Wednesday, 3 July 2013

New Direction

I was too aimless here to finish writing anything here, so I decided to give myself more aim on a new blog:

I made myself a cute banner and everything.

Thursday, 2 May 2013

A few final thoughts or mortgages.  Let's compare some scenarios.

First, let's look at upgrading your first home.  We'll imagine that you bought a home that you could more-than-afford with the intention of buying a home that you can't currently afford in the future.  Over five years your salary, and thus the amount you can spend on your mortgage, goes up 10%.  At the same time you build equity in your first house.

I calculated how much you would be able to afford to pay on that new home after five years, as a proportion of how much you paid on your first home.  This gives an idea of how much you will be able to upgrade.  The answer depends on how much you "underspent" on the first home.  The cut-off where you get a better upgrade with a high interest rate is around 90% of your maximum ability to pay.  That is, again, if you 300 currants a month then if you choose a mortgage that costs 270 or less then you'll be able to upgrade your home more with a high interest rate than a lower one.  If you pay 290 a month for your mortgage then you are better off with a low mortgage rate, if you pay 230 then the lower mortgage rate is much better.

As we saw before, a 10% increase in your payments on a mortgage with 12% interest makes a very big deal in terms of paying it back, but the same payment doesn't make such a big difference with lower interest rates.

Next, what if the value of your house goes up or down when you own it?  Remember in my first post that I specifically said that I was interested in houses as primary residences, which means that, generally speaking, the value of your house will go up and down with the market so the realtive buying power of your investment won't change that much over a short number of years.

I calculated a few different scenarios.  In each scenario you are selling your house and moving to a new one after five years.  We can look at three different possibilities - you are upgrading (buying a house of about 50% higher value), relocating (buying a house of the same value) or downsizing (buying a house of 30% less value).  We can look at the situation where you are maximizing your mortgage to pay the most you can for the house, and where you are buying more conservatively so that you can afford to pay your mortgage down faster (you contribute 10% or 20% more than your mortgage payment per month).  We can look at a situation where housing prices go up 20% or down 20% over those five years, where your salary increases 10% or does not increase, and where interest rates go up or down over that same time.

That's a lot to vary so I can't possibly lay it all out here, but I can do some of the basics.  I set the loan-to-value ratio at 95%, gave you a 10% raise over the five year period before you move, assumed you have to pay around 8% closing costs between fees and taxes, also assumed you were going to buy the biggest house that you were allowed to with your salary, and considered that you were willing to finance your new home at 25-years amortization (even though you were already 5 years into your original 25 years).  With a 3% interest rate you could afford a home about 15% more expensive than your original one in five years.  With a 12% rate you could only upgrade the value by 6%.

In my last post the magic formula for making 12% interest better was paying about 10% more than your basic mortgage payments.  So let's try those numbers again, but this time you only want to get a mortgage that is 91% of the size of the largest one you can afford.  Now with a 3% interest rate you can afford to buy a home worth up to 28% more than your original purchase.  With a 12% interest rate you can upgrade you home by 24% - much closer together, but still in favor of lower interest.  One of the biggest factors in this is closing costs, another is refinancing at another 25 years rather than 20 years.

If the market goes up or if it goes down it negatively affects your ability to upgrade your house.  I know that sounds odd but it if the market goes up and your salary doesn't go along then your ability to make a mortgage payment is reduced.  If the market does down then after only 5 years the sale of the place might not cover your current mortgage which will mean you can't afford a down payment on a new place.  With the other assumptions I've given, the market rising 20% or falling 20% means you will either have to stay put or downgrade your house.  At 10% you have very slight leeway to improve.  What is interesting, though, is that even with a maximum mortgage, w=the high interest rates are better for you than

the low ones whether the price of homes goes up or down.

If interest rates change by going up then having bought a home five years before is a bit of a problem.  You could find yourself unable to renew your mortgage because it is too costly to do so.  You are penalized by the higher price of money but don't benefit from the lower prices of homes.

If interest rates go down you get a big payoff.  The value of your home will rise as people can afford more and more, but the amount you have to pay won't go up a cent.

Since we can expect that consumer interest rates will never dip below zero percent and we know that historically they haven't gone above twenty, we can deduce that when interest rates are lower there is more room to grow and when interest rates are higher there is more room to shrink.

