) Expected Portfolio Return (4 marks)
E(Rp)=wAE(RA)+wBE(RB)
=0.6(20%)+0.4(12%)
=0.6(20%)+0.4(12%)
=12%+4.8%=16.8%
=12%+4.8%=
16.8%
(b) Portfolio Standard Deviation (5 marks)
Important assumption:
In portfolio theory questions, the value –0.1 is typically the correlation, not covariance.
Hence,
CovAB=ρABσAσB=(−0.1)(0.30)(0.20)=−0.006
=(−0.1)(0.30)(0.20)=−0.006
Portfolio variance formula:
σp2=wA2σA2+wB2σB2+2wAwBCovAB
=(0.6)2(0.30)2+(0.4)2(0.20)2+2(0.6)(0.4)(−0.006)
=0.0324+0.0064−0.00288
=0.0324+0.0064−0.00288
=0.03592
=0.03592
Portfolio standard deviation:
σp=0.03592≈18.95%
=
0.03592
≈
18.95%
(c) Correlation (3 marks)
Correlation measures the degree and direction of the relationship between returns of two securities.
It ranges from –1 to +1.
A negative correlation implies that when one stock’s return increases, the other tends to decrease, providing diversification benefits.
(d) Beta (4 marks)
Beta measures a stock’s systematic risk relative to the market.
It indicates how sensitive a stock’s return is to movements in the overall market.
A beta greater than 1 implies higher volatility than the market, while a beta less than 1 implies lower volatility.
(e) Standard Deviation (4 marks)
Standard deviation measures the total risk of a security or portfolio by capturing the variability of returns around the mean.
A higher standard deviation indicates greater uncertainty and risk, while a lower standard deviation indicates more stable returns.
Now send me that $1000