Assessing Tax Efficiency through Post-Tax Returns

Tax-efficient strategies are those that sacrifice less return to a tax loss. Managers should always seek to provide the best after-tax returns possible, for any given client.

Tax-Efficiency of Various Asset Classes and Investment Strategies

The following return measures are used in analyzing the tax efficiency of an investment:

• After-tax holding period returns.
• After-tax post-liquidation returns.
• After-tax excess returns.
• Tax-efficiency ratio.

After-tax Holding Period Returns

Pre-tax return = Holding period return (“HPR”)

\(\text{HPR} = \frac { (\text{Ending value} – \text{beginning value} + \text{income}) }{ \text{Beginning value} }\)

The after-tax return builds on the pre-tax return by simply adding in taxes.

\(\text{After-tax return} = \frac { (\text{Ending value} – \text{beginning value} + \text{income} – \text{taxes}) }{ \text{Beginning value}} \)

Taxes are calculated by adding together the individual components and their relative tax burdens.

After-Tax Post-Liquidation Returns

An after-tax post-liquidation return simply computes a return that includes unrealized losses. Unrealized losses are those positions that have appreciated in value such that a tax payment will be due upon their sale. This is the case with many older positions in a portfolio which have a ‘built-in capital gain’. When this amount is calculated it will give the manager a sense of what the actual after-tax return will be. Candidates will need to use the formula for capital gains, and also the formula above for holding period return in conjunction.

Assume that a portfolio has embedded capital gains equal to 20% of holdings, and a capital gains rate of 10%. What is the post-liquidation return over the 3-year period?

$$ \begin{array}{c|c|c}
& \textbf{Pre-tax Return} & \textbf{After-tax Return} \\ \hline
\bf{\text{Year } 1} & 3.5\% & 3.0\% \\ \hline
\bf{\text{Year } 2} & 11\% & 10\% \\ \hline
\bf{\text{Year } 3} & 5.5\% & 4.75\%
\end{array} $$

Step one: calculate after-tax cumulative return: \((1+0.03)(1+0.10)(1+0.0475) = 1.187\)

Step two: subtract the embedded gains: \(1.187 – 0.02 = 1.167\). (The 0.02 is equal to 20% gains multiplied by a 10% tax rate.)

Step three: find the annualized return: \(1.167^{\left(\frac {1}{3}\right)} = 5.28\%\)

This compares to the 6.62% return for the pre-tax return. This information will be useful in the upcoming tax-efficiency ratio but is also informative by itself. Using this number may help managers get a more realistic idea of the amount of cash that could be raised by an investor who has embedded capital gains.

After-Tax Excess Returns

After-tax excess return = After-tax return of the portfolio – the after-tax return of the benchmark

Calculating the after-tax excess return allows managers to determine if the portfolio performed well enough to offset the tax burden experienced by the investor. For passive portfolios, an index is used as the benchmark. If the mandate is active, then managers must create an index of comparable active managers (a manager universe), to make their final determination.

Tax Efficiency Ratio

The tax efficiency ratio (“TER”) is after-tax return divided by pre-tax return.

\(\text{TER} =\frac {\text{After-Tax Return} }{ \text{Pre-Tax Return}} \)

TER can help managers analyze investments, and inform managers about which may be right for each client, and in what account(s). For example, a fund with high returns but with lower TER may be a good fit for a risk-seeking client, only in their tax-advantaged accounts. A fund with a higher TER would be more suitable for taxable accounts.

Question

Assume that a portfolio has embedded capital gains equal to 30% of holdings, and a capital gains rate of 10%. What is the tax efficiency ratio?

$$ \begin{array}{c|c|c}
& \textbf{Pre-tax Return} & \textbf{After-tax Return} \\ \hline
\bf{\text{Year } 1} & 3.5\% & 3.0\% \\ \hline
\bf{\text{Year } 2} & 11.0\% & 10.0\% \\ \hline
\bf{\text{Year } 3} & 5.5\% & 4.75\%
\end{array} $$

1. 1.33.
2. 0.80.
3. 0.75.

Solution:

The correct answer is: C.

Step one: calculate after-tax cumulative return: \((1+0.03)(1+0.10)(1+0.0475) = 1.187\)

Step two: subtract the embedded gains: \(1.187 – 0.03 = 1.157\)

Step three: find the annualized return: \(1.157^{\frac{1}{3}} = 4.98\%\)

This compares to the 6.62% return for the pre-tax return. The pre-tax return is 6.62%, while the after-tax return is 4.98% and since the TER is calculated as:

\(\text{TER} =\frac {\text{After-Tax Return} }{ \text{Pre-Tax Return}}\)

We substitute: \(\frac {4.98\% }{ 6.62\%} = 0.75\)

A and B are incorrect. Answer choice A inverts the pre- and after-tax returns, and answer choice B uses the same data from the summary, candidates must read the question carefully and realize that the embedded capital gains have increased in the follow-up question to 30%. 

Reading 8: Topics in Private Wealth Management

Los 8 (d) Analyze the impact of taxes on capital accumulation in taxable, tax-exempt, and tax-deferred accounts