Mortgages - fair assessment or usury?

[Winston Gutkowski]

Martin Vajsar wrote:I've always thought that "compound interest" means "interest from interest" (and so does Wikipedia). Over time, it can get really big (it's geometric, not linear, series). That's different than borrowing money at rate X and lending it at rate X+Y.

Ah, but even I know that paying back a loan at that rate is NOT arithmetic, even if the original interest rate sum is. I also wonder if it isn't part of advertising mythology ("2% above prime").

If you measure it against one businesst transaction (the mortgage), then you might be somewhat right. But it is much more usual - and, in my opinion, much more correct - to measure the profit against the money you've invested (ROI). And in this measure, the profit is proportional to the remaining debt.

Ooof (I assume you're talking about the lender's ROI). Even more reason to keep it as high as possible then, no?

Unless every remortgage is part of a larger process that takes into account the borrower's ongoing relationship with the lender (including money they've already paid), rather than simply a new contract, then you may be right; but I don't think it's a standard requirement (do tell me if I'm wrong).

I too think this is a great discussion. It has, at the very least, made me to try to look at the entire mortgage industry from a wider point of view.

Glad you're enjoying it.

Winston

[Winston Gutkowski]

Piet Souris wrote:Well, as I explained, risk is only one part that determines the actual interest. That particular part is called 'credit spread'. But if lending is your business, you would also want to earn a living. And you have your expenses.
As always: it is paying off to try to see things from the perspective of the other party. If you know the reasoning,
ask yourself: if I were that banker, would I behave differently?

A very good question, and possibly what's at the heart of this thread.

The problem is that it gets into more philosophical questions like: "What is a loan?". Presumably, the idea is that there's some mutual benefit to both parties in the process; otherwise it seems unlikely that they would ever have happened. And if that's the case, is it reasonable to use words like "indentured"? This would suggest that the process is simply a one-way transaction that benefits the borrower at the expense of the lender, when my argument is that it's actually probably the reverse.

My question to you, as the maths expert here (and it's a tough one): Are the formulae that you've learned as an actuary the only interpretation that can be put on a loan?

Lloyd's "names" (almost all, very rich people) were successfully able to argue back in the 90's - after several major disasters that hit Lloyd's in quick succession - that "indenturement in perpetuity" (ie, indenturement of family) ran contrary to modern ethics and, while I disliked their crowing at the High Court result and their "beggars with top hats" intensely, I do understand that it was a landmark case in our understanding of "what a loan is".

Winston

[Martin Vashko]

Winston Gutkowski wrote:

Martin Vajsar wrote:I've always thought that "compound interest" means "interest from interest" (and so does Wikipedia). Over time, it can get really big (it's geometric, not linear, series). That's different than borrowing money at rate X and lending it at rate X+Y.

Ah, but even I know that paying back a loan at that rate is NOT arithmetic, even if the original interest rate sum is. I also wonder if it isn't part of advertising mythology ("2% above prime").

True. I did forget. But the compound interest (in the Wikipedia's sense) gets geometrically larger with time, whereas here it would get geometrically larger with every new bank in the chain. And while there are many months in 30 years, there probably aren't that many banks involved in my mortgage. The final rate would surely look different then.

Ooof (I assume you're talking about the lender's ROI). Even more reason to keep it as high as possible then, no?

Yup. Until banks find a way to profit from me without lending me money, they'll try (among other things) to sell me a mortgage. Car manufacturers are trying to sell me a car. I don't see how that should be particularly bad; when I don't want a car, or a mortgage, I don't get one.

If you think people are tricked into getting mortgage, now that would be something different. Should state prevent people who didn't pass a test on financial literacy from taking mortgages?

Side note: I've got a second mortgage (and a second flat) by now, so I'm a glaring example of the principle you're talking about But I have a funny story to share - when I negotiated my first mortgage, it took some painful work to get all the details fixed. When finally I had it all done, I was already past some terms and needed to have it signed really fast, but I've still asked to get the contract with me to read it over weekend. This request caused such a disarray in the bank that I still think I was the first customer who actually asked for it. Looks like most folks sign even the mortgage contract without ever reading it. I fortunately learnt to read everything I sign (even the small print) before getting burned, but I feel this is a rare exception, not the rule. I believe this should be one of the basic things schools should teach. Perhaps students should be required to sign an exam protocol at the exit exam, those who would sign without reading it would fail....

