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Mortgages - fair assessment or usury?

 
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This question is for the financial mathematicians out there, and was prompted by this topic, and in particular the last post (by Piet Souris, who seems to know his financial formulae).

I have often thought that the standard repayment schedule for loans and mortgages borders on usuary because the borrower's repayment schedule:
(a) Delays significant reduction in principal for a very long time.
(b) Is almost always covered by a lien on the thing for which the loan was needed, reducing the lender's risk in a way that is NOT reflected in the formulae themselves.
(c) Benefits the lender most, in normal times, when the borrower defaults; particularly if they do so during the first two-thirds (or so) of their schedule.

I suspect also that the tensors in the standard formulae also promote greed (as if there weren't enough stimuli for that already ) to the point where lenders overreach themselves by borrowing in order to lend, resulting in things like the latest banking crisis.

I should say that I'm no economist, but it seems to me that, in mathematical terms, many interpretations could be put on what a loan actually "is", and that the standard approach is unduly penal on the borrower, requiring him/her to take on risk and liability and time that stretches out into a future that is very difficult for humans to comprehend, particularly in markets that have a lot of sharks around.

I've read a bit about Islamic banking, and also about savings-based lending schemes like the JAK bank, and wonder if these couldn't be implemented or standardised for us all.

Being a confirmed sceptic of capitalism, I also have no notion that greed (or indeed "enlightened self-interest") learns from its mistakes, so I'm most interested in what people think about the mathematics.

A TGIF topic for anyone who's interested.

Winston
 
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Winston Gutkowski wrote:I should say that I'm no economist, but it seems to me that, in mathematical terms, many interpretations could be put on what a loan actually "is", and that the standard approach is unduly penal on the borrower, requiring him/her to take on risk and liability and time that stretches out into a future that is very difficult for humans to comprehend, particularly in markets that have a lot of sharks around.


I think you're mixing two things. Firstly, there definitely are people who take mortgages without understanding it completely or at all. The only remedy here is not to allow such people taking mortgages. Would they be better off? I dunno.

Secondly, the mathematics. I do believe that the standard formulae reflect the fact that if the bank didn't borrow the money to you, it could invest it somewhere else and get appropriate interest. Difference between the interests should correspond to differences in risks, and the mortgage rates might be a bit unfair in this sense, but at least in my country I don't think it would be much (the mortgage rates are currently slightly over 3% at this time; I personally have a mortgage with a rate close to 4%). For unsecured loans that value is at least two to three times as much. Given the current economic situation the question is whether the mortgages aren't actually safer than government bonds and should therefore get a better rate.

If you want to borrow a lot of money for a long time, you'll pay a lot of interest. I don't see any way to go around it, since the borrower could do something better with his money than part with them for several decades.

(a) Delays significant reduction in principal for a very long time.


Some banks offer different payment schemes, such as paying fixed amount of the principal plus all of the interest for that period; you're repaying the debt much faster and pay much less in total, but the initial payments are skyhigh.

(b) Is almost always covered by a lien on the thing for which the loan was needed, reducing the lender's risk in a way that is NOT reflected in the formulae themselves.


The difference in rates for unsecured loans is significant (see above). Whether the rates accurately reflect the inherent risks is a different question, which I don't feel knowledgeable enough to try to answer.

I do see one significant difference between European and American mortgage system. In Europe, when you default on your mortgage, your property is auctioned and the proceedings are used to repay the debt and fees. If it is not enough (and quite often it is not, as selling a property in an auction is not the best option), you still owe the bank the rest. In the USA, if you default on your mortgage, your bank gets the house and you don't owe it anything. This is certainly a safer alternative for the borrower, but it also contributed significantly to the depth of the USA mortgage crisis - as soon as your house value plummets below what you owe to the bank, you're better off simply walking away. That further depresses property prices, which results in a positive feedback system.

(c) Benefits the lender most, in normal times, when the borrower defaults; particularly if they do so during the first two-thirds (or so) of their schedule.


I don't see how the lender benefits when the borrower defaults. Could you elaborate a bit on it? (If this was true, I generally wouldn't expect the banks to refuse mortgages to people with inadequate income.)

I've read a bit about Islamic banking, and also about savings-based lending schemes like the JAK bank, and wonder if these couldn't be implemented or standardised for us all.


If I understand it right, you don't pay interest on your loans, but you also don't get any interest on your deposits, and you're obliged to put in as much money as you borrow. This doesn't sound bad, as you can save the difference between deposit rate and mortgage rate, which is significant. But at the same time, if you don't have enough saving points accumulated, you're obliged to repay your debt and save at the same time. That could be a lot of money, couldn't it? And at the same time, your savings are not appreciated at all, so the inflation goes against you, whereas with a mortgage, inflation helps you. After factoring the inflation in, you might find that the deal is still better than mortgage, but perhaps by substantially less than you'd expect.

If we'd able to run economy without inflation, now that would be something different, but it will probably require more changes than this.
 
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Well, as a Humanist, I'm going to have to go with usuary. Capitalism has given us predatory lending, unfair and illegal foreclosures, a world wide recession, and a never ending cycle of debt for the very poor (people and countries alike). During the latest US government shutdown, food centers were closed while the congressional gym and swimming pool remained open as an "essential" service.

From a mathematical perspective, it seems that lending formulae are hit and miss. I remember asking friends in the financial industry how simple interest is calculated and came up with different answers. Urban legend has it that Einstein was once asked to calculate simple interest and it was beyond his skills.
 
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Robert D. Smith wrote:I remember asking friends in the financial industry how simple interest is calculated and came up with different answers. Urban legend has it that Einstein was once asked to calculate simple interest and it was beyond his skills.


I would say that this is because no one, not even clerks, calculates interests by hand nowadays, computers do it. The math behind it (Mortgage calculator) is comparable to that behind Special relativity, and much, much, simpler than General relativity. So even if the Einstein legend was right, I'd say the problem was he wasn't clear about the rules, not the math.
 
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> Well, as a Humanist

Robert, the dictionary entry you sent us to has 5 definitions of “Humanist”. Which one is yours?
 
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Thanks Winston, for this very interesting topic.

First of all: Martin gave an excellent reply, to which I have nothing to add.

So, let me focus a little bit on how a mortgage interest is determined. As an old actuary,
if you call 57 old (I do!), the traditional education was mostly concentrated on the liability
side of the (insurance) balance, leaving the asset side to all those 'greedy investment people'.
In the last 15 years I have witnessed a substantial change in the actuarial business, where
it became mandatory to also have at least a decent understanding of the asset side of things.
And fascinating as this world is, it is very complex, and the math used is also very complex.

Let me ask you a question: suppose you have some spare money, put in a drawer in your house,
and seeing that is does not generate any interest there, you start looking for some ways to
invest your money. Now, you have two options:

1) bring it to the bank. That is safe, of course, and they grant you a yearly 3% interest.
2) lend it to some company that needs the money to finance their activities, and that company
also grants you 3% (well, if they haven't gone bust, that is).

What would you do? Well, I read that you are a scepticist when it comes to Capitalism and greed,
so I am not sure what you would do, but the general opinion is that given a certain yield, you invest
the money in the safest possible way.

So, that company has no choice. If it wants to attract money, they must pay an interest rate that is
above the so called 'safe rate'.

How much? That depends. Suppose you estimate the chances for that company to go bust within the
next year to be 20%. So you start to do some simple maths.

a) going to the bank will grant you q interest
b) lending it to the company against p interest will give you an expected amount of: 0.8 * p
c) so, you say: q = 0.8p therefore p = q / .8
d) and if you had millions of such transactions, that p would be okay. But if you have only one
or at most some of these investments, then your risc goes up; the volatility (or standard deviation)
is very high. So, chances are you put p = q / 0.5

And that is only the beginning of how interest rates are determined.
Because the company that lends money for mortgages faces all kinds of risc, it has to maintain
some buffer, for adverse situations. This buffer is probably provided to the company by shareholders.
Now, these shareholders have the same reasoning: they invest their money into a risky business,
and therefore demand a dividend that is twice the 'safe interest', otherwise they
might as well put in on the bank.
So, in order to pay this dividend, and since you cannot invest this buffer in some risky other investments,
this dividend has to come from somewhere. From where? Well, from the person that already had
to pay p instead of r.
So, p becomes now the old p + some extra for the dividend.
(this 'extra' being termed 'cost of capital').

