On Hedge Funds

OK kiddies, time to discuss business, but I promise this post will quickly degenerate into something a bit more light-hearted.

As some of you out there in the Good Dinosaur readership world (now with a Facebook Group and a Facebook Page. What's the difference, you ask? Who knows! Join / Fan them both!) I've ventured out and started a company. As mentioned in a previous post, I've experienced some struggles with getting the mish-mash of thoughts up in my head-space down into one of those so called “plans of business”, or for our Spanish readers, “plans de business.”

I've done some research on how to write a business plan and even found some services that offer a template you can drag and drop information into and, presto, instant business plan! While this would have be an easy solution, it did not seem like a great idea. After all, it is my company's business plan and my company, like a beautiful snow flake fluttering in the cool Vermont winter air, is unique from all others and should not, nay, cannot be expressed via a boiler plate document.

One article I've grown particularly fond of is the Harvard Business Review posting on How to Write A Great Business Plan. It describes the mindset to take and what to cover when writing a business plan:

• Describe the market you are entering
• Explain the opportunity that you are seeking to capture
• Illustrate how you will accomplish your vision
• Tell your readers who you and your team are

Quick, clean, and to the point! How do you like them apples?

Well, in my past employment-life I spent most of my days reading over business plans, so I wondered why I did not have a better grasp on how to conger these documents into existence. And then it hit me. All the business plans I'd viewed were for start-up hedge funds, and business plans for these companies are unique little beasts.

Lets see how a typical hedge fund business plan would be composed if we followed the HBS recommended method. Lets first layout the basics of our fictitious fund:

1. The Name. Select a name for our new fund, the more old-money sounding and urbane the better. Expensive vacation destinations are a good choice, as are street names, or city locations. Make sure to add “Capital” to the end!

Example. Lincoln Square Capital, LLC

2. The Logo. Pick a logo that looks solid and sophisticated, and employs grey-scale (colors are for hippies, and hippies aren't skilled at managing money).

Example.

Ok! We are now set to move on to the rest of our business plan:

• The Market: Here we state the basics about the hedge fund industry. Really, all that is ever described is the overall size and who can invest.
  
  
  Example. The hedge fund market is large and expanding, quickly approaching $2 trillion in assets under management. Hedge funds are large, unregulated pools of capital that seek to invest in attractive opportunities and make the funds' investors a boat load of cash. The minimal investment in most hedge funds often begins at $500,000 so only rich people should really continue reading.


• The Opportunity: In this section we typically see a quick claim that through well disciplined investing, an investor in the fund stands to gain handsomely.
  
  
  Example. Please see the accompanying graphic to illustrate the opportunity presented by investing in Lincoln Square Capital, LLC:
  


• How we will do it: This section is pretty standard, the example below best depicts how this part is handled.
  
  
  Example. Please see the accompanying graphic to illustrate our investment technique:
  Thank you. Now give us money.


• Our Team: This is the most important section, but fortunately, follows a Mad Libs format and really only describes one person: the fund's founder. Let's all play along!
  
  1. Small investment bank name. Example: Morgan Stanley
  2. Trading-oriented job name. Example: Convertible Bonds Trader
  3. Better investment bank name. Example: Goldman Sachs
  4. Hedge fund name. Example: SailFish
  5. Number between 10-30. Example: 20
  6. Number between 1-1000. Example: 618
  7. Pick either “Park” or “Madison”. Example: Madison
  8. Ivy League college name. Example: Princeton University
  
  Now lets see how we did!
  
  
  Example. Jonathan Smith founded Lincoln Square Capital, LLC in 2009. Prior to founding Lincoln Square Capital, LLC, Jonathan worked at (1) Morgan Stanley as a (2) convertible bonds trader. After several impressive years of service he moved on to (3) Goldman Sachs. Next, Jonathan jumped to the prestigious hedge fund, (4) SailFish, where he achieved annualized returns of 25% (assumes (5) 20 times leverage).
  
  Seeking to capitalize on his unique talents and money management capabilities, Jonathan launched Lincoln Square Capital, LLC, headquartered at (6) 618 (7) Madison Avenue. The fund is currently accepting qualified investors.
  
  Jonathan is an esteemed alumni of (8) Princeton University and enjoys polo and wine.

As a bonus, stealthily posting a picture to a non-descriptive Flickr account that illustrates, in addition to the impressive credentials listed, that the fund manager might be related to The Most Interesting Man In The World always helps. Add an anonymous posting to Seeking Alpha, DealBreaker, or any other finance oriented website with a link to the aforementioned picture to generate greater interest in the fund.

Example.

Commenter #17: "Looks like Jonathan at Lincoln Square knows how to water ski"

And that's it! We are done! In short, a business plan for a hedge fund has little to it. The main product / service that gets the lion share of coverage in a typical business plan write-up is shrouded in secret. Like a magician, a fund manager will never divulge how his investment magic works. So the entire section on the service / product is encased in a "black box," leaving little else to cover.

Maybe I should forget this whole “regular business” stuff and just start a hedge fund? I already know how to market it.

