The typical Canadian mortgage matures in 5 years or less. Why can't Canadians get (say) 30 year mortgages? I used to think that the answer was "inflation", or "inflation uncertainty". Now I don't. Now I think the answer is "Section 10 of the Canada Interest Act". Which we should abolish.
Why can Americans get 30 year mortgages? I used to think the answer was "some sort of implicit subsidy by Fanny and Freddy". Now I'm not so sure.
This post is mostly about Canada. But it has implications for Americans. On reading US comments and responses to my previous post, I get the impression that there's a general assumption that the US 30 year mortgage only exists because of government support. I'm not sure that's right. Or rather, it may depend on what sort of 30 year mortgage we are talking about.
We really need to distinguish "closed" from "open" mortgages.
A 5-year "closed" mortgage means the interest rate is fixed for 5 years. That's the typical Canadian mortgage. If you want to pay it off earlier, you have to compensate the lender by paying the difference between the old and new interest rates over the remaining term of the mortgage. That means you never have any incentive to renew a mortgage if interest rates fall.
A 30 year "open" mortgage means you can pay it off any time you like. So if interest rates fall, you have an incentive to renegotiate the mortgage and take advantage of the new interest rates. That means the interest rate you pay cannot rise, but can and probably will fall. That's the typical American mortgage.
The 1880 Section 10 of the Canada Interest Act puts a maximum penalty of 3-months' interest on repaying any loan over 5 years after 5 years have passed. That's a small penalty, and it would take only a small fall in interest rates to make it worthwhile for a borrower to exercise his option to renegotiate created by Section 10. In effect, closed mortgages of longer than 5 years are effectively banned in Canada. All mortgages longer than 5 years are effectively open mortgages, whatever the contract says.
There is a market in open mortgages in Canada, but nearly all are for very short terms, like 6 months or 1 year.
In Canada: open mortgages for longer than 1 year fail the test of the market; and the market for closed mortgages for longer than 5 years is effectively banned.
What are the implications for Americans? The typical American 30 year open mortgage would probably fail the test of the market. But a 30 year closed mortgage might very well pass the test of the market.
Why do I think a 30 year fixed rate closed mortgage might meet the test of the market, if it weren't banned in Canada by Section 10? Because it meets the desires of both borrowers and lenders, or at least some borrowers and lenders.
Let's start with the borrowers. We are born with a long position in human capital, and a short position in housing. We will need somewhere to live for the rest of our lives. Buying a house is a way to cover your short position in housing, and protect yourself against the risk that future rents may rise. If our only asset is human capital, the stream of our future wage income, but we can't sell our human capital in the futures market, the next best thing may be to finance the house with a 30 year mortgage with a fixed interest rate. (The ideal mortgage would be one where the monthly payments were positively correlated with our wage income, but that vehicle might not exist). A variable rate mortgage might be better, if the level of interest rates were positively correlated with the level of our wages (as opposed to the rate of change of our wages, i.e. wage inflation), but they might not be. And the market shows that more Canadians chose a 5 year fixed than a variable rate mortgage. And the open mortgage is a weird hybrid, that is fixed when interest rates rise, but variable when interest rates fall. Except for people planning to sell their house in the next year, who want to minimise the hassle of dealing with a closed mortgage, I can't think why it would meet the needs of borrowers. And it fails the test of the market, at terms longer than 1 year.
Now the lenders. People about to retire at 65 need a safe investment for the next 30 years or so. Or the pension plans that offer them a life annuity need a safe investment. Except for the fact that mortgages are typically not indexed for inflation, a 30 year fixed rate closed mortgage looks close to ideal. And if the Bank of Canada sticks to its 2% inflation target, this concern matters less than it did in the past. If all fluctuations in nominal interest rates are due to fluctuations in real interest rates, and not to fluctuations in expected inflation, as they should be under credible inflation targeting, then variable rate mortgages will not provide a good inflation hedge, and will create risk of real interest rates fluctuating.
If a good seems to meet the needs of potential buyers, and sellers, but doesn't exist in the market, the presumption should be that the fact that Section 10 of the Canada Interest Act bans the good is the reason why it does not exist.
But what if I want to move house in the next 30 years? No problem, and it isn't a problem in Canada already, if you want to move house in Canada before your 5 year mortgage is up. Mortgages can be transportable (you take them with you to the new house), or assumable (the new buyer, OAC, takes over your mortgage). Really, mortgages are just like fridges and stoves in that regard. You don't get a 10 year stove because you think you will move in 10 years. And if you want to sell and rent? Can't you just use the proceeds to buy a bond, and leave the bond as collateral for your mortgage? And if you suddenly win the lottery, and want to pay off your mortgage? You can always pay the interest rate differential, plus any transactions costs.
Canada Deposit Insurance Corporation insures GICs of 5 years or less, but not longer than 5 years. That might also be part of the explanation why Canadian mortgages are 5 years or less. Banks borrow at terms up to 5 years, so want to lend at terms up to 5 years. Maybe.
Eric Lascelles of TD has written an excellent primer (pdf) on the Canadian mortgage market (with some comparisons to the US).
I thank all the commenters on my previous post for excellent comments that helped me write this post. Blogging is a team-effort. Comments are integral to blogging. That's how we can cut across disciplines and areas of expertise. And we need to. That's worthy of a post sometime.
Worthwhile Canadian Initiative 
@Adam P: You write ‘lower interest rate, lower inflation rate state goes with lower real income growth (real income doesn’t have to fall, it just needs to grow less than expected).’