I have only tipped a few of many layers that determine the mortgage interest. Last year a guy
working in this department gave us actuaries a college how this mortgage business works.
For this, they form joint ventures, called 'Special Purpose Vehicles', that were formed to attract
money and shuffling around a lot of cashflows. Well, I remember getting headaches of all these complexities
and actually getting the feeling of 'greedy semi-crooks', just like you have ;)

To be more concrete: given the fact that banks can borrow money from the ECB (the European Centrl Bank)
at an all time low interest rate (I think it is 0.25%), obtaining cheap money is no problem.
And indeed, current mortgage interest of about 4-5% certainly is felt to be too high.

Another fact is that, under current European rules, banks must drastically increase their buffers, so that
tax payers are less likely to save a bank when that bank gets into troubles. And, guess where that
money is partly coming from? Extra profit of course.

But then: when I bought my first house, in the early eighties, mortgage rates were around 8%, and currently
I pay 3.7%, so I am not complaining.

Then on the risk a mortgage company faces. I will talk about the situation in Holland, it might be completely
different in other countries. (By the way: is what Martin describs, about 'walking away' and then the bank owns
the house, correct? What if you default in year 30 of a mortgage with 30 year duration? Incredible)

In Holland, when I bought my house, the rules for getting a mortgage were pretty strict:
- you could borrow no more than 70% of the auction price (see Martins reply, here called 'execution price')
- the mortgage could not be higher that 3 times your annual income
- and if you were a pair (say man/wife) then only the highest income of the two was taken into
account

But in the nineties, all these rules were 'liberalized'. In fact, banks could do whatever they pleased
and given the boom in house prices, banks would lend up to 110% of the (too high) price of a house.
The general thought was that since house prices were going skyhigh, that 110% would soon be below
the value of that house. But in the recent years, we saw a sharp decline of house prices.

What I am trying to make clear, I guess, is that the determination of mortgage interests is
a very complex process, of which greed is certainly a part.

But then, it can't be denied that capitalism has brought us (in the western world) a lot of good.
People tend to work harder and more efficient when they have a personal interest, rather than
when you do it, say, for the state. So, in general, society also profits. But the two facts, greed
and the lust for power, make it a bit like a nuclear plant: very rewarding, but please
make sure that we have a lot of safety built-in (which with capitalism, is a very big question).

And finally: we cannot blame a poor simple mathematical formula for the 'r' bing unreasonably high,
in the same way that you cannot blame your car when you are speeding!

Greetings,
Piet

Edt: that's nice. Had to change 'r' to 'q' otherwise my text was inacceptable
 
Winston Gutkowski
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Martin Vajsar wrote:I think you're mixing two things. Firstly, there definitely are people who take mortgages without understanding it completely or at all. The only remedy here is not to allow such people taking mortgages. Would they be better off? I dunno.


Me neither, but can you honestly say that any 25 or 30 year-old knows what their life is going to be like when they're 55 or 60?

If you want to borrow a lot of money for a long time, you'll pay a lot of interest. I don't see any way to go around it, since the borrower could do something better with his money than part with them for several decades.


Could they? Then why don't they? I suspect because it's far better for them to lend it to you.

And unless I'm wrong, repayment calculations assume that all (or a significant portion) of that principal is re-invested, rather than providing income, which seems to me to be a lender's paradise that bears very little relation to reality. Furthermore, the terms and mathematics of repayment are decided solely by the lender, with the borrower simply given the choice of whether to take it or leave it.

I don't see how the lender benefits when the borrower defaults. Could you elaborate a bit on it? (If this was true, I generally wouldn't expect the banks to refuse mortgages to people with inadequate income.)


OK, let's assume that Martin takes a loan to buy his house at 5% over 30 years. Things go just fine until halfway through when he runs into difficulties (illness, lay-off, whatever). At this point the bank has received income virtually equal to the original loan (about 96%), but Martin has only paid off about a third of it (actually, slightly less). The bank has thus already made about as much money as it's ever likely to out of the agreement, particularly when depreciation and inflation are taken into account; so it stands to reason that the bank has far more interest in Martin being solvent for the first half of his loan than the second.

It would be interesting to know just how many (or what proportion of) long-term loans actually go to term.

Don't get me wrong. I'm not saying that lenders shouldn't make profit, or take on all the risk; it just seems to me that the "standard" maths (and/or the assumptions on which it's based) are biased in favour of the lender. In turn, I suspect that promotes concentration of "riches" (equity, money, etc - I'm not sure of the economics term) in the hands of those who already have it, which sounds like the recipe for an anthill society to me.

As someone once said: Show me a man who's trying to make money, and I'll show you a free-marketeer; show me a man who's got money, and I'll show you the worst protectionist bastard there is.

But thanks very much for your comments. Much appreciated.

Winston
 
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Winston Gutkowski wrote:

Martin Vajsar wrote:I think you're mixing two things. Firstly, there definitely are people who take mortgages without understanding it completely or at all. The only remedy here is not to allow such people taking mortgages. Would they be better off? I dunno.


Me neither, but can you honestly say that any 25 or 30 year-old knows what their life is going to be like when they're 55 or 60?.



First of all, most mortgages have a fixed interest rate for only,say, 10 years.

And indeed, buying a house is one of the biggest investments you're ever likely to do. So, therefore, you must very eriously
think about what you are getting in to. But then again, you pay a huge amount of money, but then, you own a house!
The idea is that you can sell the house when needed.

I

If you want to borrow a lot of money for a long time, you'll pay a lot of interest. I don't see any way to go around it, since the borrower could do something better with his money than part with them for several decades.


Could they? Then why don't they? I suspect because it's far better for them to lend it to you.



Well, it is just one kind of investment. So they don't. It is a wise thing to have a broad renge of investment,
to pread your risks.

And unless I'm wrong, repayment calculations assume that all (or a significant portion) of that principal is re-invested, rather than providing income, which seems to me to be a lender's paradise that bears very little relation to reality.


Indeed, gained interest is re-invested, although part of it will be spent on salaries, dividend, et cetera.
And if there is one company that charges unrealistic high mortgage rates, then find some company that offers lower rates.

Furthermore, the terms and mathematics of repayment are decided solely by the lender, with the borrower simply given the choice of whether to take it or leave it.


? The terms, yes, but the maths? These arise from Mathematics.


OK, let's assume that Martin takes a loan to buy his house at 5% over 30 years. Things go just fine until halfway through when he runs into difficulties (illness, lay-off, whatever). At this point the bank has received income virtually equal to the original loan (about 96%), but Martin has only paid off about a third of it (actually, slightly less). The bank has thus already made about as much money as it's ever likely to out of the agreement, particularly when depreciation and inflation are taken into account; so it stands to reason that the bank has far more interest in Martin being solvent for the first half of his loan than the second.



I think you are misinterpreting the very nature of 'interest'.
first of all, they reward the lender for making available the money in the first place. It's nothiing else than hiring someone to do some work for you and aying him
Second, the lender faces a risk, namely the defaulting borrower. Fo this risk, he wants to be paid.
Lastly, a lender also wants some compensation for inflation.

It would be interesting to know just how many (or what proportion of) long-term loans actually go to term.


Houses are bought and sold again. So, many mortgages are paid back at once and/or renewed. Just look around in the neighbourhood you live in:
you will see many 'for sale' signs.

Don't get me wrong. I'm not saying that lenders shouldn't make profit, or take on all the risk; it just seems to me that the "standard" maths (and/or the assumptions on which it's based) are biased in favour of the lender. In turn, I suspect that promotes concentration of "riches" (equity, money, etc - I'm not sure of the economics term) in the hands of those who already have it, which sounds like the recipe for an anthill society to me.


If you DO want to blame the maths, blame guys like Newton, Gauss, Poincaré, for having developed all these maths!
Dn't blame Java if you make a programming error!

