Linear Bilevel Programming Problem †Free Samples to Students

Question: Discuss about the Linear Bilevel Programming Problem. Answer: Introduction: Efficient Frontier can be defined as the group of optimum portfolios, which can produce highest expected return for a certain risk level. It can be also used for deriving the lowest risk for a specific rate of return. Capital Allocation Line is the graph, which use to measure the risk level of risk-free and risky investments. It exhibits the return level, to be earned, by investing in an asset, with certain risk level (Jahanshahloo et al. 2012). Three Asset Portfolio: The efficient Frontier and Capital Allocation Line for the portfolio investment, consisting Australian Share, Australian Bond Australian Cash Deposit, are shown in the following graph as per the given data:- The Bordered Covariance for the weighted portfolio is as follows:- Bordered Covariance Matrix for Target Returns Australian Shares % Return Australian Bond return Cash Rate % Average Return Weights 0.005721334 0.111759778 0.882518888 0.005721334 0.015827457 0.031526222 0.107188438 0.111759778 0.031526222 0.677137386 1.693218413 0.882518888 0.107188438 1.693218413 15.34825795 1 0.154542116 2.40188202 17.1486648 The Correlation Matrices for the targeted return from the portfolio is also shown below:- Correlation Matrix Australian Shares % Return Australian Bond return Cash Rate % Average Return Australian Shares % Return 1 0.304528514 0.217476748 Australian Bond return 0.304528514 1 0.525224579 Cash Rate % Average Return 0.217476748 0.525224579 1 Four Asset Portfolio: When the international shares are included in the above-mentioned portfolio, the efficient frontier and the capital allocation line would be as follows:- The Bordered Covariance for the equally weighted portfolio amongst four assets is as follows:- Bordered Covariance Matrix for Target Returns Australian Shares % Return Australian Bond return Cash Rate % Average Return International Shares % Return Weights 0.005721253 0.111759531 0.882519216 0 0.005721253 0.015827005 0.031525703 0.10718695 0 0.111759531 0.031525703 0.677134395 1.693215304 0 0.882519216 0.10718695 1.693215304 15.34826937 0 0 0 0 0 0 1 0.154539658 2.401875402 17.14867162 0 The Correlation Matrix for the targeted return from the four asset portfolio is also shown below:- Correlation Matrix Australian Shares % Return Australian Bond return Cash Rate % Average Return International Shares % Return Australian Shares % Return 1 0.304528514 0.217476748 0.717272355 Australian Bond return 0.304528514 1 0.525224579 0.26015471 Cash Rate % Average Return 0.217476748 0.525224579 1 0.341160259 International Shares % Return 0.717272355 0.26015471 0.341160259 1 It can be stated that from the above graphs and the tables that at the return level of 9.5%, the optimum portfolio will not include the international shares (Aggarwal et al. 2012). Reference List: Aggarwal, R., Kearney, C. and Lucey, B., 2012. Gravity and culture in foreign portfolio investment.Journal of Banking Finance,36(2), pp.525-538 Jahanshahloo, G.R., Vakili, J. and Zarepisheh, M., 2012. A linear bilevel programming problem for obtaining the closest targets and minimum distance of a unit from the strong efficient frontier.Asia-Pacific Journal of Operational Research,29(02), p.1250011