Judge Holden

Judge Holden: Moral law is an invention of mankind for the disenfranchisement of the powerful in favor of the weak. Historical law subverts it at every turn. A moral view can never be proven right or wrong by any ultimate test. A man falling dead in a duel is not thought thereby to be proven in error as to his views. His very involvement in such a trial gives evidence of a new and broader view. The willingness of the principals to forgo further argument as the triviality, which it in fact is, and to petition directly the chambers of the historical absolute, clearly indicates of how little moment are the opinions and of what great moment the divergence thereof. For the argument is indeed trivial, but not so the separate wills thereby made manifest. Man's vanity may well approach the infinite in capacity but his knowledge remains imperfect and howevermuch he comes to value his judgements ultimately he must submit them before a higher court. Here there can be no special pleading. Here are considerations of equity and rectitude and moral right rendered void and without warrant and here are the views of litigants despised. Decisions of life and death, of what shall be and what shall not, beggar all question of right. In elections of these magnitudes are all lesser ones subsumed, moral, spiritual, natural.
Blood Meridian


Little Bill: "I don't deserve this, to die like this..."

Munny: "Deserve's got nothing to do with it."
Unforgiven

In the novel there is an investment bank where one of the trading units gets requests from its clients to price their illiquid inventory. (This is an exercise that occurs in real life, because the clients have to mark to market, and for some assets there is no market. So they go out and get bids from a couple of banks, and then mark at the average of these two prices). This trader puts in incredibly low-ball prices. One bank prices a security at $92. He prices it at $50, leading to a mark to market price of $71. The trader knows that with such a low price, the client will be forced into liquidation mode. The trader positions his book for the forced sale that he helped precipitate, generating big profits from his scheme. This is fiction. But if we have learned one thing over the past couple of years, in the world of finance truth can be stranger than fiction.
~Rick Bookstaber

Where to begin? 1st I will say that I have a post coming forthwith about the Tarot card game in Blood Meridian as a microcosm or vignette for the entire novel.

Now though I wanted to further explore the notion of good and evil set forth in these various stories from above. The first two are obviously close in genre but I believe the third to be in the same strain of logic. All try to deal with fairness or merit or mitigations of circumstance, but all in all the three come back to the ultimate logic of games and the men that play them. In the Judge's opinion the world revolves around games with war being the makind's opus. He would revel in Munny's logic that even though Little Bill may be the more exemplary character it does not matter. Once he kills Ned, he enters a new game with Munny. The terrible violence that is the climax of Unforgiven can all be avoided. Munny has the blood money for killing the two wayward cowboys. He can return to his family and move to San Fransisco. However, as Holden lauds above, "A man falling dead in a duel is not thought thereby to be proven in error as to his views."

One could even bring in a fourth story, or, parable as it were, of the Pharisee and the Tax Collector. "The Pharisee stood and prayed to himself like this:‘God, I thank you, that I am not like the rest of men, extortioners, unrighteous, adulterers, or even like this tax collector. I fast twice a week. I give tithes of all that I get.’ But the tax collector, standing far away, wouldn’t even lift up his eyes to heaven, but beat his breast, saying, 'God, be merciful to me, a sinner!' I tell you, this man went down to his house justified rather than the other (former); for everyone who exalts himself will be humbled, but he who humbles himself will be exalted."

The parable means that even though the Indians in Blood Meridian and Little Bill in Unforgiven lead moral lives, that without besetting themselves humbled before God they suffer as well. In Blood Meridian the only God described is war. Quite a twisted way in which McCarthy uses the logic of Jesus in Judge Holden's ode to war.

Which brings us to the last passage. Should Bookstaber's hypothetical be taken with a dim view? Should the capital markets just be considered another game, one in which men put up bold stakes, though not as bold as a pound of flesh? Holden and Munny would hold that just because the client is in the right without a recourse there is little that he can do, except stop arguing and start mining for his pound of flesh. It seems as though the capitalist system follows along the logic of Munny and Holden up until a point, to quote Satjayit Das "we rip their f&cking faces off!" However, in the end the bankers are scolded, and settlements issued. A wizened person would state that there is still an temporal distortion though. The clients can be swindled and then have their monies returned but there is still a point in time between the swindle and the discovery that bankers can maximize and do. (e.g. Bonuses vintage 2006-2008)

At a party one evening I remarked to a friend "Ever get the feeling that the societal rules are arbitrarily effective pieces of figmentation? That is, it is the only idea of retribution or the fear thereof that deters you from doing whatever it is you feel you want to do. However, mitigating that fear is the idea that there is a temporal distortion and in that episode imagine what you can get away with until society catches up with you... that my friend is the basis of evil."