 
Winston Gutkowski
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Piet Souris wrote:Thanks Winston, for this very interesting topic.


I thought you might like it.

So, let me focus a little bit on how a mortgage interest is determined. As an old actuary,
if you call 57 old (I do!), the traditional education was mostly concentrated on the liability
side of the (insurance) balance, leaving the asset side to all those 'greedy investment people'.


Interesting. And BTW, I'll be joining the 'Heinz' club next June.

Let me ask you a question: suppose you have some spare money, put in a drawer in your house,
and seeing that is does not generate any interest there, you start looking for some ways to
invest your money. Now, you have two options:


Oddly enough, I was in precisely that situation back in 2007. What I actually did was to invest in bank shares after the first big drop, on the assumption (badly wrong as it turned out) that they couldn't get much worse.

However, unlike most investors, I regarded it as a 5-year plan (now a 7-year plan ), so I wasn't unduly bothered back in 2008/9, when my investment was worth about 30% of my original stake. Currently, I'm now showing roughly a 10-15% profit (it varies day by day - nature of the beast) which, while not as good as I'd hoped, is still probably better than most businesses over the period; and certainly better than if I'd left it "in the drawer" (or a bank).

Also, my investment was one that I could afford (and was prepared) to lose - that's the nature of "money in the drawer" - which I suspect is not true of lending banks; although I also suspect that this is where these "buffer" funds you speak of are so important.

And finally, I like to think that, in my tiny way, I've contributed to the stabilization of the sector, because I've invested in shares, not in derivatives or other "get rich quick" schemes that simply shuffle money around while somebody (now including governments) rake off a percentage in the process.

And maybe that's my question: Should profit be the only motive when you invest (or lend)? I certainly want institutions to be lending money, but it seems to me that there's a "greater good" that gets lost if greed is the only driving force behind it.

As to the rest of your post: Fascinating. I'm clearly going to have to read a lot more.

Thanks a lot.

Winston
 
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Winston Gutkowski wrote:Currently, I'm now showing roughly a 10-15% profit (...)


WHAT?!?!?!? You old (but not so very old!) capitalist!

But indeed: the adage is: newver gamble on money that you cannot afford to loose.
 
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Winston Gutkowski wrote:And maybe that's my question: Should profit be the only motive when you invest (or lend)? I certainly want institutions to be lending money, but it seems to me that there's a "greater good" that gets lost if greed is the only driving force behind it.


Risk is a motive when you invest or lend too. So no .

Seriously though, a bank is a business. If you borrow from friends/family, the goals are different. This is part of the reasons that credit unions operate differently than baks. (I mean a real credit union where people have some other connection.)
 
Winston Gutkowski
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Piet Souris wrote:First of all, most mortgages have a fixed interest rate for only,say, 10 years.


Thus, surely, increasing the uncertainty for the borrower?

And indeed, buying a house is one of the biggest investments you're ever likely to do. So, therefore, you must very eriously
think about what you are getting in to. But then again, you pay a huge amount of money, but then, you own a house!


Ah, but do you? As far as I can see, that "ownership" only entitles you to sell it again when you decide. In difficult times, not only can the lender assume that right, in Europe it doesn't even necessarily clear your debt.

Well, it is just one kind of investment. So they don't...Indeed, gained interest is re-invested, although part of it will be spent on salaries, dividend, et cetera.


Yes, but the assumption is that they have re-invested it; and that's what I take issue with.

And if there is one company that charges unrealistic high mortgage rates, then find some company that offers lower rates.


Despite the fact that that "lower rate" company may be miscalculating their risk? Again, I thought this was what prompted the last 6 years of "toxic debt".

The terms, yes, but the maths? These arise from Mathematics.


No, they arise from maths based on specific assumptions. My worry is not that the maths is wrong, but that it's based on assumptions that are biased in favour of lenders - or possibly, ones that promote greed.

I think you are misinterpreting the very nature of 'interest'. first of all, they reward the lender for making available the money in the first place. It's nothiing else than hiring someone to do some work for you and aying him


I think you'll have to explain that one to me, because I don't see any "compounding" involved in paying someone a salary.

Second, the lender faces a risk, namely the defaulting borrower. Fo this risk, he wants to be paid.


Which, at least in terms of property, is surely covered by the lien. Since, at the start of the agreement, it can be reasonably assumed that the borrower has nothing and the lender has everything, the lien simply exchanges money for equity. And in addition, the lender receives additional income proportional to the interest rate (actually, proportional to the rate over the assumed term). Where's the risk? Surely not in an agreement like that.

Lastly, a lender also wants some compensation for inflation.


And there, unfortunately, is where my maths fails me. I certainly agree that it's a factor, but I simply don't know how one goes about calculating that sort of risk.

Houses are bought and sold again.


Ah, but that wasn't my question - "How many mortgages actually go to term?" - To clarify: How many (or what proportion of) mortagaes are actually repaid exactly according to schedule - ie, Martin makes his first payment of a 30-year mortgage in January 1980, and his last in December 2009, never missing a payment or selling before time? My suspicion would be very few.

Yet the mathematics is based on precisely that schedule; and who benefits from variations to it?

Great discussion. Hope you don't mind me remaining a sceptic.

Winston
 
Winston Gutkowski
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Piet Souris wrote:WHAT?!?!?!? You old (but not so very old!) capitalist!


Yeah, it's a heavy cross for us "trendy lefties" to bear.

But indeed: the adage is: newver gamble on money that you cannot afford to loose.


And I suspect that that's where a lot of our current problems stem from. Leverage only goes so far.

Winston
 
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I think there's another factor in many people's deliberations over whether to take on a mortgage: what's the alternative? We all need somewhere to live, and we all need to consider how we'll pay for our living expenses when we're too old to work.

Here in the UK, property prices are still rising faster than earnings, despite various temporary fluctuations in recent years. So if you want to buy a house in the UK, it's better to buy it as soon as you can afford it, because if you wait too long your earnings and savings may not rise enough to keep up with the increased cost of property. For example, when we bought our house (with a mortgage) 14 years ago, it was priced at around 5 times the average wage hereabouts. Now it's supposed to be worth more like 10 times the average wage because the house price has risen but wages have not. If we'd waited 14 years, we probably still couldn't have saved enough to make up the difference, so we'd never have been able to afford the house. My wife would love to move back to the area of London she grew up in, but it would be impossible for us to afford it: economic cleansing at work.

Meanwhile, rents are out of control in most places where you'd actually want to live and be able to find work, partly because so many people can no longer afford to buy their own place. So if you are waiting to buy a house when you have enough savings to minimise the mortgage, you may never be able to save enough cash to do so. My monthly mortgage payment is half what it would cost to rent a house like mine (which is nothing special I hasten to add!). So despite the interest rates etc, a mortgage may still be the cheapest practical way to put a reasonably secure roof over your head.

And if you are thinking ahead to how you will live when you're older, then you need to ask how you will pay your rent if you don't buy a place while you're still working. This is especially true in the UK, where the state pension is one of the worst in the developed world and private pensions rely on the casino mentality (and questionable competence) of the financial services industry. Again, a mortgage may be a crap deal in principle, but in practice it's better than struggling to find extortionate rents on a fixed pension income when you're old, or living with the uncertainty of 6 month tenancies and the constant risk that your landlord will decide to make some money by selling your rented home out from under you (which happened to us twice in the 3 years before we bought our own place).

It's discussions like thsi that make you realise you are now officially Middle-Aged!
 
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Winston Gutkowski wrote:OK, let's assume that Martin takes a loan to buy his house at 5% over 30 years. Things go just fine until halfway through when he runs into difficulties (illness, lay-off, whatever). At this point the bank has received income virtually equal to the original loan (about 96%), but Martin has only paid off about a third of it (actually, slightly less). The bank has thus already made about as much money as it's ever likely to out of the agreement, particularly when depreciation and inflation are taken into account; so it stands to reason that the bank has far more interest in Martin being solvent for the first half of his loan than the second.


So according to this scheme, after 15 years the bank got its investment into my mortgage almost back (96% of it). However, if the bank invested that amount into 15 years of government shares instead (say, not the Greek ones ) with 2% p.a. (see, substantially lower than my 5%), by now it would have some 135% of its original investment. So there is a difference.

