Power of Expectations

 

    Here in BC we have had a wild week - Floods have taken out nearly every major highway between the lower mainland and the interior. On the island, flooding has bottlenecked traffic between the south island and the remainder of the island. 

    Now the fear - because of these wiped out highways in the interior - and with the bottleneck over the Malahat, there is a rumour circulating that we will have a major gas shortage! 

    Let's be clear - there will be supply chain stresses, but given the routing of major pipelines and truck routes, here on the island, there would be little reason to expect a major fuel shortage. That is, we may witness constant demand for fuel, and a slight decrease in the ability to supply, which would be reflected in a small period of excess demand which would be corrected with an increased price. (below)

Excess demand, caused by supply shortage due to weather events. 

Given the Excess Demand, prices increase, and the new equilibrium is realized.

    Given this scenario, we would expect a slight period of excess demand (nothing that current station reserves couldn't handle), and then witness a bump in the price come next shipment. 

    But let's look at the power of expectations!

     Presume, for a second that the above scenario is purely rumoured, and that in reality we are so well stocked, and supply chains are so robust that the effect of this weather event is marginal and will have no real impact on fuel markets. If the above scenario is false, but people expect there to be a shortage, they will act as if there is a shortage.

    Some people legitimately need gas today. Others will be fine to wait till tomorrow, others are fine to wait 3 or 4 days or more. But, if everyone now believes that a fuel shortage is imminent, they believe that if they wait they will either (A) not be able to get gas because none will be left, or (B) have to pay more for the same gas compared to today. 

    So what does a rational individual do? they rush to buy gas today to ensure they can get the gas! Unfortunately, everyone does this causing a spike in the quantity of gas demanded. So now, in one day we witness, say, 4 days' worth of gas demand accumulating at once! (below).

    Keep in mind, what was initially a, relatively, tiny amount of excess demand in the imagined shortage case, in now a large excess demand due to this "run" on gas stations. In this case, many gas stations may not have the excess inventory on hand to meet such a surge in demand, causing the shortage to become increasingly apparent, and reinforcing people's expectations that there is in fact a gas shortage. I first heard rumour of this gas shortage at 11:00 am. by 3:00pm 2/5 gas stations I passed were sold out of gas, the remainder had line ups extending for blocks. Keep in mind, this is the same day - so this shortage is not caused by supply chain troubles, but purely due to a surge in demand due to expectations!

    In this scenario - we imagined that the gas shortage was entirely fictitious, but believed by the masses. we now see that simple belief or expectation can create a shortage thereby reinforcing our prior belief - we have just created a self-fulfilling prophecy! forcing a shortage of fuel, ultimately resulting in a spike in the price. 

    What happens if the fuel shortage was not fictitious, but rather starts as a rumour and proves to be a true supply shortage? 

    Then we get both scenarios playing out in tandem resulting in a case of large excess demand, forcing mass shortages and causing the biggest increase in the price (below).

    

    The above case is the likely outcome. That is, we are likely expecting a slight shortage, due to supply chain problems caused by weather. Our reaction to this will cause a surge in demand, we will likely witness a large shortage causing a large boost in price. 

    The best-case scenario is if everyone went about getting gas as if nothing was going to happen. If this occurred, we would only witness an outcome like we saw in scenario one, with a slight shortage and a slight bump in price. The problem is that everyone who was planning to get gas on days 2, 3 or 4 would be worse off versus just getting gas today - worse off because they would pay a marginally higher price. Thus, everyone acts today, creating a shortage, and creating a drastic boost in the price for everyone. 

    Thoughts? Feel free to comment below.

 

CMHC must be abolished before it craters Canada's economy

    I was recently handed this article from the national post making the claim that the CMHC needs to be abolished. While I agree with Sabrina that the CMHC is contributing to the problem I hardly believe that the abolishment of the CMHC is the solution. 

    What is CMHC? 