Overall through all of this I've found only one case where lower interest rates are better for home buyers.  That is the case where the home buyer buys the largest house they can possibly afford, pays their minimum payment only, and then wants to upgrade to an even larger house.  Of course that is only a good scenario if mortgage rates stay low.  If they go up, or if the market goes down, then this very unstable scenario leads to a disaster.  We've seen such a disaster quite recently.

In the end, low interest rates are not good for home buyers except for those home buyers who wish to always remain with large debt loads as they constantly move from one place to another over many years, always paying the most they can towards their mortgage.  These people, however, are essentially renters who have chosen to have hundreds of thousands of dollars in debt, they aren't really home owners because they aren't moving towards owning a home.

As I said before, if you are buying a home, all other things being equal, the lower the interest rate you can negotiate the better.  But the idea that interest rates going down is a good thing for you - well, "other things being equal" doesn't really hold up.


Thursday, 25 April 2013

Saving for a Down Payment

So what about down payments?  Last time I said that they either came out even or that they worked out better for you when interest rates were higher.  That's because there are two kinds of assumptions that I can make when analyzing them.

My goal in comparing high to low mortgage rates is that I am trying to hold all the other factors that you can control equal.  One factor that you can't control is how much someone else is willing to bid for the house, which means that lower interest rates will mean higher house prices.  Another factor you cannot control is the down payment required by the bank.

Usually down payments are measured as percentages of house prices.  Currently in Canada you need a down payment of at least 5% but the higher the down payment the better off you are in terms of insuring your mortgage.  We'll use the same numbers as last time - 25-year amortization period, 300 currants a month to spend on mortgages - and then consider once again the 3% interest vs. the 12% interest scenarios.  Add to this a requirement of a 5% down payment.

In order to make that down payment you'll have to save money.  While you are saving money you are going to have to pay rent.  Let's say that while renting you manage to set aside 50 currants a month to save for a down payment.  If the bank is charging 3% interest for a mortgage, they surely aren't paying out very much at all.  They probably pay you something around 2 percentage points less.  That means at a 3% mortgage rate (so a 1% interest rate on your own investments) you will have saved up for a down payment after 62 months.  That's just over five years.

If the banks were charging 12% for a mortgage and paying out 10% then you would need to save for only 27 months, two and a quarter years, before you had 5% of the value of your home.

The huge difference is because of the different cost of the house.  With a cost of 63.5k you would need to save up more than twice as much as you would with a cost of 29.8k.  It also matters that you are earning more interest.  With 12% mortgage rates by the end of the second year you've earned 21% interest on the money you deposited during the first month.  Since you're deposting only 50 currants that's only 10, but it's something.

With a 3% mortgage rate after two years you've only earned 2% interest on the initial deposit.  You've earned a mere 5% interest on the initial deposit after the full five years.  The thing about 1% interest rates is that it takes a long time before you even notice the compounding.  In fact, because the amount of interest paid is rounded, it is possible that it doesn't compound at all over such a short number of years.

Basically you need to save up much longer to afford a down payment on your home purchase when interest rates are lower.  The down payment required is higher and you earn less interest while you are saving.

Now I mentioned that there is another way to look at this where there is basically no difference between the two rates.  And that is to say that if two people both had equal opportunity to save up a down payment ahead of time then they will have down payments of equal size which will essentially add to the maximum loan they are allowed to take out to determine the price of the home.  That is, if we assume that people have five years to save up a down payment then under the higher interest rate everyone will have a higher down payment available, which will mean everyone will need that down payment to compete with one another.

This uses the same competitor-is-probably-in-the-same-boat-as-you methodology I used yesterday.  In this case, though, it ignores the fact that you and whoever is competing with you for the house are both in the same boat - you both have to delay your decision to buy a home for an amount of time it takes to save up a down payment.  Even if the interest rate doesn't affect your ability to compete for the house you want, it still might mean you'll be bidding on a house you want years later.

One possible argument is that because low interest rates make it harder to save up a down payment they will also lower the price of houses.  After all, if the bank demands a 5% down payment then only those people who can afford such a down payment can bid.  So in addition to being capped by the income of the people who are interested in buying, the value of a home is capped at 20 times the down payment available to the people buying.