A variable rate mortgage does provide higher consumption to the borrower in the situation you mention – the rate goes down with lower real income growth. It adjusts automatically, assuming the monetary authorities respond to lower inflation by lowering rates.
This is one of the advantages: there is no need to have an open mortgage to benefit from falling inflation (income growth). Except that in the case of the fixed rate mortgage, the borrower has to exercise the option to refinance – and, for another fixed rate, pay the option price again.
“But I still can’t see any assumptions under which the open mortgage would dominate both fixed closed and variable. ”
Re-read my argument, it’s because the open mortgage gives a higher expected consumption growth rate than the variable mortgage plus the downside insurance which is valuable to a risk averse agent. (The variable mortgage does, I agree, provide consumption insurance.) Your argument that full consumption insurance is optimal is only valid assuming a fixed expected value of consumption. Here we are comparing two possibilities with different variances of consumption but also different expected values, thus which is better will be determined by the preferences of the borrower.
Now, of course it’s all in the pricing. The degree of risk aversion vs the option price will determine which is preffered but it should be very, very easy to see that a moderately risk averse borrower may prefer the open mortgage to either of the others.
PS: let’s imagine for a second that we agree that depending on the pricing and the consumption risk that agents face, either of the mortgages might dominate the others. For open mortgages, how do we go from “sometimes better and sometimes worse” to “weird, stupid and dangerous”?
@Nick: yes, in a fairly simple model of asset pricing, the variable rate mortgage is carried at book value (ceteris paribus). There is also no expectation that borrowers will refinance except in the case of spread compression (hence reducing earning assets which would have to be lent at new prevailing rates … which can roughly be assumed to be lent at the same rate for new variable rate loans).
An extreme example of the issue with US fixed rate mortgages is that servicing portfolios (which is no longer the mortgages, but the contract to service an existing pool of e.g. Fannie and Freddie mortgages on a fee for service basis) fluctuate wildly with repayment expectations. (Because as rates go down, it is assumed more mortgages will be refinanced, hence reducing the size and the expected present value of the existing pool – in the rising interest rate scenario, they go up in value).
Just as an example of how a bank/financial institution can work, I work for one that prices and places effectively all of its non-treasury loan assets to re-price to six-month Libor. Likewise all borrowings. Fixed rates, foreign currency, EVERYTHING is swapped and/or hedged to get back to the base currency/term. Options to repay are typically done on a complete ‘make whole’ basis (equivalent to paying for cancelling the existing swaps or funding arrangements, like buying back the borrower’s own bonds at current market prices – which would have gone up if fixed rate and interest rates have fallen). And yes, the loans – all floating – would generally be priced at outstanding principle (less reserves), ignoring the more complicated accounting cases and whether hedges would be applied directly against the loan or liabilities going up and down separately (but with, theoretically, same net effect).
Nick: “So the borrower’s consumption would rise in very good states. And full insurance being optimal, he wouldn’t want to pay an amount equal to the expected value for that to happen.”
that’s the point, the variable rate mortgage gives both lower variance of consumption and lower consumption growth rate. The open mortgage gives a higher variance to the consumption path but also a higher growth rate. It is easy then to choose values for risk aversion coefficients and consumption paramters that make the open mortgage dominate.
GA, you’ve comletely misunderstood the argument.
PS: I was responding just now to GA @2:10pm.
We were posting at the same time.
PPS: at 2:25pm (just above) when I said “The open mortgage gives a higher variance to the consumption path but also a higher growth rate” that is relative to the variable mortgage.
Relative to the fixed rate closed mortgage the open mortgage gives both higher expected consumption growth and lower variance. Thus the closed mortgage is entirely dominated by the open mortgage!
@Adam: I get, I just believe you’re not accounting sufficiently for the up-front cost of the option (it reduces consumption now) nor the cost of refinancing each time to benefit from the open option. Whether one can choose parameters to make it dominate may be possible, but I still think this hasn’t got to the point where one can say “financial institutions can or will offer this at reasonable prices.” Even if the borrower might prefer.
Adam: I have re-read your original argument @12.45, and I’m still not getting it.
All three consumption streams (for each of the three types of mortgage) should have the same expected value, given a risk-neutral, competitive lender.
Since the actual interest paid on an open mortgage will tend to fall over time (it will fall unless interest rates rise faster than the falling value of the option), the open mortgage will tend to give a rising consumption stream over time, if real wages have no up or down trend. That may be a good or bad thing. It is usually a bad thing, if the borrowers rate of time preference proper equals the interest rate. But in any case, an upward or downward trend in mortgage payments, wages, and consumption, can presumably be offset by varying your savings outside the mortgage.
What am I missing?
I see fixed as reducing borrower default risk and open as reducing borrower timing risk, adjustables being preferred but caps not necessarily providing sufficient limits to avoid potential loss, so open as insurance worth paying for by preventing catastrophic loss even if expensive. Extreme at 30 though simple to analyze, a sufficiently long adjustable should do as well or better. We buy fire insurance though we don’t expect to profit from it.
@Nick:
When you mention life annuities, I must mention that I have life insurance training. The life annuity market in Canada is actually underdeveloped. Canada Life holds 40% of the market share, IIRC. Canada has shown itself to be averse to purchasing life annuities for a couple of reasons.
1) Life Annuities are one of two options for taking an income from an RRSP, the other being a RRIF. RRIF’s are far more popular because you can structure them to create an inheritance, whereas life annuities revert to the insurer on the annuitants death. Furthermore life annuities have generally had poor indexation options and with Canada’s history of inflation prior to the 1990’s RRIF’s have been seen as a better option for income. There is also the fact that the bull market of the 1990’s led many financial advisors to counsel their clients to pursue active management. This of course entails higher fees. This is not a coincidence. “Financial Planner” = “Salesman”. Canadians would be very much better off if they kept this in mind at all times.
