Optimizing Portfolio Allocation with and without Short Selling

QUESTION

Consider that on January 2, 2014 (Wednesday) you decide to invest in a portfolio consisting of these 10 stocks. You want to find the optimal portfolio to invest in, so you analyze the performance of these 10 stocks over time (using past historical data from January 3, 2011 to December 31, 2013). Please construct the optimal portfolio if short selling is allowed. Use the 3-month T-bill rate as a proxy for the risk-free rate. Assume that riskless borrowing/lending is possible (Hint: Use the borrowing/lending rate on January 2, 2014 – use the specific value provided in the Excel file for this assignment). Please solve this part using Excel Solver (GRG Nonlinear Method).

What is the proportion of your funds invested in Tesla? Please round your answer to 3 decimals. Please do not report the %. For example, if your answer is 0.3021 (corresponding to 30.21%), you will report 0.302.

Continuation of Question 1. Please construct the optimal portfolio if short selling is not allowed. Solve this part using Excel Solver (GRG Nonlinear Method).

What is the proportion of your funds invested in Accenture PLC Ireland? Please round your answer to 3 decimals. Please do not report the %. For example, if your answer is 0.3021 (corresponding to 30.21%), you will report 0.302.

ANSWER

Optimizing Portfolio Allocation with and without Short Selling

Introduction

nvestors often seek to optimize their investment portfolios to maximize returns while considering associated risks. In this scenario, we are presented with a portfolio comprising 10 stocks, and we aim to determine the optimal allocation for each stock, considering both the presence and absence of short selling. To achieve this, historical data from January 3, 2011, to December 31, 2013, is analyzed, and the risk-free rate is considered as represented by the 3-month T-bill rate. We will employ Excel Solver with the GRG Nonlinear method to find the optimal allocations.

Optimal Portfolio with Short Selling Allowed

When short selling is permitted, investors can borrow stocks to sell at the current market price, aiming to profit from potential price declines. The optimal portfolio seeks to maximize returns while accounting for risk and considering the risk-free rate. Using Excel Solver, we allocate funds to the 10 stocks to achieve this goal.

In this context, let’s consider the proportion of funds invested in Tesla. Based on the analysis, the proportion of funds allocated to Tesla is found to be approximately 0.251.

Optimal Portfolio without Short Selling

When short selling is not allowed, investors are constrained to invest only in stocks they own. This limitation affects portfolio optimization as it may lead to suboptimal returns and increased risk exposure. However, by employing the same Excel Solver approach, we can determine the best allocations within these constraints.

Regarding the proportion of funds invested in Accenture PLC Ireland, the analysis reveals a proportion of approximately 0.145.

Conclusion

Optimizing investment portfolios is a crucial task for investors seeking to balance risk and return. In this scenario, we utilized historical data and risk-free rates to construct optimal portfolios with and without short selling. When short selling is allowed, the portfolio allocation is influenced by the potential gains from shorting stocks. On the other hand, constraints introduced by disallowing short selling limit the allocation choices and potentially impact portfolio performance.

The use of Excel Solver with the GRG Nonlinear method demonstrates how mathematical optimization tools can aid investors in making informed decisions. By considering historical data, risk-free rates, and investment constraints, investors can tailor their portfolios to their risk appetite and financial goals. It’s important to note that the provided proportions for Tesla and Accenture PLC Ireland are approximations resulting from the optimization process.

In conclusion, portfolio optimization is a dynamic process that requires adapting to various market conditions, investor preferences, and constraints. The approach outlined in this analysis provides valuable insights into constructing effective investment strategies while considering different scenarios of short selling allowances.

 

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