There may be some merit to this argument.  With lower interest rates it is harder to save up large chunks of money, so people are less likely to have large down payments, which means that housing prices might be capped by down payment size rather than income size.  Personally I don't think this reflects the reality of the current housing market.  When 40-year amortizations were allowed people took advantage of them, which shows that people are willing to make a house much more than a 25-year investment.  That means that saving up for five years to afford a down payment might be well within what people are wiling to do.  I also don't think it is a coincidence that low down payment requirements have come hand-in-hand with lower interest rates.

Of course once we start talking about the reality of the housing market our entire simple model falls apart - and even if low interest rates and low down payments occurred as part of the same policy, that doesn't mean there couldn't be a different policy in the future.  I can't deny the possibility that under some sets of circumstances down payment size would be more of a limiting factor on mortgages than income, especially if rental prices are very high so people who aren't buying have trouble saving.  And obviously if a down payment of 10%, 15% or 20% were required then the size of down payments might be severely limiting.  As an exercise, you could brainstorm other factors that might contribute housing prices being limited by the size of the down payments that buyers can afford!

I still want to construct some scenarios about the market going up and down and "building a nestegg" by paying down your mortgage, so I'll probably keep talking about mortgages for at least another post,


Wednesday, 24 April 2013

Low Interest Rates! A Good Time to Buy!

It should be obvious from the title of this post that I have no idea what I am doing with this blog.  Basically the problem I've run into is that I don't have a lot of numbers to analyze in my life.  I get to do a tiny bit of analysis at work, but really no one is interested in in-depth thinking about complicated issues.  That's a big reason why I've been very attracted to video games, they give me complex systems to think about and I can apply my analysis.

The housing market is another complex system that I live with.  Not that I am a great buyer and seller of real estate, but I do own real estate and I do have a mortgage to pay off.  And since pretty much all analysis of home buying is done to confirm the biases of banks or political parties, why not take a meaningful look at the effect the low interest rates really have on an individual's position in the housing market.

Because that's really what's missing from the perspective taken on low interest rates by the reports you see in the media.  You aren't a speculator (if you are, then enjoy your fountains of cash), you are a person who needs a place to live.  You are going to have to pay for that place to live either through rent or by purchasing it.  When you sell that place to live you are going to have to rent or purchase another place to live.  When you die your inheritors might sell the place you own and split the cash, but while you are alive you are always going to need a place to live.

So people with financial backgrounds tell us the most obvious thing in the world: If you are going to take out a huge loan, the lower the interest rate the better it is for you.

They then translate that into the statement: Interest rates are low, it's a good time to buy.

But there is a missing premise in there.  To get from A to B, you need to include the following: The interest rate is not going to affect the size of the loan you need to take out.

And that just isn't true.

If you are buying a house in Canada then your mortgage will likely be insured by the Canadian Mortgage and Housing Corporation.  In order to be insured the mortgage must follow certain rules.  You need a down payment of a certain size, the amortization period must be below a certain amount, the monthly payment can't exceed a certain fraction of your income.  If you are not in Canada you will not be subject to CMHC rules, but presumably whatever bank you are dealing with will have their own rules; it's a lot harder to find a zero down mortgage with no proof of income today than it was in 2006.

What's important to understand is that while we usually think that our mortgage payments are determined by the size of the mortgage we take out, it is just as valid to think that the size of the mortgage we can take out is dependent on what we are willing to pay each month.

So how much is this house you want going to cost?  Because it is essentially up for auction, it is going to cost you however much the next most interested buyer is willing to pay for it.  The particular auction system probably means it's even a little more expensive than that, but we'll ignore that difference for now.Who is this next-most-interested-buyer?  They are most likely someone who, like you, needs a mortgage to buy their home.  They are, therefore, most likely someone who is subject to the same mortgage rules as you are - they have equal access to good mortgage rates, they have to put down a down payment of a certain size, and they have to have an income high enough for the bank to approve their mortgage payments.

Furthermore, they may be someone who makes pretty much the same amount of money as you do - after all, they found themselves looking at a house with the same list price as you.  Besides, if they have far less money than you then they are not really a competitor for the home.  If they have far more then you aren't really a competitor.

