Q5 Question 5 Note: You may type your responses to each part in the spaces provide below. Alternatively, you may upload your handwritten and scanned answers to each question part below. Q5.3 to Q5.5 are to be answered independently of each other. The return on the market portfolio has a standard deviation of 25%. Angela has borrowed $10,000 (at the risk-free rate), to which she has added $25,000 of her own funds and invested the whole amount in the market portfolio (this information relates to Q5.1 and Q5.2 ONLY)

Q5.1 What is the standard deviation of Angelas portfolio? Show your calculations.

Q5.2 Angela wishes to change her portfolio from having $35,000 in the market portfolio so that the standard deviation of its return is 20% but she also wants her portfolio to remain fully diversified. Briefly outline how she should change her portfolio so that the standard deviation of the new portfolio has a standard deviation of return of 20%. Explain the transaction(s) that Angela needs to do to achieve this outcome. Be precise. Show your calculations.

Q5.3 Assume there are many risky assets available to investors, but investors are not able to borrow or lend. Both Samuel and Keith are risk-averse investors, but Samuel is less risk averse than Keith. Show that Samuel and Keith will invest in different portfolios and that Samuels optimal portfolio will have a higher expected return than Keiths optimal portfolio.

Q5.4 An equally-weighted portfolio contains ten securities, each with a standard deviation of returns of 40%. If the pairwise correlation of returns for these securities is 0.7, calculate the resulting portfolios standard deviation of returns. Show all calculations.

Q5.5 Justin has a portfolio consisting of $10000 invested in Vaccine Technologies Ltd (VTL) shares, $24,000 invested in Air Travel Ltd (ATL) shares and $6000 invested in Big Bank Finance Ltd (BFL) shares. The estimated betas of these shares are 1.6, 1.1 and 0.9 respectively. Calculate the beta of Justins portfolio. Show all calculations.