# New C.D. Howe report - "The Piggybank Index"



## MoneyGal (Apr 24, 2009)

The C.D.Howe Institute has released another report on retirement income. 

In it, they suggest that Canadians need to save between 10 and 21% of pre-tax income annually from age 30 to age 65 in order to replace 70% of their working income in retirement. 

I'm a little baffled at some of their conclusions and underlying assumptions, and I'd appreciate the opportunity to think this through with others. Thoughts?


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## steve41 (Apr 18, 2009)

One issue that gets overlooked is the effect of inflation. Not only is the fudging of inflation by using a real rate instead of a nominal rate problematic, but the fact that, whereas inflation might run at 2%, an individual's salary will grow at a higher rate. The study as I read it, took the latter into account. (salary grows at 3%, inflation was 2%)

This makes a huge difference in any type of lifetime projection. In the early years, the savings rate will be very small (even zero) and in the latter stages (pre retirement) your savings rate will be in the 25% range.

Of course, when you include a house purchase in the mix, the savings rate during the latter working years (after the mortgage is paid off) can climb even higher. Throwing the TFSA in for good measure, and things can get real messy.


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## MoneyGal (Apr 24, 2009)

Steve: unspool this a bit more for me, please. 

They used what they say are inflation-adjusted rates (hence, not nominal rates for investment and wage growth). 

So I don't understand your comment - explain, please?


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## steve41 (Apr 18, 2009)

OK... I find that inflation and interest rates are separate and distinct entities. I treat them separately... when I force an inflation adjusted net income, I inflate that income need and treat the rates as nominal. When you treat inflation by adjusting the nominal rate as a 'real' rate, it doesn't make much difference over a short time frame, but when you treat inflation and market growth as separate and distinct over long time frames, the 2 models diverge. It is not a big deal, but is one of my peeves.

The other issue (salary grows at a higher rate than inflation) is more important.


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## MoneyGal (Apr 24, 2009)

OK, unspool even more. 

I understand that inflation and asset growth are distinct phenomena. However, in a model which holds rates (of growth and inflation) constant, what difference does it make if you use a single, inflation-adjusted rate or set the inflation assumption separately from the investment return? 

Can you explain with examples how the models diverge?

I should also ask about the "wage grows higher than inflation" peeve too. What is your issue with that?


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## CanadianCapitalist (Mar 31, 2009)

MoneyGal said:


> I'm a little baffled at some of their conclusions and underlying assumptions, and I'd appreciate the opportunity to think this through with others. Thoughts?


I took a quick look at the report and nothing really jumped at me. If I may ask, what conclusions or underlying assumptions do you find baffling?


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## CanadianCapitalist (Mar 31, 2009)

steve41 said:


> OK... I find that inflation and interest rates are separate and distinct entities. I treat them separately... when I force an inflation adjusted net income, I inflate that income need and treat the rates as nominal. When you treat inflation by adjusting the nominal rate as a 'real' rate, it doesn't make much difference over a short time frame, but when you treat inflation and market growth as separate and distinct over long time frames, the 2 models diverge. It is not a big deal, but is one of my peeves.
> 
> The other issue (salary grows at a higher rate than inflation) is more important.


Inflation and interest rates are linked together. They may diverge in the short-term but closely follow each other over the long-term. 

I think you are saying that compounding real rates at 1% produces fairly close results when interest rates are 3% and inflation is 2% but diverges when interest rates are 13% and inflation is 12%. Fair enough. But I suspect you won't get dramatically different results and we are looking for an approximate answer anyway.


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## Four Pillars (Apr 5, 2009)

I'm starting to ignore any CD Howe reports. I don't know what their agenda is but common sense is not on it. 

Need 70% replacement income in retirement? Maybe yes, maybe need more, most people will need less.

They seem to assume that you can't save for retirement outside your rrsp/tfsa. I don't see why not.


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## MoneyGal (Apr 24, 2009)

Sorry. No intent to be cryptic - I just wanted to see what others might say. 

My issues are:

1. Whether people need 70%, 50% or some other rate in retirement is not the issue for me. The issue is that 70% is presented without discussion as THE ideal rate, and there is only one passing mention of another rate - 60%. I think the assumption of static rates through what can be a long period of retirement is one of those "rules of dumb" and I don't understand why they would not at least acknowledge that this is a fundamental assumption to their model, _and it might not be apppropriate_. 