Unless every remortgage is part of a larger process that takes into account the borrower's ongoing relationship with the lender (including money they've already paid), rather than simply a new contract, then you may be right; but I don't
think it's a standard requirement (do tell me if I'm wrong).

Yes, it is practically a new contract. But the parameters are different: I've already paid some of the principal, so the new debt will be lower, the ratio to the house price better and therefore I might get a better rate. And I'll probably want to pay in shorter time. If none of the original parameters change (the overall time, the rate), I'll end up paying the exact same amount each month. But I'll pay much bigger share of principal each month, mainly because there are now 20 years to go instead of 25 (though we used 30 years as an example earlier, I didn't take 30 years mortgage, it would be too costly overall).

There is no fundamental reason to take into account the money I've already paid: it is just the interest and a part of the principal I had to pay according to the contract. That I paid improves my credit score, but that's about all.

I really don't see how paying off the mortgage prematurely would benefit the bank. To the contrary, if the mortgage ends, it needs to find a new use for the repaid principal. I think there is some point in here where we don't understand each other.

Presumably, the idea is that there's some mutual benefit to both parties in the process; otherwise it seems unlikely that they would ever have happened. And if that's the case, is it reasonable to use words like "indentured"? This would suggest that the process is simply a one-way transaction that benefits the borrower at the expense of the lender, when my argument is that it's actually probably the reverse.

(Sorry for mixing quotes from different posts, if it gets cumbersome, I'll cease.)

So the lender does not benefit from the mortgage? I think I did benefit, as I couldn't buy a flat otherwise. I like my flat. I'll post some photos sometime

This is pretty philosophical, actually. What is the fair price of anything? Should bread be sold at different prices to people with different income?

My question to you, as the maths expert here (and it's a tough one): Are the formulae that you've learned as an actuary the only interpretation that can be put on a loan?

Though you haven't addressed me, and I'm by no means an expert, I'll try: not necessarily, I'd say, but all the formulae a bank will accept will follow a basic principle: you'll pay the interest from the amount you're owing. I believe a bank might even allow you to postpone your payments by several years completely, but I'm pretty sure that the amount you'd have to pay eventually wouldn't please you.

Edit: I've misunderstood the question apparently. It's getting late I'd say there is unlimited number of interpretations of anything.

[Piet Souris]

Winston Gutkowski wrote: (...)
The problem is that it gets into more philosophical questions like: "What is a loan?". Presumably, the idea is that there's some mutual benefit to both parties in the process; otherwise it seems unlikely that they would ever have happened.

Well, thre is certainly a mutual benefit.
The theory behind it is based on the assumption of 'benefit curves' (hope I'm using the correct English names here).
Such a curve is a function that values the amount of money, this 'value' being your sense of hapiness.
Such curves must have two characteristics:

- more money ==> higher value i.e. the function is strictly monotone increasing
- the more money you have, the less you gain from extra money ==> the second derivative is negative

or in short: such a 'benefit curve' is concave and positive. Of course such functions are hypothetical, but they
form the basis that makes things like loans and insurances possible.

And I do not have any reason to doubt that there is such a mechanism in real life.

Take for example the recent hype around the Apple iPhone and iPad.
Now, Apple haters alway say that these Apple products are way too high priced, and
they may have some good points here. But the true Apple fan values his/her Apple machine
so much, that they are willing to pay double the price, so much pleasure do they get
from their Apple. In this case both parties benefit.

The same holds for a mortgage. Martin pointed it out already. Yes, you are the weaker party,
and yes, you get to pay interest, possibly interest that you feel is too high.
BUT: it enables you to buy your own house, now, instead of saving for it for the next fifteen years!
And when the conditions underlying the mortgage are not outrageous, then again, both parties benefit.

And the final factor which tops it all: whenever people are involved, you will see
that people behave irrational. I have always wondered how it is possible that we launch a rocket,
and two years later that same rocket encounters a meteorite somewhere in space, lands on
it and taking pictures, while at the same time, we do not know tomorrows stock exchange prices.

Indeed, it's getting philosofical, and it's getting late, and indeed: great discussion.

Greetz,
Piet

[Winston Gutkowski]

Piet Souris wrote:Well, as I explained, risk is only one part that determines the actual interest. That particular part is called 'credit spread'.
But if lending is your business, you would also want to earn a living. And you have your expenses...

Sure, but if I'm buying a house, should I expect to be funding your lifestyle?

A mortgage agreement is quite specific: "You agree to pay x percent on this repayment schedule". My question is not, and has never been, "is the agreement document fair?"; it's much closer to:

Are the rules of engagement fair?

