The relationship between capital structure and portfolio management is a crucial intersection of corporate finance and investment theory. Capital structure—the mix of debt and equity financing—directly affects a firm’s risk-return profile, influencing cost of capital, financial flexibility, and market valuation ( Brealey, Myers, & Allen, 2020 ; Ahmed et al., 2024 ). In contrast, portfolio management focuses on selecting and combining assets to achieve the optimal balance between return and risk, guided by the principles of Modern Portfolio Theory ( Markowitz, 1952, 1991 ; Statman, 2019 ). Understanding how a firm’s financing decisions interact with portfolio-level risk-return optimization offers valuable insights for both corporate managers and investors.

Traditional capital structure theories, including Modigliani and Miller’s (1958) irrelevance proposition, the trade-off theory ( Kraus & Litzenberger, 1973 ), the pecking-order theory ( Myers & Majluf, 1984 ), and agency cost theory ( Jensen & Meckling, 1976 ), provide complementary perspectives on how leverage impacts firm value. Recent empirical evidence suggests that while pecking-order behavior often dominates in practice, trade-off considerations remain important, especially when accounting for taxes, bankruptcy costs, and financial flexibility ( Frank & Shen, 2016 ; Dang et al., 2020 ).

Most classical models, however, treat debt and equity in isolation from portfolio risk considerations. Integrating Modern Portfolio Theory into capital structure analysis allows for a more unified approach—treating debt and equity as a two-asset portfolio whose weights can be optimized to minimize the Weighted Average Cost of Capital (WACC) for a given expected return ( Rubinstein, 1973 ; Huang & Ritter, 2022 ). By applying mean-variance optimization and solving via a Lagrangian function, firms can identify the capital structure point that lies on the efficient frontier, thus achieving both cost minimization and risk control.

Recent studies have explored this integration further. For example, Li and Shi (2021) demonstrate that portfolio-based capital structure models can better capture market volatility effects on firm value, while Baker and Wurgler (2020) show that market timing and behavioral factors also influence leverage decisions in ways consistent with portfolio optimization logic. Dynamic approaches, such as those by DeAngelo and Roll (2015) , highlight how firms adjust capital structures over time in response to changing market conditions and internal constraints.

Furthermore, broader portfolio innovation, such as Hierarchical Risk Parity (HRP) and machine learning–based optimization models, illustrates modern advances in risk minimization—though largely within asset manager rather than firm-level contexts ( de Prado, 2016 ). These techniques motivate our approach of adopting mean-variance optimization at the corporate balance-sheet level.

This paper builds on these insights by proposing a quantitative framework that explicitly combines capital structure theory with portfolio optimization methods. The proposed model treats debt and equity as correlated portfolio assets, uses mean-variance analysis to model risk-return trade-offs, and applies Lagrangian optimization to determine the optimal leverage that minimizes WACC for a target return. By doing so, the model bridges a theoretical gap, offering a rigorous, closed-form method that aligns corporate finance decisions with portfolio optimization principles.

Major Assumptions:

Derivation of the Model:

First: Estimating rates of return, variances and covariance

The rate of return on bond and stock are estimated as:

$R_{dt}=\frac{B_t-B_{t-1}}{B_{t-1}}$(1)

$R_{et}=\frac{S_t-S_{t-1}}{S_{t-1}}$(2)

Where, d = debt, e = equity, B = market price of bond, and S = market price of stock.

${\sigma }^2\left(d\right)={\displaystyle {\sum }_1^n\frac{{\left(R_{dt}-R_d\right)}^2}{n-1}}$(3)

${\sigma }^2\left(e\right)={\displaystyle {\sum }_1^n\frac{{\left(R_{et}-R_t\right)}^2}{n-1}}$(4)

Where ${\sigma }^2$= variance, $R_d$ and $R_e$ the mean of $R_{dt}$ and $R_{et}$.

Finally, the covariance between debt and equity is given by

$Cov\left(d.e\right)={\displaystyle {\sum }_1^n\frac{\left(R_{dt}-R_d\right)\left(R_{et}-R_e\right)}{n-1}}$(5)

Second: Given

${\sigma }^2=W_d^2{\sigma }_d^2+W_e^2{\sigma }_e^2+2W_d{W}_{e}Cov\left(d.e\right)$(6)

Where $W_d$ and $W_e$ are the weights of debt and equity, which are given by $W_d=\frac{d}{d+e}$, and $W_e=\frac{e}{d+e}$, subject to

$W_d+W_e=1$(7)

Forming Lagrange function as L, we have

$L=W_d^2{\sigma }_d^2+W_e^2{\sigma }_e^2+2W_d{W}_{e}Cov\left(d.e\right)+\lambda \left(W_d+W_e-1\right)$ (8)

Taking the partial derivative of L with respect to $W_d$, $W_e$ and $\lambda$, we get

$\frac{\partial L}{\partial W_d}=2W_d{\sigma }_d^2+2W_{e}Cov\left(d.e\right)+\lambda =0$ (9)

$\frac{\partial L}{\partial W_e}=2W_e{\sigma }_d^2+2W_{d}Cov\left(d.e\right)+\lambda =0$ (10)

$\frac{\partial L}{\partial \lambda }=W_d+W_e=1$ (11)

Rearrange in Matrix form we have

$\left[\begin{array}{ccc}2{\sigma }_d^2& 2Cov\left(d.e\right)& 1\\ 2Cov\left(d.e\right)& 2{\sigma }_e^2& 1\\ 1& 1& 0\end{array}\right]\left[\begin{array}{c}{W}_d\\ W_e\\ \lambda \end{array}\right]=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]$ (12)

Using Cramer’s rule we solve for $W_d$ and $W_e$, the optimal weights of debt and equity:

$W_d=\frac{{\sigma }_e^2-Cov\left(d.e\right)}{{\sigma }_d^2+{\sigma }_e^2-2W_d{W}_{e}Cov\left(d.e\right)}$(13)

$W_e=\frac{{\sigma }_d^2-Cov\left(d.e\right)}{{\sigma }_d^2+{\sigma }_e^2-2W_d{W}_{e}Cov\left(d.e\right)}$(14)

Hence,

$W_d+W_e=1$ or $W_e=1-W_d$(15)

These optimal weights will achieve the minimum cost of capital hence maximize the value of the firm.

An empirical test was conducted to validate a model for determining the optimal weight of debt for corporations. ¹The analysis utilized data from the Egyptian securities market, with a focus on companies listed on the EGX30 and EGX70 indices.

The objective of the analysis was to use the collected data to estimate the optimal weight of debt $W_d$.

The relationship between capital structure and portfolio management is multifaceted and critical for financial decision-making. A firm’s capital structure significantly affects its risk profile, stock price volatility, and cost of capital, all of which are crucial inputs for portfolio construction and management as demonstrated, there is no one-size-fits-all approach; portfolio managers must carefully consider the capital structure of firms and its implications for risk and return. By integrating modern portfolio theory with capital structure principles, this paper offers a model to optimize the debt-equity mix, minimize the WACC, and thereby maximize firm value. The statistical evidence overwhelmingly suggests that the model is exceptionally good, performing its function with a high degree of accuracy and reliability. The high correlation, strong predictive power, and low error rates, further supported by the regression analysis, affirm that the model is both powerful and valid for empirical work. Future research could further explore how the interaction between capital structure and industry-specific factors influences portfolio performance. Furthermore, emerging approaches in behavioral and macro-finance may shed light on how investors perceive and react to capital structure in their decision-making.