The data set required for the completion of the Applied Problems and the Portfolio project can be obtained from the course website. The EXCEL file contains sheets labelled:

DAILY WEEKLY MONTHLY

Presenting your solutions to the applied problems

1. Each group is responsible for its allotted problems.
2. All group members will receive the same mark.
3. All presentation must be done on PowerPoint. Here are a couple of tips to transfer information from other programs.
- When pasting any object from WORD or EXCEL always use Edit -> Paste -> Special -> Picture option
- You can transfer a whole (or part) of any screen to PowerPoint via MS Paint.
- 1. Open Paint (Programs -> Accessories -> Paint)
- 2. Go to the screen you wish to copy
- 3. Press the Print Screen key
4. Go to paint
- 5. Paste in paint
- 6. Cut in paint and copy into PowerPoint
4. Aim to take a between 2 and 5 minutes for presentation
5. Content. In order to obtain a high mark you need to.
- State the question,
- Briefly explain the steps taken in completing the requirements of the question,
- Set out the results of your computations and state your conclusions, trying at all times to relate your results back to the lecture material and any relevant theoretical consideration

Plot the growth rates of the two series, on the one graph against time.

Why does the gap between the two series increase as time progresses?

Q4. Use the Monthly data to compute the average annual growth of the (1) S&P Price and (2) S&P Accumulation indices.

Q5. Use the Monthly data to calculate the average annual growth of the (1) All Ordinaries Price and (2) All Ordinaries Accumulation indices

Q6. Use the Monthly data to plot the growth of $1

(1) invested in the shares that make up the S&P 500 Accumulation index

(2) invested at the average annual rate of growth.

Q7. Use the Monthly data to plot the growth of $1 (1) invested in the shares that make up the All Ordinaries Accumulation index (2) invested at the average annual rate of growth.

Q8. Show that the average of the period by period returns on the S&P 500 accumulation index is consistent with the growth of the index from the first to the last observation.

Q9. Use the Monthly data to plot the growth of a unit invested in the S&P 500 Accumulation index (1) in USD and (2) in AUD.

Q10. Use the Monthly data to compute average annual continuously compounded rate of return on an S&P investment (1) in USD and (2) in AUD.

Q11. Use the Monthly data to plot the growth of a unit invested in the MCSI India Total Return Index (1) in INR (Indian rupees) and (2) in AUD.

Q12. Use the Monthly data to compute average annual continuously compounded rate of return on an investment in Indian stocks, (1) in INR and (2) in AUD.

Q13. Use the Monthly data to plot the growth of a unit invested in the Singapore Straits Times Accumulation Index (1) in SGD and (2) in AUD.

Q14. Use the Monthly data to average annual continuously compounded rate of return on an investment in Indian stocks (1) in SGD and (2) in AUD.

Q15. Using monthly data, produce a histogram comparing the expected rates of return on share investments in Australia, US, Singapore and India, for a domestic resident of each of these countries.

Q16. Using monthly data, produce a histogram comparing the rates of return on share investments in Australia, US, Singapore and India, for a resident of Australia.

Q17. Use the Monthly data to compute a series of continuously compounded returns for the All Ordinaries Accumulation index. What are the per annum expected return, variance of return and the standard deviation of return for the series?

Q18. Use the Monthly data to compute the annual standard deviations of returns for (1) the Singapore Straits Times Accumulation Index, (2) S&P Accumulation index, (3) the All Ordinaries Accumulation index and (4) the MSCI Indian Total Return index in their own currency?

Q19. Use the Monthly data to compute the annual standard deviations of returns for (1) the Singapore Straits Times Accumulation Index, (2) S&P Accumulation index, (3) the All Ordinaries Accumulation index and (4) the MSCI Indian Total Return index in AUD?

Q20. Compute some statistics to show how monthly S&P500 equity returns are distributed?

Q21. Are monthly S&P500 accumulation index equity returns normally distributed?

Q22. Use the CHI squared test for goodness of fit to check whether the monthly S&P500 accumulation equity returns are normally distributed?

Q23. Does the Jarque-Bera test confirm the Goodness of Fit test of normality results for the S&P500 accumulation index?

Q24. Are monthly ASX All Ordinaries accumulation index equity returns normally distributed? Use (1) eyeball analysis on a plot (2) the CHI squared test of fit and (3) the Jarque-Bera test to check whether the monthly ASX All Ordinaries accumulation equity returns are normally distributed?

Q25. Leptokurtosis (too many extreme observations) is often observed in financial market returns. Use the monthly ASX Australian All Ordinaries Accumulation data to compute (1) the number of observations that are outside the two standard deviation range from the mean (2) the ratio of the number of observed observations in these tails compared with that expected under a normal distribution.