Let's say your house-competitor both make 1000 currants a month.  The CMHC says the most they are allowed to pay for their mortgage is 30% of their income - 300 currants (it's actually 32%).  The CMHC says that they you are allowed to amortize the mortgage over 25-years.  The bank is offering a 3% fixed rate.

So how much is your house competitor able to pay for the house?  They can offer 63,545 currants.  So, if they really want the house, you are going to have to offer more than that.  What would happen if the bank were offer a 12% fixed rate?  Then your house competitor would be able to offer a maximum of 29,756 currants.

Note that either way, in order to match that offer what you need to do is pay 300 currants a month for 25 years at the end of which you own the house.  In one scenario you own a house that you paid 63.5k for and in the other you own a house that you paid 29.7k for, but let's remember that what you really own is a place to live where you no longer have to make mortgage payments.

Pay off your mortgage faster!
"But," the standard thinking goes, "With lower interest rates you can pay off your mortgage faster!"  This is somewhere between completely false and an outright lie.

Here is what it means that you pay down your debt faster with a lower interest rate.  Say you buy that house for 300 currants a month over 25 years.  If interest rates at 3% then after 10 years you will have paid off nearly 32% of your total debt.  If interest rates are at 12% then you will have only paid off 13% of your total debt.  That first case sounds a lot better, right?

But remember, at 3% your initial loan was 63.5k, while at 12% it was 29.7k.  The actual amount of money you still owe after 10 years is 43,565 currants if the interest rate was 3% but it's only 25,840 currants if the interest rate was 12%.  And remember that you still have the same income as you did, 1000 currants a month.

Though you pay off your debt faster as a percentage, at all times your actual debt will be higher because the loan was larger to begin with.

It's quite possible that you can pay more than the guidelines say for your maximum payment.  Just because the bank won't give you a mortgage with a monthly payment more than 300 currants a month doesn't mean that you can't set aside another 10, 20 or 30 currants to get out of debt faster.  Suppose you can pay 30 currants more, so you are able to pay 10% more than your required payment - let's also assume that your bank allows you to do this, but I think at this point most mortgage agreements would allow at least this much flexibility.

If you can pay 10% more than your mortgage payment then under a mortgage at 12% you will be paid off in less than 15 years.  If your mortgage rate was 3% then you'd still be in debt after 20 years - you would barely finish paying your mortgage any faster at all.  Suppose instead you could increase your payment by 25%.  In that case the 12% mortgage is done after 9 years while you'll still be paying off your 3% mortgage for more than 15.

Conversely if you reduced your payments a person with higher interest rate would suffer more than a person with a lower one, but if you can't make your mortgage payments then the consequence is the same regardless of the interest rate.

A similar result is that if you want to be mortgage free within 10 years instead of 25 you can make a much better offer at 12% than at 3%.  In the 12% interest rate housing market, the person who wants a 10-year mortgage can pay 72% of what the person willing to take a 25-year mortgage can.  This certainly means they get a smaller place.  with 3% interest wanting a 10-year mortgage means that you can only pay 49% of what you'd be able to pay for a 25-year mortgage.  You probably can't afford anything in remotely he same category.

But wait, you say, what about the next best alternative?  After all, you could invest that money instead of paying down your mortgage and if mortgage rates are higher than you could get more interest for your investment.  There are two problems with this line of thinking.  First, it is unlikely that you can invest money at a higher interest rate than the interest rate the bank is charging on mortgages.  The bank is in the mortgage business to make money, if they could invest the money elsewhere and get more back from it then they wouldn't need to give you the mortgage in the first place.  But if you are just the sort of genius who sniffs out incredible investment opportunities (you are almost certainly not, by the way) then those investment opportunities are going to pay you more if interest rates are higher.  Since the amount of money you have to invest is a fraction of your paycheck, not a function of interest rates, the higher the interest rate the better it is for you as an investor.

Someone might argue that we do not see this direct relationship between housing prices and interest rates.  Housing prices did not go down when interest rates went up in the 80s and they did not go up massively when interest rates went down.  Furthermore, in recent years in many places housing prices have gone up a lot even though interest rates, inflation and wages increases have all remained very low.

To that I point out that I am using a very simple model to show the effect of asingle variable.  Reality is much more complex.  Looking at interest rates and home prices they are at least correlated in the right way.  The price of homes is very heavily influenced by things like CMHC and banking practices, as well as wages.