Moreover, my house will be sold at auction and used to repay my remaining obligations. I'll get whatever remains. The problem here is that selling the house quickly is bad for me, I would be better off to foresee the situation and arrange it so that I can sell the house in more favorable terms. (This is why I always tried to be able to live off savings for at least half a year, but this belongs more to the other question of people being able to understand all the risks involved in mortgage.) However, selling the house quick hurts me, but my loss here is not the bank's profit.

Now, the bank might make me pay fines and other contractual fees, and I'd say that his is a murky area which does pose some ethical questions - it has been shown, for example, that credit card rules are skewed in a way that hurts poor people disproportionally, and I wouldn't be too surprised if the banks rip the mortgage defaulters too. Also, as the principal decreases over time, the associated risks do get lower as well. In a fair world, this probably would be reflected in the rates. In real world, banks give better terms to first-time customers (at least in my country), so they do the exact opposite, but I can go to another bank and become first-time customer again

Ah, but that wasn't my question - "How many mortgages actually go to term?" - To clarify: How many (or what proportion of) mortagaes are actually repaid exactly according to schedule - ie, Martin makes his first payment of a 30-year mortgage in January 1980, and his last in December 2009, never missing a payment or selling before time? My suspicion would be very few.

Yet the mathematics is based on precisely that schedule; and who benefits from variations to it?


Well, I personally plan to repay the mortgage much sooner, and only chose long period to protect myself from a strike of bad luck. If I chose shorter period, I'd end up paying the bank less - substantially less - in total, but I could get into trouble in my income faltered. I intentionally chose what I saw as the safer way. Should the bank "subsidize" my decision to play it safe somehow? I believe I got better rate, since I had more than adequate income for my mortgage, so perhaps the subsidizing does happen in a way, actually (playing the devil's advocate here ).

Winston Gutkowski wrote:

I think you are misinterpreting the very nature of 'interest'. first of all, they reward the lender for making available the money in the first place. It's nothiing else than hiring someone to do some work for you and aying him


I think you'll have to explain that one to me, because I don't see any "compounding" involved in paying someone a salary.


I may be wrong here, but I think there is no compounding in mortgage. Every month, I pay the interest from exactly the amount of money I owe to the bank. Compounding would arise if I haven't paid the bank enough to cover the interest due. In this case, the unpaid interest would add to my debt and next time I'd pay interest from the interest, resulting in "compounding". But this is not the normal flow of things in mortgages.

Interesting discussion, really! I wonder how you always come up with such a catchy topic!
 
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Jeanne Boyarsky wrote:Risk is a motive when you invest or lend too. So no .
Seriously though, a bank is a business. If you borrow from friends/family, the goals are different. This is part of the reasons that credit unions operate differently than baks. (I mean a real credit union where people have some other connection.)


I hate to say, but that sounds to me like simply hoisting the white flag and saying 'Yes. Profit is all'.

Assuming that a liberal society is intended for the greater good, then simply chasing a buck seems a rather poor technique; and I doubt that it's what Adam Smith or Thomas Paine had in mind.

Personally, I've always liked the Quaker business model: Quality goods sold at reasonable profit. They wouldn't barter, because their assumption was that the asking price was fair. They were, however, one of the first Christian sects to accept that profit of any kind was justified. They were also a major factor in the social changes that took place in the 19th century in the UK (health care, social housing, working conditions). Unfortunately, the flagship companies like Cadbury's and Rowntree have all been sold off to conglomerates whose motives are nowhere near as lofty. The only one left that I know of is Clark's shoes.

It seems to me that we've lost the "enlightened" part of "enlightened self-interest". Maybe that'll change when China becomes the #1 power (around 2025 from what I can gather), but I doubt it. I don't trust "state" capitalism any more than I do individual.

Winston
 
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Piet Souris wrote:(By the way: is what Martin describs, about 'walking away' and then the bank owns
the house, correct? What if you default in year 30 of a mortgage with 30 year duration? Incredible)


Well, according to what I've read, this is what happens when the price of the house is lower than the remaining debt. In my country, this would leave me still owing to the bank (and I do see this quite a bit unfair, as I'm taking some burden of risks that I believe genuinely belong to the bank), while in the US I wouldn't have any remaining liabilities - according to what I've read, people were just dropping the keys into the mailbox and going away.

I don't know what happens when it is the other way round, but I assume that you generally should be able to sell the house on your own terms and then just repay the bank the remaining debt.
 
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chris webster wrote:I think there's another factor in many people's deliberations over whether to take on a mortgage: what's the alternative? We all need somewhere to live, and we all need to consider how we'll pay for our living expenses when we're too old to work.


Surely just another point that weighs on the side of the lender? You, as the borrower, are faced with only two choices - take it or leave it - regardless of how you feel about the maths (or, as we've been discussing, the assumptions that those maths are based on).

For example, when we bought our house (with a mortgage) 14 years ago, it was priced at around 5 times the average wage hereabouts. Now it's supposed to be worth more like 10 times the average wage because the house price has risen but wages have not.


And I think you'll find it's a trend that has basically been going since the end of WW2 in most Western countries. Furthermore, it only increases the power of the lender - even I understand basic supply-side economics.

And if you are thinking ahead to how you will live when you're older, then you need to ask how you will pay your rent if you don't buy a place while you're still working. This is especially true in the UK, where the state pension is one of the worst in the developed world and private pensions rely on the casino mentality (and questionable competence) of the financial services industry.


Don't get me started. Seems to me that, since the "Iron Lady", Britain can't decide whether it's American or European, and is currently stuck somewhere in the mid-Atlantic. In the short term (no Euro), it seems to have helped; but long-term...? I simply don't know; but I hope I never see people living on the street like they do in the US and Canada. That, to me, is failure.

It's discussions like thsi that make you realise you are now officially Middle-Aged!


Join the club mate, and welcome.

Winston
 
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Martin Vajsar wrote:So according to this scheme, after 15 years the bank got its investment into my mortgage almost back (96% of it). However, if the bank invested that amount into 15 years of government shares instead (say, not the Greek ones ) with 2% p.a. (see, substantially lower than my 5%), by now it would have some 135% of its original investment. So there is a difference.


But only if you assume that:
(a) They would have done it.
(b) They guessed correctly over the 15 years that it took you (I hope you don't mind me using your name ) to fail.
And that's my problem with the maths: It assumes a perfect (or near-perfect) scenario for the lender.

Moreover, my house will be sold at auction and used to repay my remaining obligations.


Which, to me, says that the lender has actually assumed no risk at all. He simply has "money to lend".

Well, I personally plan to repay the mortgage much sooner, and only chose long period to protect myself from a strike of bad luck. If I chose shorter period, I'd end up paying the bank less - substantially less - in total, but I could get into trouble in my income faltered.


And there is precisely where my example comes into play. Once they have received a reasonable proportion of the loan in service payments, they couldn't care less whether you resell the house or simply default on your loan. The mechanics for them are exactly the same, except that in the latter case they get their residue from an auction rather than a re-sale. And in the second half of your loan, the chances are that it will be better for them if you default (less risk).

If you sell your house early, regardless of whether it's the best thing for you or not, their yield on that loan is WAY better than the nominal 5% that they were going to get had you gone to term. Hence my question.

I may be wrong here, but I think there is no compounding in mortgage.


Then I fear that you're very naive. It's certainly true that you don't pay as much as the simple compound calculation for total (and why would you?), but I suspect that every tensor in the algorithm that you do pay is biased in favour of the lender. And if anyone (Piet?) can prove me wrong, I'd like to hear about it.

Interesting discussion, really! I wonder how you always come up with such a catchy topic!


Glad you're enjoying it. Dub me "naive capitalist".

Winston
 
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Winston Gutkowski wrote:I hate to say, but that sounds to me like simply hoisting the white flag and saying 'Yes. Profit is all'.

Assuming that a liberal society is intended for the greater good, then simply chasing a buck seems a rather poor technique; and I doubt that it's what Adam Smith or Thomas Paine had in mind.


