Question

a. If variance of asset A is 0.04 and variance of asset B is 0.02, what is the correlation between the two assets? Assume covariance between the 2 assets to be 0.015. Show how you found the values.

b. Suppose a portfolio has expected return of 15% and volatility of 30%. How can you combine this portfolio with the risk-free asset to create a portfolio with 10% expected return? Risk-free asset has expected return of 3%.  Show how you found the values. Describe the steps.  

c. Write all the steps (i.e., the first method used in the example shown in videos/Excel) used in finding variance-covariance matrix directly from returns. Which steps can be skipped in Excel? Write the steps in plain English.

d. What are the diagonal entries of a variance-covariance matrix? If you have two assets with correlation of 0.65 and variances of 0.03 and 0.04, what would be the entries in the variance-covariance matrix (write in terms of (1,1), (1,2), (2,1), (2,2) where the first value refers to row number and the second value refers to column number)? Show how you found those values.

e. What is the difference between minimum variance frontier and efficient frontier?

Answer 1

A.

the variance of asset A is 0.04 and variance of asset B is 0.02, the correlation between the two assets is =

0.015/((0.04)^0.5*(0.02)^0.5)=0.53

Co-relation=Covariance(X,Y)/(S.D of X*S.D of Y)

[S.D (Standered Deviation=square root of variance]

B.

If we invest 25% in asset A and B , and rest 75% on risk free invest then we can generate 10% return from the portfolio.

Let assume A&B total contain x% and risk free asset hold 100-x%

then,

x%*15%+(100-x%)*3%=10%