Other Return Measures

Other Return Measures

Gross and Net Return

The gross return is what an asset manager earns before subtracting various costs such as management fees, custody fees, taxes, and other administrative expenses. However, it does account for trading costs such as commissions.

Gross return does not consider management or administrative costs. For this reason, it is a suitable metric for assessing and comparing the investment expertise of asset managers.

Net return is a metric for how much an investment has earned for the investor. It considers all administrative and management costs that reduce an investor’s return.

Pre-tax and After-tax Nominal Return

Unless otherwise stated, all returns are nominal pre-tax returns in general. Depending on the jurisdiction, different rates apply to capital gains and income. Long-term and short-term taxes may also be applied to capital gains.

The after-tax nominal return is determined by subtracting any tax deductions applied to dividends, interest, and realized gains from the total return.

Real Returns

Returns are typically presented in nominal terms, which consist of three components: the real risk-free return as compensation for postponing consumption, inflation as compensation for the loss of purchasing power, and a risk premium. Real returns are useful in comparing returns over different periods, given that inflation rates vary over time.

Recall the relationship between the nominal rate and the real rate:

$$\text{(1+ Nominal Risk-free rate)=(1+Real risk free rate)(1+Inflation premium)}$$

We can find the connection between nominal and real returns by considering the real risk-free rate of return and the inflation premium. This relationship can be expressed as:

$$(1+\text{Real Return})=\frac{(1+\text{Real risk-free rate})(1+\text{Risk premium})}{1+\text{Inflation premium}}$$

Real returns become particularly useful when you want to compare returns across various time periods and different countries. This is especially important when returns are shown in local currencies and when inflation rates vary from one country to another.

After-tax real return is the amount the investor receives as payment for delaying consumption and taking on risk after paying taxes on investment.

Leveraged Returns

If an investor uses derivative instruments within a portfolio or borrows money to invest, then leverage is introduced into the portfolio. The leverage amplifies the returns on the investor’s capital, both upwards and downwards.

The leveraged return considers the actual return on the investment and the cost of the borrowed money. The cost of borrowing and financing fees are subtracted from the overall return produced by the investment to determine the leveraged return.

Using the borrowed capital (debt) increases the size of the leveraged position by the additional borrowed capital.

Intuitively, the leveraged return is given by:

$$\begin{align}R_L&=\frac{\text{Portfolio return}}{\text{Portfolio equity}}\\&=\frac{\left[R_P\times\left(V_E+V_B\right)-(V_B\times r_D)\right]}{V_E}\\&=R_P+\frac{V_B}{V_E}\left(R_P-r_D\right)\end{align}$$

Where:

\(R_L\) = Return earned on the leveraged portfolio.

\(R_P\) = Total investment return earned on the leveraged portfolio.

\(V_B\) = Value of debt in the portfolio.

\(V_E\) = Value of equity in the portfolio.

\(r_D\) = Borrowing cost on debt.

Example: Calculating Leveraged Return

For a $250,000 equity portfolio with an annual 9% total investment return, 40% financed by debt at 6%, the leveraged return would be:

$$R_L=R_P+\frac{V_B}{V_E}\left(R_P-r_D\right)=9\%+\frac{$100,000}{$150,000}\left(9\%-6\%\right)=11\%$$

Question

A $7,500,000 equity portfolio is 35% financed by debt at a cost of 5% per annum. If the equity portfolio generates a 9% annual total investment return, the leverage return is closest to:

A. 11.15%.

B. 14.00%.

C. 8. 25%.

The correct answer is A.

$$\begin{align}R_L&=R_P+\frac{V_B}{V_E}\left(R_P-r_D\right)\\&=9\%+\frac{\$2,625,000}{\$4,875,000}\left(9\%-5\%\right)=11.15\%\end{align}$$