Part A

The standard deviations of shares A, B and C are 20%, 15% and 30%, respectively. You want to make a portfolio combining these three shares. The correlation matrix of these three shares is as follows:

Share	A	B	C
A	1.0	-0.6	0.1
B	-0.6	1.0	0.6
C	0.1	0.6	1.0

You have $1 million to invest in these three shares in the following proportions:

Share	Weights
A	0.30
B	0.20
C	0.50

Using the above data, answer the following questions:

1. Calculate the covariance matrix for the three shares
2. Estimate the contribution of each share to the portfolio variance
3. Calculate the percentage contribution from each share to the portfolio variance
4. If you want to reduce the portfolio variance which share would you replace with a share that has a lower contribution.

Part B - Derivative applications

You are interested in creating a levered version of an ETF. The ETF has a Sharpe ratio of 0.70 and an annual return standard deviation of 30%. The risk free rate is 4%. You have $100,000 to invest. You want to borrow $400,000 at the risk free rate and invest the total amount in the ETF. Calculate the expected return and Sharpe ratio of the levered portfolio and compare the Sharpe ratio of the levered portfolio with the above Sharpe ratio.

Part A The standard deviations of shares A, B and Care 20%, 15% and 30%, respectively. You want to make a portfolio combining these three shares. The correlation matrix of these three shares is as follows: Share A B A 1.0 -0.6 0.1 B -0.6 1.0 0.6 0.1 0.6 1.0 You have $1 million to invest in these three shares in the following proportions: Share A B Weights 0.30 0.20 0.50 Using the above data, answer the following questions: Calculate the covariance matrix for the three shares IL Estimate the contribution of each share to the portfolio variance Calculate the percentage contribution from each share to the portfolio variance If you want to reduce the portfolio variance which share would you replace with a share that has a lower contribution IV. Part B - Derivative applications You are interested in creating a lovered version of an ETF, The ETF has a Sharpe ratio of 0.70 and an annual return standard deviation of 30%. The risk free rate is 4%. You have $100,000 to invest. You want to borrow $400,000 at the risk free rate and invest the total amount in the ETF. Calculate the expected return and Sharpe ratio of the levered portfolio and compare the Sharpe ratio of the levered portfolio with the above Sharpe ratio