Winston

[Winston Gutkowski]

Martin Vajsar wrote:If you think people are tricked into getting mortgage, now that would be something different.

I'm not sure if "tricked" is the right word, but I have no doubt that people can be talked into it. After all, I (and I assume you) are computer programmers with a reasonable grasp of maths (and a tenuous grasp of even the stuff we haven't been taught), but we need a Piet to tell us what the maths actually is.

Should state prevent people who didn't pass a test on financial literacy from taking mortgages?

Please. I know MBA's who wouldn't know their arses from their elbows. A good businessman (in the truest sense of the word) isn't born to it; he's made. In ancient times a man could become a patrician by being a good bricklayer, having a lot of kids, and being on the right side in a war. These days, the establishment would like you to think it takes an MBA to know if you can fart or not.

I suspect a proper businessman (and probably a lot of borrowers too) can smell a bad loan or debt at twenty paces the way you or I can smell bad code; and they don't need Harvard grads to tell them why.

At the same time: the maths is important; and (at least to me) interesting.

Winston

[Winston Gutkowski]

Martin Vajsar wrote:I've misunderstood the question apparently. It's getting late I'd say there is unlimited number of interpretations of anything.

OK, so do you agree with my contention that the mathematical interpretation we use for loans is the most favourable one to the the lender? And if not, can you tell me why it isn't?

Simply put: I want to hear the mathematical "lenders lament". And if you can't come up with that, a good example will do.

As you say, it's late. I look forward to your (and, I'm sure Piet's) responses.

Winston

[Greg Charles]

Put me firmly in the camp that loan amortization is math, not usury. The principal declines slowly at first because you have a lot of money borrowed. Annoying? Yes, I hated how slowly my loan went down in the first decade. That's how the math works out though. I'd like to be able to fly too, but this dang gravity has me pinned to the ground.

However, it's beyond question that pre-collapse mortgage lenders preyed on naive borrowers, encouraging them to take on more debt than they could handle. That's also not usury as I understand it, but I'm glad we're starting to develop regulations to prevent it.

[Martha Simmons]

Are you guys working on breaking the World Record for "The Mos Boring Thread Ever"?

Anyway, here is my modest contribution:

"MORTGAGE
Etymology
From Anglo-Norman mortgage, Middle French mortgage, from Old French mort gage ("death pledge"),
http://en.wiktionary.org/wiki/mortgage

[Winston Gutkowski]

Greg Charles wrote:Put me firmly in the camp that loan amortization is math, not usury. The principal declines slowly at first because you have a lot of money borrowed. Annoying? Yes, I hated how slowly my loan went down in the first decade.

Hi Greg, and thanks for your post. Tell me: Did you take your loan to term?

Also: Do you simply accept the maths because, like me and probably most of us, it's simply "what you've been taught"? Or is there truly no other interpretation to it?

I'm still struggling with Piet's formulae, and I'm quite sure that a lot of thought went into them; I just wonder how much of that thought was put in by borrowers rather than lenders.

Winston

[Winston Gutkowski]

Martha Simmons wrote:Are you guys working on breaking the World Record for "The Mos Boring Thread Ever"?

Hey, nobody said you had to like it. And since it's plainly interested you enough to post, your post itself would seem to be a contradiction.

Like the dictionary link though; it never occurred to me to look up the derivation.

Winston

[Pat Farrell]

Wow, long thread with a fair amount of mis-information. In the US, the typical mortgage is paid off in about 7 years. Varies a bit with recessions, interest rates, etc. Very few people keep their house for 30 years, so the 30-year mortgage is more nominal than real. 40 years ago, the standard mortgage was 20 years. The longer terms were made popular when interest rates were high.

In 1980, a mortgage would have a rate of about 21%.

Calculating a mortgage payment is simple. Its not about compound interest, unless you miss a payment. Every month, you pay the interest for the month, and a bit of principal. In the first years of a 30 year mortgage, you pay next to nothing on the principal. A few tricks, mortgages are calculated on a 360 day year, and every month has 30 days.

Right now, interest rates on mortgages are nearly free. But in normal times, the actual monthly payment difference in a 15-year, 20-year, and 30-year mortgage are not very big. The short 15 year deal will save you at least 60% of the total cost.

Someone up thread said that you can default on a 30 year mortgage in the 29.5'th year. Sure you can, but at that time, you only owe a tiny amount, your payments are nearly all principal and you only have six more to go.