For a company, yes profit is all. It's a bit more complicated than that as it is profit over the long run. That's what prevents a company from charging you $100 and sending you a pile of poo. Well ok, fraud laws help there too. But it isn't in a company's interests to profit at the expense of making the company look so bad that customers won't come back and will tell their friends. Companies need to invest in their future and future profitability.

I don't believe that "profit it all" precludes social. Companies support charities. Granted they do it for PR and tax deductions. And some *people* at companies think about the greater good. If they are high up enough in the company, you get the company looking at the global good. But that isn't the job of the company. It's something nice that happens.

By the way, when we say "company", I'm thinking of a corporation. Obviously, a non-profit will have a different view of social causes.
 
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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.

It's a bit more complicated than that...


Well, glad we're agreed on that at least; but I think that your idea of what constitutes a "business" is a bit simplistic. Canada, for example, has Crown Corporations, which are 'not for profit' - as opposed to non-profit - that have to conform to a lot of rules; not the least of which is that they employ Canadian labour for a lot of their services. I believe the US Postal Service is run on similar lines, although if you're a diehard Reaganist, you may simply view it as another "arm of government" forgetting, in the process, its storied history.

I don't believe that "profit it all" precludes social. Companies support charities...


This is an argument that dates back to the 1920's, and here I'm absolutely on the side of the Socialists.
Nobody wants charity; they want jobs. And a rich government that can't be bothered to even provide them with shelter when times are tough has, as far as I'm concerned, failed in its duty to its citizens.

Winston
 
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First of all, this answering thing is a nightmare, when you have to make a lot of quotes.
After having spent two hours answering Winston and sending my response, this nasty Censor'
refused to send my answer, because it has spotted a loose 'are' somewhere. And then Strictly
come dancing' started, only to find that I've lost my complete answer. Grrr,

Nevertheless, I tried to reinstate all, but I see that there have been some other reactions as well.
So, my answer may contain some things that have already been discussed, and I'll come back to these
if necessary, but here goes:

Winston Gutkowski wrote:

First of all, most mortgages have a fixed interest rate for only,say, 10 years.



Thus, surely, increasing the uncertainty for the borrower?



Well, the borrower might also benefit, when interest rates have dropped. There are no certainties in life, that's a fact.
Suppose: you can borrow money, and either you pay 3% per year, interest being determined after every year, or you can
fix this fixed interest period for 30 years, interest being 5%. Which of the options would you prefer?
I bet, if someone can afford paying 5%, then that person goes for that option: ease of mind.

Winston Gutkowski wrote:

And indeed, buying a house is one of the biggest investments you're ever likely to do. So, therefore, you must very seriously
think about what you are getting in to. But then again, you pay a huge amount of money, but then, you own a house!



Ah, but do you? As far as I can see, that "ownership" only entitles you to sell it again when you decide. In difficult times, not only
can the lender assume that right, in Europe it doesn't even necessarily clear your debt.



True, but that accounts for a lot of things. It is in principal not different from borrowing money to buy a car, or a decent new computer.
If you are facing financially difficult times, you have to sell some property to meet the debts. The only special thing with mortgages is the
amount involved.

The American system seems very odd to me. A collateral, like a house, makes the risk for the lender smaller, so the interest
will be less. Nevertheless, the borrower has the obligation to pay everything back, and the value of the collateral is taken into account.
In the American system, if I understand Martin correctly, you simple swap your obligation for the collateral, no matter what
the remaining value of that obligation is. Now, that's what I consider to be a big risk for the borrower.

Winston Gutkowski wrote:

Well, it is just one kind of investment. So they don't...Indeed, gained interest is re-invested, although part of it will be spent on salaries, dividend, et cetera.



Yes, but the assumption is that they have re-invested it; and that's what I take issue with.

And if there is one company that charges unrealistic high mortgage rates, then find some company that offers lower rates.
Despite the fact that that "lower rate" company may be miscalculating their risk? Again, I thought this was what prompted the last 6 years of "toxic debt".



Hmm.. well, if you compare two products, one cheaper than the other, is it always true that the cheaper one is of less quality?

The 'toxic' part was primarily based on the fact that mortgages were sold to people who, given their income, should never have had this mortgage.
And besides, If I recall correctly, these American mortgages really were incredible: low payments in the first years, and then a big increase later.
This is what you call "a market going nuts". Therefore, some strict govrnment institue should look upon the mortgae industry.

Anyway, if you borrow money from a company that goes bust, that is not your concern. You have a mortgage contract, and that remains valid,
no matter what. At least, here in Holland.

Winston Gutkowski wrote:

The terms, yes, but the maths? These arise from Mathematics.



No, they arise from maths based on specific assumptions. My worry is not that the maths is wrong, but that it's based on assumptions that are biased in favour of lenders - or possibly, ones that promote greed.



Let's recall the formula I gave in the topic you referred to:

Loan = Payment * a(n,q)

This formula has two assumptions:
a) the payment P is paid at the end of each period
b) that the interest rate all over ("internal rate of return") is 'q' per time unit.

This formula depends in no way on assumptions that underly the determination of 'q' .
If you agree on paying the loan back in some other way, the formula changes accordingly. For instance, if you pay P in the first 10 years,
and 2P thereafter, the formula becomes:

L = P * a(10, q) + A(10,q) * 2P * a(n-10,q)

Winston Gutkowski wrote:

I think you are misinterpreting the very nature of 'interest'. first of all, they reward the lender for making available the money in the first place. It's nothiing else than hiring someone to do some work for you and paying him



I think you'll have to explain that one to me, because I don't see any "compounding" involved in paying someone a salary.



First of all, if your business is in selling mortgages, then your costs are mainly twofold: you have to pay interest or dividend to
those who supplied you the Capital, and second: you have to make a living (and so do the people you employ, let alone the office
from which you run your business). These costs you have each year, and therefore you need income each year to finance this i.e.
some surcharge on the interest rate.

Winston Gutkowski wrote:

Second, the lender faces a risk, namely the defaulting borrower. Fo this risk, he wants to be paid.



Which, at least in terms of property, is surely covered by the lien. Since, at the start of the agreement, it can be reasonably assumed that the borrower has nothing and the lender has everything, the lien simply exchanges money for equity. And in addition, the lender receives additional income proportional to the interest rate (actually, proportional to the rate over the assumed term). Where's the risk? Surely not in an agreement like that.



Well, that depends. First of all, under normal circumstances, you do your monthly (quarterly/yearly) repaiments, so your debt decreases, while the house remains its value
(or, increases in value). But there are a lot of mortgges in which you only pay interest, and never pay any amortizations. These mortgages are
purely based on the fact the the house will always be at least as valuable as the debt.

Now, that sounds incredible, but it is quite common in Holland. The point being that Holland is one of the very few countries where interest paid on
a mortgage is deductible from the income tax. So, it is beneficial to keep the debt as high as possible. But the problem with this is
when house prices drop. You will have a big problem selling your house then, since you will remain in debt.
And, given his problem among others, we lost the Triple A status yesterday, by S&P.
And so there are now much stricter rules for mortgages: people have the obigation to pay at least 50% of the mortgage back
within the next 30 years, income tax reduction will be limited, the amount to be borrowed will be limited, et cetera.

Winston Gutkowski wrote:

Lastly, a lender also wants some compensation for inflation.



And there, unfortunately, is where my maths fails me. I certainly agree that it's a factor, but I simply don't know how one goes about calculating that sort of risk.



Well, that's no problem. We simply create millions of curves, and let the computer run through all these scenario's.
We do this usually for interest curves and mortality curves for the next 80 years, inflation, currently, is fixed at some amount.
(We are critized for this by the reviewers of our systems, so we will have to do something about that in the near future).

The idea is not so difficult: say, you have some distribution, for instance, normal, Poisson, Shifted Gamma, whatever.
You draw, say, 100.000 values, and do your calculations. Variables are mean and variace.
Suppose that, instead of drawing numbers, you draw curves, each curve being a possible scenario for the next 80 years.

