Question 9

Consider the following expected returns, volatilities, and correlations:

Stock	Expected Return	Standard Deviation	Correlation with IBM	Correlation with Alphabet
IMB	3%	5%	1.0	-1.0
Alphabet	10%	20%	-1.0	1.0

1. Consider a portfolio consisting of only IBM and Alphabet. Calculate the percentage of your investment (portfolio weight) that you would place in IBM stock to achieve a risk-free investment. Show all your working.
2. Based on your finding in Part (a), what is the expected return of your portfolio? What is the risk free rate in this market, assuming the market is efficient and perfect?
3. Consider a portfolio consisting of only IBM and Alphabet. Calculate the expected return and standard deviation on such a portfolio when the weight on IBM stock is 60%, 80%, and 100%.
4. Based on your answer in Part (c), identify the efficient portfolios consisting of onlyIBM and Alphabet, when the weight on IBM stock is 60%, 80%, and 100%.
5. Assume that the correlation betweenIBM and Alphabetis - 0.5 and the expected returns and standard deviations for these two stock remain same. Consider a portfolio consisting of onlyIBM and Alphabet.

Calculate the expected return and standard deviation on such a portfolio when the weight onIBMstock is 60% and 80%.

Comparing with answer in Part (c), what can you conclude?