In the US, we have a cartel that pushes people into mortgages and single family homes. This is good for the real estate agents, banks, construction workers, developers, road builders etc. The public policy claim is that having people with mortgages makes for more stable community. And it forces savings.

The reality is that if you move every 7 years, the savings are suspect. What having a mortgage does for sure is lock you into the house if times get bad. Hundreds of thousands of folks in Detroit and other rust belt cities could not just move to where the jobs were, because they were stuck with a mortgage on a house that they could not sell.

If you are a reasonable risk, the bank will not foreclose on your mortgage. They will work with you. Most of the stories in the media are about folks who could not afford the house they bought. When times/money got tight, guess what? they could not afford their homes. Duh, they should have kept renting.

If you think your job might go away, or that you may move to another city for employment, rent, don't buy.

[Martha Simmons]

Winston: And since it's plainly interested you enough to post, your post itself would seem to be a contradiction.

Oh. A contradiction was spotted on the corner of Meaningless Drivel and Disappearing Posts alley... Ok. I guess, the question is: Is a contradiction in Meaningless Drivel a contradiction in any meaningful sense of a "contradiction"?

Hey, nobody said you had to like it.

I do, it's just that I have a primitive brain, so your discussion is frustratingly complex = meaningless for me. Two-three centuries ago there was a tradition in my country: when a new family was formed, the whole settlement would provide free labor for one day, and one day was enough to build a house for aforementioned happily married. Well, at least this is the legend.

Now explain to me, please, in as primitive terms as it's humanly possible: in which exactly direction did we progress since then?

[Martin Vashko]

Winston Gutkowski wrote:

Martin Vajsar wrote:I'd say there is unlimited number of interpretations of anything.

OK, so do you agree with my contention that the mathematical interpretation we use for loans is the most favourable one to the the lender? And if not, can you tell me why it isn't?

Not exactly. I really meant that there are unlimited interpretations of any observation, and we generally use Occam's razor to choose the simplest one and stick with it.

One of the interpretations of mortgage formulae is that the debtor pays the interest from exactly the amount he owes, period. I don't think it can get much simpler than this, and so I genuinely believe this is the most fitting interpretation. Paying the interest obviously benefits the lender, not the borrower. It's the same as paying for a house benefits the seller, not the buyer. But the buyer gets the house, and that is his benefit. And in case of mortgage, the borrower gets money he didn't have, and that is his benefit.

Given the previous discussion, I believe you disagree with including risks and other components in the final rate you think the borrower shouldn't bear. If this really is the case, the problem, in my opinion, is not in the formula, but is confined to determining the fair rate.

If you still think that paying so much of interest and so little of the principal at the beginning of the mortgage is unfair, I think you should try to justify why the lender shouldn't get paid all of the interest he is entitled to based on the - now presumably fair - rate.

[Piet Souris]

Still doubting the maths, I see. Now, I will try to focus clearly on the reasoning, and then to the maths
that come with this reasoning. So you can then see if you find the reasoning acceptable, and if so,
if the maths are modelling this reasoning in a fair way.

Suppose you have 1 euro to invest. You can put it as a deposito for two years, inwhich the bank grants you
an annual interest of i, compound interest. If you do that, you will have (1+i)^2, after these two years.
Now, this is a fact, so no need to discuss this.

But you have an alternative. You can lend that money to a borrower B, and he will pay you back
an amount of 2P after one year, and an amount of P after two years. You can put that first repayment (2P),
at the bank, and they will give, for a one year fixed period, an interest of j per annum.

The principle is now: both alternatives must give the exact same value after two years.

Given this principle, you start doing the maths:

Alternative 1 gives me (1+i)^2 after two years
Alternative 2 gives me: 2P *(1+j) + P after two years.

Therefore:

P * (3 + 2j) = (1+i) ^2 ==> P = (1+i)^2 / (3 + 2j)

(believe it or not, but this is very much like the original formula that started the original topic!)

Questions:
1) do you find the reasoning acceptable? From the point of view of you, the lender, and the POV of the borrower?
2) if so, do you consider the maths to be an accurate model of this reasoning?
3) if not, how would your reasoning be and/or what maths would you use?

Now, suppose that after this initial payment of 2P, the borrower comes to you, and he wants to redempt
the rest of the loan too, right now. Suppose that he will pay an additional amount X. Now you reckon:

putting 2P and X to the bank, that will give me: (2P + X) (1 + j).
So, again starting from the same principle, you have:

(2P + X) * (1 + j) = (1 + i) ^2

==> X = P / (1 + j).

