When a house with mortgage is better than a house without one

You are in the market to buy a new house. You have 10L ready cash with you and the current interest rate is 8% (Assume same rate for both lending and borrowing).

You have two options: two exactly identical houses

1. Without a mortgage, priced at 10L.
2. With a mortgage that involves interest at 5%. (The mortgage was taken at the time of low interest rate. The present value of the payments to bank comes to 10L i.e. you can make the asset mortgage free by paying the bank 10L. The mortgage is assumable. Which means that you can assume the mortgage that is in the name of the current owner.)

In this scenario it is profitable to buy the house that has mortgage. Assume the mortgage and invest the 10L at 8%. If you take the first option, you own an asset worth 10L while in the second case you own (?) an asset worth 10L plus you get interest income of (8-5 = ) 3%.

What are the flaws in this argument?

The market is efficient. The arbitrage opportunity that this situation presents will result in increase in price of the house with the mortgage to balance out the riskless profit opportunity.

Edited: As mentioned by Amit, other factors like mortgage market being less liquid and high transaction cost involved may also have an effect.

Information Age

Todays age is sometimes called Information Age. Somehow I feel that using that terminology for any period of time is incorrect. Every age is and was an Information Age. Information was priceless a thousands years ago as it is now. The only difference that I can see is that we are able to make sense of the information much more correctly and faster than ever before.

All our decision making depends on information. This relation between information and decision making presents some interesting points. Consider a simple game of Tetris. In our version of tetris we have only two types of blocks, a one square block (1s)and a two square block (2s). The pile at the bottom has two slots in which we can fit 1s (left slot) or 2s (right slot). While playing the Tetris we make the decision of where to put the shape that next comes in. Suppose you need to make the decision of where the incoming block goes without even knowing which block is the next one. We can either choose the left slot or the right slot and it will make no difference. Actually it does. Generally when we have to make a decision based on a yes/no information we assume that the probability is like a coin flip. Exactly 50%. Which is not always the case. Thus, it is possible that choosing the left slot all the time gets you a better result than 50%.

This is an example of decision making without information. The information we need to make the perfect decision is to know which is the next block. We make 1 bit of decision using 1 bit of information. Real life is not so simple, we make 1 bit of decision using a huge amount of information (e.g., hold or sell the stock). Now let us assume that we have a little more information about our Tetris game. We know which was the block that came in the previous round. It was a 1s. We also know that the probability of a 2s following a 1s is 0.9. Thus knowing that the previous block was 1s gives us a 90% surety that we can predict which the next one would be. This is not perfect but it is better than nothing.

Now suppose you have another kind of information with you. You have the source code of the algorithm that generates the block. Now you don’t have to worry about any probabilities, you can always know which the next block would be.

Thus we have a classification of information

  1. Useless information. Strictly speaking this is not information.
  2. Information that helps us make the decision with 100% certainty
  3. Information that helps us reduce the uncertainty in our decisions.
  4. And a Metainformation that helps us generate the information we need.

Thus not all information are created equal.

What do you call it when you make a decision without all the information or the Metainformation? You call it Risk. This is the basis of all the risk analysis and risk management principle. You do not have the adequate information and hence you prepare some bulshytt (Note that this word is different from the popular Bulshit) to try to help you make decision.

The reverse of this decision making process is also true. When you know a decision, it is quite possible that you can derive the information that led to the decision. This is true even when you do not take a decision. Absence of information is also an information.

Under a rational assumption, if we have 100% information we can make the correct decision and there is no involvement of subjectivity in it. This is rarely the case. This leads to what is called as Bounded Rationality in management parlance. That is we make decision with whatever information we have available to us at the moment.

Lets get to know Efficient Market hypothesis now. EMH or at least the stronger form of it asserts that market prices instantaneously reflects all the available information. There are countless ways in which this seems and is wrong. Technical Analysts believe in EMH but also believe that EMH does not affect the market instantaneously but instead happens in trends. This gives the Technical Analysts the tiny bit of time to get into the trend ahead of the others.

