(a) Using **Python** in your calculations, do the following exercises (i), (ii) and (iii).

(i) You invest $83 now and receive back a total of $83.64 after 28 days. What is the yield on your investment?

(ii) You receive 6.5% per annum on a 138-day deposit. What is the effective rate? What is the daily equivalent rate? What is the 138-day discount factor?

(iii) What is the NPV of the following cashflows using an effective annual interest rate of 10% per annum?

Now: -$105

6 months: -$47

12 months: -$47

18 months: -$47

24 months: -$47

36 months: +$450

(b) Use **Excel** to do this question. It is 1 January 2017 and Mary has just bought a condominium for $2 million. She has succeeded in securing a loan of 70% of the purchase price, payable over 30 years. She will start paying the instalments at the end of the month. The interest rate is 1.6% per annum.

(i) Compute the monthly instalment she has to pay.

(ii) Calculate the outstanding principal balance at the end of one year.

(iii) Draw up a table showing the month-by-month instalments broken down into interest paid, principal repaid, and principal outstanding at the end of each month.

(a) Using **Python**, do the following exercises (i) and (ii).

(i) What are the weighted arithmetic and geometric means of the following numbers, given the following weightings?

12 (weighting 11%)

7 (weighting 19%)

13 (weighting 7%)

1 (weighting 23%)

10 (weighting 16%)

15 (weighting 3%)

4 (weighting 21%)

(ii) What is the volatility of the portfolio consisting of the following two assets?

Current value Volatility

A: 2 million 8.1%

B: 3 million 15.4%

Correlation between A and B: + 0.37

(b) Anna is a novice stock investor, having just graduated from the University. She has one stock, X, in her portfolio currently and is looking to build a portfolio of stocks. She is considering adding one more stock into her portfolio and is examining three possible stocks, A, B and C. These 3 stocks have identical characteristics and she is indifferent between the three stocks. She has found the following data on these three stocks:

Covariance between X and stock A = 0.72

Variance of A = 0.81

Covariance between X and stock B = 0

Variance of X = 0.64

Variance of B = 0.30

Covariance between X and stock C = -0.40

Variance of X = 0.64

Variance of C = 0.25 and X and C are negatively correlated.

Apply the relevant formula to compute the portfolio risk in each of these cases, using appropriate values where available from the question. Which stock should she choose? Explain your choice.