Chandan Dubey

# Taking inflation to the extreme

Taking a situation to the extreme, in some cases, helps explain it better. A very good example is the Monty Hall problem. I came across it when the professor of my probability course gave it as an exercise. The solution of the problem is very surprising and I urge you to solve it for yourself before looking at the explanation below.

The problem is posed as a game played between you and a computer. Suppose that there are three identical rooms with doors that are controlled by the computer. Two of the rooms have a goat inside, but the third has a Porsche. You have no knowledge about the contents of any of the rooms but the computer has. The game has four steps (a) You pick a door, (b) The computer picks one of the two leftover doors and opens it; revealing a goat, (c) The computer gives you an option to switch to the other door, and (d) The computer opens the door you picked and you get the content of the room.

Step (b) needs some additional explanation. There are two situations. In Step (a) you might have picked the door with the Porsche behind it. In this case, the computer picks a door at random out of the other two i.e., picks one of the two with probability 1/2. In Step (a) if you pick a door with a goat behind it, then out of the two left-over doors, only one has a goat. The computer then opens this door to reveal a goat.

Rationally, you want to win the Porsche. The question is: in Step (c) should you switch the doors ?

Taking this situation to the extreme might help you make a decision. Instead of three doors, consider 100 doors with 99 goats and 1 porsche. In Step (b) computer opens 98 of the left-over 99 gates. Do you switch the doors in Step (c) ?

***

World War I was an expensive affair. The participants spent more and more money in the hope that they will be able to collect it from the group that lost the war. The German side lost and were demanded to pay nearly \$64b. The GDP of Germany was \$12b before the war and \$64b was an extremely steep sum.

Germany had financed most of the war by printing money. It had expanded its money supply by 400% and the prices were nearly 10 times in 1920 compared to 1913. Instead of trying to rebuild its finances, the Germany took the easier way of inflating away the debt by printing as much money as needed. In fact, some claim that the Germans intentionally destroyed their economy to obviate the need of paying reparations.

The amount of inflation can be gathered from the fact that after the war \$1 was worth 8.91 marks and on Nov 12, 1923 it was worth 630b marks. In Nov, just as the new currency Rentenmark was introduced, the mark fell some more. On Nov 14, it was at 1.3 trillion; on Nov 15, it was 2.5 trillion and on Nov 20, it was trading for 4.2 trillion !

In 1922, nearly 1 trillion marks were printed. In the first six months of 1923, the amount rose to 17 trillion (see Lords of Finance by Liaquat Ahamed, page 93-94).

***

Printing money, in simple terms, is a way to transfer wealth from the savers to borrowers. In the spirit of taking situations to the extremes, we can look at Germany and see what happened.

The savers of Germany (among them: teachers, civil servants, scientists, doctors, workers) were hit the hardest. They had invested all their life savings into government bonds and saving accounts. The careful accumulation of the money amounted to naught. A thousand mark bond from 1914 was still worth the same in 1923, but a loaf of bread cost in billions of marks. It is not difficult to see that the middle class Germany was reduced to indigence and penury.

The debtors (among them: the industrialists, real estate owners, risk takers with large debt) flourished and made like robbers. Their assets increased in price because of the inflation while their debt was worth nothing. A debt of 1000 mark in 1913 was still worth 1000 mark in 1923 (except that one has to pay the interest during the intervening 10 years). The debtors benefited from buying hard assets on margin.

***

Real-estate companies are excellent hedge against inflation. A real-estate company owns buildings and lands. This is a capital intensive business and generally the company has to take a lot of debt to finance the acquisition of new houses and new land.

Inflation will profit this company on two fronts (a) the prices of its assets increase, and (b) The debt will be worth a lot less.

For example, if you took 8.9 mark in loan and bought a piece of land in 1918 Germany then in 1923 the land will be worth a lot, while the loan will be still worth 8.9 marks !

