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31 VOLATILITY... AFTER TAXES! In an environment in which savings accounts have different tax characteristics, the Institut québécois de planification financière and the CFA Institute recommend considering the latent income taxes in asset allocation for a better representation of purchasing power. The impact of income taxes on various savings vehicles can be summed up as follows: David Truong CIWM, F.Pl., M. Fisc. Advisor, Expertise Center National Bank Private Banking 1859 Savings account Face value Return Risk (β, σ) TFSA 100% 100% 100% Deferred plan (RRSP, RRIF, LIRA, LIF, etc.) 1 – Estimated effective rate in retirement 100% 100% Investment account Bonds 100% 1 – Marginal rate 1 – Marginal rate Equities 100% 1 – Marginal rate/ deferred 1 – Marginal rate/ deferred We often talk about after-tax return but rarely of after-tax risk. Return is the very first thing advisors and clients look at when assessing portfolio performance. In a situation where latent income taxes have to be considered, the return on an RRSP or a TFSA presents similar characteristics. The expected return on a portfolio, before or after taxes, is similar because it is the increase in the value of the plan. Take, for example, an RRSP that is earning a return of 11%. After taxes, the RRSP also posted an 11% increase in relation to its net value. Likewise, a 6% TFSA offers a 6% increase in relation to its net value. With a non-registered investment account, however, unlike a TFSA, the increase is not equal to the return earned, because you have to take into account the income taxes payable on the return. Furthermore, those income taxes vary depending on the type of income. Since taxation is annual and is added to other personal income, we are using the marginal tax rate for our calculations. The after-tax return for a non-registered account for a year can be summed up like this: Variables G, D and I stand for the rates of return earned on capital gains, dividends and interest, respectively. R stands for the income tax rate, here either the marginal rate or the marginal dividend rate. We can therefore conclude that TFSAs and deferred plans are identical in terms of the change in return. Only investment accounts differ in this regard, because the income must be reduced by the latent income taxes. After-Tax Risk Risk measures are statistical measures that provide historical predictors of investment risk and volatility. There are several measures for calculating portfolio risk, but the most well-known are standard deviation and beta. 1. Standard Deviation The standard deviation of a portfolio is a weighted combination of the securities' variances adjusted by their covariances. That means that the overall variance of the diversified portfolio is lower than a simple weighted average of the individual variances of the securities in the portfolio. The individual variances of the equities can be calculated using a normal distribution. For the variance of a portfolio that holds many securities, the marginal contribution of one security to the total risk of the portfolio is measured using the covariance of the return on the security and the return on the portfolio. It is important to return to the source of the mathematical formulae, because that allows you to understand how the tax rates are applied. Since we can calculate historical after-tax returns, we can apply the after-tax standard deviations based on the type of account. a) Standard Deviation in Deferred Plans and TFSAs For deferred plans and TFSAs, since the after-tax return is the same as the before-tax return, the FEATURE ARTICLE

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