Question

would you please show the work

Assuming a normal distribution for the returns on investment, if the mean return is 12% and the standard deviation of returns is 6%, what is the probability of earning 0% or less?

The returns on two stock have a correlation of 0.50. One stock’s returns have a variance of 100%2 while the other has a variance of 81%2 . What is the covariance between the stocks’ returns?

A portfolio is comprised of $400 invested in stock A, which has an expected return of 10%, and $300 invested in stock B, which has an expected return of 15%. What is the expected return on the portfolio?

A portfolio is construct of 40% in the market portfolio and 60% in the risk-free asset. If the return on the Market portfolio is 10%, the return on the risk-free asset is 3%, and the standard deviation of the market portfolio’s returns is 20%. What are the return and standard deviation of returns of the portfolio?

Answer 1

Assuming a normal distribution for the returns on investment, if the mean return is 12% and the standard deviation of returns is 6%, what is the probability of earning 0% or less?

Z=(R-mean)/standard deviation
=>Z=(0%-12%)/6%
=>Z=-2
Pr(R<0%)
=Pr(Z<-2)
From the table, we see that Pr(Z<-2)=0.02275

The returns on two stock have a correlation of 0.50. One stock’s returns have a variance of 100%2 while the other has a variance of 81%2 . What is the covariance between the stocks’ returns?

Covariance=correlation*sqrt(variance of one)*sqrt(variance of other)=0.50*sqrt(100%%)*sqrt(81%%)=0.0045

A portfolio is comprised of $400 invested in stock A, which has an expected return of 10%, and $300 invested in stock B, which has an expected return of 15%. What is the expected return on the portfolio?

Expected return=(amount in Stock A*expected return of Stock A+amount in Stock B*expected return of Stock B)/(amount in Stock A+amount in Stock B)=(400*10%+300*15%)/(400+300)=12.14%

A portfolio is construct of 40% in the market portfolio and 60% in the risk-free asset. If the return on the Market portfolio is 10%, the return on the risk-free asset is 3%, and the standard deviation of the market portfolio’s returns is 20%. What are the return and standard deviation of returns of the portfolio?

Expected return=proportion in market portfolio*market return+proportion in risk free asset*risk free asset return=40%*10%+60%*3%=5.80%

Standard deviation=proportion in market portfolio*standard deviation of market portfolio=40%*20%=8.00%