Q26. Compute the ratio of extreme observations in the distribution of monthly returns from the US, Australian, Singaporean and Indian accumulation indices.

Q27. Using the Monthly S&P500 Price index compute a continually compounded return on equity for each month. Use this data to compute the number of runs of positive and negative returns.

Q28. Does the result of a runs test support an hypothesis of independence of monthly S&P500 Price Index returns?

Q29. Using the Monthly ASX All Ordinaries Price index to compute a continually compounded return on equity for each month. Use this data to compute the number of runs of positive and negative returns.

Q30. Does the result of a runs test support a hypothesis of independence of monthly ASX All Ordinaries Price index returns?

Q31. Compute the correlation between Monthly S&P Price Index returns with those of last month. Is there any evidence of non-independence of returns?

Q32. Compute the correlation between Monthly ASX All Ordinaries Price Index returns with those of last month. Is there any evidence of non-independence of returns?

Q33. Comment on US interest rate trends as evidenced in the monthly 10-year bond yields.

Q34. Use the runs analysis to check whether 10-year bond yields are independently distributed

Q35. Use the Monthly data on 10 year US bond yields to compute a monthly bond return series. What is the per annum expected return on bonds and the standard deviation of that return?

Q36. Compare the average and the standard deviation of adjusted US bond returns with their equity equivalent returns computed from the S&P500 Accumulation index?

Q37. Examine the distribution of the excess of US equity return over US bond return.

Q38. Is the mean and standard deviation of return of the excess of US equity over US bonds of the previous question consistent with the theory of combinations of random variables?

Q38. Is the mean and standard deviation of return of the excess of US equity over US bonds of the previous question consistent with the theory of combinations of random variables?

Q39. What is the theoretical probability that a portfolio of US equity will provide superior returns to a portfolio of US bonds over the next;
(1) one year?
(2) five years?
(3) ten years?

Q40. How long does your investment horizon need to be before the probability that equity beats bonds exceeds 90%?

Q41. Compute the correlation between the continuously compounded monthly returns for equity (S&P500 accumulation) and bond returns (as computed in Q35). Comment upon the sign and size of the correlation number.

Q42. Compute the average return and standard deviation of a portfolio containing 1/2 bonds, and 1/2 equity. Plot, in return standard deviation space, the portfolios of (1) 100% equity,
(2) 100% bonds and (3) 50% bonds/50% equity. Is there any evidence that the diversified portfolio is in any way superior to either of the undiversified portfolios?

Q43. Is there any statistical evidence of expected return instability in the monthly S&P500 Accumulation returns?

Q44. Is there any statistical evidence of instability in the variance of monthly S&P Accumulation returns?

Q45. Plot the cumulative continuously compounded return for each of the 15 stocks.

Q46. Compute the per annum expected return and standard deviation for each of the 15 stocks.

Q47. Arbitrarily choose three stocks from the weekly data set. What are the risk, expected return and individual share weights for the absolute minimum risk portfolio (3 STOCK CASE)?

Q48. Plot in the risk (standard deviation), expected return space each of the 15 shares. Which shares are mean-variance efficient?

Q49. What are the weighting's of each share in "best" 15 stock portfolio yielding an expected return of 10%pa?

Q50. Graph the minimum risk frontier for short sales allowed combinations of the 15 stocks. Q51. Find the weights for the short sales allowed, 15 share MVP portfolio.

Q52. Show that an equally weighted portfolio lies inside the minimum variance frontier

Q53. Use the weekly data on the S&P500 Composite Price Index and on the exchange rate to compute weekly continuously compounded returns for a "typical" US stock in the domestic currency. Compute annual expected returns and standard deviation of returns for each foreign index asset.

Q54. Add the US asset to your 15 stock short sales allowed portfolio. Identify the best portfolio with an expected return of 10%p.a.. How much risk was eliminated with the addition of the US asset?

Q55. On the same graph, plot the minimum variance frontier for

1. the 15 asset short sales allowed portfolio
2. the 16 asset portfolio (includes the US asset)

Q54. Add the US asset to your 15 stock short sales allowed portfolio. Identify the best portfolio with an expected return of 10%p.a.. How much risk was eliminated with the addition of the US asset?

Q55. On the same graph, plot the minimum variance frontier for

1. the 15 asset short sales allowed portfolio
2. the 16 asset portfolio (includes the US asset)

Q58. Compute and plot the short sales allowed minimum variance frontier where the sum of the weights of the banking stocks is restricted to be 25%. Compare this frontier with the unrestricted frontier.

Q59. Compute the weights associated a short sales not allowed portfolio yielding a return of 10% p.a. Comment upon the differences between this weight vector and its short sales allowed equivalent.