So as a society we have evolved from our anarchic roots. It is just that we have not yet perfected the ability to provide justice in the most timely of manner. There is one last point I would like to ponder. The last point I wanted to touch upon is how in a contract it is easy to assume that there are two parties to the contract. Much like the Judge points out in his duel example. However, in these times this is not so. There is always a third-party, i.e. the government, who has to enforce the contract or provide the means in which to rectify the obligations. This is important as it drives the distortion of justice inherent in society currently, as it is always reactive justice.

Addendum:
This just in from Vanity Fair.

A money manager I spoke to described his meeting late last year with Jane Mendillo, who in July 2008 became president and chief executive officer of Harvard Management Company. Knowing that Mendillo was trying to unload assets, he offered to buy back Harvard’s sizable stake in his private fund. As he recalls, the surreal dialogue went something like this:

He: “Hey, look, I’ll buy it back from you. I’ll buy my interest back.”

She: “Great.”

He: “Here, I think it’s worth—you know, today the [book] value is a dollar, so I’ll pay you 50 cents.”

She: “Then why would I sell it?”

He: “Well, why are you? I don’t know. You’re the one who wants to sell, not me. If you guys want to sell, I’m happy to rip your lungs out. If you are desperate, I’m a buyer.”

It doesn't matter who is correct, whether the assets are worth 1.00, 1.11, or 50 cents. When the margin call comes you must submit yourself to a gamble that subsumes correctness.

Liquidity, or not. The difference between market making and frequent trading

Liquidity is ephemeral. It is there until it isn't, a real chocolate teapot that disappears when it is most needed. I am not sure how much of this has reached main stream media (MSM) but in the trading world this story is huge and it deals with the current liquidity providers high frequency traders.

Let's think about logging into your E*Trade account, with a few clicks you can buy a lot or an odd lot of shares of your latest stock tip. In a few moments you have your confirmation and I wish you great success in your endeavor. This is how trading is done across the capital markets, no? Ummm... no. IPO's, bond trading to cite some examples is not as clean. The imaginary stock trade is facilitated by a market maker. You want to sell, she will buy. You want to buy, she will sell. At least this is how it worked in the old days. A quick aside, the reason there are market makers is that they take a spread on each transaction, the buy and sell offers are a penny to a few pennies apart, thus the market makers is incented to trade as often as possible but not take positions. They act as a wholesaler with an inventory of certain securities that they sell and buy to make a market. BTW, this is lucrative career.


Now though, 70% of the trades are facilitated by high frequency traders. (HFTs)
Now I don't want to beat on Goldman Sachs but they trade their own accounts (Principal) more than the next 6 firms combined. They act as suped-up Hoover running trades and being paid by the exchange to do so. One interesting fact dug out today involved much maligned CIT. The company was bailed out by its creditors, but during the period in which its future was up in the air the stock traded down below a dollar. Who cares, that is expected. Well, except that exchanges will not pay the liquidity rebate of .003 cents per share unless the stock is above a buck. Thus, as it trades around the dollar mark remember that it is not because of a fundamental value, instead it is following the fundamentals of high frequency trade economics.

So we have moved from a visible market mechanism, the bid spread amount to the exchange rebates for HFTs. While it also difficult to become a market maker it is near impossible to become a HFT. You need a space race-sized budget to build up your computer speeds, you need to secure space near the exchange as the trades are done in microseconds, in short you need to be RenTech or Goldman Sachs.

In summation, there are three main points buried in this post:
A) There is a conflict of interest at the exchanges as the exchanges allow these HFTs unprecedented access to the exchange that the lay retail and institutional investor cannot afford or have access to.
B) Is this the best way to run an exchange, through a hidden rebate to HFTs
C) If 70% of the trades are noise, or worse front run trades by the HFTs how much of the assets value is decided by the noise and how much by its inherent value surmised by the efficient markets hypothesis. (EMH)

Correlation in everything

PARKING rates are holding firm despite the economic downturn, according to Colliers International, a property company. European cities have some of the highest daily parking rates, with Amsterdam and London coming out on top. Tokyo is the most expensive place to leave your car outside Europe. Honolulu is second behind New York among America's cities. Drivers in London fork out the most for a monthly unreserved space. The cheapest parking in the survey is in India, where a spot in Chennai costs 96 cents a day. ~The Economist

Felix Salmon pointed this out in his blog links the other day and with a quick rebuke marked that the series relationship between daily parking rates and monthly parking rates was highly uncorrelated. Normally I would take his word at gospel but perhaps I should be more skeptical. (In general as opposed to explicitly when reading Felix's work.) So I quickly entered the data into a spreadsheet and looked at an x-y scatter plot. While it was true that the regression line did come out with a less than desirable r-squared figure of 59.97%, which in lay terms means that the line can explain almost 60% of the variance of the points from the "best-fit" linear regression line produced. So Felix is correct not much of a natural correlation, so much for those who love to extrapolate out series.