    CMHC, or the Canadian Mortgage and Housing Corporation is a Crown Corporation created shortly after world war two to assist returning vets to purchase homes. This was initially needed as banks were reluctant to lend to returning vets and government (taxpayer) insurance was needed to entice banks to issue these mortgages. 

    

    In this way CMHC insures certain mortgages, thereby indemnifying the banks from loss in the case of default. This program was initially well-founded and justified as it provided the banks with the peace of mind required to lend, and it allowed many returning veterans the peace that comes through homeownership. 

    As time went on, CMHC expanded their program from vets to the greater population expanding its mortgage insurance to all Canadians looking to buy their first home. Now initially that was the catch, the insurance was available to people looking to buy their first, starter, home and this had many conditions attached to it, maximum price, couldn't have owned a home in Canada in the last X many years, etc. etc. At this point, the program was a helpful tool to assist first-time homebuyers in getting into the market and becoming homeowners with as little as a 5% downpayment.

    Time continued to progress, and CMHC continued to expand their program. The expanded program now allowed for the purchase of any residential property with as little as 5% down, Vacation properties, Rental properties, or just speculative purchases could be financed with as little as 5% down. Further, the max price cap was removed, so now all of Canada's residential inventory was able to be purchased for a minimum of 5% down, for a brief stint pre-2009 one could even purchase with 0% down while receiving a cash kickback from the bank.

    The problem with all this is hopefully clear. Individuals with the means can speculate, or purchase additional properties with very little "skin in the game", banks are happy to lend this money because they are indemnified from loss, so the money keeps rolling out to buy more and more houses while the taxpayer keeps backing the risk. 

    Fast forward to 2018 and the government introduces further legislation giving the government an equity stake in new purchases. which gives the government further interest in ensuring that real estate prices never come down.

    In this sense, it seems clear the CMHC is part of the problem of our current housing crisis. I say "part of" because the supply side is arguably just as big, if not a bigger problem. But despite CMHC's role - Is abolishing the CMHC really going to be beneficial?

    I would argue that abolishing the CMHC would cause more harm than good. If abolished, we have two scenarios that begin to appear. 

    (A) we have a period with no mortgage insurance, where we revert to standard mortgages requiring a minimum of a 20% downpayment in order to be financed. In this case, the only individuals who would be able to buy, or re-purchase within this market are those who already have the means. This would create increasing distributional problems with inequality, at a time when we are all painfully aware of the inequality present in society around us. 

    (B) Private insurers step into the space vacated by CMHC and begin to offer a similar service to that which CMHC had offered.

Under scenario (B) if these private insurers mirror the offerings of CMHC, we end up with the same scenario as we have now, but at least with the benefit that the taxpayer is no longer backing the risk in the case of a crash. That is, we still have the undue surge in demand by allowing banks to allocate capital to the real estate market through risk-free loans, which to be honest creates an interesting distortion in financial markets, but that is for a different conversation. 

    In this case, I am not in favour of abolishing the CMHC, no insurance would create lots of problems while having private insurers step in would only help in the sense that it takes the risk off of the tax-payer and onto private enterprise (assuming no eventual bailouts).

    I would call, not for an abolishment of the CMHC, but a return of the CMHC to its earlier mandates. In assisting Canadians with their first home purchase up to a regional price cap. In my mind, there is no reason why the government should be providing financial assistance to those who want to speculate in the housing market. there is no reason why the government should be providing financial assistance to those wanting to purchase a vacation cabin or a rental income property. In my mind the program should exist to aid Canadians in achieving homeownership, not to aid Canadians in making money off of the real estate market. 

    Thoughts? feel free to comment below.  

    

COVID False positives.

 

Source: BCCDC

I have often been forwarded articles like this one here which is stating the large probability of receiving a false negative on a COVID-19 test.

This, at first light, appears to be a huge problem.

From the article, we have the reported probability of receiving a false positive based on how many days you have had this disease for:

Day 1 of disease: 100% chance of false positive.