It might also be argued that while lower interest rates will push prices up over the long term or in a steady state, it is still the case that if interest rates are lower this week you are better off this week than last week.  In a way that's true.  If you negotiate the whole deal and fix the price of the home and then go to the bank and find out that they are going to charge you a lower interest rate than you thought then you a better off paying less.  But I don't think it takes a huge amount of time for interest rate changes to creep into housing prices.  As long as people are competing for houses, the maximum amount each person can afford will affect the actual amount paid.  The maximum amount that a person can afford is affected instantly by a change in rates.

Next time I'm going to talk about down payments.  As far as I can tell, they are either a wash or they once again favour high interest rate environments.

I am not a financial professional and I would love to hear why I am wrong.


Tuesday, 16 April 2013

Don't Starve

Don't Starve is set to be released in a week.  This is strange because you've been able to buy it and play it for some time now.  I guess it's good of them, though, to call the initial release a beta.  It would have been nice if the recent Sim City release was called a beta considering that it didn't work.

For those of you who were Glitch fans, Don't Starve hits some similar notes.  The biggest difference is that there are bees and you get honey from their nests.  Well, I guess the biggest difference is that the game is unforgiving and intensely lethal.  And when you die instead of going to purgatory and returning you are simply dead.  You can start another game, that one is over.

The similarity is that Don't Starve is very much a game of exploration.  You click things to see what will happen and combine items to have interesting effects.  It's just that sometimes what happens is that you go to a screen that says, "You survived 0 days."

I think that death really helps the exploration part of the game, though.  When you explore it is exciting.  Finding out new things has a real cost.  The better you get at the game the less there is to find out but the most costly it is to try since you get to a point where you generally spend the first part of the game doing the same thing as last time.

I unlocked three characters, each of which has their own advantage.  One of them is immune to fire, one grows a beard, and one is visited by the ghost of her dead twin sister at night sometimes.  It is a game where these three advantages are relatively equal - though very different.

I haven't played in a week or two now, I think ultimately it may have been a passing phase.  But I did put in more than 50 hours of play and I think I'll go back to it in a while to see what has been added to the game in the release version.

I don't like to give advice about this sort of thing because I don't have any reason to think that you enjoy the same things about games as I do.  So instead of making a suggestion, I'll just say that I enjoyed playing the game without doing any external reading about it, just discovering everything on my own.  This is a game about a journey, not about a goal.  In the end, you are just going to die, might as well get the most out of the experiment.

Wednesday, 10 April 2013

Women in Gaming and Very Narrow Arguments

I read an article on Rock Paper Shotgun about why they intend to keep talking about sexism in gaming.  I don't normally read that site, so I can't tell you whether anything else they write is worth reading, but I understand that they write a lot about video games.

What I found particularly good about the article is that it ends with a list of arguments that you should not bother making if you don't like a gaming site talking about sexism.  The article points out that the majority of these arguments are crafted to attempt to sideline any useful discussion, or to call into question the validity of the discussion to begin with.

In particular, I was very happy to see, "People are exaggerating on both sides," on that list.  That's a good argument to be aware of because it comes up in arguments about all kinds of controversial subjects.  Someone trying to sound very smart or very grown-up says that the whole argument is nonsense because people only ever take extremist positions.  Of course in reality on any controversial subject the people who take extremist positions get too much attention and the people who are trying to talk things over and understand them get too little.  That doesn't mean that the latter group doesn't exist.

I did think that something was missing from the list, though.  Unfortunately when you are trying to defend your position from jerks it is often necessary to fill your argument with all kinds of acknowledgements and disclaimers so that you don't give them anything to hold on to.

If you make an argument that people don't like, what you'll hear back is that in  one sentence in one paragraph what you said wasn't exactly true.  Or that one analogy you made isn't really a strong analogy.  Or that one fact you sited is from a source of questionable reliability.