***

Let us come back to the Monty Hall Problem. The solution to the problem is that switching at Step (b) is the correct choice. This way you double the probability of winning the car.

This answer is counterintuitive, even after some serious mental exercise. The car is either behind the door you chose or not. How can showing a goat in one of the remaining rooms change this fact ?

Taking the case to the extreme with 100 rooms explains why switching might help. The probability of picking the right door in Step (a) with the Porsche behind it, is 1/100. After the computer has shown 98 goats by opening 98 of the remaining 99 rooms, we have 2 left-over closed doors. If we pick one randomly among these two, the chance of hitting the Porsche is 1/2 (there are two gates and Porsche is behind one of them).

Let us answer the original problem more formally.

There are three ways of hiding the Porsche among the three rooms. If you pick the door with the Porsche in Step (a), switching in Step (c) makes you win a goat. If you pick the door with a goat in Step (a), then switching in Step (c) makes you win a Porsche. The probability that you picked the room with Porsche in it - in Step (a) is 1/3. The probability of picking a door with a goat behind it is 2/3 in Step (a). So, switching the door in Step (c) will make you win with probability 2/3, while staying with the same door will make you win with probability 1/3.

Chandan Dubey
I invest because I want to be free by the time I reach 40 years of age i.e., 2025. My investment style is to find a small number of bets with large margins of safety. I pay a lot of attention to management and their incentive. Ideally, I like to buy owner operator businesses. I am fortunate to have a strong inclination towards studying. I aid my financial understanding by extensive reading in psychology, economic, social sciences etc.

 Currently 3.50/512345 Rating: 3.5/5 (22 votes)

Denggi - 5 years ago    Report SPAM
Hi Chandan

I'm curious about the debtor scenario you mentioned. How would the interest rates have been at the time? Would the increased interest repayments (assuming interest rates went higher in tandem with inflation) have been enough to negate the increase in value of the property?

Holding an asset and a fixed rate loan would have given amazing results of course. A person could have even made money taking a car loan. :)
Rollling - 5 years ago    Report SPAM
Am I that bad on probabilities?

You have 3 doors. You chose one probability 1/3 of being right. Computer gets the remaining two probability 2/3 of getting the Porshe.

Computer randomly opens one of its two doors. There's a goat. Which means that your probabilities of getting the porshe are now 1/2 and the computer probabilities are also 1/2. As such changing doors wouldn't hurt but wouldn't help either. Your probability isn't static.

The same happens with 100 doors. you have 1/100 probability and computer 99/100. If the computer opens 98 doors with goats then in the end there only remains 2 doors. So your probability of being right is now 1/2 equal to the PC. AS LONG AS the pc is opening doors randomly

About the rest: true and that's why the german fear debt so much (and I agree with them even if I'm portuguese and that means I'm earning less day by day to pay other peoples debts -since I'm against this overspending for years)

ps: if I'm wrong on the probabilities problem please explain.
Batbeer2 - 5 years ago
>> Am I that bad on probabilities?

Yes ;-)

Play this game with someone. Unless you happen to have a big house, a porsche and some goats, use three inverted, opaque cups. One with a coin underneath. Your partner has knowledge of where the coin is and you don't. Try to pick the right cup ten times. Stick to your original choice. You will probably find your average is less than 50%. This is probably what you were expecting; you aren't that bad after all.

Then try it ten times by consistently "swicthing" to the remaining cup. You will probably score better than 50%.

With 100 doors; Munger says invert:

Lets say you picked door number 6. Unless you picked the right door to begin with (1%), the computer has no choice but to eliminate all the wrong doors. The single remaining door (in this case number 57) represents the 99% chance that you didn't pick the right door to begin with.

With three doors, the door the computer leaves represents the 66% chance you didn't pick the right door to begin with.

Batbeer2 - 5 years ago
On topic....

I've seen > 400% annual inflation. It's bad for everyone. Yes, if you have a load of fixed rate long-term debt, that "evaporates". Within a couple of years you are in the same position as the savers; no meaningful debt and probably no meaningful income either. The point here is that hyperinflation is bad for everyone. The whole economy resorts to barter trading.