To picture this: suppose you have a function f(t), of which you know that f(0) = 0 and f(T), for some T, is drawn from a normal distribution, with mean mu(T), and variance sigma(T).
To calculate integrals for such functions, you need the Itoh calculus (one of those nasty maths I had to bcome acquainted with some years ago).
This is rather different (and much more complex) than the everyday Rieman or Stieltjes integrals.
Anyway, what I do for a living nowadays, is valuating the liabilities of our huge pension insurance protfolio, and also valuing the guarantees
that we have give in the past on these insurances. For this, we have lots of scenario's: mainly interest and mortality. And we also measure
how sensitive our outcomes are to small changes in the assumptions. And a lot more.
But I digress.

Winston Gutkowski wrote:

Houses are bought and sold again.



Ah, but that wasn't my question - "How many mortgages actually go to term?" - To clarify: How many (or what proportion of) mortagaes are actually repaid exactly according to schedule - ie, Martin makes his first payment of a 30-year mortgage in January 1980, and his last in December 2009, never missing a payment or selling before time? My suspicion would be very few.



Well, the mortgage contract is rather explicit on this. The only occasion where the normal redemption scheme is not followed is when the mortgage is paid back at once
(by selling the house, or when the borrower dies and has an insurance for that), or when the borrower defaults.
If I take myself as an example: my mortgage ends in less than two years from now. I hve never paid any redemption, but I have a life insurance that
pays out the mortgage when I dy, or when I am still alive in less than two years from now. So I guess I am one of those for which the
mortgage is repaid according to scheme. But I have no idea of the total figures, no.

One final reason to end a mortgage prematurely: when interest rates have dropped so far, that it is worth taking a new mortgage and redempt the old one.
However, there ís usually a big fine to pay. making it usually unattractive. (and there is some very good reason for that fine,
which I can explain, if you are interested).

Winston Gutkowski wrote:Yet the mathematics is based on precisely that schedule; and who benefits from variations to it?



Let's take this situation into consideration:
1) the duration is 2n years, interest rate is q, loan is L
2) we pay back a fixed amount P, under the assumption that we pay it back in the next 2n years.
3) But after n years: we pay at once tthe remaining value A, without any fine

Now, what will be P and what will be A?
first: we determine P:

L = P * a(2n, q) ==> P

Then, we determine A
After n years, the borrower has still to pay P for the next n yars, the present value at that time being P * a(n,q), so that's the remaining value A

You see, whether P gets paid for 2n years, or redempted after m years, has no effect at all on the maths.

Even stronger: most mortgage contracts are for a fixed period of, say, 10 years, after which you usually renew your mortgage
(with a new interest rate), or you can redempt it without fine.

Winston Gutkowski wrote:Great discussion. Hope you don't mind me remaining a sceptic.



I don't blame you, rest assured!

 
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Piet Souris wrote:First of all, this answering thing is a nightmare, when you have to make a lot of quotes.
After having spent two hours answering Winston and sending my response, this nasty Censor'
refused to send my answer, because it has spotted a loose 'are' somewhere. And then Strictly
come dancing' started, only to find that I've lost my complete answer. Grrr,


Oh NO. Don't worry, you're not alone even on this thread (it happened to me too).

Unfortunately, it's getting a bit late here, so I hope you'll excuse me if I reply tomorrow; it looks like I may have a bit of maths to digest anyway (hope I'm up to it, with me 'A'-Level stuff).

And thank you to everyone who's participated - especially those who I disagree with. I haven't even looked at the usual Java forums today because I've had so much fun answering posts here, which probably says as much about "Meaningless Drivel" as it does about me or me trendy-lefty opinions.

Winston
 
chris webster
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Winston Gutkowski wrote:[...as it does about me or me trendy-lefty opinions.

Winston


Sadly, I can barely remember when genuinely left-of-centre opinions were remotely "trendy" in the UK!
 
Jeanne Boyarsky
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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.
 
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Piet Souris wrote:True, but that accounts for a lot of things. It is in principal not different from borrowing money to buy a car, or a decent new computer.
If you are facing financially difficult times, you have to sell some property to meet the debts. The only special thing with mortgages is the
amount involved.

The American system seems very odd to me. A collateral, like a house, makes the risk for the lender smaller, so the interest
will be less. Nevertheless, the borrower has the obligation to pay everything back, and the value of the collateral is taken into account.
In the American system, if I understand Martin correctly, you simple swap your obligation for the collateral, no matter what
the remaining value of that obligation is. Now, that's what I consider to be a big risk for the borrower.


Different than a car. A car decreases in value the second you drive it off the lot. And is guaranteed to keep decreasing in value as the loan goes on. A house count go up, down or stay the same. Or it could be seized by another creditor (I think.)

But yes, it is a big risk for the borrower.
 
Martin Vashko
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Coincidentally, a related article is in the latest issue of The Economist: http://www.economist.com/news/finance-and-economics/21590927-modern-proposal-ancient-roots-cap-and-tirade
 
Piet Souris
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Jeanne Boyarsky wrote:

Piet Souris wrote:True, but that accounts for a lot of things. It is in principal not different from borrowing money to buy a car, or a decent new computer.
If you are facing financially difficult times, you have to sell some property to meet the debts. The only special thing with mortgages is the
amount involved.


Different than a car. A car decreases in value the second you drive it off the lot. And is guaranteed to keep decreasing in value as the loan goes on. A house count go up, down or stay the same. Or it could be seized by another creditor (I think.)


Not in principal. In both cases, you borrow money and you pay it back according to some scheme. That's what I meant.

Now, the idea behind borrowing money to finance some purchase is that the pay back scheme must follow the nature of the purchase.
In that way, you will feel the true cost involved of that purchase.

In the case of a car, indeed, the value of the car decreases every second, and after 10 years or so, the car has no remaining value, therefore
it would be wise to make sure that after that period, you have no remaining debt. I remember some collegues way back that increased their
mortgage to finance a new car, because mortgage rates were very low, and the value of the house had increased sufficiently.
Now, is that wise? Even when you consider that the interest for a borrow solely for a car is way higher?

Following this idea: since a house price does not decrease (well, that was the believe for many years, at least) one could argue that a mortgage
does not need to be amortized at all. You just pay interest and that's it. Would you want such a mortgage? If not, why not?

Anyway, and reading the article Martin is referring to: I certainly can sympathize with Winstons feeling about mortgage companies. It sure
is a one way traffic: they determine the mortgage rates, and while for them a mortgage is every day business, for you (in general, not you, Jeanne!)
it is a very big moment in your life. And I certainly feel that mortgage rates are higher than they should be.
But then again, I can remember mortgage rates were above 10% (even above 20% in the UK), in the early eighties, so compared to that:
what is the problem?

Greetings,
Piet
 
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The article I was referring to highlights one aspect I wanted to mention earlier (and then forgot): there are loans on the market which have much, much worse rates and overall conditions than mortgages. And even when there is no lien, the situation in my country is that the borrower can lose his house over such debts anyway, since the debtor's property can be seized, even when it was not a collateral in any of his loans (notsure whether this is a universal concern, though). I do think that these payday lenders are clearly unethical and should be heavily regulated - regulated away if need be. They are invariably taking advantage of the poor financial situation and lack of understanding of their hapless customers.

If we assume that it is at all possible (or ethical) to administer an interest on the debt, and the issue is just the rate, then I'd say mortgages lie on the more ethical end of the specter of the financial products (much better than credit cards, in my opinion). In my own case: average inflation in my country over last four years was around 1.9%, which means that real mortgage rate I was paying was not around 4%, but close to 2%.

I believe that mortgages appeared on Winston's radar mainly because the sums involved are so high Perhaps the underlying issue behind the mortgage concern is the affordability of housing in general?
 
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Martin Vajsar wrote:I believe that mortgages appeared on Winston's radar mainly because the sums involved are so high Perhaps the underlying issue behind the mortgage concern is the affordability of housing in general?


Yup. That's definitely a big part of my concern, but I also think that the lender's 'risk' is overassessed. Apart from the past 5 years - and possibly even including it - I can't think of any other 5-year period since 1945 in which property in the West hasn't kept up with inflation.
That being the case, and assuming that mortgages involve a lien that covers the remaining principal - especially when the borrower is usually also required to provide a deposit - Where is the risk for the lender? Unless I'm very much mistaken, most of our current problems stem from the fact that lenders have not been lending 'money in the drawer', but rather money that they've borrowed.