And again the same questions:
1) do you find the reasoning acceptable? From the point of view of you, the lender, and the POV of the borrower?
2) if so, do you consider the maths to be an accurate model of this reasoning?
3) if not, how would your reasoning be and/or what maths would you use?

Next scenario: after one year, the interest rate for the second year has dropped to 0.5j per annum. That's unfortunate,
of course, for you. But what about the calculation of X? Would you change that to:

X = P / (1 + 0.5j), or would you keep the original X?

What would you do? Try to get X = P / (1 + .5j) and reducing some of your loss? After all, it is the borrower who wants
to break the contract.

Final scenario: that borrower B has not a very reliable reputation. You estimate the change of recieving the first 2P
to be p1, and for the final payment P to be p2.

If you take that into account, keeping i and j unchanged, how would you do the maths now?
Same question, but let us keep P unchanged, and assume that i and j are changed proportionally: what interest rates
would you now have? Can you say that the increase in interest rates in this sum is a 'risk' surcharge? If so, do you think
it is justified to let B pay that risk surcharge?

Well, that should make the reasoning and the maths clear.

<LOL>
@Martha: and? Did we succeed in breaking this World Record? At least we should come close!
@Pat: you are right. It has most definitely, absolutely, guaranteed, nothing to do with compound interest
</LOL>

[Pat Farrell]

Piet Souris wrote:in which the bank grants you an annual interest of i, compound interest.

I know you are really just trying to simplify to make the example easy to follow.

In the real world, bank loans are quoted as annual interest, but typically compounded daily. Sometimes they even use continuous compounding. So that makes my earlier post incorrect. On day two you do owe the interest on day one.

[Martin Vashko]

Winston Gutkowski wrote:I suspect a proper businessman (and probably a lot of borrowers too) can smell a bad loan or debt at twenty paces the way you or I can smell bad code; and they don't need Harvard grads to tell them why.

It's true that in the US mortgages were sold to people who clearly shouldn't have them. I do see the greed in this one - the thinking probably was "at worst (or perhaps 'probably', which would make it even worse) they won't pay, but we don't care, as we get the house".

Forcing the lender - somehow - to take some loss - nontransferable to the borrower (it's actually pretty difficult to ensure this) - when the borrower defaults might perhaps help to avoid such behavior. It could be limited in a way - say, lender whose ratio of foreclosures exceeds some limit would have to pay a fine (so that the banks theoretically wouldn't need to increase the rates).

The problem with schemes that punish wrong business decisions is that they make things much worse during economic downturns - not only that the bank has losses from investments, cannot sell new mortgages, foreclosures sometimes do not bring in all of the debt - the bank furthermore has to pay fines. I'm not completely up-to-date with the EU deficit penalties, but they are an example of such policy.

[Pat Farrell]

Winston Gutkowski wrote:I suspect a proper businessman (and probably a lot of borrowers too) can smell a bad loan or debt at twenty paces the way you or I can smell bad code; and they don't need Harvard grads to tell them why.

This is true. In the "sub-prime crisis" the problem was not that the businessmen thought that the loans were good. Rather they knew that the borrowers could not afford the loans. The only way that the loans worked financially was in the underlying value of the house price increased substantially every year. Plus, the lenders were directed by Congress to make more risky loans. Congress didn't phrase it that way, what they said was you only make loans to white folks with good jobs. Make more loans to folks with bad jobs and folks with brown/black/yellow/orange/purple skin.

The only rational thing for the lenders to do was to charge very high interest rates to offset the risk. Sadly for all of us, they didn't raise them high enough to reflect the real risks.

Thus, they were shocked, shocked that there was gambling in this establishment.

[Greg Charles]

Winston Gutkowski wrote:

Greg Charles wrote:Put me firmly in the camp that loan amortization is math, not usury. The principal declines slowly at first because you have a lot of money borrowed. Annoying? Yes, I hated how slowly my loan went down in the first decade.

Hi Greg, and thanks for your post. Tell me: Did you take your loan to term?

Also: Do you simply accept the maths because, like me and probably most of us, it's simply "what you've been taught"? Or is there truly no other interpretation to it?

I'm still struggling with Piet's formulae, and I'm quite sure that a lot of thought went into them; I just wonder how much of that thought was put in by borrowers rather than lenders.