2. Their definition of saving "enough" for retirement uses the annuity factor - that is, how much could you buy as a retirement income stream if you purchase a single premium annuity at age 65. Except I don't know anyone who does that, plans for that, or advocates that. OF COURSE if you suggest that saving sufficiently is defined as "saving enough to buy an annuity that replaces 70% of your pre-retirement income" most people will fail, and fail miserably. But since when was buying a SPIA the only retirement income strategy? [scratches head]


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## steve41 (Apr 18, 2009)

OK.... I am in transit for a day (fambly emerg) so I can't do much.

Here are two runs (age 35-age 95) taking a $1M chunk of capital and solving a 'die-broke' plan for 5% nominal rate & 2% inflation by differentiating the two and a second run where I eliminate inflation and turn the rate to 3% (real rate)

When you examine the behaviour of the capital under the nominal scenario, it will grow slightly before it starts to shrink. The 'real' rate projection behaves differently.

Nominal
Real

Not a big deal, however they do diverge. 

(I only recently started to unravel the 'real' vs 'nominal' rate/inflation issue, so bear with me. I have always treated rate and inflation as two separate entities, and never thought there was a problem except over long time frames.

I will plug back into the thread later tomorrow.


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## CanadianCapitalist (Mar 31, 2009)

steve41 said:


> OK.... I am in transit for a day (fambly emerg) so I can't do much.
> 
> Here are two runs (age 35-age 95) taking a $1M chunk of capital and solving a 'die-broke' plan for 5% nominal rate & 2% inflation by differentiating the two and a second run where I eliminate inflation and turn the rate to 3% (real rate)
> 
> ...


Of course it does. It doesn't seem like you have adjusted the net to estate for inflation in the nominal scenario. You are not doing an apples-to-apples comparison here.


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## brad (May 22, 2009)

MoneyGal said:


> The issue is that 70% is presented without discussion as THE ideal rate, and there is only one passing mention of another rate - 60%.


Not really true: in their discussion of assumptions up-front, they state:

"TARGET RETIREMENT INCOME:4 The higher the targeted fraction of pre-retirement earnings to be replaced during retirement, the higher the fraction of earnings a person must save every year. We provide calculations for different target replacement rates. We start at 70 percent, usually considered the “gold standard” rate, along with a 60 percent replacement level (Table 1). We also provide calculations for a moderate 50 percent replacement rate in Appendix C." To me this doesn't imply that they're saying 70% is what people should aim for.

The focus of this report is "how much do you need to save in order to achieve a given targeted fraction of pre-retirement earnings?" I think they're clear that choosing the actual target is up to you. It would of course be nice if they explained some ways to figure out what your target should be, but that's not really the topic of this report.


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## MoneyGal (Apr 24, 2009)

Once again, I fail at close reading skills. I still don't like, however, the suggestion that 70% - or any constant rate - is the "gold standard" for replacement rates. (Not sure what smiley is appropriate here.)


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## steve41 (Apr 18, 2009)

> Of course it does. It doesn't seem like you have adjusted the net to estate for inflation in the nominal scenario. You are not doing an apples-to-apples comparison here


"Net to estate" in my model has no PV/FV connotation. It is purely what the estate will see after tax should the subject die at any point along the way.

Remember these two runs are ultra dumbed down. I have removed taxation (this $1M chunk of capital is a de facto TFSA) and the CPP and OAS have been removed. Since there is no tax, the net to estate is the value of the capital at that point in time.

The behaviour of the capital as it grows and shrinks under an indexed withdrawal scheme is completely accurate in the 'nominal' pdf (inflation and interest rate are separate and distinct). The 'real' pdf represents what the capital does when you approximate the effect of inflation by changing the rate from nominal (5%) to real (5%-2%)

My theory is that the behaviour of the capital in the 'real' model follows a nice simple spreadsheet financial formula while the behaviour of the capital in the nominal pdf, while accurate, is hard to emulate using a simple spreadsheet financial function.

As I said, over short time frames it isn't a big deal, but over a long stretch (60 years in this case) it can diverge.


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