2) Pension funds in this country are generally structured as trusts. While Sun Life does offer a Group Annuity product to trade away pension risk through a group life annuity, the pension industry has generally seen this sort of product as an extremely expensive option. My brother is an accountant and he has told me that companies strongly prefer to keep their funds (even pension funds) under direct control. Again I believe they prefer to run an aggressive strategy in order to increase the rate at which they may discount contributions.
I find this lamentable because this annuity product has Assuris protection. In the case of default (which would have to be Sun Life in this case) you are guaranteed an income of 100% up to $60,000/year and are guaranteed 85% of your income above that. This is light-years ahead of the Ontario Pension Benefit Guarantee Fund and is available in all provinces.
@anon:
Here is a good jump-off page.
http://www.canadianmortgagetrends.com/canadian_mortgage_trends/2008/04/fixed-or-variab.html
Dr. Moshe Milevsky is the leading light in this area of research.
@GA:
Here’s a good interview with the VP of CMHC, Pierre Sarre. http://www.canadianmortgagetrends.com/canadian_mortgage_trends/inside-cmhc.html.
In addition to high-ratio insurance, CHMC offers “portfolio” insurance to lenders who wish to optimize their risk and capital usage. This is a policy paid for strictly by the lender, the borrower never sees it.
@determinant: Thanks for the cite. It’s certainly a much higher percentage of mortgages insured than I realised at about 2/3s, but not all.
Nick@09:06AM:
But what if discount factor differs between lender and borrower? In your numerical example, I believe that the discount factor of both lender and borrower is assumed to be 1. However, if lender’s discount factor is 0.7 instead of 1, he will set the interest rate of the open mortgage as 5.26. (In general, if lender’s discount factor is d, the interest rate will be set as (10+6d)/(2+d).) In that case, if borrower’s discount factor is 1, then he will choose the open mortgage over the other two.
Nick@3:03pm,
Let’s take your example from before with a Phillips curve added. The borrower has a current real incomeof 100 (measured in units of the consumption basket excluding housing) and spends 50 on the mortgage leaving a consumption of 50 plus the house. Since in all cases the housing conumption is the same we’ll just say he has consumption of 50.
Now, tomorrow two states are possible each with 50% probablility. In the boom state his income goes to 101 but rates rise as well. In the recession state his income falls to 99 but rates fall as well.
Let’s suppose, for simplicity, that the rate changes are such that a variable rate mortgage fully insures consumption, thus in the boom state mortgage payments to the variable mortgage go up by 1 and in the recession state the variable mortgage payment falls by 1.
Now, let’s see how the mortgages do:
Boom:
Variable mortgage: income 101, payment 51, consumption 50.
Closed Fixed : income 101, payment 50, consumption 51.
Open Fixed : income 101, payment 50, consumption 51
(since open acts like fixed when rates go up).
Recession:
Variable mortgage: income 99, payment 49, consumption 50.
Closed Fixed : income 99, payment 50, consumption 49.
Open Fixed : income 99, payment 49, consumption 50
(since open acts like variable when rates go down).
Thus, as I said before, when income and rates fall the open insures consumption just like a variable rate mortgage but when income and rates rise the variable mortgage reduces consumption while the open mortgage allows the extra income to be consumed.
Since both states have 50% probability we get:
Variable mortgage: mean consumption 50, variance 0
Closed Fixed : mean consumption 50, variance 1.
Open Fixed : mean consumption 50.5, variance .25.
It should be quite obvious that whatever numbers we chose for how mortgage payments change with rates that it will always be the case in this two state world that the open mortgage dominates the closed mortgage and depending on risk preferences may well dominate the variable mortgage.
Adam: those numbers for the boom can’t be right. An open fixed mortgage must have a higher initial rate than a closed fixed. Because otherwise the lender is providing the option for free. With a risk neutral lender, all three mortgages must have the same mean consumption. So in a boom, where interest rates rise, the borrower with the open mortgage, who does not exercise his option, must face higher payments and lower consumption than the borrower with a fixed mortgage.
A risk neutral lender would require the mean payments be the same for all 3 mortgages, and so the mean consumption would be the same also.
In a 2 state world (boom or bust), the open mortgage would give the same interest rate as the variable in the boom. You would need a 3 state world (boom, bust, or middling) to distinguish all 3 mortgages. In boom: fixed beats open beats variable. In bust, variable=open beat fixed. In middling, fixed=variable beat open.
himaginary: sorry, you lost me there. I will try to think about it.
Yes Nick, you’re right on the means, my mistake.
So, price the open mortgage so it costs .5 units more in all states (say). The mean consumption is the same for all mortgages yet the open mortgage dominates the closed, due to its lower variance, right?
So, in this example the variable rate mortgage dominates all.
That still leaves two points, first of all if I recall you have actually been claiming (on the other post) that closed mortgages should dominate open ones, is that not right?
Second, we seem to be moving further and further from “weird, stupid and dangerous”, do you not agree?
PS: I did say several times yesterday that it will depend on how the pre-payment option is priced. My guess is that we could in fact produce examples where the open mortgage is best.
Nick@08:55AM:
Let me clarify a bit.
