Merry Christmas!

To all who read my blog, the ardent few of you and the many passerbys, Merry Christmas! I hope you all have a safe and happy holidays with family and friends. Probably no updates until after new years when I start my new co-op. So if not, happy new years as well.

Option Model Updated

I’ve continued to work on my option pricing model and have updated it. It now calculates the option greeks theta, vega, gamma, and delta as well as showing you payoffs. I’ve also added one option strategy payoff and profit loss page for a butterfly spread. The link is the same. I will repost it here.

12 period Binomial and Black-Scholes Model

EDIT: This was updated again as of 12/21/2010. Fixed some of the modeling problems with vega/theta/gamma/delta.

More Updates: Added put delta and theta, changed up some of the colors and a bit of the layout. Removed Value Graph and went with P/L instead. The rest was mostly cleanup. Overall very satisfied with what I have. Going to continue to add more as I go along.

Some Ideas:
More Strategies (Iron condor, strips/straps/straddle, strangles, etc…)
Greeks for each strategy
Ability to make custom strategies
Implied vol calculations
GARCH Volatility forecasting
Monte-Carlo sims.
Probability graphing.
A lot of this will take VBA and Matlab knowledge to complete but I hope to address a lot of this just a few months from now.

12 Period Binomial and Black-Scholes option Pricing model

I’ve been trying to brush up on my excel modeling skills and I’m hoping to do a collab with Greg Williamson, a buddy of mine from NEU, on a DCF and ratio valuation model as well as some other portfolio optimization models (like asset allocation and incorporation of securities like bonds and derivatives into a portfolio). I’ve seen some black-scholes calcs up but almost zero (free) binomial option pricing models. I think I understand why now, because it took me forever today to get this up and running. Anyway, here is a link (and it will also be posted in the models section) to my current incarnation of the black-scholes and binomial option pricing models in excel. I’m hoping to do a bit more work in Matlab using matricies as I compile more complex data and teach myself a little bit more about how to use it. Need to learn VBA as well. It’s a great thing I love using excel because that’s going to be the bulk of my job for the next six months.

John Hancock Asset Allocation

So  I just accepted a job offer for a co-op position (6 month internship) on John Hancock’s asset allocation team. I’m extremely excited and was elated to get a call back on the same day extending me the offer. The team works on asset allocation utilizing a “fund-of-fund” style model whereby they create diversified mutual-fund portfolios by investing in lower-level mutual funds that are target-sector (such as mid-cap, large-cap, emerging markets, fixed income etc…) specific. The team does both quantitative and qualitative higher level macro analysis and sets up strategic asset allocation for all of the funds managed by John Hancock. They have target-risk and target-date funds which cover a broad swath of equities and fixed income.

To me, the position was a perfect fit and sounds like it will be an amazing opportunity to learn. Asset allocation is one of the most complex parts of investment and the challenge of learning how it’s done is one that I can’t wait for. I knew the right job would come a long, and this couldn’t be a better time. I start in January and will hopefully have a lot more to write about going forward as my knowledge of the markets and asset allocation grows.

Corporate tax shelters and reduced competition

Over at Macroeconomic Resilience, Ashwin Parameswaran comments on how crony capitalism can reduce stability and macro-resilience by limiting the new entrants into industries which need competition. The thought-provoking article along with a post at Dues Ex Macchiato on Google and the Double Irish had me thinking about the unintended consequences of industrial policy like competitive taxation between nations.

Google is one of the world’s largest tech firms, with a market cap of $181.7 billion and a net-income over over $6 billion  in 2009.  However, thanks to a tax scheme known as the Double Irish, they were able to reap a tax savings of over $3 billion over the past 3 years.  Thanks to the ridiculously low corporate taxes of Ireland, and the way in which their tax code is structured, Google is able to be taxed at only around 2.5% of its total European earnings.  This is simply one example of how many firms use competitive corporate tax rates (and tax havens) to increase their bottom line. The Double Irish is also odd on its face given the fact that Ireland’s beggar-thy-neighbor policy should be quite inflammatory to the EU nations which had to bail them out.

While many on the right would most likely claim a “triumph of the free-market over government intervention,” competitive taxation can lead to highly undesirable outcomes and decrease competition and increase monopoly power of incumbent firms. I will try here to create a conceptual framework where we can understand how this happens.

My hypothesis for the mechanism by which competitive tax rates discourage competition in foreign nations is thus:

1) The foreign tax loophole can only be taken advantage of by those who have the scale to make it profitable (i.e. legal fees and other costs are eclipsed by tax savings). Incumbents are at an advantage in this regard.

