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Basic Question 2 of 11

Christopher owns two risky assets, both of which plot on the security market line. Asset A has an expected return of 12% and beta of 0.8. Asset B has an expected return of 18% and a beta of 1.4. If Christopher's portfolio beta is the same as the market portfolio, how much does he have invested in Asset A?

A. He has 1.33 invested.
B. He has 0.67 invested.
C. He has 1.67 invested.
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User Contributed Comments 21

User Comment
kalps a calculation would have been nice
Aimy 0.8*X+1.4*(1-X)=1, X=0.67
mtcfa An easier way to do this is: you can nix C and E right off the bat since you can't have more than 100% in any one stock. To have a portfolio beta of 1, you know you have to have more invested in stock A (it's beta is less than 1). Therefore, B is the only logical answer.
myanmar mtcfa: the way you're thinking is the right one for the exam
julamo exactly, except for 1 thing: you know you need to have more invested in stock A, but not because its beta is less than 1, because its beta is closer to 1 than the beta of asset B.
akanimo The key thing in this question is to remember that MARKET BETA = 1 and the portfolio weighting should result in a weighted beta = 1 ... rest is arithmetic.
MUTE Correct! akanimo
Rotigga Let X = % allocated to Asset A;
(1-X) = % allocated to Asset B
--> X*(0.8) + (1-X)*(1.4) = 1
--> 0.8(X) + 1.4 - 1.4(x) = 1
--> 0.4 = 0.6X
--> X = 0.667
julescruis Thank you for your comments they really helped...
Smiley225 have to apply the shortcut from mtcfa!
bmeisner mtcfa's last point is incorrect so you really shouldn't follow his way. He says that since stock A's beta is less than 1 you have to have more of it. That's simply not correct! What if the Beta of A was 0.2? Then the answer would require more of stock B!

I did this problem in my head (no calculator or paper needed for this simple math) because since you need beta = 1 then to get to 1 when you have one asset at 0.8 and the other at 1.4 you are going to need 2x as much of the 0.8 asset to balance off the 1.4 asset. Therefore 2/3 of your portfolio has to be in A. 2/3 * 0.8 + 1/3 * 1.4 = 1
danrow good question!
zeiad beta=1
so
a/b =12/18=.667 ?
mattg You can't have over 100% of your portfolio invested, rock on mtcfa! Don't do math unless you have to
mazen1967 WaBa+WbBb=1
wa+wb=1
waBa+(1-Wa)Bb=1
WaBa+Bb-WaBb=1
Wa(Ba-Bb)=1-Bb
Wa=(1-Bb)/(Ba-Bb)
Wa=(1-1.4)/(.8-1.4)=.67
shajidubai think about graph; the portfolio beta is in between, so no chance of weight going above 1, so only choice is 0.67
johntan1979 Shortcuts = easiest ways to fail

Know your formulas. Know your calculations. Exam questions won't be as easy as this one.
jonan203 jesus guys, of course you can have more than 100% of your portfolio invested, it's called margin and it REDUCES your EQUITY.

johnnyboy is right again, KNOW THE FORMULAS OR FAIL!

and don't assume these basic review questions will be anywhere near the level of difficulty on the real exam.
birdperson you can have over a 100% in a stock, you just need to be short somewhere else to make it balance...
khalifa92 @ mtcfa & myanmar: you are wrong here, you can have more than 100% invested in one stock if the other stock is borrowed instead of lending (eg):
E(R)= -0.5 ( 5% ) + 1.5 ( 10% ) = ...
margin or levereged position.
khalifa92 my previous comment is unrelated to this question, but just to clarify a point so don't get confused and ignore it.
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I am happy to say that I passed! Your study notes certainly helped prepare me for what was the most difficult exam I had ever taken.
Andrea Schildbach

Andrea Schildbach

Learning Outcome Statements

explain the capital asset pricing model (CAPM), including its assumptions, and the security market line (SML)

calculate and interpret the expected return of an asset using the CAPM

CFA® 2024 Level I Curriculum, Volume 2, Module 2.