So the discussion of the actual issue - in this case that women in gaming are too often insulted, dismissed, valued for their appearance instead of their accomplishments, etc. - has to be sidelined by endless acknowledgement of obvious truths.  John Walker who wrote the piece even included the parenthetical comment, referring to how he has been abused for talking about sexism: "I’m not going to fret about saying, 'But of course not as bad as…', because of course it’s not as bad as…"

So even though he does not want to spend time talking acknowledging that we shouldn't get into a who-suffered-more contest, he basically has to give a nod to such contests in order to exclude himself from them.  If he were instead writing an article about oranges he would not have to specifically comment that he didn't want to make his article about which professional wrestler he liked best when he was a kid.  The article is full of this and so it ends up being fairly long-winded and cumbersome.  The very direct message of the article doesn't get much space.

But all of this elaboration and clarification end ups being ineffective.  He brings up a book that I think I would like to read entitled, "Why Are All the Black Kids Sitting Together in the Cafeteria."  He brings the book up specifically to borrow one analogy from the author of the book.  If the comments were enabled, one person would criticize him because "his analogy" (an analogy he didn't make between female gamers and black high school students) is flawed - girl gamers aren't segregated from guys - and another person would criticize him for comparing the abuse suffered by a group of attractive, white, middle- and upper- class women to the abuse suffered by blacks during segregation (the fact that the book is not about segregation, and that this is not an accurate description of the population of female gamers wouldn't matter).

There is always room to attack some narrow point, and those arguments always seem to derail the discussion.  So what I'd really like to add to the article is not another message to people making bad arguments, but a message to people who read them.  Whenever someone takes a long article or comment and argues with select sentences from it, the first thing you should ask yourself is not whether this person has a legitimate beef with those particular sentences, but whether it makes any difference to the overall point.  Rather than sidetracking the entire discussion into fact checking the seventh sentence of the third page, we could just say, "I'm not sure if you are right, but even if you are I don't see how it affects the overall point of the article."

Also, this article is another great reason to miss Glitch.  I don't think I was ever part of a discussion in Glitch, even on the forums, where I felt like someone was dismissed or belittled for being female.  I'm sure such discussions happened somewhere in Glitch, but in the forums for many games the only threads that _don't_ contain abuse against women are the ones in which everyone assumes that all speakers are male.

Thursday, 4 April 2013

Going Crazy, Playing Diablo 3

Have you ever felt like your brain, in a desperate attempt to explode forth from your body, is going to smash into the front of your skull so hard that it will cause your back to snap and your entire body to fold up and implode in on itself leaving only a pale sphere hovering where your stomach used to be?

I've been playing Diablo 3 recently.  Diablo 3 is a fairly good game that was very nearly ruined by the auction house (the one for in-game currency, not the real money one) and the goal of incorporating competitive PvP.

The PvP thing is not mentioned as often as the auction house thing.  Something that is actually very disappointing about Diablo 3 is that there is almost nothing to analyze, numerically speaking.  More than any other game I've ever played it really highlights the tension between "balance" and fun.  By tension I mean that balance isn't fun at all.  Forget about balance, just make everything awesome.  Basically balance is only important for PvP.  When you play against a computer you can just set the difficult how you like it, or use console codes in single player mode if you really want to, or use mods.  Of course you can't do those things in Diablo 3.

People talk a lot about the auction house, but essentially the biggest problem it created is that the most efficient way to make your character more powerful is to log out for several months.  The endless recycling of items on the auction house means there is rapid deflation of prices on everything other than the very, very best gear.  Right now if you have a few hundred thousand gold you can buy yourself a set of equipment that will easily beat inferno difficulty, but months from now you'd be able to buy better things, and then even better months from that.  In fact, once you've levelled a character to 60 you can just never play again, knowing that you are improving your character about 80% to 85% as efficiently as you would if you were playing 10 to 20 hours a week.

The story also goes completely off the rails in act 2.  It makes no sense whatsoever.  Belial is the lord of lies, but the only thing he seems to be actually lying about is being good at lying.  In reality he is the lord of smashing you to bits with his gigantic arms.

Ultimately Diablo 3 should be seen as an exercise in living in the moment.  If you can manage to live in the moment then you have have fun as your cute little wizard drops meteors on hundreds and hundreds of zombies and demons.  But while you try to do that, your attention will be constantly tugged at by all of the facts about the past and the future that should add up to ruin your experience.

Because of the problems with the game I can't see myself going on with it much longer - I've played and quit before.  But I'm sure that even if I leave it behind again soon, a few patches from now I'll start another level 1 character and play for a while.  Go little wizard!