Flash Boy Velocity Problems
The new book by Michael Lewis
“Flash Boys” discusses how Wall Street is now using faster cables between
Chicago and New Jersey to trade faster.
A millisecond or two does not seem like much time but Wall Street firms
can make a lot of money buying and selling quickly.
A firm that has knowledge of a large buy order at $20 per share may be able to snap up all available shares at $19.9 and screw their customer and that is what modern Wall Street is all about.
A firm that has knowledge of a large buy order at $20 per share may be able to snap up all available shares at $19.9 and screw their customer and that is what modern Wall Street is all about.
Here is the cite to Flash Boys on Amazon:
It is a highly entertaining
and informative book.
I have written a finance math problem that explains why Wall Street firms are willing to pay a lot of money to make quicker trades.
http://dailymathproblem.blogspot.com/2015/03/aflashboysfinanceproblem.html
This post uses the issues raised by Flash Boys to motivate velocity and distance problems. Velocity and distance problems are generally motivated by problems pertaining to falling balls or rockets so these problems are a bit different.
Question: The new fiber line between Chicago and New
Jersey was able to transmit trade information in 13 milliseconds. The line was 827 miles long? What is the speed of messages on the new
line? Express the answer in miles per
second and kilometers per second.
Answer: There
are 1000 milliseconds in one second so it should take 13/10000 seconds to
travel the 827 miles. This means the
trade is traveling at 827/0.013 miles per second.
827/0.013 is equal to 63,615
miles per second.
There are 1.60934 kilometers
in a mile. This means that the trades
travel at 102,379 kilometers per second.
Question: Prior to the construction of the new line trade information between Chicago and New Jersey took between 14.6 and 17.0 milliseconds to arrive depending upon what line was used? Assume that all messages travel at the speed calculated in the previous question. (I am not sure whether this assumption is correct but some lines are straighter and shorter than others so this problem is predicated on the assumption that differences in travel time are due to length of line.)
How long is the line where it
takes 14.6 milliseconds to make the trip?
How long is the line where it takes 17.0 milliseconds to make the trip?
Answer: WE know that Distance is equal to speed x
time. Speed is 63,615 miles per
second. Time is either 0.146 seconds or
0.017 seconds.
Calculation of Distance
Message Traveled In X Seconds


Seconds

0.0146

0.017

Speed Miles Per Second

63,615

63,615

Distarnce Miles

Seconds * Speed

Seconds * Speed

Distance Miles

929

1081

At 0.0146 seconds the cable
is 929 miles. At 0.017 seconds the
cable is 1081 miles.
This could also be solved as
a ratio problem.
D1/S = 827/0.013 =
D2/0.0146 = D3/0.017
So
D2 = 827
x 0.146/0.013 = 929
D3 =827 x 0.017/0.013 = 1,081
Question: The actual distance between New York and
London is 5576 kilometers. Assume there
is a direct shortest distance cable between the two cities and that the message
travels at the speed specified in the first question. How long does it take for the message to
travel from New York to London? How
long does it take for the message to arrive if the route is 10 percent longer
than the direct route?
Answer:
Below is the calculation of
the time it takes a message to travel from New York to London, assuming the
same speed as in the Chicago to New Jersey problem.
Calculation of Time it
Takes Message to Travel from New York to London


Direct Route

10% More than
Direct Route


Distance In Kilometers

5576

6133.6

Kilometers Per Second

102,379

102,379

Time Traveled In Seconds

D/V

D/V

Time Traveled in Seconds

0.05446

0.05991

Note there are 1,331
kilometers in 827 miles. The ratio of kilometers for New York to London to
Chicago to New Jersey should equal the ratio of the time traveled on the two
message trips
(5576/1331) =
(X/0.013)
So the direct New York to
London trip should take
(5576/1331) x 0.013 = 0.0544 seconds.
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