2) Smaller incumbent firms in the same industry will return lower margin from engaging in the tax shelter but it will be forced to do so to stay competitive

3) The smallest of firms – typically new entrants into the industry – will have even lower margin when trying to take advantage of the loophole

4) Only global, incorporated firms, can take advantage of the loophole, thus non-global competitors lose out.

Any new entrants or smaller competitors (such as companies like Red Hat) have an inherent disadvantage to firms in its industry which employ this strategy since the cost to set up the strategy initially can divert resources which might have been better spent on research and development. What confirms, to me, that incumbent firms earn out-sized benefits from running such a tax strategy is that all of the largest firms use it, solidifying their place in the global economy. Companies like Microsoft, Apple, IBM, Oracle, Pfizer, and Eli Lilly all employ the Double Irish and Dutch Sandwich which allow them to reap huge tax savings. These tax savings also work in another way to reduce the competition in industries. They inflate earnings thus driving up stock prices and lowering borrowing costs for incumbent firms. While new entrants do not have this advantage, incumbent firms can take advantage of low borrowing costs to continue to increase their market share and drive out competition.  As firm monopoly power increases it becomes harder and harder for new entrants to disrupt this. Tax havens and loopholes only facilitate this movement towards a less dynamic and resilient economy.

While I discuss international tax havens here, I wonder if this might possibly be teased out in state-wide data of industry entrants as competitive tax-loopholes were enacted by different states using econometric analysis and data on firm creation and bankruptcy.

Perhaps WTO policy should be revamped in light of both the Chinese Currency manipulation and the banana-republic style tax codes of many countries to include regulations on tax codes and and currency pegging in order to achieve a nations economic policy. We can see that the effect of ridiculous tax codes in Ireland have not helped it in the least.

Not much to write about as of late

I’m truly sorry I haven’t taken the time to update my blog. I just haven’t had much to write about that isn’t already written about. I will try to update with links and what not that I find interesting. When I make blog posts I really try to find a topic I care about and something that I think I have a different or novel take on. I think I want to start expanding upon some other posts and I’m trying to wrap my head around a few things. As it gets closer to finals I will have little else to do but study, although reading textbooks sometimes does bring things to light.

These past few weeks have been a struggle for me, going through interview after interview only to find either the job wasn’t right for me, or I wasn’t right for the job. I’ve come to the realization that much of the financial world doesn’t want thinkers as much as they want doers. While I am both, I love the non-mainstream theoretical side of finance and economics. I love exploring and poking around trying to understand different topics. I would love to find a position which allows me to do this, which is very much one of learning but learning that is geared towards achieving a goal for the firm. I’d love to find a job where my insight and enthusiasm translate into action. Perhaps I look for too much at this stage in my career. Perhaps I need more education.  I try to be open and honest with interviewers but many times it’s met with a dismissive and almost “why are you so different?” tone and body-language.

Finding a job which appreciates both insight and conviction in those insights has been a challenge but I hope to find it soon.

Pricing Bonds

On my recent mid-term exam in Risk Management the class was given a question which read:

A 10-year, 8% coupon bond (paid annually) currently sells for $90. A 10-year, 4% coupon bond (paid annually) currently sells for $80. What is the 10-year zero interest rate?

This had me thinking, how do you do this problem? The solution given by the Professor was thus: You Sell the 8% and buy 2 of the 4 percent (or vice versa buy/sell). You then calculate the cash flows which cancel out, except for the ending cash flows of 2*100e^-rt and 100e^-rt. So you get 100e^(-10r) = 70 which comes out to r = .035667 or 3.5667%. I started to wonder whether or not there was another way, using calculus, to do this, but instead you could price ANY bond with the same maturity but a change in the coupon rate so long as you have two bonds which are identical except for their coupon rates. This is because the coupon rate acts as a scalar which creates a linear variation in the price of the bond when C changes.

The natural response was to use partial differential equations, but I realized quickly I didn’t even need to do this. The solution worked out very much like the Cobb-Douglas TFP problem I had looked at earlier in the week, which gave me insight  into how derive a theoretical pricing for the bond and finding the n-maturity zero coupon rate.

First we must define the present value of the coupon payments which is given by the formula

(1.1)

Where C is the coupon payment in dollar value, r is the rate of interest or discount rate, and t is the amount of time.

Since C is held constant throughout we can then take C out from the summation to yield the formula

(1.2)

Now here one might be tempted to find the Pv using partial differentials of C, r, and t, but that is not required. Instead we can set the summation as a constant and have the price change simply as a factor of C to yield:

(1.3)

To find how the present value of the coupons change as C varies we take the differential and yield the ordinary separable differential equation:

(1.4)

Which then becomes the first order linear differential equation:

(1.5)

Now we define the formula for the present value of a Bond given by the equation:

(2.1)

Par = par amount of the bond (the initial value of the bond, typically 100, 1000, etc…)

N = value at termination

We use this formula to bootstrap the zero yield curve.