So let's extrapolate out the series to see what happens. Taking the daily rate and multiplying it by 30 days to see what happens. Obviously if you pay up front you should be expected to earn a discount. Also by purchasing in bulk and thus giving the merchant sticky expected cash flows, which the merchant can extrapolate to his peril, you should also receive a discount.


Now the series looks much more promising. Below is a graph of the monthly discount from paying up front versus paying the daily rate 30 times. You can see the discount's median is almost 64% and the average is about 57%. The series is also drawn from the above table so you can see that as the daily rate drops so does the discount, which is also expected because price levels matter. I am quite certain Felix wrote this in passing as he boarded his plane for Beijing but I think he may have written too quickly without a full analysis.

Stock Market Monkeys

Once upon a time a man appeared in a village and announced to the villagers that he would buy monkeys for $10 each.

The villagers, seeing that there were many monkeys around, went out to the forest, and started catching them. The man bought thousands at $10 and as supply started to diminish, the villagers stopped their effort. He further announced that he would now buy at $20. This renewed the efforts of the villagers and they started catching monkeys again.

Soon the supply diminished even further and people started going back to their farms. The offer increased to $25 each and the supply of monkeys became so little that it was an effort to even see a monkey, let alone catch it!

The man now announced that he would buy monkeys at $50! However, since he had to go to the city on some business, his assistant would now buy on behalf of him.

In the absence of the man, the assistant told the villagers. “Look at all these monkeys in the big cage that the man has collected. I will sell them to you at $35 and when the man returns from the city, you can sell them to him for $50 each.”

The villagers rounded up with all their savings and bought all the monkeys.

Then they never saw the man nor his assistant, only monkeys everywhere!

Now you have a better understanding of how the stock market works.

Source: Unknown H/T Prieur

Duration or if you prefer the Price-to-Dividend Yield

Duration is an economic/finance term used to describe when the average payment will be made on a bond. This is a gross simplification, but useful to describe it in lay terms. So if you have a zero-bond, that is one that does not pay out a coupon, the only payment is when the security matures and then pays its face value. So if it is a 5 year zero, then obviously you on average get your repayment in the 5th year. Simple, eh? Well, when you have coupon payments this averages move up closer to the present day depending on the relative size of the coupon to the final payment. The ultra-cool aspect of this is that when you match when you need your money back to a security's duration than interest rate changes will not affect you, that is you are immunized. This is because the loss that you are receiving by the relatively lower coupon rate when interest rates rise is made up by the reinvestment of the coupons in the higher current interest rate. However, I didn't want to follow fixed income with this post and instead wanted to look at equities.

So you can also apply this logic to equities. So I did so for the S&P500 index. I went to Standard and Poor's website, http://www2.standardandpoors.com/portal/site/sp/en/us/page.topic/indices_500/2,3,2,2,11,29,2002,0,0,0,1,0,0,0,0,0.html and searched around a bit to find the historical dividends and the price index. So I looked at the year-end price level and the year-end dividends paid in the past 4 quarters. Here is the chart I made.
The axis starts with the current price-dividend ratio and goes back until 2002. As you can see over the past 7 1/2 years the ratio has been above 50 until 2008, this era covers post-9/11 and the dot-bomb era. More incredulous when the trough of the equity market was in 2003 the ratio was at its highest level. So maybe the rally over the past 5 years did not really make much sense. Hindsight being 20-20 and all.

So applying the immunization concept to these numbers, it means that on average you would receive your money back by investing in the S&P500 anywhere from 50 to 60+ years in the future. Mad! Now the ratio fell to its lowest in December where it was 31.82 and now is at 35.03. That means if you plan on retiring in 35 years, the change in interest rate levels will not affect your investment. This makes the huge implicit assumption that the dividends and prices will remain at a constant ratio over that period. Neither I, nor anyone else should, believe that to be the exact case but this is a useful exercise in maintaining our bearing when viewing the equity markets. This information is most useful to investors who are about 30 years old, any older than that and you would need to have considerable more invested in shorter duration bonds to match your expected retirement date.