A warehouse full of spare tyres and/or medical supplies and/or tools (hacksaws, shovels, chainsaw parts) are what you want.
Cdubey - 5 years ago    Report SPAM
@Denggi: The interest rates for the banks were as follows

1914-1921 5%

1922 12% in November

1923 Bank interest rate rises to 19% in January, 30% in April, 90% in September.

(Source)

Even assuming 100% interest rate every year from 1918 to 1923, you would have spent at most 6x8.91 marks on 8.91 mark loan taken in 1918.

Still far from being 1.3 trilion !

Rollling - 5 years ago    Report SPAM
@ Batbeer " [color=#333333; font-size: 12px; line-height: 18px; text-align: justify; ">the computer has no choice but to eliminate all the wrong doors. " - then it's not random! obviously if it's not random then the probability 1/100 remains... he however said " the computer picks a door at
ps: about the inflation... everybody get's hurt... some less than the others... the fixed rate endebted at least end up with little debt
Batbeer2 - 5 years ago
From the article: >> You have no knowledge about the contents of any of the rooms but the computer has.

Cdubey - 5 years ago    Report SPAM
@Sky: If I am correct, you do not understand all the steps of the game.

The computer *knows* what lies behind which door. Let us number the doors 1, 2 and 3. Suppose in Step (a) you picked door 1. The computer looks at door 2 and door 3 and sees what is behind them. There are two different cases. Case A: The car is behind door 1. In this case, door 2 and door 3 have goats behind them. The Computer picks one of 2 and 3 randomly with probability 1/2 and reveals a goat. Case B: The car is not behind door 1. In this case, either 2 or 3 has a goat behind it. The computer then picks among 2 and 3 the door with goat behind it. He then opens this door to reveal a goat. In Case B, the behaviour of the computer is not random !

So, the computer picks a gate at random only when you have picked the door with the car in Step (a). Otherwise, computer opens the gate with the goat behind it.

When the problem is with 100 doors then after you pick a door in Step (a), there are two different situations again. Case A: You picked the door with car behind it. In this case, the computer picks 98 out of the 99 doors randomly and opens them - revealing goats behind each one of them. Case B: You picked a door with a goat behind it. In this case the computer is not random. He has to open 98 doors and they all should have a goat behind it. So, he has to *eliminate all the wrong doors*.

A good discussion on the Monty Hall problem is here.
Superguru - 5 years ago    Report SPAM
real estate and gold should be good inflation hedge. Did Japan have inflation?

I also read somewhere during QE1/2 - Bernanke saying QE is not same as printing money.
AlbertaSunwapta - 5 years ago    Report SPAM
If it smells like a goat, or bleats like a goat, it probably is a goat. So there you go, your odds just improved. Now, if only I knew what a Porsche smelled like for a bit of certainty. :-)

... the value of a bit of extra research before placing a bet.

Now, two goats under the right economic circumstances might be worth more than a Porsche. If held, one tends to destroy earnings power and the other grows it.

As for gold... The problem is not the holding of it in high inflation but the divesting of it after it has proven itself "invaluable". Real estate might lag inflation but in disinflation it is unlikely to collapse, if at all, as dramatically as gold. "Gold bugs" will find it near impossible to sell their position until they've loss much of their hedging benefits.
Brucechin - 5 years ago    Report SPAM
Bayesian theory shows that the opened door containing the "goat" has given you more information, that which you did not have at the beginning. Thus, with this new information you should act and choose another door. Using 100 doors
Dr. Paul Price - 5 years ago    Report SPAM

The problem in the USA with owning highly appreciated real estate due to inflation?

Government reassessments will ramp up property taxes on your phantom gains and you may not have the cash needed to remian in your home.

This is exactly what happened to many people in the housing bubble. Hyper-inflation would make it much, much worse.