###### Sensitivity Analysis, Scenario Analysi ...

Simulation analysis, scenario analysis and sensitivity analysis are all stand-alone risk measures that... **Read More**

Some cost factors must be considered when trading in ETFs. They can either be **implicit costs**, e.g., tracking error, bid-ask spread, premium or discount to NAV, portfolio turnover, and secured lending; or **explicit costs**, e.g., management fees, commissions, and taxable profits or losses to traders.

From the investor’s perspective, these cost factors can either be positive or negative. Positive costs may include premiums and taxable profits, whereas the rest are negative costs.

We will illustrate the effect of management and trading costs by calculating the round-trip and holding period costs.

Suppose an investor pays a commission of $4 on a $10,000 trade. Additionally, he pays a 0.12% bid-ask spread. The investor’s round-trip trading cost is *closest to*:

$$ \begin{align*} \text{Round-trip trading cost } (\%) & = \left(\text{One-way commission } \%\times2\right) \\ & +\left(\frac{1}{2}\text{Bid}-\text{ask spread } \%\times2\right) \\ \text{One-way commission} & = \frac{$4}{$10,000}=0.04\% \\ & =\left(0.04\%\times2\right)+\left(\frac{1}{2}\times0.12\%\times2\right) \\ & =0.20\% \end{align*} $$

Suppose an investor pays a commission of $4 on a $10,000 trade. Additionally, he pays a 0.12% bid-ask spread. The 4-month, 12-month, and 2-year holding period of the investor with an annual fee of 0.18% is *closest to*:

$$ \begin{align*} \text{Holding period cost } (\%) & = \text{Round-trip trade cost } (\%) \\ & + \text{Management fee for period } (\%). \end{align*} $$

The holding period costs for:

$$ \begin{align*} \text{4-month holding period cost }(\%) & = 0.20\%+\left(\frac{4}{12}\times0.12\%\right)=0.24\% \\ \text{12-month holding period cost } (\%) & = 0.20\%+\left(\frac{12}{12}\times0.12\%\right)=0.32\% \\ \text{2-year holding period cost }(\%) & = 0.20\%+\left(\frac{24}{12}\times0.12\%\right)=0.44\% \end{align*} $$

The trading costs and the management costs can be obtained, as shown in the following table.

$$ \begin{array}{c|c|c|c} \textbf{Holding Period} & \textbf{4-month} & \textbf{12-month} & \textbf{2-year} \\ \hline \text{Commission} & 0.08\% & 0.08\% & 0.08\% \\ \hline \text{Bid-Ask Spread} & 0.12\% & 0.12\% & 0.12\% \\ \hline \text{Management Fee} & 0.04\% & 0.12\% & 0.24\% \\ \hline \text{Total} & 0.24\% & 0.32\% & 0.44\% \end{array} $$

Therefore,

**For the 4-month holding period**:

$$ \begin{align*} \text{Trading cost } \% \text{ of the total} & = \frac{0.20\%}{0.24\%}=0.83\% \\ \text{Management fees } \% \text{ of the total} & = \frac{0.04\%}{0.24\%}=0.17\% \end{align*} $$

**For the 12-month holding period**:

$$ \begin{align*} \text{Trading cost } \% \text{ of the total} & = \frac{0.20\%}{0.32\%}=0.625\% \\ \text{Management fees } \% \text{ of the total} & = \frac{0.12\%}{0.32\%}=0.375\% \end{align*} $$

**For the 2-year holding period**:

$$ \begin{align*} \text{Trading cost } \% \text{ of the total} & = \frac{0.20\%}{0.44\%}=0.45\% \\ \text{Management fees } \% \text{ of the total} & = \frac{0.24\%}{0.44\%}=0.55\% \end{align*} $$

From the above calculations, note that for holding periods of 3 and 12 months, trading costs represent the largest proportion of annual holding costs (0.83% and 0.625%, respectively). Moreover, for a three-year holding period, management fees represent a much larger proportion of holding costs (0.55%), excluding the compounding effect.

## Question

Jayson Smith is an investor who pays a commission of $8 on a $22,000 trade. He also spends 0.14% on the bid-ask spread. Smith’s round-trip trading cost is

closest to:

- 0.036%.
- 0.248%.
- 0.212%.

Solution

The correct answer is C.$$ \begin{align*} \text{Round-trip trading cost } (\%) & = \left(\text{One-way commission } \%\times2\right) \\ & +\left(\frac{1}{2}\text{Bid}-\text{ask spread } \%\times2\right) \\ \text{One-way commission} & = \frac{$8}{$22,000}=0.036\% \\ & =\left(0.036\%\times2\right)+\left(\frac{1}{2}\times0.14\%\times2\right) \\ & =0.212\% \end{align*} $$

Reading 40: Exchange Traded-Funds, Mechanics and Applications

*LOS 40 (f) Describe the costs of owning an ETF.*