Winston

No, I'm not old enough yet to have taken a 30 year loan to term. Anyway, I'm selling the first place I owned. The house I live in now though, I will take to term unless I pay it off early. I don't intend to move again.

The idea that I only accept the "fairness" of an amortization schedule because I've been taught to is ridiculous. Were you taught your time tables, or the quadratic formula, or a Taylor series. Do you accept them only because you were taught them? Do you believe there is a fairer value of pi or Napier's constant out there?

At the beginning of a loan, you have a lot of money borrowed, so most of your payment goes to interest. Towards the end of the loan, you have just a little money borrowed, so most of your payment goes to principal. If you wanted to reduce your principal by a constant rate through the life of the loan, you would have to start with a big payment, and reduce it each period as the principal decreased. I prefer fixed monthly payments.

There's plenty of guilt to hang on lenders, without blaming them for math. They pushed interest only loans, low or no down payments, balloon payments, low initial rates that could grow after some years, etc. All of these things were fine when housing prices kept rising. You could always sell the place and pay off the loan, or just refinance it, and maybe even take out some of the new equity to finance a nice trip or big screen TV. Yea! Money for nothing! It didn't last though, and all the sub-prime loans made the collapse spectacular.

[Pat Farrell]

Greg Charles wrote:Yea! Money for nothing!

Figure out how to make it work and you'll be rich.

[Winston Gutkowski]

Piet Souris wrote:Suppose you have 1 euro to invest...

Sorry for late reply. I was away again yesterday.

Piet: Thank you. Finally an explanation I can get my feeble brain around. And yes, now it does make much more sense.

Why? Because it's a statement of what the lender could reasonably be expected to get from the income for the loan, rather than the principal. Secondly, it seems to confirm my assertion that, unless someone gets greedy or doesn't do their job properly, there isn't actually much risk involved.

As to the rest: I realize that my thinking is simplistic, and I certainly wouldn't want to live in a world where there was no incentive to lend; but it still bothers me that under the standard schedules it takes so long to reduce principal. Perhaps the only alternative is some sort of 'tapered' scheme where payments start out high (or higher) and gradually drop off, maybe within defined limits, so that the principal gets reduced more evenly. Again, my maths isn't good enough to confirm or deny it, but I suspect that a deviation of as little as ±5% about a 'mean' payment could flatten out the principal reduction quite significantly.

Anyway, thanks again.

Winston

[Robert D. Smith]

Jeanne Boyarsky wrote:

Winston Gutkowski wrote:

Jeanne Boyarsky wrote:For a company, yes profit is all.

Hmm. Unabashed capitalism. So presumably, things like toxic dumping and sweatshop labour are simply "friendly fire". They can, after all, simply be put down to pursuit of profit, and are still actually legal in many countries.

But coming back to less emotive subjects: What about exportation of labour? It's the backbone that is likely to turn China and India into the next #1 and 2 powers in the world over the next 50 years. Are you happy with that? Is that what you see as the "triumph of capitalism"?

Personally, I have no vested interest in who is "top dog", and I have no notion that they will do any better or worse than the US or England before them; but as a Western liberal, I worry about a future that is governed by countries where people can simply disappear, or where 90% of the wealth is owned by 5% of the population. And we (or the "profit is all" motive) will have been responsible for it.

Winston

Taking this part of the discussion to the Rattlesnake Pit. (This is a forum that will be made available on January 3rd - Jumpin JForum Day.) Moderators have access to it now as a preview so Winston and I can continue this part of the debate until then. The Rattlesnake Pit is for political or controversial topics. Which is clearly where Winston and I have gotten.

But Jeanne, these are the bits I want to follow. By 3 January this topic will (most likely) be dead.

[Winston Gutkowski]

Robert D. Smith wrote:But Jeanne, these are the bits I want to follow. By 3 January this topic will (most likely) be dead.

Nothing to stop you reviving it on the 4th. Or starting an MD thread along the same lines before then.

I actually think it was a very sensible thing to do. This thread is quite specific; that post was merely an anti-capitalist rant on my part (I'm the "old Liberal" that Winston Churchill warned about )

Winston

[Greg Charles]

The idea of reducing principal by the same amount is interesting, and not so hard to calculate assuming we let ourselves cheat and use an online amortization calculator like the one at http://www.myamortizationchart.com/.