However we know that the summation is equal to equation 1.3 and we can also more generally say that the final coupon payment is captured in the eq. 1.3 as well. Therefore the equation we are left with is:

(2.2)

After getting this equation we want to see how the Present Value of the bond varies as the coupon payment varies, so we get the partial differential equation:

(2.3)

which becomes the ordinary differential equation

(2.4)

(2.5)

We see that equation 2.5 = equation 1.5. Thus we can postulate that the present value of the bond varies linearly when C changes. Therefore we can create a general equation to find the present value of a bond for any C when t and r of 1…n  are held constant. This equation is the linearized equation of the bond price given an initial value.

(3.1)

Csub1 = New coupon payment

dC = CsubZero – C1

PvBond(CsubZero) = value of the bond at initial coupon payment.

One can then set eq. 2.2 = eq. 3.1 to yield this equation:

(3.2)

To solve for the zero coupon rate we set C(1) = 0 to get

(3.3)

You can then solve for r using normal algebraic methods.

DCF Model updated

My DCF model has been updated with more automation, calculation of CAGR, and an example with numbers.

Finally, a Libertarian I can (somewhat) agree with

For the most part, I disagree with the entire conservative/libertarian notion of completely free markets. I also really disagree that free-markets create exogenous social-change within a population (such as in the case with slavery, civil rights, feminism, or the “hippy” movement) and that the government is the only oppressive force is society.

Kerry Howley, an editor at Reason magazine, who happens to coincidentally be my cousin, has views that I can actually agree with. Broad social change isn’t brought about by an exogenous factor, such as the “market mechanism” but is endogenous coming from within the populous. However, societal values and social norms can also be just as oppressive as government legislation.

While Jim Crow was codified into law, it was ingrained into society not because of law but because of accepted social norms in the south. It was, and in many places still is, accepted that blacks were inferior to whites – less intelligent, less trustworthy, more violent, etc… And that blacks, in turn, should be subservient to their white counterparts. The question is, how do we deal with these social norms and a culture which supports oppressive behavior? With an oppressive culture – from it will stem an oppressive government, being that government is simply a collection of individuals who share like views and decide to thus codify these views into some sort of law. But even without government the idea that the oppression would stop because of the market-mechanism just doesn’t hold water. People can be quite irrational and choose to deny service or give service to individuals, irrespective of the economic consequence – due to societal pressure to do so. In fact, the collusion of a society against a certain group can cause the group to be oppressed, even when adjusting for the economic consequences which could be ambiguous in either direction.

In the following article Kerry expresses her concern for the typical libertarian dismissal of social norms as an oppressive force and road block to the true libertarian vision of freedom. Where her and I differ is the prescription. I believe government gives even undeserved groups the ability to petition and change oppressive social norms through the force of law. Without government, by what mechanism do we have to oppose oppressive social norms. The supply/demand dynamics of a free-market system may not be the cure-all. It would not stop lynching, beatings, and certainly would not stop segregation.

The government is a tool, which can be both good and bad. It can be used as a tool for oppressive legislation (such as Jim Crow and the Patriot act) or it can be used as a tool that secures the right of an individual to participate fairly – and freely – within a market. The Government, just as the market, is ambiguous in its aims. But the market cannot be guided without the rule of law – and it becomes subject to irrationality, biases, and prejudices of man.

The article can be found here – http://reason.com/archives/2009/10/20/are-property-rights-enough

I encourage you to read it, as she explains, more eloquently, her ideas than I ever could.

We’re All Cultural Libertarians

Freedom is about more than just the absence of government.

Kerry Howley

“It was amazing to me how quickly she overturned the power structure within her family,” Leslie Chang writes in Factory Girls, her 2008 book on internal migration within China. Chang is marveling at Min, a 17-year-old who left her family farm to find work in a succession of factories in the rapidly urbanizing city of Dongguan. Had Min never left home, she would have been expected to marry a man from a nearby village, to bear his children, and to accept her place in a tradition that privileges husbands over wives. But months after Min found work in Dongguan, she was already advising her father on financial planning, directing her younger siblings to stay in school, and changing jobs without bothering to ask her parents’ permission.

New Page! Excel spreadsheets.

I’ve posted up a new page which will contain any and all excel spreadsheets/models I create. Feel free to browse through (the link is at the top of the page under the website title).