**I.Introduction**

Taxes are clearly an important part of any investment strategy for taxable investors. Harvesting losses, deferring gains can add value to a portfolio. But what impact do taxes have on arriving at the long term strategic asset allocation decision?

**Conclusion**: taxes have an impact not only on return but also on risk. This fact mediates the impact of taxes on asset weights, as the relative efficiency of assets is roughly the same before and after tax.

**II. Asset Allocation: The Basics**

- Asset allocation is complicated but essentially consists of 2 steps:

(i) formulating views about asset class performance in the future

(ii) constructing portfolios based on those views

- Taxes affect the first step, but how much do they affect the second?
- Notably, in all of the complicated portfolio construction process, 4 things matter:

(i) investor objectives: how much risk am I willing to bear? (post-tax)

(ii) asset risk: how risky is each asset on the margin and what is its risk ranking?

(iii) risk-adjusted returns: what is the level and ranking of risk-adjusted returns? In the classic mean variance problem, this can be expressed as efficiency (excess return over risk)

(iv) portfolio risk: how do the assets fit together in terms of risk and return? Here correlation is a critical input.

**III. Taxes: An overview**

- In the US, three types of taxes are considered:

(i) taxed as ordinary income (either interest/yield or short-term gains)

(ii) taxed as dividends or long-term gains

(iii) state taxes

- The other consideration is how much positive and negative returns can be offset in each category.

**IV. Tax Impact on Returns**

- Three key factors in determining the “effective tax rate” for a particular asset class:

(i) turnover of the portfolio

(ii) yield and dividend rates

(iii) tax rates

- The impact of turnover

(i) Definition

(ii) Does turnover imply the proportion of cap gains which is short-term? No.

(iii) If turnover is independent of tax considerations, then short-term gains will approximately = Turnover^2

(iv) Note: in practice managers might be more than simply random in managing tax implications of trading strategies which will reduce this further

- Putting it together

(i) Based on the three assumptions above, we can calculate an effective tax rate

(ii) In this case, returns will be (1-Effective Tax Rate) Pre-tax Return

(iii) This is the conventional stopping point: some assets are more heavily taxed than others and therefore should be penalized in the portfolio construction process

**V. Risk: The Forgotten Quantity**

- Two important components of risk: volatility and correlation
- Volatility

(i) Key point is taxes “shrink” not only returns but also volatility of returns

(ii) Key assumptions: losses can be roughly offset with gains

(iii) Result is that volatility shrinks *at the same rate* as returns

(iv) This in turn means that the *efficiency* of a particular asset class is held roughly constant before and after tax

(v) Only impact on asset allocation therefore will be the ranking of assets in terms of risk but not in terms of efficiency (in other words, it can potentially move the place on the frontier that the asset sits, but not the average level (ranking versus penalization)

(vi) Possible exception: if *sources* of volatility are not proportional to sources of return. As an example, consider bonds. Yield is a large component of return but a very small component of marked-to-market and trading volatility. If this is true, then volatility might change at a different rate than return.

- Correlation

(i) Key point: correlation is unaffected by taxes as well

(ii) Why? Correlation is unaffected by multiplying

**VI. Conclusion**

Key thing missing in conventional wisdom and the classic approaches is that taxes affect risk as well as return. This mitigates the impact of taxes on choice of portfolio weights.