A portfolio selection problem arising from real-estate investments

  • Shaun Butler Stellenbosch University
  • Kit Searle School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh
  • Philip Christian Malan Stellenbosch University


Investments have been used as a medium to mitigate the effects of inflation for many yearsand it is expected that they will be used for many years to come. Not only do investmentsallow for an opportunity to increase the net worth of a sum of money, they also allow fora source of passive income. With every investment, however, there is an associated riskbut, higher risks are typically associated with a more enticing reward. From the broadscope of potential investment opportunities, the primary focus of this paper is to considerinvestments within the realm of real estate.Although property investments have the potential of generating a satisfactory return andmay generally be considered a safe investment, as with any investment, poor decisionmaking may still results in the loss of capital. A multi-period portfolio selection model mayassist a potential investor in determining an optimal investment plan. The multi-periodportfolio selection model considers the future value and rental incomes of a set of potentialproperties, in determining the optimal investment plan over a given time horizon, aimed atmaximising the expected net present value of the portfolio. The quality of the investmentplan, however, is dependent on the accuracy of the predicted future value and rental incomeof the properties under consideration. Therefore, in order to determine these future valuesaccurately, a time series forecasting model is proposed. The forecasting model predicts thevalues for property values and rental income over a selected time horizon, which serves asinput to the multi-period portfolio selection model.In short, the goal of this paper is to apply suitable time series forecasting methods in orderto generate predicted values with an acceptable accuracy, to serve as input for a multi-periodportfolio selection model to determine an optimal investment plan as output.


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