[lead]The allocation to stocks and bonds in a portfolio is usually a decision made without considering taxes. For retirees this could be a mistake.[/lead]

Bob has $500,000 in his registered savings plan (RRSP) and $500,000 in a taxable account. Bob’s RRSP is invested in bonds and his taxable account is invested in stocks. Alice has $1,000,000 in an investment account which she has split equally between bonds and stocks. Do Alice and Bob have the same asset allocation and are they taking the same risks?

The predominant view is yes to both questions: Alice and Bob both have an asset allocation of 50% equities and 50% bonds and are therefore exposed to the same market risk. This is a view that ignores taxes, or equivalently, assumes that the effective tax rate on deposits and withdrawals is zero. In this world, the risk to the portfolio value and the risk to income from the portfolio is the same. That is not the world most investors inhabit.

How might taxes impact an investor’s asset allocation? We can get an idea by imagining a world of very high marginal taxes. In the (absurd) extreme of 100% marginal tax rates, all of Bob’s RRSP belongs to the Canada Revenue Agency. In this situation, Bob may have a pre-tax asset allocation of 50% equity, 50% bonds but his after tax income is coming solely from the equity portfolio and his after-tax income is 100% exposed to equity risk. By focusing solely on the tax on withdrawals from an RRSP we highlight that taxes matter, not that RRSPs are a bad idea: when considered over the investment lifecycle tax advantaged investments are a good thing but we need a means of evaluating their impact on after-tax income which is, ultimately, what retirees spend.

Tax Equivalent Wealth

A full accounting of the impact of taxes should include the impact of taxes not just on withdrawals but on deposits and the tax deferral in between. A general treatment would consider the different tax regimes of RRSPs, tax free savings accounts (TFSAs) and corporate holdings. Since bonds and stocks have different tax treatments, the asset mix within each of these accounts also needs to be considered. The asset location decision (which investment goes in which account) now is intertwined with the asset allocation decision (how much should be allocated to equities and bonds). Give this complication, it is easy to understand why the tax impact on asset allocation has been largely ignored.

To the rescue comes research1 that provides two useful simplifications.

The notion of tax equivalent wealth. A dollar deposited in a tax advantaged account is converted to an equivalent amount deposited in a taxable account that would generate the same after-tax retirement income. This is the tax equivalent wealth of the account. In general, we would expect the tax equivalent wealth of an RRSP to be greater than the RRSP value (or else why invest in RRSPs?).
The asset location decision between the tax equivalent wealth accounts can be considered independent of the asset allocation decision.

Let’s use Bob’s savings experience as an example.

Bob’s Z factor

Bob built his RRSP portfolio by saving regularly, always buying bonds. In our simple example, we will assume his savings can be represented by a single bond purchase, 30 years ago and all the return comes in the form of interest payments. We will skip the details, but it is then easy to calculate a ratio, which we will call the Z factor, which tells us the value of bonds that Bob would need to generate the same after-tax wealth 30 years later. We assume Bob paid 45% tax when saving and 25% on withdrawal in retirement. We calculate this ratio below for interest rates of 3%, 4% and 5%.

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Bond Return 3% 4% 5%
Z factor2 1.12 1.29 1.47

Source PWL calculations

So, for example, if interest on the bond averages 4% then, for every $1 invested in Bob’s RRSP, he would have to invest $1.29 in a taxable account to get the same after tax value. The Z factor accounts for the value of the deferred tax within the RRSP, counterbalanced by the income tax payable upon withdrawal. For shorter savings periods or lower interest rates, the benefit of the tax deferral might outweigh the tax on withdrawal so the Z factor is less than one. For a full consideration of the benefit of using an RRSP we must include the benefit of being able to contribute pre-tax dollars. Our example, with Z factors close to unity, highlight that in a low interest rate environment like today’s, almost all the benefit of investing in bonds in an RRSP comes from the tax refund – a reminder that this should not be seen as a “gift” from the CRA to boost spending on a vacation or a dream kitchen!

To get $1 after tax contribution into Bob’s RRSP requires only $0.55 pre-tax, with the government providing the additional $0.45 through the tax refund. In other words, Bob’s contribution is leveraged by 1/(1-0.45).

Now we get to the key question: how much would Bob have to contribute in a taxable account to get the same after tax benefit that he will get from his RRSP?

If WR is Bob’s after-tax RRSP contribution then he would need to contribute WI after-tax dollars in a taxable account to get the same after tax benefit where:

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and t is the marginal tax rate during accumulation³.

Recall that we considered Bob’s RRSP, currently valued at $500,000 to have grown from a single bond purchased 30 years ago when he was paying 45% tax. Assuming a 4% interest, we can calculate Bob would have needed $152,602 in his RRSP 30 years ago to grow to $500,000 in his RRSP today. We also know the Z factor equals 1.29, so we can calculate the tax equivalent wealth, W_I:

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Let’s assume that Bob also had $152,602 in equities in a taxable account 30 years ago. He would have a total asset allocation of 50% equities, 50% fixed income. On a tax equivalent basis his RRSP is actually worth $194,277, meaning that had Bob not used the RRSP he would have needed taxable assets of $194,277 to generate the same after tax income in retirement. His total tax equivalent wealth is $346,879 and the tax equivalent asset allocation is 44% equities and 56% fixed income. Bob’s spending power in retirement has a lower equity allocation and a lower risk than his pre-tax asset allocation would indicate.

A world of Z factors?

A completely general treatment would compute Z factors for any mix of bonds and equities in any tax advantaged account (RRSPs, TFSAs, and corporations) but that is not necessary to draw some general conclusions:
If you are saving to generate future income, and Z>1, assets held within a tax advantage account will have a greater impact on retirement income than the pre-tax asset allocation suggests.
Specifically, if you follow the recommended strategy of locating bonds preferentially in tax advantaged accounts, then the volatility and return of after tax retirement income behaves as if the asset allocation had a higher allocation to bonds than the pre-tax asset allocation would suggest.

Often when investors are looking for options for additional retirement income they consider taking more portfolio risk by increasing the equity allocation. As we have illustrated, there may not be a simple relationship between a change in pre-tax asset allocation and after tax income. Although simple models can provide general insights, comprehensive financial planning that accounts for the interplay of all the factors that contribute to a sustainable retirement income, not just taxes and asset allocation, remains the best solution for selecting the optimum strategy for individual investors.

¹ Huang, J. 2008. Taxable and tax-deferred investing : A tax-arbitrage approach Review of Financial Studies,21,2173-2207

² Z = (1 – T) * ^etrN, where T is the tax on withdrawal, t is the tax during accumulation, r is the bond interest and N is the savings period.

³ If we were considering TFSAs rather than RRSPs then
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where W_{S is the contribution to the TFSA.}