Day 4 of disease: 67% chance

After symptoms begin to show (When you would likely then go to get a test) 

Day 5 of disease 38%

Day 8 of disease 20% 

As I said, this appears to be frightening. Of those getting the test (who have symptoms) something close to 2 out of 5 tests will say that the person is COVID negative when in fact they have the disease.  

So let's work through this. Let's say that you are sick (or someone in your family is sick) and you decide to get a COVID test. You go through the process, get your brain tickled, then get the phone call later that evening. Good News. The result is negative. 

But then you read this article. Are you actually COVID free? or did you just receive a false negative? What is the likelihood that you actually have COVID given that you received a negative test result?

Well, we can actually work this out quite easily. 

Let's first utilize our general multiplication rule for events that are not mutually exclusive:

This says that the probability that both events A and B occur is the probability of A occurring multiplied by the probability of event B occurring, given that, A has already occured. To put this into a more straight forward sense:

Let suppose you have a cooler of beverages. 3 colas and 4 rootbeers. The probability you reach in (without looking) and pull out a cola and a rootbeer is a probability you pull out a cola and then the probability you pull out a rootbeer, given that, you have already pulled out a cola.  

Now the important piece to remember is that this goes both ways.

The probability, P(Cola and Rootbeer) is identical to the opposite P(Rootbeer and Cola). that is, the order is not necessarily important, as long as we finish with one of each. 

Thus we have that:

Why is this helpful to us? 

Almost there - let's open this up, define (A) and (B), and then things should start to become clear.

Where if we set: (A) = "Covid" or (C) and (B) = "Negative test" or (N) we obtain:

From here we can work through what we know (or can find out) in order to answer our question.

What was our question again? 

What is the likelihood that you actually have COVID given that you received a negative test result?

Right, that is, we are looking for P(C|N) so we need to determine values for all the other variables:

• P(C)
• P(N)
• P(N|C)

So how do we go about solving all this?

Well, let's start out with P(C). Currently, there are just over 100k active cases in BC. Given a population of just over 5 million that puts you at about a 2.5% chance of having COVID.  Yes, exposures, or area in which you live/work/play is going to impact this, but we don't have that, so let's keep it simple. 

 

Let's then take a look at P(N). in total, just over 2 million tests have been done in BC (2 336 090), with just over 200K of those being a positive result (217 485) that is we can work out the P(+) to be 9.3%. Using our compliment rule, we can then obtain the P(N) to be 1-P(+) or 90.7%. 

Finally, we need to determine the P(N|C) That is, what is the probability you get a negative test result given that you have COVID. 

Hey, that is our false-negative rate as reported above. Let's start by using the 38% false negative. so summarizing all this we have:

• P(C) = 0.025
• P(N) = 0.907
• P(N|C) = 0.38

We can then re-arrange our above formula to solve for P(C|N) and then make the appropriate substitutions.

Making our substitutions:

What does this mean? it means that given the low rates of actual COVID occurrence in the province and despite the relatively high rates of false negatives. the probability that you actually have COVID given that you received a False-negative is only 1%. That is reasonably low. 

What about if you had a test on day 4 (Pre-symptoms) which when you think about it, is extremely quick for you to realize - notified of an exposure (X) days ago, feeling fine, but will book a test just the same:

Again, despite the alarmingly high false-negative rate. the probability that you actually have COVID given that you received the negative test result is exceptionally low (less than 2%) 

Okay; so what is the moral of the story.

Articles like this come out - and they end up breeding fear and distrust of the tests - potentially leading to people not taking the tests at all. They may think the test is not worth it, the results are meaningless. This of course is problematic in determining caseloads, tracking spread, and combating and turning the tides for this disease. 

Despite these high rates of false negatives. This is still an extremely useful tool and an extremely valuable resource to utilize in our fight against COVID. 

Now - if infection rates were to skyrocket. suppose that instead there was an 80% chance that you had COVID. At that time we would have to question whether or not this test was effective, as the false-negative rate would be extremely problematic. But with our current "low" relative caseloads and infection rates, this large of a false-negative is not a huge concern.