It was reported this week that after nine decades of operating in Australia, Ford will shut down production in the country due to the strength of the Australia dollar and high costs, particularly wages. Ford reported that production costs in Australia "are twice that of Europe and nearly four times higher than in Asia." The factories are planned to close within 3 years.
Strength of the Australian dollar would make it more costly to operate there. How exactly has the Australian dollar fared against other major currencies? The AUD-USD is currently around 0.97. This is actually on the lower end of the 52-week range, and further down from the peak of around 1.10 reached in mid-2011. However looking at the 5 year chart, AUD-USD was as low as 0.6 in late 2008. Since the start of 2011, it has been steadily strong at above 1. Looking at AUD-JPY, again a similar strengthening trend can be observed. After hovering around 80 for most of mid-2009 to mid-2012, it has surpassed 100 this year and currently is around 97.78. Finally, looking at AUD-EUR, the pattern can be seen as it has strengthened from around 0.5 in late 2008 to currently around 0.75, although it was as high as 0.85 in mid-2012.
Sources:
Friday, May 24, 2013
Thursday, May 23, 2013
Mixed Headlines Regarding Housing Market
There were mixed headlines regarding the house market today. Sales of new homes in the United States climbed to an annualized rate of 454,000 in April. This was the second highest monthly figure since July 2008. Year-over-year, the median selling price increased 14.9% to $271,600, which is the highest on record. Partially fueling the rising demand are the low interest rates. This week the average 30-year fixed mortgage rate was 3.59%.
Despite these news, limitation on home supply is put by the lack of equity to sell homes. In a report released by Zillow (NASDAQ: Z), a real estate information provider with a "database of more than 110 million U.S. homes," keeping the property listing tight are the "about 22 million Americans ... [who] lack enough home equity to move." The report stated that 44% of homeowners with mortgages had less than 20% equity in their home, and 20% is usually required to purchase a new home. This figure includes 13 million Americans, or a quarter of homeowners with mortgages, who were underwater, or owed more than what their homes are worth. Zillow projects that by Q1-2014, only about 1.4 million homeowners will regain positive equity.
Sources:
Despite these news, limitation on home supply is put by the lack of equity to sell homes. In a report released by Zillow (NASDAQ: Z), a real estate information provider with a "database of more than 110 million U.S. homes," keeping the property listing tight are the "about 22 million Americans ... [who] lack enough home equity to move." The report stated that 44% of homeowners with mortgages had less than 20% equity in their home, and 20% is usually required to purchase a new home. This figure includes 13 million Americans, or a quarter of homeowners with mortgages, who were underwater, or owed more than what their homes are worth. Zillow projects that by Q1-2014, only about 1.4 million homeowners will regain positive equity.
Sources:
Tuesday, May 21, 2013
A Look into Venture Capital Firms Behind Tumblr
Yahoo's acquisition of Tumblr was a boon for many, including Union Square Ventures and Spark Capital, the two venture capital firms who made initial investments into Tumblr during its infancy. The combined investments of $10 million translated to 47% ownership of the company, giving them a 50-fold return in the recent deal with Yahoo that valued Tumblr at $1.1 billion. The deal was also a spark for the New York start-up community, as Tumblr represents the "largest venture-backed purchase for a New York company."
Union Square Ventures, based in New York, describes itself on its website as a "small collegial partnership that manages $450,000,000 across three funds" and invests in companies that "create services that have the potential to fundamentally transform important markets." Spark Capital, based in Boston, manages about $1.5 billion. Common across both funds include Twitter.
On Tuesday, the front page of Union Square Ventures highlights the Tumblr acquisition, which characterizes Tumblr as "world's greatest platforms for self expression." Tumblr has 108 million blogs across its network, and generates about $13 million in revenue annually, which is the amount Yahoo generates daily. Nevertheless, it is the younger audience and mobile users whom Yahoo seeks to attract through this acquisition.
Sources:
Union Square Ventures, based in New York, describes itself on its website as a "small collegial partnership that manages $450,000,000 across three funds" and invests in companies that "create services that have the potential to fundamentally transform important markets." Spark Capital, based in Boston, manages about $1.5 billion. Common across both funds include Twitter.
