Leverage (finance)

Financial leverage is the use of borrowed funds, debt, or other financial mechanisms to increase an investor's or company's exposure to an asset or investment relative to the amount of capital directly contributed.

Leverage can magnify both gains and losses.

A simplified leverage relationship is:

$\text{Leverage}=\frac{\text{Total Asset Exposure}}{\text{Investor Equity}}$

where:

• $\text{Total Asset Exposure}$ = total value of assets or positions controlled;
• $\text{Investor Equity}$ = capital contributed by the investor or equity holders.

Leverage in investing

An investor can use borrowed funds to purchase securities, thereby controlling assets with less capital than would be required for an unleveraged investment.

A simplified balance-sheet relationship is:

$\text{Assets}=\text{Debt}+\text{Equity}$

Therefore:

$\text{Equity}=\text{Assets}-\text{Debt}$

For an investment purchased using borrowed funds:

$\text{Leverage}=\frac{V}{E}$

where:

• $V$ = market value of the investment;
• $E$ = investor's equity.

Example

Suppose an investor contributes $5,000 of personal capital and borrows an additional $5,000 to purchase securities worth $10,000.

The leverage ratio is:

$\text{Leverage}=\frac{\mathrm{\$}\mathrm{10,000}}{\mathrm{\$}\mathrm{5,000}}=2$

The investor therefore has 2:1 leverage.

If the securities increase in value by 10%, their value becomes:

$\mathrm{\$}\mathrm{10,000}\times 1.10=\mathrm{\$}\mathrm{11,000}$

Ignoring interest, transaction costs, and other expenses, investor equity becomes:

$\mathrm{\$}\mathrm{11,000}-\mathrm{\$}\mathrm{5,000}=\mathrm{\$}\mathrm{6,000}$

The investor's return on the original $5,000 equity is:

$\frac{\mathrm{\$}\mathrm{6,000}-\mathrm{\$}\mathrm{5,000}}{\mathrm{\$}\mathrm{5,000}}=20\mathrm{\%}$

Thus, a 10% increase in the underlying asset produces a 20% return on the investor's original equity in this simplified 2:1 leveraged example.

If the securities instead decline by 10%:

$\mathrm{\$}\mathrm{10,000}\times 0.90=\mathrm{\$}\mathrm{9,000}$

Investor equity becomes:

$\mathrm{\$}\mathrm{9,000}-\mathrm{\$}\mathrm{5,000}=\mathrm{\$}\mathrm{4,000}$

The resulting return on equity is:

$\frac{\mathrm{\$}\mathrm{4,000}-\mathrm{\$}\mathrm{5,000}}{\mathrm{\$}\mathrm{5,000}}=-20\mathrm{\%}$

Leverage therefore magnifies the percentage gain or loss relative to the investor's equity.

Leverage and return on equity

For a simple leveraged investment, ignoring financing costs:

$R_E=\frac{V_1-V_0}{E_0}$

where:

• $R_E$ = return on investor equity;
• $V_0$ = initial asset value;
• $V_1$ = final asset value;
• $E_0$ = initial investor equity.

If the initial leverage ratio is:

$L=\frac{V_0}{E_0}$

and the asset return is:

$R_A=\frac{V_1-V_0}{V_0}$

then, in the simplified case where debt remains constant and financing costs are ignored:

$R_E=L{R}_A$

This illustrates why leverage magnifies returns on equity.

Leverage with borrowing costs

When borrowed funds carry interest, the effect of leverage depends on both the asset return and the financing cost.

A simplified leveraged return on equity is:

$R_E=\frac{V_0{R}_A-D{r}_D}{E_0}$

where:

• $D$ = amount of debt;
• $r_D$ = borrowing cost;
• $R_A$ = return on the underlying asset.

Using:

$V_0=D+E_0$

the relationship can be expressed as:

$R_E=R_A+\frac{D}{E_0}(R_A-r_D)$

This shows that leverage can increase the return on equity when:

$R_A>r_D$

and reduce the return on equity when:

$R_A<r_D$

before considering taxes, transaction costs, and other factors.

