question on portfolio management

[vitamin]

could someone please help me on this:
On page 303 of Schweser book 3 on portfolio management - explanation on concept checker #7: do we assume that the market beta is one? I’m not sure where is the 1 coming from.
thanks!
vitamin

 

[cfasf1]

beta of stock AT is 1.25 and it’s weight in the portfolio is .67
beta of stock HC is .5 and its weight in the portfolio is .33
beta of this actively managed portfolio is 1. (weighted average of above) that explains the first 1
and market beta is 1, by definition, i think. so yes, we do assume market beta is 1.

 

[dinesh.sundrani]

Portfolio Beta, by def, is Covariance(return
, return)/ Var
hence, Market beta is Covariance(return, return)/ Var
Covariance of anything with itself is variance of that thing…
therefore,
Covariance(return, return) = Var
hence,
Var/ Var = 1
So I think we should assume that market beta is always 1 (weather it’s given or now)
But, if anobody could confirm this for sure??
- Dinesh S

 

[busprof]

Dinesh is correct. But you don’t need the math to see it. – Beta measures the relationship of an asset’s risk premium to the risk premium of the market. So, by definition, the risk premium of the market MUST BE equal to the risk premium of the market (they’re the same thing). So, the market beta MUST be one.