CollegeJobConnect Beta

I'm excited to bring you news on GoodDinosaur's newest corporate sponsor, the CollegeJobConnect!



The CollegeJobConnect is an exciting new web-service that connects college undergraduates and employers. Currently, there are few avenues for college undergraduates to make the jump from academics to a professional career. Similarly, there are few options for employers to recruit undergraduates, and those that do exist are costly and inefficient.

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We are breaking down barriers and providing connectivity to an under-served, under-recognized talent pool. By organizing the college demographic into one location and providing employers with unprecedented and easy access, the CollegeJobConnect will be the go-to place where talented, educated individuals are discovered and hired.

Triangle Problem + Solution

Question: "If you break a straight line randomly in two places, what is the probability that you can form a triangle from the resulting three pieces?"

Please provide the proof + code for a simulation of 10,000 trails! Will post the solution tomorrow so get crackin!

------------------------------------------

Solution:

• View The Proof
• View The Code

First off, congratulation are in order to a Mr. Paul R. and a Mr. Dan D. who both successfully utilized the higher power of numbers and reached the correct answer. A slow clap to you both. A special mention is in order for a Mr. Frank I. who uncovered about 80% of the solution, and to a Mr. Elliot G. who at least attempted the problem (percentage of success was not capable of being calculated for this last attempt).

The Proof. We first have to determine what, when given three different lines of varying lengths, is required to construct a Triangle? In order to create a triangle from three different lines of varying lengths, we need the following condition to hold:

Long side < short side + medium side

Now, looking at the posed question, lets say that the stick’s length is L, and we have two random breaks, a and b. We can draw the following representation:


We can see that, in this case, a < b. We can also see that there are three lengths that result from this break, x, y, and z. We have the following equations now:

1. x + y + z = L
2. a < b
3. x = a
4. y = b – a
5. z = L – b

So we have to think about the value-space that a and b can take on, namely that 0 < a < L and 0 < b < L, or graphically:


This is a representation of all possible values a and b can take on. Now let’s assume that x >= y >= z so from the starting condition that must be fulfilled to make a triangle, we have:

x < y + z => a < (b – a) + (L – b) => a < -a + L = a < L/2

So in order for a triangle to be the result, a must be less than half of the entire length. Furthermore, because x = a and x is the largest, y and z must also be less than half of length L. We see that no single side can be greater than or equal to L/2 if we want to be able to make a triangle from the sides.

So we can update our equations:

1. x + y + z = L
2. a < b
3. x = a and x < L/2
4. y = b – a and y < L/2
5. z = L – b and z < L/2

So we can now update our set of values drawing – we know that a < b and a < L/2 from updated equation #3, so:


The values of that a and b can take on, when a < b, that will produce a triangle are now outlined in green. Next, from updated equation #5 we have that L – b < L / 2, which equals b > L / 2:


The values of that a and b can take on, when a < b, that will produce a triangle are now outlined in green. Finally from updated equation #4 we have that b – a < L / 2, which equals b < a + L / 2 (this is a linear condition – line has a slope of 1 and b intercept of L/2:


So the area that meets all of these conditions is our winner (in green):


Which we can see is equal to 1/8 (0.125) of the possible values.

However, remember that this assumes that a < b, and because we know that a and b are both random numbers, they are interchangeable, so we can also have the following situation:


So this scenario must be taken into account. We now assume a > b, which yields the following starting equations:

1. x + y + z = L
2. a > b
3. x = b and x < L/2
4. y = a – b and y < L/2
5. z = L – a and z < L/2

We are still working with the same initial work space for a and b, but we have a different limitation being applied, namely a > b.

If we rearrange all these new equations as we did above, we arrive at the following conditions:

Starting Condition: a > b
From #3: b < L / 2
From #4: b > a – L / 2
From #5: a > L / 2

Which we can plot graphically:


And the only area of intersection for all equations mirrors what we found before, reflected across the line b = a:


Finally, we combine both scenarios for a > b and b < a and the resulting areas that satisfy our starting stipulation (long < medium + short), and we get the following result set:


Which yields and answer of 1/8 + 1/8 = 1/4 or 0.25 or 25%. So if you break a straight line randomly in two places, the probability that you can form a triangle from the resulting three pieces is 25%.

The Code. The code to run the simulation. This is written in Ruby.

#!/usr/bin/ruby
numOfTrials = 10000
numTriangles = 0

numOfTrials.times do

# generate two random breaks, ordered
breaks = [ rand, rand ].sort

# load the length calculations via the breaks into an "lengths" array
# order the lenghts
lengths = [

breaks[0] ,
breaks[1] - breaks[0] ,
1 - breaks[1]

].sort

# add 1 to triangle var if we have a triangle
numTriangles += 1 if lengths[2] < lengths[0] + lengths[1]

end

pct = numTriangles.to_f / numOfTrials * 100

puts "Number of Trials: " + numOfTrials.to_s
puts "Number of Triangles: " + numTriangles.to_s
puts "Percentage: %" + pct.to_s

Running this simulation produces results that cluster around the expected value of 25%.