived_user]

Onda wrote: my calculation- 0.0269 = squared root of SEE over 59 and 4.27%

Are you sure that there’s only one independent variable (i.e., did they state that explicitly)?

Onda wrote: my calculation- 0.0269 = squared root of SEE over 59 and 4.27%

Where did you get 59?
Using your formula, what’s the value of SSE?
What’s the total sum of squares (TSS)?

 

[archived_user]

Actually, it shouldn’t be 59; it should be 58 because they told us we have two parameters hence, its 60-2=58
Using the formula, I get SSE= 0.04196938
TSS wasnt given to us

 

[archived_user]

So, how do you use SSE to get the idiosyncratic risk?

 

[archived_user]

Quick question. Isn’t SSE the diosyncratic risk because our goal is to minimize it as much as possible ?
Second, thats what I got for SSE=0.04196938 which is different from 49% given in the solution and I dont get where I messed up

 

[archived_user]

Onda wrote: Quick question. Isn’t SSE the diosyncratic risk because our goal is to minimize it as much as possible?

It is idiosyncratic risk. However, the reason isn’t that our goal is to minimize it.

Onda wrote: Second, thats what I got for SSE=0.04196938 …

Which is correct.

Onda wrote: … I dont get where I messed up

Evidently the question was intended to mean “What percentage of the total variance is idiosyncratic?” That isn’t clear from what you wrote. You calculated the SSE, but not the percentage of TSS that SSE represents.
Where did you get this question?

 

[archived_user]

in the curriculum in regards to quants. Reading 4, example 4 on page 254

 

[archived_user]

What’s the exact question it asks?

 

[archived_user]

Regression Statistics
Multiple R = 0.7131
R-squared = 0.5086
Standard error of estimate = 0.0269
Observations= 60
Alpha: 0.0031( intercept ); 0.0070 ( standard error); 0.4429 9 ( t stat)
Beta 0.9068 (coefficient); 0.1170 ( standard error) ; 7.7504 ( t stat)
Question: How much of RBC stock’s excess return variation can be attributed to
company-specific risk?

 

[archived_user]

The question is not well worded: it would be reasonable to interpret it either as how much absolute variation, or as what percentage of the total variation. On the real exam I would expect there to be no such ambiguity.
Nevertheless, when they give you three answer choices that are all percentages, you can be sure that they meant the latter interpretation, not the former.