On Tuesday, the front page of Union Square Ventures highlights the Tumblr acquisition, which characterizes Tumblr as "world's greatest platforms for self expression." Tumblr has 108 million blogs across its network, and generates about $13 million in revenue annually, which is the amount Yahoo generates daily. Nevertheless, it is the younger audience and mobile users whom Yahoo seeks to attract through this acquisition.
Sources:
Saturday, May 11, 2013
Column Generation Illustration
This example illustrates the first few steps of using column generation method to solve an integer program. In particular, this is a cutting beam example, where given beams of length L = 100, determine the minimum number of beams to satisfy demand of size n_i for length d_i: n1 = 21, d1 = 13, n2 = 39, d2 = 31, n3 = 61, d3 = 36, n4 = 14, d4 = 45
The initial objective function is to minimize x1 + x2 + x3 + x4, given the following constraints:
Objective value is 135. This is the dummy case where no cutting takes place. The dual solution is (1, 1, 1, 1), so the next LP to solve is: max p1 + p2 + p3 + p4 subject to 13*p1 + 31*p2 + 36*p3 + 45*p4 <= 100. The solution is (7, 0, 0, 0), and since the objective value of 7 is greater than 1, continue. Add this column in the next run. The pattern generated here (7, 0, 0, 0) means that 7 pieces of length 13 will be cut from the stock, whose length is 100.
Now with the addition of a new variable, minimize x1 + x2 + x3 + x4 + x5, given the following constraints:
The objective value has decreased to 117, and the dual solution is (1/7, 1, 1, 1), so the next LP to solve is: max 1/7*p1 + p2 + p3 + p4 subject to 13*p1 + 31*p2 + 36*p3 + 45*p4 <= 100. The constraint is the same as the earlier maximization problem. The solution is (0, 3, 0, 0), so this would be the next column to generate, given that the the objective value of 3 is still greater than 1. Continue this process.
The initial objective function is to minimize x1 + x2 + x3 + x4, given the following constraints:
| 1 | 0 | 0 | 0 | >= | 21 |
| 0 | 1 | 0 | 0 | >= | 39 |
| 0 | 0 | 1 | 0 | >= | 61 |
| 0 | 0 | 0 | 1 | >= | 14 |
Objective value is 135. This is the dummy case where no cutting takes place. The dual solution is (1, 1, 1, 1), so the next LP to solve is: max p1 + p2 + p3 + p4 subject to 13*p1 + 31*p2 + 36*p3 + 45*p4 <= 100. The solution is (7, 0, 0, 0), and since the objective value of 7 is greater than 1, continue. Add this column in the next run. The pattern generated here (7, 0, 0, 0) means that 7 pieces of length 13 will be cut from the stock, whose length is 100.
Now with the addition of a new variable, minimize x1 + x2 + x3 + x4 + x5, given the following constraints:
| 1 | 0 | 0 | 0 | 7 | >= | 21 |
| 0 | 1 | 0 | 0 | 0 | >= | 39 |
| 0 | 0 | 1 | 0 | 0 | >= | 61 |
| 0 | 0 | 0 | 1 | 0 | >= | 14 |
The objective value has decreased to 117, and the dual solution is (1/7, 1, 1, 1), so the next LP to solve is: max 1/7*p1 + p2 + p3 + p4 subject to 13*p1 + 31*p2 + 36*p3 + 45*p4 <= 100. The constraint is the same as the earlier maximization problem. The solution is (0, 3, 0, 0), so this would be the next column to generate, given that the the objective value of 3 is still greater than 1. Continue this process.
Thursday, March 21, 2013
Interest Rate Swap and Swaption
Interest rate swap is also known as plain vanilla swap, or fixed and fixing swap. It is the exchange of cash flows on a notional value (say $1 million) given a fixed interest rate (say 3%), for the cash flows from on the same notional value given a floating interest rate (say LIBOR + 0.5%). The notable aspect is that the notional value never gets traded, and thus is rather arbitrary. Over the life of the swap, the payments are made to the counterparty at intervals that are usually 6 months. The swap benefits entities that may want more exposure or mitigate exposure to interest rate risk.
