Portfolio Management

[gazhoo]

An investor put 60% of his money into a risky asset offering a 10% return with a standard deviation of returns of 8%, and he put the balance of his funds in the reisk free asset offering 5%. What is the expected standard deviation of the portfolio?

how do you get the answer?

 

[petprin]

It's 8%*0,6=4,8% (linear proportion)

 

[gazhoo]

yea, that's the right answer but could you explain it please?

 

[hoffmag2]

Portfolio Std. Dev =

([w^2*Sdev^2] + [w^2*Sdev^2] + [2*w*w*r*Sdev*Sdev])^1/2
1 2 1 2 1 2

Put the numbers underneath to designate which asset they belong to...

Since you know that Rf asset has a standard deviation of 0, You can drop out the second and third part...

(.6^2 * .08^2)^1/2 = 4.8%

 

[hoffmag2]

doesn't look like my ones and twos lined up where I had them...but hopefully you get the gist...

 

[gazhoo]

what is ^?

 

[hoffmag2]

"to the" so x^2 is x squared. y^3 is y cubed.

its the square root of the basic portfolio variance formula....

http://en.wikipedia.org/wiki/Modern_portfolio_theory

 

[petprin]

See Volume 4, page 256-257

 

[gazhoo]

there's got to be a simpler explanation..pl

 

[lijodotcom]

Remember that the Std. deviation of a risk free asset is 0. If you use 0 in the portfolio std deviation formula you will see that only the risky asset part of the formula gives a value.

 

[approaching_c]

this is one of those things i love about PM, and why i don't mind studying PM at all, but i mind studying most other CFA materials. it's so neat and makes perfect sense. and by substituting portfolio std dv. into the portfolio returns equation you get the equation for CML, which you do not have to memorize!! it just makes sense, unlike everything i tried to cram into my brain for FSA, which never ends up staying inside my head.