So, let's say the loan period is 360 months (30 years) and the starting principal is 360,000. For a normal fixed rate loan at 3.5%, the monthly payments would be 1616.56. For the first payment, 566.56 of that would go to principal. If we want to reduce principal by 1,000 per month, then we'd have to increase our first payment to 2050.00, so that's about a 25% increase. Each month, we'd be able to reduce our payments until the final month would just be 1000.00 and change.

It gets a bit uglier if the interest rate is 5.5%. The monthly payments are now 2044.04, and only 395.85 goes to principal. We'd have to raise our first payment to 2648.19 to accomplish our goal of reducing principal by 1000.00, which is almost a 30% increase. The higher the interest rate the more you'd have to increase your early payments to keep principal declining by a fixed amount each month.

In practice, no lender is going to give a loan with terms like those. However, at least in the U.S., you're free to pay above the monthly payment to reduce principal faster. That means you could simulate the fixed rate of principal decline if you felt like doing that ... until finally the principal got low enough that paying by your method would mean paying less than the monthly payment. At that point the lender would squawk, and you'd have to pay that monthly payment anyway. The result would be you'd pay off the loan before the end of the 30 year term. That's also OK and free of any penalty for any loan I've been involved with.

[Matthew Brown]

I think Greg's analysis shows why that's not generally how mortgages work. Many (most?) people will expect their incomes to grow over time - even if only in line with inflation. So picking a payment schedule that means your repayments decrease over time isn't very sensible, because it's at the start of the term that you expect to have most difficulty meeting the payments. So such a schedule will decrease the amount you can afford to borrow in the first place, because it's those first payments that are the constraint.

In the UK you can also repay early, unless you're locked into a deal. For example, when we bought our house we took out a deal that fixed our interest rate for 5 years (I think), to make things predictable. During those five years there was a penalty for overpaying more than a small amount. Since those five years have been up we've been had no restrictions on overpayment (which, now, we can afford to do).

[Winston Gutkowski]

Matthew Brown wrote:So picking a payment schedule that means your repayments decrease over time isn't very sensible, because it's at the start of the term that you expect to have most difficulty meeting the payments.

Which is presumably just one area where actuaries come in: in calculating the payment that someone is likely to be able to make.

I'm also not talking about a linear reduction in principal, but what about something in between?

Based on one of those mortgage calculators, 100,000 @ 5% over 30 years comes to about 536/month. Assuming that our "borrower" could stand an extra 27 (+5%) to begin with, what about a progression where payments reduce linearly from 563 at the start to 509 at the end? I bet the loan would be paid off a few years earlier and the principal reduction curve would be flattened.

Now this is where my maths falls down, but I'm pretty sure that you could then reduce the mean payment to a figure where the +5 to -5 reduction results in a term completion of exactly 30 years, so I can't imagine that it would cause particular hardship to the borrower at the start, and his/her payments would still remain fairly constant.

I'm sure there's all sorts of other things I've missed out, but it seems like something that might be worth considering.

Winston

[Pat Farrell]

Winston Gutkowski wrote:Which is presumably just one area where actuaries come in: in calculating the payment that someone is likely to be able to make. I'm also not talking about a linear reduction in principal, but what about something in between?

I'm a bit confused by your use of the term actuaries here. In the US, an actuary is a statistician working for an insurance company. They calculate when you are likely to die, get in an accident, get sick, etc. They have no roll in mortgage calculations.

A mortgage interest rate is the price that the lender (aka bank) sets to reflect your risk of default. This is mostly based on your salary, down payment size, savings amount, current debt level, time on job, time since moved and other small stuff. If you die, that has no impact on the mortgage, your estate deals with that. Its usually done by an Excell spreadsheet, there is not much judgement allowed. The lenders are under fairly severe restrictions these days, they don't get much chance to think.

[Martin Vashko]

Generally speaking, the faster I pay off the mortgage, the cheaper it becomes - I'll save on the interest.

Winston Gutkowski wrote:I'm also not talking about a linear reduction in principal, but what about something in between?

Everything "in between" will result into decreasing payments (at one end we have decreasing payment scheme, at the other fixed payments scheme). But if I have decreasing payments and my disposable income is not decreasing, I'm missing out an opportunity to pay the mortgage faster, which is bad for me (see above). I'm afraid the fixed payments scheme is actually the most suitable for an average mortgagee (assuming he chose the right amount he is able to pay each month).

The best strategy as a customer, in my opinion, is to make sure that I can put in irregular payments without penalty. That way I can settle down for a regular payment that I'll likely be able to pay even in bad years, and allows me to put up any surplus I can afford in good years. Banks usually want to limit the ability to pay the mortgage faster*; see Matthews post. I have the exact same condition. However, at the exact occasion when the fixed period ends, I can repay any portion of the remaining debt without penalty.