Swaption is an option on the swap, whereby the writer has the option but not the obligation to enter into a swap agreement by a certain date. But furthermore, the contract specifies whether the buyer will be the recipient of the fixed or floating rate cash flows.
Sources:
Swaption is an option on the swap, whereby the writer has the option but not the obligation to enter into a swap agreement by a certain date. But furthermore, the contract specifies whether the buyer will be the recipient of the fixed or floating rate cash flows.
Sources:
Tuesday, March 19, 2013
Simulation of Simplified Version of Showcase Showdown Using MATLAB
See previous related post: Showcase Showdown Analysis: Circular Reasoning and Oscillating Nash Equilibrium
In the show The Price Is Right, contestants spin the Big Wheel, which has 20 sections randomly distributed, from 5 cents to $1.00 in 5-cent increments. The objective is to get the highest amount without going over $1, with one initial spin and an optional second spin. Clearly the first contestant is at a disadvantage, as the later contestants simply opt for the second optional spin if the first spin is not enough. For the first contestant, there needs to be a strategy consisting of a critical value for the first spin, at or above which the second spin is not preferred, as the probability of going over is too high. It's also a discrete case, as the critical value can only be from 5 to 100, in increments of 5.
In the actual show, there are three contestants. For the sake for simplicity, only two contestants are assumed in this simulation. In the case of tie, rerun the trial. For each possible critical value from 5 to 100 cents, 1 million trials are run in this Monte Carlo simulation to determine the winning percentage of player 1 under that strategy.
Here's the graph with the critical point on the x-axis and the winning percentage on the y-axis:
The maximum occurs at critical value of 55, corresponding with a winning percentage of 45.55%. At a value of 50, the winning percentage is up there at 45.22%. Even closer is 45.52% at a value of 60. The winning percentage gradually tapers off. Even at a value of 70, the winning percentage is still at 44.25%. Here's the MATLAB script to generate the data and graph:
In the code above, simply vary the value of n to change the number of trials at each strategy. Of course, this optimal strategy will be different if the third contestant is taken into consideration in the actual game.
In the show The Price Is Right, contestants spin the Big Wheel, which has 20 sections randomly distributed, from 5 cents to $1.00 in 5-cent increments. The objective is to get the highest amount without going over $1, with one initial spin and an optional second spin. Clearly the first contestant is at a disadvantage, as the later contestants simply opt for the second optional spin if the first spin is not enough. For the first contestant, there needs to be a strategy consisting of a critical value for the first spin, at or above which the second spin is not preferred, as the probability of going over is too high. It's also a discrete case, as the critical value can only be from 5 to 100, in increments of 5.
In the actual show, there are three contestants. For the sake for simplicity, only two contestants are assumed in this simulation. In the case of tie, rerun the trial. For each possible critical value from 5 to 100 cents, 1 million trials are run in this Monte Carlo simulation to determine the winning percentage of player 1 under that strategy.
Here's the graph with the critical point on the x-axis and the winning percentage on the y-axis:
The maximum occurs at critical value of 55, corresponding with a winning percentage of 45.55%. At a value of 50, the winning percentage is up there at 45.22%. Even closer is 45.52% at a value of 60. The winning percentage gradually tapers off. Even at a value of 70, the winning percentage is still at 44.25%. Here's the MATLAB script to generate the data and graph:
x = zeros(1,20);
y = zeros(1,20);
for crit = 1:20
x(crit) = 5*crit;
n = 1000000;
win = zeros(1,n);
for i = 1:n
done = false;
while ~done
firstSpin = ceil(20*rand)*5;
if firstSpin >= x(crit)
playerOne = firstSpin;
else
playerOne = firstSpin + ceil(20*rand)*5;
end
if playerOne > 100
playerOne = 0;
end
playerTwo = ceil(20*rand)*5;
if playerTwo < playerOne
playerTwo = playerTwo + ceil(20*rand)*5;
end
if playerTwo > 100
playerTwo = 0;
end
if playerOne > playerTwo
win(i) = 1;
done = true;
elseif playerOne < playerTwo
done = true;
end
end
end
y(crit) = sum(win)/n;
end
plot(x,y); grid on; xlabel('player 1 critical point'); ylabel('player 1 winning percentage')
In the code above, simply vary the value of n to change the number of trials at each strategy. Of course, this optimal strategy will be different if the third contestant is taken into consideration in the actual game.
