Portfolio Return / Portfolio Risk

CFA Level I
#1

I am quite unsure of the following::

An investor wants to invest in index by borrowing 35% at the Risk Free Rate. Expected Return of the index is 14% & Standard devisation is 18%, the risk free rate is 7%. What is the expected return & Standard deviation of the portolio?

A: Port Return = 11.55%, Port Risk = 11.70%

B: Port Return = 11.55%, Port Risk = 18%

C: Port Return = 16.45%, Port Risk = 24.30%

Could you please break down simplistically how to calcualte this.

Thanks,

#2

Expected return = -0.35(7%) + 1.35(14%) = 16.45%

Variance of returns = (-0.35)²(0%)² + (1.35)²(18%)² + 2(0%)(18%)(0) = 0.059049

Standard deviation of returns = √variance of returns = √0.059049 = 0.2430 = 24.30%.

#3

Hi S2000,

Thanks for the response. I apologise but i’m still a little unclear of your calculations. Please bear with me.

Why have you done one calculation of -0.35 x 7 & then another of 1.35 x 14.

II’m not following your var calcualtions either.

Sorry, but can you please elaborate?

Thanks a lot!

#4

The portfolio return is the weighted average of the returns of the constituent securities. In this case the weight on the risk-free asset is -35% (you’re borrowing 35%), and the weight on the risky asset is 135% (your total portfolio (100%) plus the 35% you borrowed).

#5

thank you.

#6

My pleasure.