Investment Finance-II - Assignment Example

INVESTMENT FINANCE-II ASSIGNMENT Contents Contents 2 Part A 4 Answer HPR, AAR and GAR 4 a) 4 b) 5 c) 5 d) 6 e) 6 Answer – 2: Daily Value at Risk 6 a) 7 b) 7 Answer – 3: Portfolio Selection 7 a) 7 b) 8 c) 8 Answer – 4: The Capital Asset Pricing Model 9 Part – B 9 1. Modern Portfolio Theory 9 2. The Capital Asset Pricing Model 11 3. The CAPM and Multifactor Models 13 References 15 Part A Answer – 1: HPR, AAR and GAR The company selected for Part - A is AMP Ltd. It is a financial services company headquartered in Sydney, Australia. a) The monthly HPR (Holding Period Returns) can be calculated using the following formula: HPR = (end period value – initial value)/initial value The data for HPR is the adjusted close price of AMP Ltd starting from July 2013 to June 2015. The results of the calculation are summarized graphically below: b) Variance, standard deviation, maximum and minimum is calculated using the following formulas, Standard deviation = ; in excel, SD = stdev (array of numbers) Variance = (SD)2 Maximum = max (array of numbers) Minimum = min (array of numbers) The results of calculation is summarized and shown below:- Summary Statistics Returns Mean 0.014290 Standard Deviation 0.061411 Sample Variance 0.003771 Minimum -0.096096 Maximum 0.161179 c) The arithmetic average and geometric average of returns are calculated in excel using the functions AVERAGE (array of numbers) and GEOMEAN(array of numbers) and the results are shown below: d) Based on the given problem the number of shares bought are 11,055 as shown below: The number of shares is calculated by diving available funds with adjusted close price. e) Based on the given assumptions the total gain will be $ 23,598 as shown below, The total gain or loss is calculated using the following formula, Capital gain/loss = Total value after brokerage fee – original investment Answer – 2: Daily Value at Risk Another company selected from a different GICS is QBE Insurance Group Limited. a) b) Answer – 3: Portfolio Selection a) The correlation and covariance of returns are calculated using the excel functions CORREL (array 1, array2) and COVAR (array1, array2) b) The efficient portfolio returns are calculated using various weight combinations: c) The minimum variance portfolio weights for the portfolio of two stocks are: Answer – 4: The Capital Asset Pricing Model Part – B 1. Modern Portfolio Theory The Modern Portfolio Theory (MPT) was written by Harry Markowitz in an article in the year 1952. The significance of this theory lies with the fact that it examines the whole economy and the entire market by emphasizing on correlation between investments. The correlation reveals the amount that can be expected from different investments in various assets. The main variables observed in the MPT theory are volatility, risk and return. The MPT uses risk as a parameter to estimate whether the value of investment will go down or up. The MPT assumes that if the investor is given choice to select from two investment portfolios, then he will select the one having minimum risk due to risk adverse nature. Alternatively, investors will undertake more risk only if there is more returns. The unsystematic risk can be diversified while the systematic risk or market risk is non-diversifiable1. The benefits of diversification are: Using the concept of MPT investors can minimize risk through diversification Diversification also allocates investment into different asset classes that ensures better returns than investment in single asset2 The MPT helps the investor to build a portfolio that nearly equals efficient frontier3 The actual Markowitz portfolio models are represented below: The correlation and covariance of stock returns of AMP and QBE helped to determine the amount that the investor can expect by investing in these assets. The changes in value of one asset are compared to another. The correlation between AMP and QBE is less than 1 which signifies that changes in value of one will not affect the other stock. In other words, if the stocks of AMP are low, then its effects will be nullified by increase in stocks of QBE. 2. The Capital Asset Pricing Model The CAPM theory is very useful for determining the required rate of return of an asset. This model is important because it considers the sensitivity of asset with respect to market risk4. The various assumptions of CAPM are: All investors, Are rational (they tend to avoid risk) Expect to maximize economic utilities Want to diversify risk across various assets Have no influence in controlling asset prices as they are risk takers Can borrow or lend unrestricted amounts at risk-free rate The various components of CAPM theory are, 1. Risk-free rate – This is generally the 10 year bond issued by the government which has no credit risk. For question – 4 (part A), the risk-free rate is 2.5% per annum. 2. Beta – It measures the sensitivity of stock with respect to market risk. If the value of beta is more than 1, then the stock will react more aggressively compared to market. Conversely, if beta is less than 1, then the stock will have less volatility. The beta of AMP and QBE are 0.0024 and -0.00215 respectively. 3. Risk-premium – It is the difference between stock return and risk-free return. That is, how much the investor can expect returns above the risk-free rate5 The formula of CAPM is , where, E(R) = expected return Rf = risk-free rate E(Rm)-E(Rf) = risk premium The advantages of CAPM over MPT are: 1. MPT does not consider systematic risk or market risk while CAPM considers market risk 2. MPT assumes that investors do not need to pay taxes which is not realistic 3. The calculation of MPT is based on past performance to measure return and risk correlation. This is not the case for CAPM as it considers market return and stock return. 3. The CAPM and Multifactor Models The Fama-French three factor and multifactor model explains the return and risk of stocks using the following formula:- The various components of this model are:- 1. Rf (Risk-free rate) – It is the assured return that the investor can expect without taking any risk 2. Km – It is market return 3. β – Analogous to classical beta but may not be equal 4. SMB – Small market capitalization 5. HML – High book-to-market ratio 6. α – portfolio performance 7. bs and bv – Linear regressions (can have positive and negative values) The major risk factors and assumptions of Fama-French Model are:- 1. Asset pricing is rational 2. The Fama-French model describes returns but the investors can act irrationally and chase higher premiums 3. The average returns on book-to-market stocks can be overstated which is risky 4. If the market portfolio is not observable then multifactor model could provide better estimates 5. There are no transaction taxes The main difference between CAPM and multifactor models are:- 1. One of the main limitation of 3-factor model is data mining as the returns are book-to-market ratio they are likely to be artifacts 2. CAPM is still preferred to calculate cost of equity because it is more practical and the cost of 3-factor model to determine expected return is not justified 3. CAPM uses only a single factor that is proportional to systematic risk 4. The 3-factor model also considers the impact of portfolio managers on the portfolio as different managers has different appetite for risk tolerance6 References Altwies, Diane and Frank, Reynold. Achieve CAPM® Exam Success: A Concise Study Guide and Desk Reference. Florida: J. Ross Publishing. 2010. Amenc, Noel and Sourd, Veronique. Portfolio Theory and Performance Analysis. New Jersey: John Wiley & Sons, 2005. Brigham, Eugene and Michael, Ehrhardt. Financial Management: Theory & Practice. Boston: Cengage Learning. 2013. Davies, Greg and Servigny, Arnaud. Behavioral Investment Management: An Efficient Alternative to Modern Portfolio Theory. New York: McGraw Hill Professional. 2012 Hughes, Duncan. Asset Management in Theory and Practice. New York: New Age International. 2005. Levy, Haim. The Capital Asset Pricing Model in the 21st Century: Analytical, Empirical, and Behavioral Perspectives. Cambridge: Cambridge University Press. 2011. Read More