Time Difference: New York & Sydney
Calculating the time difference between New York and Sydney is tricky, not only because both cities observe daylight saving time, but they also are on the opposite hemispheres, so one city's summer is winter for the other. Sydney is GMT +1000 and New York is GMT -0500, yet the time difference between the two cities is rarely 15 hours.
For New York, DST is observed from the second Sunday in March to first Sunday in November. For Sydney, DST is observed from the first Sunday in October to the first Sunday in April. For the sake of convenience, the four relevant Sundays for 2013 are as follows: March 10, Nov 3, Oct 6, and April 7, respectively.
Sorting the dates by groups:
Sources:
For New York, DST is observed from the second Sunday in March to first Sunday in November. For Sydney, DST is observed from the first Sunday in October to the first Sunday in April. For the sake of convenience, the four relevant Sundays for 2013 are as follows: March 10, Nov 3, Oct 6, and April 7, respectively.
Sorting the dates by groups:
- Jan 1 to March 10: Sydney on DST, New York off DST --> 16 hour difference
- March 10 to April 7: both on DST --> 15 hour difference
- April 7 to Oct 6: Sydney off DST, New York on DST --> 14 hour difference
- Oct 6 to Nov 3: both on DST --> 15 hour difference
- Nov 3 to Dec 31: Sydney on DST, New York off DST --> 16 hour difference
Sources:
Time Difference: New York & London
The time difference between New York and London is crucial, especially for the financial service sector. For most of the year, London is 5 hours ahead of New York. However, while both areas observe daylight saving in summer, the onset and ending dates aren't exactly aligned, causing a shift in the time difference for moments in the spring and fall.
In the United States, daylight saving begins on the second Sunday in March, and lasts until the first Sunday in November. In Britain, it begins on the last Sunday in March, and lasts until the last Sunday in October. So in all, daylight saving in London begins later, and ends earlier. During those gap periods, New York is only 4 hours behind London, as opposed to the 5 hour difference, when both cities are on daylight saving or when both cities are off. Because there isn't a moment at which London is on and New York is off daylight saving, the London - New York time difference will never be 6 hours.
In conclusion, the time difference between New York and London is as follows:
In the United States, daylight saving begins on the second Sunday in March, and lasts until the first Sunday in November. In Britain, it begins on the last Sunday in March, and lasts until the last Sunday in October. So in all, daylight saving in London begins later, and ends earlier. During those gap periods, New York is only 4 hours behind London, as opposed to the 5 hour difference, when both cities are on daylight saving or when both cities are off. Because there isn't a moment at which London is on and New York is off daylight saving, the London - New York time difference will never be 6 hours.
In conclusion, the time difference between New York and London is as follows:
- First Sunday in November - second Sunday in March: 5 hour (both off DST)
- Second Sunday - last Sunday in March: 4 hour
- Last Sunday in March - last Sunday in October: 5 hour (both on DST)
- Last Sunday in October - first Sunday in November: 4 hour
Quick Glance into Ryanair
Ryanair, the Dublin-based airliner known for its operation of low-cost passenger airline service, is in the news for signing an order from The Boeing Company worth $15.6 billion. Ryanair is one of the few airliners that orders exclusively from Boeing, and has now expanded its fleet by 30% to over 400 units in order to grow its capacity to over 100 million across Europe by 2018. Boeing (NYSE: BA), which has seen its stock price soar by over 10% in the past month to close at around $85, welcomed the news, as its Commercial Airplanes CEO Ray Conner remarked the Next-Generation 737 "as the most efficient, most reliable large single-aisle airplane flying today," which "has been and will continue to be the cornerstone of the Ryanair fleet."
Ryanair Holdings (NASDAQ: RYAAY), the holding company for Ryanair, has market cap of around $12 billion. Its net profit margin in Q4-2012 fell to 1.87% after posting 12.76% for Q3. A visit to Ryanair's website indeed illustrates the low-cost business that it operates. There's a roundtrip from London to Dublin one month in advance available for only 44 GBP. On flight search websites that offer comparison, it becomes even more evident that the $56 value is significant that of its competitors, including $194 from British Airways. The low fares do come at some costs though; as users go on the website to search for flights, they are prompted to enter a "security code," which is obtained by viewing a short advertisement. Nevertheless, the colossal deal was signed today in New York.
