ECON1095: Quantitative Methods In Finance - Finance Assessment Answer

Subject Code: ECON1095 Internal Code: F_AI_EJDB_AG

Quantitative Methods In Finance - Finance Assessment Answer

Assignment Task: QUESTION 1 An investor is considering putting additional funds into the Australian share market; to assist with this decision she analyses the continuous daily returns for S&P/ASX 200 - PRICE INDEX (MKT) from 19 February 2018 to 19 February 2019 using Excel’s Data Analysis/Descriptive Statistics. This data is available in ECON1095 Data Sem 1 2019.xlsx. (a) Calculate the 95 % confidence interval for the daily returns for MKT over this period. (b) The investor decides that she will only put extra ECON1095: Quantitative Methods In Finance - Assessment Answer money into the Australian share market if she can rule out negative returns. The average daily returns for the sample period should be above zero. Therefore, the question is, ‘have the daily returns for MKT been far enough above zero for the investor to be confident that they will not go below this level?’ Test to see whether the daily returns on MKT are less than or equal to zero using a level of significance of That is, conduct the following test, Ho: <= 0, H 1: >0. Would she invest further in the Australian share market using this rule? (c) Test to see whether the daily returns on MKT are normally distributed using the Jarque-Bera test. This should be done in Excel, by calculating the Jarque-Bera statistic using the formulas from the notes and Excel’s Data Analysis/Descriptive Statistics. 2 Using the results of this test, comment on the accuracy of the probabilities you calculated in parts (a) and (b) of this question. QUESTION 2 Suppose a hypothetical individual’s Utility (U) can be explained through their consumption of two goods (X1 & X2) such that: Check your answer using the solver in excel. To do this open a new spreadsheet and insert names for X 1 and X 2 in cells B2 and C2 and the starting values for these variables of 1 in both cells B3 and C3 and name these cells Xone and Xtwo. In cell B6 type the formula for the utility function, = 0 (Xone^ 1 )*(Xtwo^ 2 ) and name this UU. In the cell,  B9 type the formula for the budget, =6.5*Xone+4.5*Xtwo and name this BB. Next, go to the solver and set the target cell UU equal to maximum by changing Xone and Xtwo. Then add the constraint that BB = 2000, then solve. When given the solver results ask for the sensitivity report as this gives. QUESTION 3 (please use EXCEL for this question). Although the conclusion from QUESTION 1 may have been to not put additional funds into the Australian share market, with the lower value of the Australian dollar the investor is ‘bullish’ about the 32 Australian listed Basic Materials shares. Therefore, she decides that a portfolio of these types of shares could present profit opportunities in the future. Using data on the Unadjusted Share Prices and the same sample period as earlier, follow the instructions below to construct an efficient frontier for the proportions of your funds that need to be allocated to the different Australian Basic Materials shares. There are additional instructions in Mathematical Programming notes. Calculate the average continuous daily returns, then convert to average yearly returns by multiplying each by your sample period (n). Transpose this block of cells and name the average returns Ret. Use the covariance command from EXCEL’s Data Analysis Tools to find the variance-covariance matrix for the daily returns. This matrix is symmetrical, so the missing elements can be easily filled in. Name this matrix Mvac. Convert Mac into the variance-covariance matrix for yearly returns by highlighting the cells and entering =n*Mvac [Ctrl]+[Shft]+[Enter]. Name this block Vac. Enter the initial guesses for the optimal weights for the shares and name this block of cells Wts. Transpose these weights and name this block Twts. Find the expected return for the portfolio using =MMULT (Wts, Ret) [Ctrl]+[Shft]+[Enter]. Call this cell Pret. Finding the variance of portfolio returns requires three stages. First, highlight the appropriate cells and enter =MMULT (Wts,Vac) [Ctrl]+[Shft]+[Enter]. Name this block Tvac. Second, highlight a single cell and enter =MMULT (Tvac, Twts) [Ctrl]+[Shft]+[Enter]. Call this cell Pvar. Next, find the portfolio risk, or the square root of the portfolio variance and name this cell Prsk. To ensure that the portfolio weights sum to one, enter 1’s and name this block Unit. To find the expression for the sum of the weights by entering =MMULT (Unit, Twts) [Ctrl]+[Shft]+[Enter]. Name this cell Wtcn. Using this worksheet and the EXCEL Solver Tool find the minimum risk for the funds' allocations for the various expected returns (I suggest performing the exercise for about ten different expected returns, chosen to ensure a solution can be found). In each case, you must constrain the weights so they are non-negative and sum to one. Use these values to graph the Efficient Frontier with risk on the horizontal axis and returns on the vertical axis. Write a brief report explaining how your portfolio changes as you try different expected returns. QUESTION 4  One approach to testing the validity of the CAPM is to use the two-pass method. At the first pass estimate the betas and the variance of the error terms for a number of firms. This is to be done using the same sample period as in the other questions and the daily returns for the Unadjusted Prices for the Australian Basic Materials firms and the S& P200 Index (MKT). At the second pass use these results to estimate the Security Market Line (SML). If the model is a good fit this is interpreted as an indication that the CAPM successfully explains the relationship between Risk and Return. First, calculate the continuous returns on all of the Australian Basic Material shares and the market index. QUESTION 5 The investor would like to further investigate the 32 Australian Basic Materials shares. She does this using the share returns, the MKT return and the Betas calculated in QUESTION 4, as well as the most recent AUSTRALIA BOND YIELD 10 Y - MIDDLE RATE as a measure of the risk-free rate (Rf ). Present the answers to parts (a), (b) and (c) of this question in a tabular form (cut and paste from a spreadsheet is fine). (a) Indicate which of these Basic Materials shares have outperformed, and which has underperformed the MKT? (b) Conduct hypothesis tests on the Betas of each share against unity to indicate whether the shares are ’passive’, ‘aggressive’ or ‘neutral’. This requires finding the standard error of the slope coefficients for each of your 32 market models. To do this: 1. Square root the variances of your error terms to find the standard errors of regression for the market models. 2. Divide these standard errors of regression by the standard deviation of the market returns multiplied by the square root of the sample size. This will give you the standard error of each slope coefficient, which can be used to conduct your hypothesis tests.(c) Using the Security Market Line; E(R i ) = R f + [E(R M ) - R f I assuming the share performance over the last 12-months is the best indicator of what is likely to happen in the future, obtain the expected returns for each of the Basic Materials shares 6. (d) Drawing on information from QUESTIONS 1, 3, 4 & 5 write a brief paragraph discussing the prospects for Australian Basic Materials share performance.

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