I also say (and I'm sure Piet will disagree with me ) that the standard maths involves assumptions that favour lenders, and also ensure that most of their profit is made early, rather than steadily over the entire course of the loan. Unfortunately, my maths simply isn't good enough to come up with alternatives, but I suspect strongly that there are other ways of interpreting 'what a loan is' that are less lender-centric.

Cars are a different matter, and as far as I'm concerned should be governed by a completely different set of rules (or perhaps just ones that reflect the depreciation of the asset far more severely). However, unless you're in the market for a Bugatti Veyron, the sums involved are also much smaller and, perhaps more importantly, so is the time period.

BTW: Great article. There are also links on the right-hand side of the page to others that also cover some of the broader things we've discussed; but Jeanne's quite right: I'll keep the political stuff for a separate thread.

Winston

PS: (@Piet) I haven't forgotten about your post; I was out most of yesterday and simply haven't had a chance to get around to it (it's big ). I will today.
 
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Winston Gutkowski wrote:Unless I'm very much mistaken, most of our current problems stem from the fact that lenders have not been lending 'money in the drawer', but rather money that they've borrowed.


But that's a different question again. The problem with mortgage crisis, in my opinion, was that even bankers believed that property prices will go up forever, or, more specifically, the invention of tranches. (On the face of it, tranches seem like an ingenious invention. It does take some imagination to see how they could go wrong, especially in the bull market. But it was the duty of bankers - and regulators - to see it, and they failed.)

I really don't see any difference for individual mortgage here in whether the bank is lending me its own money or borrowed money. With borrowed money, it has to pay interest to the original lender. With it's own money, it forgoes any interest it might have earned if it invested the money elsewhere. In both cases, mortgage interest rate will cover the "price of the money" plus earnings for the bank, plus (oh, here we go ) risks.

I also say (and I'm sure Piet will disagree with me ) that the standard maths involves assumptions that favour lenders, and also ensure that most of their profit is made early, rather than steadily over the entire course of the loan. Unfortunately, my maths simply isn't good enough to come up with alternatives, but I suspect strongly that there are other ways of interpreting 'what a loan is' that are less lender-centric.


I'll disagree too. I'm pretty sure that each month I pay the interest from exactly the amount I'm owing that month - at exactly the rate I've agreed with the bank beforehand. Yes, in the first year I've paid much bigger interest than in the last year, but in the first year I've owed much more money than in the last year. Thus, the debt doesn't decrease linearly (and I believe this is one of the reasons for your grief). Some banks do allow to choose a different repayment schedule, you quite certainly could find a bank which would allow you to pay fixed amount of principal plus interest each month, but the problem with this scheme is that the payments would decrease rather quickly, so the next year you could afford to pay much bigger part of the principal with the same income. The typical mortgage scheme smooths this effect over the entire duration of the mortgage, so that the amount you pay each month is fixed. That probably suits most folks best, I'd say.

You might be right that the distribution of the risks for the lender is not constant in time. In the beginning, it is probably highest, and it decreases as the debt itself decreases. Moreover, someone who has paid the mortgage for fifteen years without problems is certainly less risky a debtor than someone without any credit history at all. But I believe that these things actually are factored into the rate, especially since mortgages are typically renegotiated every few years.

I don't deny that the lender has an upper hand, but this is where competition comes into the picture. I was able to negotiate off a few tens of a percentage point off my mortgage, but the discussion was about what a competitor would offer me, not about the risk assessment of my profile.
 
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Piet Souris wrote:... only to find that I've lost my complete answer.


I don't want to derail this topic, but let me point out that there are extensions for many browsers that are able to recover the text you've typed into a form when something bad happens. I, personally, am using Lazarus for Chrome.
 
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Martin Vajsar wrote:I really don't see any difference for individual mortgage here in whether the bank is lending me its own money or borrowed money.


You don't? I do, because it increases their risk.

With borrowed money, it has to pay interest to the original lender. With it's own money, it forgoes any interest it might have earned if it invested the money elsewhere.


So surely, in the former case, the cost of that money is compounded? And I can't imagine any person or institution whose motive is profit not passing on that cost to the borrower, not to mention the cost of insurance against the added risk.

Now I understand that it may not be most efficient to require that 100% of a lender's money be "in the drawer", but why should I, as a borrower, assume the cost of a risk that I have absolutely no control over? The bank decided to borrow money in order to lend it to me - indeed, in the case of a retail bank, they've probably borrowed some of that money from me - but why should that change the cost of my agreement with them? I still don't see the risk to them when, in the case of property and unless they get greedy, they are virtually guaranteed not to lose on the transaction. They simply have access to funds (and interest rates) that are not available to the rest of us mere mortals.

You might be right that the distribution of the risks for the lender is not constant in time. In the beginning, it is probably highest, and it decreases as the debt itself decreases. Moreover, someone who has paid the mortgage for fifteen years without problems is certainly less risky a debtor than someone without any credit history at all.


Sure they are, but that has less to do with the fact that they're any less at risk of running into difficulties than it has to do with the fact that the bank has already made as much profit as it's ever likely to out of the agreement.
In the above example, the bank has already made 96% of the original loan, and stands to receive a further 67% if the borrower defaults (or resells). Total: 1.63 * principal. If the loan goes to term they will receive ≈1.93 * principal, but it will take them another 15 years to do so, so it could well be argued that the bank is actually losing in the last half of the agreement; particularly when inflation is taken into account.

Hence, I'm quite sure, why banks are more than happy for you to rewrite mortgages, or to pay off your current one and assume a larger debt in search of your "dream house".

Great discussion though.

Winston
 
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It is still straight forward maths.

Now, as you will no doubt know, there are many different types of loans. I once knew the English terms, but I've forgotten
most of them. So, when in doubt, do not hesitate to ask what I am talking about.

Type one: zero coupon loans (or in short: zero's)
These types of loan are very important in the valuation of so called 'market value of liabilities'.
The loan has the following characteristics:
- there's the loan at t = 0, and there's only one repayment, after n years
- no other payments take place
- the one payment after n years is of course determined by the value of that one payment.

The maths are simple. We have the loan L, and the one payment P, at time n.
We then have:

L = P * A(n, i), and from this you are able to calculate the interest 'i' here. This interest 'i' (and I am being
very careful here not to use the letter 'r', otherwise this nasty Censor will give me some bad times) is
the IRR, the all over interest. This 'í' is NOT the interest for each single year of the n years involved.

Now, this type of investment is ideal for quarantee situations. Suppose I am an insurance company, and someone pays us a single premium
at t = 0, to get some lump sum in n years from now. Think of someone paying for a pension scheme.
For this single premium, we can buy a zero loan with duration n. That will have an interest í' involved, and thus,
we are able to 'guarantee' an interest 'í' over these n years. Since there are no in between payments, we do not
have to worry about the interest that we would be able to make when re-investing these in between payments.

Zero's are very easy to obtain, for periods of up to 40 years. For each duration, you would have different 'i's.
These í's are derived from so called 'swaps', where two parties agree to pay each other cashflows, for a certain
period. Both parties agree on some fictional amount, the 'Notional', and party A pays a fixed interest to party B, and
party B pays a floating interest to party A. This floating could be the six mont's LIBOR, or EURIBOR, for instance.
These swaps are determined such, that at t = 0, both series of payments have the same present value.
These swaps are very easy to get for most durations, and from these swaps the interest rates for zero's is derived.

/************************************************/

Another important type of loan is the annuity, most mortgages come in the form of such an annuity.
We have a durantion n, a loan L, a, say, yearly payment P, and an interest rate i.
The maths are simple:

L = P * a(n,i) or P = L / a(n,i).

Now, you may wonder, in these payments P, what exactly is the amortizing part, and what is the interest part?
Let us denote the amortization part in payment t by: Am(t).