Sources:
Ryanair Holdings (NASDAQ: RYAAY), the holding company for Ryanair, has market cap of around $12 billion. Its net profit margin in Q4-2012 fell to 1.87% after posting 12.76% for Q3. A visit to Ryanair's website indeed illustrates the low-cost business that it operates. There's a roundtrip from London to Dublin one month in advance available for only 44 GBP. On flight search websites that offer comparison, it becomes even more evident that the $56 value is significant that of its competitors, including $194 from British Airways. The low fares do come at some costs though; as users go on the website to search for flights, they are prompted to enter a "security code," which is obtained by viewing a short advertisement. Nevertheless, the colossal deal was signed today in New York.
Sources:
- http://www.forbes.com/sites/davidewalt/2013/03/19/boeing-lands-a-15-6-billion-737-order-from-ryanair/
- http://www.nytimes.com/2013/03/20/business/boeing-secures-15-6-billion-order-from-ryanair.html?_r=0
- https://www.google.com/finance?q=NYSE%3ABA&ei=yKFIUfj7HZL-rAGRew
- https://www.google.com/finance?q=NASDAQ%3ARYAAY&ei=vpZIUai9A4eNrAH9rgE
- https://www.bookryanair.com/SkySales/booking.aspx?culture=en-gb&lc=en-gb
- http://www.skyscanner.com/flights/lond/dub/130420/130427/airfares-from-london-to-dublin-in-april-2013.html
Thursday, March 7, 2013
Acceptance Rejection Method for Simulation
In simulation, use the acceptance rejection method to simulate a random variable X with density f(x), for which there is no direct method to use the inverse transformation to generate it. However, suppose that there is a known algorithm to generate random variable Y with density g(x) such that f(x) / g(x) is bounded, that is f(x) / g(x) ≤ c. To find c, take the derivative of f(x) / g(x) to find the maximum value. Here's the algorithm:
- Generate Y according to the known algorithm
- Generate U, the uniform distribution from 0 to 1
- If U ≤ f(Y) / c*g(Y), then set X = Y
- Otherwise, start all over
Note that to produce each copy of X, the loop runs until condition 3 is satisfied. In the end, c become the average number of runs to produce a copy of X. In the following, a random variable with f(x) = 2x*e^(-x^2) is generated using MATLAB. The chosen g(x) = e^(-x), so f(x) / g(x) = 2x*e(x-x^2), and the maximum value c turns out to be exactly 2.
There's no way to verify that this method does indeed generate a random variable with the given f(x). Instead, to test the accuracy of the algorithm here, two values (a and b) are inputted at the end. The program first calculates the integral of f(x) from [a, b], or the probability that X falls between the range of [a, b]. Finally, the program uses the simulated copies of X to count the proportion of the copies of X that fell in that interval of [a, b]. The two values should be close to each other.
func = @(x) 2*x.*exp(-x.^2);
n = 100000;
results = zeros(1,n);
numTimes = zeros(1,n);
for i=1:n
trialDone = false;
count = 0;
while ~trialDone
count = count + 1;
y = -log(rand);
u = rand;
if u <= y*exp(y-y^2)
results(i) = y;
trialDone = true;
end
end
numTimes(i) = count;
end
a = input('Lower bound for x: ');
b = input('Upper bound for x: ');
disp 'Evaluated integral using f(x): ';
quad(func, a, b)
disp 'Simulated integral using acceptance / rejection method: ';
length(results(results>a & results
disp 'Average trial runs per simulated copy: '
mean(numTimes)
Choose values between 0 and 2.5 for a and b, for over 99.8% of the data are in that range. Upon running the script using different values, the calculated integral closely matches the frequency proportion obtained from the simulation technique using the acceptance rejection method. While this does not verify the accuracy of the method, it at least illustrates that the resultant output resembles what the expected output should be. Finally, the resultant average trial runs per simulated copy hovers closely to 2 as expected.
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