How many assets are included in the no short sales allowed 10% portfolio? Compare the two sets of weights.

Q60. Compare and contrast the MVP weights for (1) the short sales allowed and (2) the short sales not allowed portfolios.

Q61. Overlay the short sales allowed minimum variance frontier on the short sales not allowed minimum variance plot. Where does the short sales not allowed restriction cause the greatest and least increase in optimal portfolio risk?

Q62. Plot the raw 3- month discount rate over the weekly data time frame.

Q63. 1. Compute weekly holding period returns for 3-month bills. What is the per annum average return and standard deviation of bill returns?

    2. Compute weekly holding period returns for 10-year bonds. What is the per annum average return and standard deviation of bond returns?

Q64. Add HPY returns for 90-day discount securities and 10-year bonds to your risk/return scatter plot of the 15 shares.

Q65. Compare the composition and risk associated with the no short sales portfolios, with a target return of 10%, constructed from (1) 15 shares, (2) 15 shares plus bonds, and 15 shares plus bonds plus 90-day securities.

Q66. Compare the composition and risk associated with the no short sales MVP portfolios constructed from (1) 15 shares, (2) 15 shares plus bonds, and 15 shares plus bonds plus 90-day securities.

Q67. Plot the minimum variance frontier for the 17-asset, no short sales allowed portfolio (1) unconstrained and (2) with the constraint that equity comprises 80% of the portfolio.

Q68. Examine and plot on a histogram the weights of a no short sales allowed portfolio, with a target return of 10%pa, (1) unconstrained and (2) with the constraint that equity comprises 80% of the portfolio.

Q69. Compute the weights of a no short sales allowed portfolio, with a target return of 15%pa, with the constraint that equity comprise at least 80% of the portfolio.

Q70. Find two portfolio target returns, one where the constraint that equity must be at least 80% is binding and one where it is not binding. For each of these two target returns, compare the (1) unconstrained weights, (2) equality constrained weights and (3) inequality constrained weights.

Q71. Plot the minimum variance frontier for portfolios with (1) unconstrained weights, (2) equality constrained weights and (3) inequality constrained weights, where the constraint is that the weight on the equity component must be at least 80%.

Q72. Compute the annual mean of each of the 15 equity for (1) the historical period and (2) the investment period.

Q73. Compute the annual standard deviation of return of each of the 15 equity for (1) the historical period and (2) the investment period.

Q74. Apply statistical test of to determine whether or not the covariance matrix in the investment period is equal to the covariance matrix in the historical period.

Q75. Plot the minimum variance frontier no short sales portfolio for (1) the historical data period and (2) for the investment period. Is there any visual evidence of a change in the minimum variance frontier between the two periods?

Q76. Find the MVP weights using the historic half data. Compute the expected return and Standard deviation of returns when these weights are applied to (1) historical data, (2) to the investment data.

Q77. Compute a portfolio of no short sales weights yielding 10%p.a using;
Wa using 2nd half expected returns, 2nd half, variances, 2nd half covariances. Wb using 1st expected returns, 2nd half, variances, 2nd half covariances

Apply both of these weights to second half data and compute the expected return and standard deviation. How close in risk and return, is (b) to (a) when applied to second half data?

Q78. Compute a portfolio of no short sales weights yielding 10%p.a. using;
Wa using 2nd half expected returns, 2nd half, variances, 2nd half covariances. Wb using 2nd half expected returns, 1st half, variances, 1st half covariances

Apply both of these weights to second half data and compute the expected return and standard deviation. How close in risk and return, is (b) to (a) when applied to second half data?

Q79. Using the ASX All Ordinaries Price index, calculate betas for the 15 shares.

Q80. Using the S.I.M. decompose each share's risk into a systematic and unsystematic component. Comment upon your results.

Q81. Estimate a SML by regressing expected return on J for the 15 stocks.

Q82. Consider two alternative portfolios

(1) An equally weighted equity portfolio,
(2) The short sales not allowed MVP computed from the first half data.

Compute the performance of these two portfolio over the 2nd half data in terms of the basis of the Sharpe index.

Q83. Consider two alternative portfolios

(1) An equally weighted equity portfolio,
(2) The first half short sales not allowed MVP

Compute the performance of this portfolio over the 2nd half data in terms of the basis of the Treynor index.

Q84. Consider two alternative portfolios

(1) An equally weighted equity portfolio,
(2) The first half short sales not allowed MVP

Compute the performance of this portfolio over the 2nd half data in terms of the basis of the Jensen index.

Q85. Use the monthly S&P500 Price index data to compute average return for each month of the year. Is there any evidence that the US share market has a January effect?

Attachment:- Applied_Problems.rar