Returns of Stocks X and Y

X Y

Average Return 19.00% 13.00%

Variance 0.09 0.04

Standard Deviation 30% 20%

Covarience 0.01

Risk-free return 3.00%

1) What is the return and standard deviation of the minimum
variance portfolio for X and Y? Ret = StDev =

2) What are the weights of the minimum variance portfolio? Wx = Wy
=

3) What is the return and standard deviation of a portfolio
composed of 30% in the minimum variance portfolio and 70% in the
risk free asset? Ret = Stvev =

4) What are the weights of a portfolio composed of the minimum
variance portfolio and the risk-free asset that has a return of
9%?? WMinVar = WRiskFree =

5b) What are the weights of a portfolio composed of the minimum
variance portfolio and the risk-free asset that has a standard
deviation of 5% WMinVar = WRiskFree =

6a) What is the Sharpe ratio of the minimum variance portfolio?
Shapre =

Community Answer

Answer:stocks returns std Dev.{:[x,0.19,0.03],[y,0.13,0.2]:}covariance : 0.01{:[" correlation "=(" Covariance "[x,y])/(sigma_(x)xxsigma_(y))],[cor[x","y]=(0.01)/(0.3 xx0.2)=0.16667]:}minimum variance portfolio:w_(A)=(sigma_(B)^(2)-cov(A,B))/(sigma_(A)^(2)+sigma_(B)^(2)-2cov(A,B))quadquadw_(B)=1-w_(A)For our problem:{:[omega_(x)=(sigma_(y)^(2)-cov(x,y])/(sigma_(x)^(2)+sigma_(B)^(2)-2cov(x,y])],[=((0.2)^(2)-0.01)/((0.3)^(2)+(0.2)^(2)-2(0.01))],[=(0.03)/(0.11)],[=0.27273%],[=0.27273=0.72727%]:}   Return of portfolic{:[ER_((p))=R_(x)w_(x)+R_(y)w_(y)],[" R- means returns "],[" w- weight "],[=(0.19)(0.27273)+(0.13)(0.72727)quad" ER-Expected return "],[=0.0518187+0.0945451],[" P - port folio "],[x","y" - stocks "],[=0.1463638]:}standard deviation{:[sigma_(p)=sqrt(w_(x)^(2)sigma_(x)^(2)+w_(y)^(2)sigma_(y)^(2)+2w_(x)omega_(y)cov(x,y))],[=sqrt((0.27273)^(2)(0.3)^(2)+(0.72727)^(2)(0.2)^(2)+2(0.27273)(0.72727)(001))],[=sqrt(0.006694348761+0.021156866116+0.003966966942)],[=sqrt0.0318181819],[=0.1783765170054]:}Answer: Return: 14.64%" Std. dev : "17.84%" rounded to "2^("nd ")" decima "weights{:[x=27.273%],[y=72.727%]:}quad" rounded to "3^("rd ")" decimial "risk free asset :" Return "=3%=0.03standand deviation =0.Risk free means there is no volatility in returny so standard deviation will be zero   {:[w_("mal ")=30%quadw_("Rf ")=70quad w" - weight "],[R_(mv)=14.64%quadR_(RA)=3%],[sigma_(mv)=17.84%quadsigma_(RA)=0%],[" R. Return "],[" a. standand deviot ... See the full answer