I assumed that 5.33% of your example in Nick@09:06AM was derived from solving the following equation:
x + (x0.5+40.5) = 5 + 5
where x is the interest rate of the open mortgage. The LHS of this equation is the total expected earning of the lender of the open mortgage, which earns x in the first year, and, x or 4, with a 50% probability of each, in the second year. And the RHS of the equation is the total expected earning of the lender of the closed mortgage or the variable rate mortgage, which earn 5 each year. For lender to be indifferent between all three mortgages, these earnings must equal.
Now, if you introduce discount factor d, the above equation becomes like this:
x + d(x0.5+40.5) = 5 + d5
If you solve this for x, you get x=(10+6d)/(2+d), which I showed in my previous comment. If you set d=1, then x=5.33, which is your example.
But, suppose that the lender’s discount factor is 0.7. In that case, x=5.26. If the borrower’s discount factor is 0.7, too, then all three mortgages have the same expected cost to the borrower, which is 8.5. However, from the point of view of the borrower whose discount factor is 1, the expected cost of the open mortgage is 9.89, whereas the expected cost of the other two mortgages is 10. So the expected cost of the open mortgage to such a borrower is lower than those of the other two mortgages.
Adam: “That still leaves two points, first of all if I recall you have actually been claiming (on the other post) that closed mortgages should dominate open ones, is that not right?”
I may have said that. If so I was wrong. All these comments have clarified my thinking. I now think that closed will dominate under some circumstances, and variable will dominate under others. I still can’t think why open should ever dominate both the other two.
“Second, we seem to be moving further and further from “weird, stupid and dangerous”, do you not agree?”
Here’s a rambling reply: about a year ago, there was talk about some financial products being, let’s say, weird, stupid, and dangerous. Like “end of the world insurance”, “financial instruments of mass destruction”, etc. They didn’t seem to serve any useful purpose, so that someone, either the buyer, or the seller, or perhaps both, must be making a mistake. Long term open mortgages look like that to me.
I could never really back up the “dangerous” part. This was a hunch. (I said in the original post I didn’t understand this bit as well as I wanted). They looked like very difficult instruments for banks to handle, and I had a hunch that in trying to handle them banks might end up doing something dangerous. I was hoping I might get more back-up for this claim in the comments.
I think I stick by the “weird and stupid” bit, unless someone can explain to me their rationale.
A better title might have been: “30 year open mortgages, WTF?”
If we take the POV of a consumer reports journalist, there is nothing strange about saying that a certain car is not a good buy, at the price. Or an industry consultant might say that a certain car is unprofitable to sell, at the price.
The economist’s POV is a bit different. Sometimes we look at a certain car and say we think that there is no price at which it could make sense both for anyone to buy and for anyone to sell. Like a sports car with drum brakes. It would only cost (say) $50 extra to put disc brakes on it, and any buyer should rationally pay the extra $50 for disc brakes. So when we see the market actually existing in one of these products, our reaction is: WTF?
Normally, when we economists see a WTF product, we think there must be something we are missing, because sellers and buyers are rational, so there must be a reason why the market produces a sports car with drum brakes, and it’s our job as economists to try to figure out what that reason is. But the first part is to explain that there is indeed a puzzle there to explain, that it is indeed a WTF product.
I think I have shown that 30 year mortgages are a WTF product. What next?
Maybe someone can come up with a deeper explanation that shows, when you add in certain tweaks to the model, they can be rational for both buyer and seller after all.
Maybe there’s some sort of legal restriction, or implicit subsidy, that explains their existence despite being a WTF product. (That’s my hunch).
Or maybe, just maybe, either buyer or seller, or both, are just making a mistake. People do make mistakes. They don’t always buy the best car, because they don’t understand cars very well. They don’t always buy the right financial instrument because they don’t understand financial instruments very well.
But I’m really still at the first stage. 30 year open mortgages are a WTF product. There’s a puzzle there. Why the F do they exist??
I’m now a bit clearer, thanks to these comments (yours especially), on what POV I am taking.
himaginary: OK. I think I follow you now.
Yep, you have reproduced the math behind my example (it took me several attempts to get it right!).
I will trust your math on your example better than I would my own math. But I trust my intuition better. And I think I’ve got an intuitive understanding of why your example works.
Here’s what my intuition tells me: some borrowers will want their payments to be rising over time (either they have high time preference, or they expect their wages to be rising over time). Others will want their payments to be falling over time (because they have low time preference, or expect their wages to be falling over time).
Open mortgages will usually tend to have payments falling over time. Some borrowers will prefer this, and this feature of open mortgages might (sometimes) outweigh the benefit of certainty of payments in a closed mortgage, and outweigh the indexation benefits in a variable mortgage.
Have I understood the intuition behind your argument correctly?
It’s clever, but I think I have a counter-argument.
If a borrower wants payments that are falling over time, he could do better still by getting a fixed interest mortgage with a variable amortisation. So the payments are time-varying but not state contingent. So he knows exactly how much he will be paying (no uncertainty), but knows the payments will trend down. (Or in the case of a variable rate mortgage, just accelerate the payments as time goes by.)
Nick: Actually, I wasn’t thinking along those lines.
Nick@07:55AM:”An open fixed mortgage must have a higher initial rate than a closed fixed. Because otherwise the lender is providing the option for free.”
What I wanted to address is this option premium. The lender sets this premium based on his time preference. What I wanted to say is that if the borrower’s time preference is higher than the lender’s one, he thinks that this premium is cheap and worth paying, because, in his POV, he can save his money compared to the alternative choice. So, making payment falling over time is not his supreme purpose; making the lowest payment is. Note that this comparison of payment involves future uncertainty, so it depends on one’s subjective discount factor.