Information has a huge impact on how you become a Goldman Sachs. What if you accept EMH and have access to that self correcting process of the market a tiny moment of time ahead of others. Well, you earn millions out of it. This is called as Flash Trading.

In flash trading, exchanges gives you access to the trading information 30 milliseconds ahead of the general public. Thus if you have a sophisticated trading algorithm and access to this information, you can identify the pattern the market is taking to adjust itself to all the information that is available to it. So now you have access to the decisions that were made but may be not the information that resulted in it. You can utilize this “decisions information” and place your decisions into the queue and earn profit. Many markets have stopped allowing flash trading, but you never know what other avenue of information use is still open.

References :

http://www.nytimes.com/2009/07/24/business/24trading.html?_r=1

http://en.wikipedia.org/wiki/Flash_trading

http://ir.nasdaqomx.com/releasedetail.cfm?ReleaseID=401816

Value At Risk

VaR is a very important concept in risk management. You can say that most of the FRM material is either a preparation to VaR or about VaR.

VaR is described in the following manner: A one week 1% VaR of 100 means that I have a 1% chance of losing more than 100Rs withing a week. This is equivalent to saying that I will lose Rs 100 or more once in a 100 weeks. When I lose more than 100, it is called VaR break.

VaR is used to plot the risk involved in any portfolio that is managed by an institution. Thus if your VaR increases beyond your risk appetite, you will have to take mitigation mechanisms, maybe by hedging or getting out of the investment altogether. VaR suffers from the “Great Intellectual Fraud” as described by Nassim Nicholas Taleb in “The Black Swan”. Since VaR is dependent on Normal distribution or its cousins (Poisson, gamma etc), it fails to consider the huge impact of a highly improbable event. VaR tells that I have a probability of losing 100 Rs or more once in 100 weeks. This “more” could be a million for all I know. Such an improbable event happening can turn the entire financial structure of a company upside down. VaR just gives you an idea of what is the probability. It is up to you to have a plan to deal with what happens when your losses exceeds the VaR.

Jorion Vs Taleb on VaR
http://www.derivativesstrategy.com/magazine/archive/1997/0497fea2.asp

New York Times article on the effects of VaR on the current financial downturn.
http://www.nytimes.com/2009/01/04/magazine/04risk-t.html?_r=1

Basis Risk

We will be taking a look at a finance related topic for a change today.

Basis is the difference between spot price and the futures price. So if S1 and S2 are two spot prices at time t1 and t2 and F1 and F2 are the futures price for a futures contract at time t1 and t2 based on the same underlying asset.

Basis at time t1 = S1 – F1 = b1

Basis at time t2 = S2 – F2 = b2

Now consider that the futures contract that we are considering expires at time t2 and we have entered into a short hedge at time t1. This short hedge is to ensure the price for an asset that we are going to sell at time t2. Now the total payoff at time t2 would be the sum of S2 (The spot price at which we are selling the asset) and any profit that we get by selling the futures at t2.

payoff = S2 + F1 – F2 = F1 + b2

The b2 is the basis risk. In an ideal hedge we would be expecting that the spot and the futures price would converge at the futures expiration date (or the date when we are selling the asset. This is the purpose of the hedge.). But there are scenarios where the S2 and F2 do not converge. Its possible that

  1. Since we did not find a futures contract expiring at the same date as the date when we are selling the asset, we purchased a futures with a little longer expiration. Hence S2 not equal to F2.
  2. The asset and the underlying asset for the futures do not match. e.g. our asset is gasoline while the contract is based on West Texas Intermediate (Texas Light Sweet) (A crude oil is called sweet if its Sulphur content is low. Less than 0.5%. Sweet oil tastes sweet hence the name.) http://news.bbc.co.uk/2/hi/business/904748.stm
  3. Transportation cost of the delivery may increase the actual cost of the asset as compared to the contract.