* If I'm not mistaken, Piet has mentioned in his earlier post that banks have good reasons to do this, I'd be interested to hear them...

[Piet Souris]

Pat Farrell wrote:

Winston Gutkowski wrote:Which is presumably just one area where actuaries come in: in calculating the payment that someone is likely to be able to make. I'm also not talking about a linear reduction in principal, but what about something in between?

I'm a bit confused by your use of the term actuaries here. In the US, an actuary is a statistician working for an insurance company. They calculate when you are likely to die, get in an accident, get sick, etc. They have no roll in mortgage calculations.

And they know nothing at all about financial maths! Let alone doing complicated mortgage calculations! And calculate when someone is likely to die?? Get off, we simply look that up in a mortality table. No, there are only three kinds of actuaries: those who can count and those who can't.

Greetz,
Piet

[Pat Farrell]

Actually, the actuaries that I've met are very sharp and do serious wizardry with statistics. They write the mortality tables.

But then, this is Meaningless Drivel

[Piet Souris]

Pat Farrell wrote:Actually, the actuaries that I've met are very sharp and do serious wizardry with statistics. They write the mortality tables

Hmm, then be prepared for a shock when you meet me...

And Martin asked why banks are generally not pleased when you redempt faster than agreed upon.
Well, it has all to do with guarantees that have been given. Either the bank (but could be any financial company)
has to pay some fixed interest itself to those who put their capital into that company. So, when the mortgagee
repays much sooner than agreed, it is very much the question whether the bank can re-invest that
money againt the rate that they themselves must pay.

But maybe it is more clear for this reason: say you have a mortgage at 10%. for a fixed 10 year period. Now,
after say 4 years, interest has dropped to 4%.
Now, if you were allowed to simply pay off the residual debt any time you like, then you could simply mortgage that residual debt
against 4% and redempt the old mortgage. Effectively, reducing the banks profitable loans.
This is one way traffic, of course. If the opposite were the case (interest going up from 4 to 10%), no mortgagee
in his right mind would do a thing like that. Therefore, redempting a mortgage outside some corridor is heavily fined.
You would probably have to pay the present value of the interest difference.

[Pat Farrell]

Piet Souris wrote:But maybe it is more clear for this reason: say you have a mortgage at 10%. for a fixed 10 year period. Now,
after say 4 years, interest has dropped to 4%. Now, if you were allowed to simply pay off the residual debt any time you like, then you could simply mortgage that residual debt against 4% and redempt the old mortgage. Effectively, reducing the banks profitable loans. .... Therefore, redeemting a mortgage outside some corridor is heavily fined

In the US, refinancing mortgages is very common. The advertise to do it on TV. Many folks do it repeatedly.

This was part of the problem with the housing bubble that burst in 2008. Lots of folks looked at their rising house value and refinanced, taking out cash and using to buy big screen TVs, new cars, etc. When the values burst, they were holding mortgages that were much larger than the house was worth.

[Piet Souris]

And so, it seems, this lengthy and interesting topic is coming to a well deserved end.
The talks were long, and I have tried to highlight some aspects of the maths involved.

This should come as no surprise. In the '90s I have been teaching 'Actuarial Calculus'.
The first three months of this in principle two year course were all about loans,
and the funny part is that the number of exersizes one can think of is practically infinite.
So, as my final contribute, and for you to see how well you know your maths, one of my
all time favorites is:

You have a normal annuity, with Loan 100.000, interest 4%, duration 30 years and yearly payment P.

- determine P (you may use an internet mortgage calculator, if you like. Note however, these were
not available to the students in the early 90's!

Now, there is a special agreement between lender and borrower:

- the amortizing part of each payment P will be paid one year ealier
- the interest part of each P will be paid one year later

What is the initial value (i.e. at t = 0) of all these payments?


Piet

[Martha Simmons]

Piet Souris
<LOL>
@Martha: and? Did we succeed in breaking this World Record? At least we should come close!

Oh, you did succeed.

I remember reading in some book that there is a certain threshold of complexity, after which the society becomes just too complex for its own good. I think we are approaching this threshold -- fast. What we really need is to return to primitives.

So, to answer the original poster's inquiry "mortgages - fair assessment or usury?" - usury.

Can some of the moderators, please, close this topic now?

(Just kidding!)