Why doesn’t the open mortgage dominate under the middle ground version of your simplified example from 906am on June 26?
Same basic facts. Period 1 rates are 5%. Period 2 rates are still 50/50 4% or 6%. Closed/Variable cost=5% and Open cost=5.33%. But period 2 rates can be further split into four possible worlds:
25%: Rates down to 4% reflecting 1% drop in inflation
25%: Rates down to 4% reflecting 1% drop in real rates
25%: Rates up to 6% reflecting 1% increase in inflation
25%: Rates up to 6% reflecting 1% increase in real rates
I’m ignoring the more interesting Phillips curve type arguments here to stick with this example and assuming we only care about the volatility of real payouts among possible scenarios. Isn’t the risk averse borrower here neutral between a Closed FRM and Variable, but prefers Open to both? For example, the real rate shock is higher in the worst case scenario for both the Closed (when inflation declines) and the Variable (when real rates increase) than in the worst case scenario for the Open.
The LIBOR Index
Libor is a bad index for floating rate loans because it is calculated from interbank borrowing rates. So even if the Bank of Canada is at zero, LIBOR (CDOR in Canada) can be arbitrarily high depending on whether banks trust each others credit. So the banks might borrow at 0 at the discount window while floating loans resetting off LIBOR can be way higher. If they were linked to the borrowers credit, that would be fine. But the fact that someone with a 25% LTV mortgage could pay 200-300 bps over the discount rate because banks suddenly become crappy credits makes no sense. And even for a Canadian 95% mortgage, CMHC is taking all the credit risk. Floating rate mortgages should be set at a fixed spread to the discount rate (or t bills). That way payments can actually go down when the Bank starts easing.
Floating, Fixed and Open…
What if I’m averse to states of the world with extremely high interest rate volatility? Personally, I find that easy to imagine since it sounds like a state of the world in which both hyperinflation and deflation become more likely. If rates haven’t changed much (just the state of realized/implied volatility is high) then nothing has changed for either the fixed or the floating mortgage. But the value of the open mortgage is through the roof because the option value is much higher. And if you’d entered into either the fixed or the floater with some trepidation, you might be feeling a whole lot more trepidation now. And even if you’d gone half fixed and half floating, it doesn’t save you from extreme states of the world – you might just be left terrified of both. So the way I see it, the open mortgage is just a view on the level of volatility. And just as I have opinions and preferences on rates, I don’t see why I wouldn’t have an opinion and preferences regarding volatility relative to the current market consensus.
Personally, I think the floater is the most neutral in terms minimizing my variance of consumption vs total consumption of the planet. I.e. I think it best allows me to maintain my relative consumption rank in society.
But if I was some kind of beta-loving, risk-seeking freak, I would go fixed. That way, as the economy rockets back to its natural 10% annual growth rate, all those open and floating rate payers will be eating my Ferrari dust even faster. And if the economy goes into a spiralling deflationary liquidity trap – well, you go big, or go home.
But if I was really risk-averse or paranoid about the ability of governments and the financial system to just work it all out in the end, I might want to get long vol and go open. Maybe I get infinite joy from being right in a state of the world where the rest of you got burned by your misplaced trust in authority. Is that not a valid form of utility?
The Preferred Investments of Seniors:
Are they really the mirror opposite of the risk-seeking fixed rate payer above (i.e. they only want to own fixed rate bonds)? What kind of hermit fixates on the absolute level of consumption? (You only want bread and water???) And has total confidence in the ability of Mark Carney to freeze inflation at 2% in perpetuity??? [Proof by incredulity]
And anyways… Doesn’t CAPM say that they (the seniors) are supposed to hold some mix of the whole market and the short rate (i.e. a floating rate note)? If they are risk averse they are supposed to hold more note, less market. But I don’t remember 30 yr fixed being on the capital-market line.
Nick @5:02pm,
Yeah, I guess we’re pretty much on the same page now. After all, my intent was never to advocate for open mortgages, I just didn’t see the argument. I’m pretty willing to believe that floating is better in most cases, for example in the UK the vast majority of mortgages are floating rate.
However, I think you’ve established “weird” but that “stupid” is still too strong. I mean, you’re initial argument for “stupid”, as I understood, was that the borrower wasted money on what was basically a lottery ticket, you said things to the effect of “why not just spend the extra .33% on a lottery ticket”. But in the recent examples you yourself observed that expected consumption would remain the same for all the mortgages, so actually the borrower isn’t throwing away money.
So, in our simple examples, at worst the open mortgage is dominated by floating because it leaves the borrower with a higher variance of consumption, it doesn’t involve the borrower spending any more money on average. That’s an important point because I’m quite sure we could construct richer examples, (more states of the world, perhaps the possiblity of an inflationary episode without income growth) where the open mortgage comes out better due to how it insures consumption in some particularly bad states of the world.
himaginary: I’m still not getting your argument. It may come to me.
dlr: I think I get your argument. But I think that in that case, a borrower would be better off getting half his mortgage closed fixed, and the other half variable. Some borrowers do that.
K: On LIBOR, yep. I see your point now. Good point. I can’t decide if you are right or not. Should the variable rate spread over (say) Tbills depend on the borrower’s credit risk, or on the bank’s credit risk, which determines the cost of the bank’s funds? Dunno.
On closed, open, or variable. If someone is risk averse for falls in consumption, and risk loving for increases in consumption (his utility function is S-shaped), that could explain open, as I said above. But he could also buy fixed, and spend the savings on lottery tickets, and get the same effect. And it’s a weird preference. The preference you are positing sounds even weirder, because it’s S-shaped like min, but S-shaped and relative too. I can’t believe that (half?) of all Americans, who take out open mortgages, have preferences like that.