Since P(t-1) = P(t) = P, we have:

P = Am(t-1) + Int(t-1) = Am(t) + Int(t)

Now, since Int(t) = Int(t-1) - i * Am(t-1) (why?). we have that:

Am(t-1) + Int(t-1) = Am(t) + Int(t-1) - i * Am(t-1), or

Am(t) = Am(t-1) * (1 + i).

So, the amortization parts form a geometric sequence.

Now, Am(1) is easy to determine: the interest part is i * L, so

Am(1) = P - i * L.

The remaining value at time t is the L - sum of paid Am(s), s = 1, ... , t.

Put this simple scheme in a spreadsheet, and see how the remaining value evolves over time. You will
notice how slowly the remaining value decreases!

/***************************/

another type of loan is the equal redemption loan.
With this type of loan, the borrower amortizes, each year, L / n, and pays interest over whatever
the remaining value is at that time.

The payments are then:

P(1) = L / n + i * L
P(2) = L / n + i * L * (n-1) / n
...
P(n) = L / n + i * L / n

Now, let's consider this from the insurers point of view. Suppose the client pays us a yearly pension premium,
for some pension at retirement. We promise to invest each premium in a 10 year equal redemption loan,
of which in the first 5 years no redemption takes place, and equal redemption within the next 5 years.
Over the whole contract period (we have these contracts with the clients, which deals with what type of
pensions are insured, how these pensions are determined, and how the financing will be).

The fun comes when we, the insurer, grants an annual interest rate of 3%, over the whole contract period.
Now, when at t = 0, interest rate are above 3%, we have no problem. But suppose that next year,
when the next premium arrives, the interest rate has gone down to below 3%? Then we are in trouble.

Not only that, but we also pay interest profits, when we make more than 3% interest on the investments.
So, interest gains we pay out, and interest losses? That is for us. Question is: can we buy some form of
protection for this? And anyway, given the contracts we have, and given current interest rates, what
is the value of these guarantees that we have given? And, when it comes to pricing, should we
put a surchage on the premiums for this guarantee, and if so, how much?

/******************************************/

You may wonder what all this has to do with Winstons initial question?

I'm not sure anymore
but first of all, to tell something of the maths involved, and secondly, why we would put some surcharge
on the premiums, in fact putting some extra interest to these investment schemes.

As I stated earlier, there are many factors that influence the determination of the interest in question.
Guarantees, current market rates, loan types, profit surcharges, dividends to pay, greed.

Greetings,
Piet
 
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Winston Gutkowski wrote:

Martin Vajsar wrote:I really don't see any difference for individual mortgage here in whether the bank is lending me its own money or borrowed money.


You don't? I do, because it increases their risk.


There is no difference. The banks 'own' money is money that belongs to the shareholders, who in return expect some dividend, higher than
risk free interest.
The exact same holds for money that the bank has borrowed itself, to finance mortgages.

 
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Winston Gutkowski wrote:Now I understand that it may not be most efficient to require that 100% of a lender's money be "in the drawer", but why should I, as a borrower, assume the cost of a risk that I have absolutely no control over? The bank decided to borrow money in order to lend it to me - indeed, in the case of a retail bank, they've probably borrowed some of that money from me - but why should that change the cost of my agreement with them? I still don't see the risk to them when, in the case of property and unless they get greedy, they are virtually guaranteed not to lose on the transaction. They simply have access to funds (and interest rates) that are not available to the rest of us mere mortals.


This is everydays life.

If you buy a new PC from company A, then in the price you pay, you pay a certain amount for the loans
that that company had to make to finance their business. For instance, the mortgage that this company
has on the shop where you bought that new PC! Now, why should you have to pay a surcharge for money
that they have borrowed, and maybe even, paying a surcharge for the risk the bank is facing...
You see, there's no escaping.
 
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Winston Gutkowski wrote:So surely, in the former case, the cost of that money is compounded?


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.

You might be right that the distribution of the risks for the lender is not constant in time. In the beginning, it is probably highest, and it decreases as the debt itself decreases. Moreover, someone who has paid the mortgage for fifteen years without problems is certainly less risky a debtor than someone without any credit history at all.


Sure they are, but that has less to do with the fact that they're any less at risk of running into difficulties than it has to do with the fact that the bank has already made as much profit as it's ever likely to out of the agreement.


It depends on what you measure the profit against.

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. It doesn't matter whether the bank has lend a million to one person, or a hundred thousand to ten different people for the same period of time. If all of them have the same rate, the income is the same too. The physical work is different, certainly (one contract or ten contracts), but it is sometimes covered by a separate fee, so all in all, the profit is just the same.

Hence, I'm quite sure, why banks are more than happy for you to rewrite mortgages, or to pay off your current one and assume a larger debt in search of your "dream house".


This doesn't prove anything: it could be as much because "larger debt means bigger profit" as "new debt means new profit".

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 perspective.
 
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Winston Gutkowski wrote: (...)
In the above example, the bank has already made 96% of the original loan, and stands to receive a further 67% if the borrower defaults (or resells). Total: 1.63 * principal. (...)


It's always compound interest.
I have given some of the elementary maths involved in loans. As you can see, it's all compount interest.

Do not confuse total yield with present values; that's really comparing apples to pears. Total yield doesnt mean anything.
It's all about the moments in time when you recieve the yields.

You might also want to have a look at the definition of 'duration' (see Wikipedia, for instance).That's kind of a first
derivative of the present value, with variable the interests involved. The duration gives some idea how
a present value is sensitive to interest changes, like a normal derivative tells something about
the rate of increase for some function.
 
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Piet Souris wrote:It is still straight forward maths.


I'm glad you think so. To me, it's extremely complex (as, I'm quite sure, it should be).

But I still don't see anywhere in those formulae where the asset (or risk) swap has taken place. As far as I can see, they are still based only on the fact that I have borrowed money; not swapped money for an asset (the house - and let's stick with property, because depreciation is likely to do me head in ).

Perhaps I need to restate the question - If:
(a) Property tends not to lose value.
(b) The lender acquires the right to sell my property should I default (or gets its resdue as part of a resale).
(c) The lender gains steady income while I am paying off the loan.
(d) The drop in my principal is not steady.
(e) I was probably required to put a downpayment on the property to start with.
Where is the risk to the lender?

The only one I can see is that they didn't do their job properly. Or that they got too greedy. Should I pay for that?

Furthermore (and this comes down to greed again), if I'm right, and most loans do NOT go to term, then the bank can claim a far greater yield on its loan base than whatever the nominal interest rate is, presumably allowing them to borrow more money at favourable rates, which they then lend to another poor sucker...

I'm being simplistic, but do you see my argument? At no point in this process do I see any assumption of actual RISK by the lender at all; all I see is a structure that requires me to pay for it, based on assumptions that I'm not equipped to question, but that I (still) suspect are strongly biased in favour of my lender.

Winston
 
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Winston Gutkowski wrote:

Piet Souris wrote:It is still straight forward maths.


I'm glad you think so. To me, it's extremely complex (as, I'm quite sure, it should be).


To me, command line commands are extremely complex to me... giving me headaches, and therefore
ever thankful that NetBeans deals with that

Winston Gutkowski wrote:But I still don't see anywhere in those formulae where the asset (or risk) swap has taken place. As far as I can see, they are still based only on the fact that I have borrowed money; not swapped money for an asset (the house - and let's stick with property, because depreciation is likely to do me head in ).

Perhaps I need to restate the question - If:
(a) Property tends not to lose value.
(b) The lender acquires the right to sell my property should I default (or gets its resdue as part of a resale).
(c) The lender gains steady income while I am paying off the loan.
(d) The drop in my principal is not steady.
(e) I was probably required to put a downpayment on the property to start with.
Where is the risk to the lender?

The only one I can see is that they didn't do their job properly. Or that they got too greedy. Should I pay for that?


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?

Now, that is hard to answer. I once had a collegue, who had some savings. So he quit the job, moved to India
or thereabout, starting a micro-loan firm, to help local people to set up their own business.
Did he succeed or did it make him happy? What interest rate did he charge (surely, he went into some risky business).
Did he come back as a millionaire, or did the local people gave him a statue?

Well, hold your breath, here comes.....

I don't know, never heard of that guy again.

Greetz,
Piet
 
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