Margin leverage

In securities markets, leverage can arise through a margin account.

A simplified margin relationship is:

$\text{Equity}=\text{Market Value}-\text{Margin Loan}$

The leverage ratio can therefore be represented as:

$L=\frac{\text{Market Value}}{\text{Equity}}$

If the market value of the securities declines, investor equity can decline more rapidly as a percentage of the original equity.

Sufficiently large losses can cause the account to fall below its maintenance margin requirement and result in a Margin call.

Operating leverage

Operating leverage refers to the effect of fixed operating costs on a company's operating profit.

A company with significant fixed costs may experience a relatively large change in operating income when revenue changes.

A simplified operating income relationship is:

$\text{Operating Income}=\text{Revenue}-\text{Variable Costs}-\text{Fixed Costs}$

The degree of operating leverage can be represented as:

$DOL=\frac{\mathrm{\%}\Delta \text{Operating Income}}{\mathrm{\%}\Delta \text{Revenue}}$

where $DOL$ is the degree of operating leverage.

Higher operating leverage can increase the sensitivity of operating income to changes in revenue.

Financial leverage

Financial leverage refers specifically to the use of debt or other financing arrangements that create fixed or contractual financial obligations.

A common accounting measure is the debt-to-equity ratio:

$\text{Debt-to-Equity Ratio}=\frac{\text{Total Debt}}{\text{Shareholders' Equity}}$

Another measure is the debt-to-assets ratio:

$\text{Debt-to-Assets Ratio}=\frac{\text{Total Debt}}{\text{Total Assets}}$

Financial leverage can increase the potential return on equity but also increases financial risk.

Combined leverage

A company can have both operating and financial leverage.

A simplified measure of combined leverage is:

$DCL=DOL\times DFL$

where:

• $DCL$ = degree of combined leverage;
• $DOL$ = degree of operating leverage;
• $DFL$ = degree of financial leverage.

Combined leverage reflects the sensitivity of earnings available to shareholders to changes in sales.

Leverage and risk

Leverage increases the sensitivity of equity returns to changes in the value or profitability of the underlying assets.

A simplified relationship is:

$\text{Higher Leverage}\to \text{Higher Return Sensitivity}\to \text{Higher Financial Risk}$

Leverage can therefore produce asymmetric practical consequences: gains can be magnified when investments perform favorably, while losses can be magnified when investments perform poorly.

Leverage and derivatives

Leverage can also arise through derivatives, because a relatively small amount of initial capital or collateral can provide exposure to a substantially larger notional amount.

A simplified notional leverage measure is:

$\text{Derivative Leverage}=\frac{\text{Notional Exposure}}{\text{Capital or Collateral}}$

The relationship between notional exposure and economic risk can vary substantially depending on the derivative, its payoff structure, maturity, volatility, and other contractual characteristics.

Deleveraging

Deleveraging is the reduction of financial leverage.

A simplified relationship is:

<math> \text{Deleveraging} \rightarrow \text{Debt Reduction} \quad\text{and/or}\quad \text{Equity Increase} \]

For an investor, deleveraging may involve repaying borrowed funds or reducing leveraged positions.

For a company, deleveraging may involve debt repayment, asset sales used to reduce debt, or raising additional equity capital.

Risks of excessive leverage

Excessive leverage can increase the probability and severity of financial distress.

Potential consequences include:

• larger losses from adverse market movements;
• higher interest expenses;
• margin calls;
• forced liquidation;
• reduced financial flexibility;
• increased probability of default;
• greater sensitivity to changes in interest rates;
• increased risk of insolvency.

During periods of market stress, forced deleveraging can also contribute to further asset-price declines.

See also

• Financial leverage
• Operating leverage
• Leverage ratio
• Margin (finance)
• Margin call
• Margin account
• Debt-to-equity ratio
• Return on equity
• Derivative (finance)
• Short selling
• Risk management
• Financial risk