Now if someone has opinions about future interest rates that differ from the market, that could explain almost anything. People take bets if they think they know better, even when they are not buying insurance by taking the bet. But the half of all American home-buyers who take out open mortgages, and buy an option on interest rates, must be bigger than the number of Americans who regularly play the option markets.
Preferred investment of seniors. But they do buy life annuities. Their fixed pension plans give them exactly that.
“Proof by incredulity”: a good morning laugh!
Adam: OK, the lottery ticket is actuarily fair. So it’s not “throwing away money”. But buying an actuarily fair lottery ticket is still a waste of money (not 100% waste) if you are risk averse. I should have been clearer.
Nick: The cost of credit is not some arbitrary number linked to supply and demand. It’s supposed to be the risk free rate plus the expected loss of the loan under the risk neutral measure. Now I agree that in times of distress, risk premia will rise even for low risk mortgages. But a zero risk mortgage (ie a 25% LTV or fully insured by someone else) is supposed to yield the risk free rate. Otherwise, there is arbitrage.
I didn’t mean to suggest that people have opinions about rates. Compared to the market, they may have different utility for different rates because of their life situations. But different utility is mathematically equivalent to a measure change, i.e. equivalent to saying that they have different expectations for rates.
Adam: The mortgages do not have have the same expected return. They have the same return (the risk free rate) under the risk neutral measure. But in the real world (by which I mean CAPM) they have a return equal to r + beta*(r_m – r) where r_m is the market expected return and r is the risk free rate. So the excess return is proportional to the extent to which they add variance to the portfolio of the average investor.
The 3 mortgage debate in general:
If we applied CAPM to the problem of choosing a mortgage, it would tell us that we should hold the same mortgages as everyone else in exactly the same proportions. But that ignores the fact that there may be regulatory constraints that prevent the market from obtaining the mortgage it wants. It might still be worthwhile looking at CAPM to tell us how we would optimize if we could.
So for our three mortgages:
Fixed 30 yr: For this one we could try to solve the problem by doing some work and calculating the empirical beta of 30 yr swap vs the whole market. But then, its the forward looking measure that matters, so we could justify just pontificating on the likely correlation. My feeling is that in a portfolio that doesn’t hold any 30 yr bonds (e.g. a younger home owner with little savings and a big mortgage), 30 yr bonds would offer good diversification (variance reducing vs the job, house, etc). And CAPM tells us that we should all hold some bonds. Paying fixed is the opposite position of 30 yr bonds and would therefore be variance increasing. Highly risk seeking behaviour. And even if one had some savings, no one would hold bonds and hold a fixed mortgage: the bonds yield less than the mortgage, just downright stupid.
Floating: Zero variance, zero beta. In CAPM this is not even an “asset”. Its just a measure of leverage.
Open: Lower variance than fixed. And the big long option position is bound to be negative beta. Is it overall negative beta? My gut feeling is yes, but I’m not certain. Still looks like a weird thing to do compared to the long bond position that you should be looking for in a diversified portfolio.
K: “Adam: The mortgages do not have have the same expected return.”
That was Nick’s restriction not mine and he got from the assumption that lenders were risk-neutral. Actually my whole argument has exactly been that the open mortgage could dominate if it hedged some risks. It’s just that the particular example didn’t show that because there wasn’t enough risk to hedge. Hence my claim that in richer framework we could easily produce an example where the open mortgage was best.
Adam: I completely agree with you. And I think aversion to volatility risk is exactly the preference that might justify going open.
Nick@07:48AM:
Let me clarify a bit, again. I was thinking in terms of Present Value of total interest payment, discounted by d. I applied that idea to your 2-year-model@09:06, and considered what happens to the three-mortgage-indifference in your model if the discount factors are asymmetric between lender and borrower.
@K:
I don’t see the problem with CDOR. I don’t know much how the guts of LIBOR works, but I do know about CDOR. Canadian interbank rates are tied in with the Large-Value Transfer System. This is the wire system which transfer guaranteed payments in Canada. It handles around 80% of the value transfer of funds each day and therefore handles most bank liabilities.
In order to operate this system, each bank (think the big chartered banks plus the Credit Union Centrals) has to pledge one of two forms of capital: collateral pledged to the Bank of Canada (Tranche 1) or interbank-pledged collateral (Tranche 2). Eligible capital is the kind used in open-market operations.
The Bank of Canada’s overnight depository rate is 0.5% below the overnight lending rate. Whenever the interbank rate gets outside of these bounds, it create an immediate and glaringly obvious arbitrage opportunity to move assets between the Bank of Canada and the interbank market, either in or out.
So the CDOR market is narrowly controlled. The only danger is when banks open up the spread of their own prime rates and the CDOR rate. They tried this at the beginning of the Credit Crisis in 2008 but the TD broke ranks and the rest followed suit immediately. Again the arbitrage opportunity (of the foot kind, this time) came into play.
Determinant:
Are you thinking about the CORRA?
I am not aware of any direct relationship between CDOR and LVTS. The relevant CDOR rates are one and three month BAs (Bankers Acceptances). This is term bank credit, like commercial paper for banks, and is not “controlled” by anybody that I know of (except maybe one infamous dealer’s swap desk). Here is a history of 3m CDOR vs OIS. OIS is a swap (3m in this case) the floating leg of which resets off the CORRA, which is an index that sets of the rate on overnight payment balances (collateralized) in LVTS (fourth graph down):
http://credit.bank-banque-canada.ca/financialconditions
So OIS vs CDOR is a good measure of the health of interbank credit. If you look at Oct 2, 2008 you can see the spike to a 106 bps differential. In normal times it is 10-25 bps. Swaps and FRNs reset off the CDOR. I am not familiar with the link to prime. But CDOR is clearly a bank credit linked rate and can deviate significantly from expectations of the risk free rate.