Rate, rate who's got the rate?

If this all seems confusing and that you've entered into a gag in Mr. Wonka's factory, you need not worry trained professionals find this baffling as well. In the last post we used a discount rate to discover what the true benefit of a security was in present value terms. Now, we need to add a bit of complexity to obtain a further degree of accuracy. So today will be about zero-rates on those risk-free securities.

First we will just assume that we know what the zero-rate is and then we can later show how to figure out the implied zero rate. The zero rate is basically what we calculated yesterday. However, coupons and dividends do not all come at the end of the security's life. So we need various zero-rates to find out what the correct price of the security is.

Given:
Zero Rate - Maturity
5.0% - 0.5 (Years)
5.8% - 1.0
6.4% - 1.5
6.8% - 2.0

Now we want to price a 2 year Treasury bond with a principal of $1,000 and a 6% coupon paid semiannually.
0.0 - ?
0.5 - 30
1.0 - 30
1.5 - 30
2.0 - 1,030. That is 1,000 in principal and 30 for the coupon payment.
We utilize the formula from yesterday and use the spot/zero-rate for each maturity.
So we find that:
30e^(-.05*.5)+30e^(-.058*1.0)+30e^(-.064*1.5)+1030e^(-.068*2.0)= 983.85
29.2593+28.3095+27.2539+899.0279=983.85

This result in and of itself is rather interesting. See the security pays 6% annual via two coupons of $30. However, it sells at a discount. This is because the majority of the bond is paid in the final payment where the interest rate is greatest and is discounted by the most periods as well. We can figure out the bond's yield maturity by utilizing a financial calculator. Entering 4 for the period, Present value of -983.85, Future Value of 1000 and Payments of 30. Then solving for the Yield to Maturity it shows 3.439% and multiplying this by two gives the annual rate of 6.89%

What happens when there is not a corresponding Treasury? That is the million dollar question.

Say you have these 5 Treasury securities:We now employ the bootstrap method.
So to find the quarterly zero-rate we know that you will be repaid your principal in 1/4 a year. Thus you gain 25 on your 975 worth of investment. If we annualize that figure you would have:
(4 x 25)/975= 10.26% Which we should change into continuous compounding.
So 4 x ln(1 +(.1026/4)= 10.13% We do the same with the other non-coupon bearing instruments and come out with continuous compounding rates of 10.47% and 10.54%. Now is where the bootstrapping begins in earnest. So the 1 1/2 year bond will pay out coupons semiannually( all Treasury securities do) so it will pay 40, then 40 and finally 1,040. So we can use the zero-rates we have already applied to find the zero-rate for 1.5 years.

40e^(-.1047x0.5)+40e^(-.1054*1.0)+1040e(-R*1.5)=960
37.9599+35.9986+1040e^(-R*1.5)=960
e^(-R*1.5)=886.0415/1040
e^(-R*1.5)=.85196
-1.5R=ln.85196
R=10.68%

Then the last one:
60e^(-.1047*0.5)+60e^(-.1054*1.0)+60e^(-.1068*1.5)+1060e^(-R*2.0)=1016
56.9398+53.9979+51.1184+1060e^(-R*2.0)=1016
e^(-R*2.0)=853.9439/1060
-2R=ln(.8056)
R=10.81%

Now we have a zero yield curve

Homework:
Calculate the zeroes for 1/2 year, 1 year, 1 and 1/2 year and 2 years.

Stupid thought of the day

Ever hear about the mathematician who drowned in the river that was on average 2-inches deep? The joke is slightly bemusing, however, it did start me pondering how the river could be set up so it could drown a man. I mean we most likely have heard that a baby can drown in two-inches of water, but a man is fairly improbable.

Here was the set up I came up with: You have a river that has the same characteristics up and down its length. So a cross-section will mimic the entire river system. It is 1,000 feet wide. The 1st section is 445 feet wide and is 1-inch deep. The middle section is 10 feet wide and is 100 inches deep, (8 1/3 feet.) The last section from the middle to the far bank is 445 feet wide and is 1-inch deep. To find the average depth of the river we add the 3 sections together after we have multiplied them by their depth. Then we divide it by the total width of the river. So

(445*1)+(10*100)+(445*1)=445+1000+445=1990
1990/1000=1.99 inches

So on average the river is 1.99 inches deep, but you can see how this can be tricky for the man fording it.