« When I chose to only deal with professionals, I never would never have thought I was choosing a life of solitude. In Canada, when we are faced with choosing between simplicity or truth, Canadians have a culture of always choosing the easy way out. » Richard Proteau (reflection on financial services and financial industry).
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What I like about coding and mathematical modelling is that it is impossible to avoid the truth. Often when I code or create a mathematical model, I am often faced with situations where the results do not fit with what I expected. Usually as a programmer, I will undergo the 5 stages of coding grief.
First I will be in denial. Certainly the code is wrong and not my expectations!
Anger, when it is impossible for me to reconcile my expectations with what my code or mathematical model has revealed.
Bargaining, should I cheat and change my code or model to get the results that would conform to my expectations?
Depression, when I realized that even with cheating, my expectations or what I believe to be true would still not be true. Depression at knowing that what I believed for so long was wrong. Why did I believe and accepted what others believed instead of checking it out myself? Depression to know if I embraced the truth, my expectations will still remain the truth out there. No amount of proof will change what is believed by others. There is profit in what is called the « convenient truth and only expenses in the real truth because investing in the truth is about long term results.
Then comes acceptance that I must embrace the truth and be true to myself; acceptance that what is believed by a majority of people; that was is promoted as the truth; that was is written as the truth by experts and specialists is often not the truth but will still dominate the market place. Embracing the truth marginalizes you.
I have come to accept that what is promoted as financial advice is in fact a system of financial principles which have been elevated to the level of dogma which is then distributed to the public through expert sources turning such dogma into a financial doctrine.
The distance that separates beliefs from truth is called ignorance and financial advice is delivered with all its flavors.
The fact is that most financial claims are unproven or unsubstantiated. I have challenged the financial industry for example to prove that Buy and Hold is better than managing the risk and returns of your investments. No experts have been able to do this. Their math is flawed, their mathematical model incomplete or I get a reference to texts written by other experts referring to other texts written by other expects… Or I get non-quantifiable claims that cannot be proven such as « people are too emotional to actively manage risk or returns… »
The last mathematical model I created was about paying your mortgage on a Bi-Weekly basis versus Accelerated Bi-Weekly basis. It is accepted as the truth that if you choose the Accelerated Bi-Weekly option, your mortgage will be paid earlier. I was very surprised when my code and mathematical model did NOT meet these expectations.
If I asked an advisor to prove that the Accelerated Bi-Weekly payment will result in the mortgage being paid earlier, most advisors would provide me with a reference to other written claims which is also based on other written claims. Their belief is that if a claim has been written over and over again, it must be true.
Some advisors who have some knowledge of math would provide me with the mathematical proof under the form of a logarithm function. However math theory is different then applied math. Your math can be good but if you apply it wrongly it will deliver you the wrong results…
What is missing from the math is the logical solution to the problem. Since the foundation of the design of a program or mathematical model is logic, it is the only way to substantiate or disprove that Accelerated Bi-Weekly payments allows you to end your mortgage early.
When you deal with logic, you have to deal with conditions (If/Then/Switch statements). You would find that for the claim that the Accelerated Bi-Weekly option results in a mortgage being paid earlier to be true, it has to meet a lot of conditions such as that the Term of the mortgage must be equaled to its Amortization.
Interestingly enough, in the United States, since there is no Term component to a mortgage and the rate is fixed (if selected) for the mortgage of 15 or 30 years (its amortization), choosing Bi-Weekly (which is always the accelerated option) will result in ending the mortgage early and the amount of interest saving and number of payments saved can be calculated mathematically without the use of a mathematical model. So the math theory is the same as the applied math.
In Canada, where the interest is fixed for a period shorter (call the term of the mortgage) than its amortization, it is impossible to know how much interest will be saved by choosing the Accelerated Bi-Weekly option as you don’t know what interest rates will apply in the futur and what term you will be choosing.
How soon will your mortgage be paid when choosing the Accelerated Bi-Weekly payment? If the initial amortization is not changed, this will depend on the last term of the mortgage. For example, at the last renewal, if a term of 1 year is selected, the earliest you can repay your mortgage is over this last term of 1 year. If you choose a term of 10 years (maximum term in Canada) as your last term, choosing Accelerated Bi-Weekly option would result in the maximum decrease in the payment period since the prepayment applies to that maximum period.
What are the mechanics?
Basically if the initial amortization is not shortened at each term renewal, the term renews on the outstanding amount of the mortgage less than what has been prepaid. It’s like triggering a tax gain and realizing it but here you are realizing the benefits of your prepayments by reducing your mortgage payment instead of paying your mortgage early.
Let’s look at an example of an Accelerated Bi-Weekly payment, for a $100,000 mortgage, amortization 30 years, fixed interest rate of 5%, Example B (USA) the term is equaled to the amortization 30 years and Example A(Canada), the term is 1 year throughout the amortization.
Example A Example B
#payment payment Balance #payment payment Balance
1 267 99923 1 267 99923
26 267 97957 26 267 97957
52 265 95851 52 267 88697
130 261 89122 130 267 88697
777 175 162 656 267 64
778 163 0 657 65 0
Please note for the sake of comparing apple to apple, interest is compounded based on the Canadian Model, Bi-Annual basis and not on monthly basis (USA).
In the USA, Bi-Weekly is equaled to an Accelerated Bi-Weekly Payment in Canada
In the USA, if you choose a ARM mortgage, then the Canada model will apply as your mortgage will now have a term. (Example 5/1 ARM : initial term 5 year renewing every year thereafter).
The Canadian model reflects what would happen in Canada. A mortgage, at the end of the term, will always renew automatically based on the mortgage conditions, If the amortization is not manually changed, then it is the payment that will change.
Well you think then the solution is simple. Why not change the amortization every year the mortgage renews? Well it does not work. It creates a problem that cannot be solved where you will either pay too much in a year (overshoot)or not enough(undershoot).The problem is that when you overshoot and you need to readjust the amortization by increasing it, you can’t do this since any increases in the amortization will be considered to be a refinance. This is where the practices and the real world result in the math theory not matching what is applicable.
The problem is that when Canadian mortgage brokers or Canadian Brokers talk about Bi-Weekly versus Accelerated Bi-Weekly and the advantages of the latter, they are referencing the USA model that does not apply in Canada. Their advice is absolutely flawed!!! It’s easier to choose simplicity and refer the USA model even if it is not true in Canada then dealing with the real truth because the mechanics of the Canadian mortgage is very complicated.
Don’t doubt for a moment that an Accelerated payment is good. It will always saves interest and allow you to prepay your mortgage. However if your mortgage has a term that is less than its amortization, it is impossible to know how much interest you will save or how fast your mortgage will be paid. It will depend on what happens in the future.