K: I agree Libor and its cousins are not necessarily the ‘best’ rate for mortgage borrowers, although it does have the advantage of being linked to the overall cost of bank funding without being too directly linked to the condition of a particular bank. It doesn’t seem to me to be necessarily ‘unfair’ (if that’s the preferred term) to link the cost of the product to the cost of producing it for the ‘average market producer.’ (Which is a kind of supply/demand test).
And I wouldn’t see a problem with, say, government dictating the use of a particular index, even the central bank rate (although this will just create a bunch of different issues in long term, they may be preferable – dunno).
But I think there’s a better solution if your real concern is volatility in the spreads as above (leading to payment shock): just introduce smoothing requirements (some kind of averaging), caps when jumps above x bps occur, or some similar. Going by gut feeling, this is going to be cheap enough and manageable enough for the banks – they just have to manage the risk with respect to the known set of mortgages resetting on a given date. (I think Canadian banks are mostly managing risks like this in normal mortgage lending, when they make an offer to lend at a rate, but the borrower benefits from any drops in the rate to closing?)
Of course, for mortgages with periodic fixed (up to five years, say), they’ve already effectively insured themselves against payment shocks except at the infrequent reset dates; while they have some residual risk for resets at these events, it’s getting close to vanishingly small. (And anyone who has a payment shock at that date can choose variable for some period and then refix later, if they really believe the issue is temporary).
In the specific series you show (thanks!), it’s worth noting that although the spread jumped (which might seem unfair), the absolute rate plummeted like a rock for about twelve months after that spike. I don’t know how many borrowers on open would be complaining through that period, but I guess not many. But yes, the spread was still higher.
Two small corrections: when I say ‘they’ve already effectively insured themselves’, I was referring to the borrowers. And for borrowers on ‘open’ during the fall in rates during 2009, I should have written ‘floating rate.’
GA:
It’s not the level of the spread as much as the dynamic I object to. And it’s not payment shocks either. If the Bank goes 300 bps, the mortgage rate should go 300 bps too. A pre-arranged five year floating rate loan should march up and down in lock step with the risk free rate. What if I lent you money for five years, but if things start going really badly for me down the road then you are going to have to really pay up for that loan. It doesn’t make any sense that you should have to make a credit evaluation of me as your lender!
If the lending rate doesn’t go down when the Bank eases, there is a serious problem with transmission of real rates into the economy. So it should be fixed vs the risk free rate from the start. And like I said: the banks are not the “producers” of mortgage credit. That job is performed by CMHC in Canada. And most of the funding is provided for free thanks to deposit insurance. This is not efficient risk intermediation. The only reason the spread only went to 106 is that the crisis wasn’t principally here. Elsewhere, the index tightened much less than the target and still lags. That’s a significant drag on stimulus.
K: As I said, I could live with the rate being tied to the risk-free. I think the cost/basis differential would end up being priced in somehow, but it’s not unreasonable as a starting point. I’m just noting that the risk is actually fairly minimal (it’s historically been for short periods that these jumps have occurred), and it could be moderated substantially with minor tweaks as I suggested above. And of course, all the Libor-likes are not based on the risk of YOUR lender, but an average of the key players (which given industry concentration in Canada may not amount to much of a difference).
Empirical question: what happened to floating rate loans in Canada during this period? Did the index being used actually jump and reflect the spread increase? Did borrowers end up bearing this? Or did the steps CMHC take to expand its coverage end up removing that (as implied by some others above, if I understood them correctly)?
As far as what actually happened to floating mortgages in Canada I’ll admit ignorance. Determinant? But the effect was big in the US where many mortgages are linked directly to LIBOR. I’m sure it was tied to CDOR in Canada or somehow to banks’ marginal cost of funding (which looks nothing like their average cost of funding). I don’t see any reason why the effect would be either small or temporary in a more Canada centric crisis. And I completely agree that the spread would be priced in – though it wouldn’t have been valued very high pre-crisis.
Well, I do disagree with your characterization of CMHC as a “producer” of credit. It’s an insurer, it enables loans to be made to a wide variety of customers at a standardized risk. It doesn’t lend any money to banks so unlike Fannie and Freddie it has less direct control over commercial rates. It’s MBS offerings aren’t large enough to dominate mortgage funding markets either.
Variable mortgages, like all commercial loans, are tied to Bank Prime, the posted “risk free” rate at the chartered banks. It’s a bit of a mystery as to how this is determined, it’s pretty much the net cost of funding plus whatever margin the banks want. This definition is important for explaining what follows.
As you see from those graphs, the interbank market follows the Overnight Rate pretty well. This is actually the worse period we’ve seen in years.
That spike in August 2008 was the “delink” period I described. The Bank of Canada cut the Overnight Rate but the chartered banks refused to cut their Prime Rates. The media screamed. The VP Finance of the Royal Bank went on television explaining her decision. During the middle of her interview she was informed that the TD had broken ranks and cut their prime rate. She immediately cut the Royal’s down too.
As for what happened to variable mortgage borrowers, as I said previously variable mortgages have fixed payment amounts and variable amortizations. When the rate increases the amortization lengthens. Banks don’t ask for more payments. As this interest rate fiasco netted itself out in short order, variable mortgage borrowers would have been none the worse off.
I think K is onto something with his talk of CAPM and beta. More of a general equilibrium analysis, where interest rate fluctuations don’t just happen exogenously, but must be caused by something.
A quibble first: “And CAPM tells us that we should all hold some bonds.”
That can’t be right? Couldn’t CAPM tell a particular, less risk-averse individual he should hold negative bonds, i.e. use leverage? Plus, someone must have a negative position in bonds, otherwise there wouldn’t be any bonds for people to buy?
If everyone had the same degree of risk aversion, and the same variance of income with interest rates, I think that everyone should hold variable rate mortgages in equilibrium.
My brain’s frozen.
Determinant: Thanks for the info. I have not really been distinguishing consistently between variable rate and floating rate, more or less assuming that both types expose both types of borrowers equally to the interest rate risk. But actually the distinction may be quite important for some borrowers – especially those most vulnerable to payment shock – whereas they may be quite indifferent to the extended tenor, at least over short time frames.
It always happens in mortgage discussions. Particularly when the US and Canada have different terminology, the discussion easily goes off the rails due to miscommunication. This isn’t the first forum where I’ve seen it.
AIUI most chartered banks don’t do floating rate where monthly payments fluctuate. This may be a market chiice because with variable rate (fluctuating amortization) borrowers get the same lower interest rate they want without the payment shock risk.
From the bank’s perspective the variable structure is better because floating rate with fluctuating payments would make a mockery of the debt service rules. A customer’s payment shock is a bank’s non-performing loan. The variable rate fixed-payment structure makes everyone happy it seems.
The people who would face rate shock would be those who have personal lines of credit and personal loans. Those do have fluctuating payments based on bank prime. But those are consumer loans.
BTW whenever a variable mortgage or loan rate is mentioned on a Canadian bank website, it will always be quoted at “Prime+1%” wherein Prime is the published Bank Prime at the top of the web page. I have never seen a Canadian bank expressly tie its personal loan and mortgage rates to an external index.
Nick,
In CAPM investments at the short rate are special since they are risk free. If you are relatively risk averse you put some of your money in the bank account (the short rate) and some in the market portfolio which includes all assets in the proportions in which they exist in the market. This includes government bonds from t-bills out to perpetuals. If you a relatively less risk averse than average, you borrow money at the short rate (line of credit, margin loan, floating rate mortgage, etc.) but still invest everything in the market portfolio. Nobody ever goes short bonds, unless the whole market is short bonds(???).
As far as someone having to be short bonds for someone to be long, you are right, it’s a bit weird. The way I think of it, companies convert assets (like talented groups of employees, business methods, IP) that are not directly investable by a generic economic agent into assets (like stocks and bonds) that are. So IBM is short IBM stock and bonds as a hedge against its organizational assets. That way the rest of us can be long. Whether short bonds is a good hedge against their assets I really don’t know, and it’s probably as long a conversation (or longer) as the one we had about mortgage borrowers. But that’s what they do, so those are the assets that are available to us.
Nick@07:48AM June 28:
Let me add one more comment. The case you discussed at Nick@05:30PM June 27 is where the borrower’s discount rate is larger than 1. Yes, in that case, the borrower prefers to have payments falling over time, and variable amortization or accelerating the payment match his demand. On the other hand, I was discussing the case where the borrower’s discount rate is still equal or less than 1, but larger than the lender’s discount rate. In that case, the borrower doesn’t prefer to have payments falling over time, so variable amortization or accelerating the payment is irrelevant.
Nick@10:14AM June 29:
I think CAPM tells us that we should have risky assets in our portfolio according to the weight as they are (i.e., market portfolio). I don’t think CAPM works the other way around, i.e., determine the proportion of the world’s risky assets according to our portfolio.
K: Got it. Long bonds and mortgages exist, and are risky, so they must be part of the market portfolio, which we all hold (with varying degrees of leverage with the safe asset). I expect I’m trying to think about both sides of the market, and asking what would exist, in equilibrium, in the market portfolio.
Yup. I agree with that. But I think I have an interesting twist. Imagine that everyone has the same risk tolerance, so everyone just has assets; no leverage or bank account savings. Then the women become less risk averse. They borrow some money at the short rate, the bank creates an equal amount of deposits, which they exchange with the men for some more of the market portfolio. So now the men have become relatively more risk averse with a smaller market portfolio and some bank deposits. All fine and consistent with CAPM.
Now imagine that instead of borrowing at the short rate, the women decide to borrow at 5 year fixed (call it a mortgage). The bank now, instead of creating an overnight deposit will create a 5 fixed rate term deposit or issue a 5 year fixed rate bond. (I know they can’t force this, but they will adjust the term debt pricing to make sure the men buy it. All modern banks will do this somehow to avoid term mismatch). So now the women hold a bigger “market” portfolio and a short position in 5 yr bond and the men hold a smaller “market” portfolio and a long position in 5 yr bond. But now, what’s happened is that no one can be holding an efficient portfolio, because they don’t all hold the same position in two risky positions: 5yr mortgage and 5 yr bond. So someone must have done something irrational. That irrational thing was to borrow fixed, thereby introducing an arbitrary position that did not belong in an efficient portfolio.
And to be clear, if the women really wanted to go fixed (i.e. they have wages that are hedged by doing that), they should first sell their long bond positions, not take out expensive fixed rate mortgages. That is a huge position change already since bonds make up a very large fraction of the market. Is the (unexplained) hedging requirement of a large fraction of the population really so big that they actually need to unload all their long bond positions and go fixed?