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Portfolio manager Stephen Goddard has run one of the best performing U.S.<br>mid-cap funds over the last three years by focusing [http://tinyurl.com/ku6vjks uggs on sale] deeply discounted companies rather than the next great growth story.<br>The $322 million Touchstone Mid-Cap Fund has returned an annualized 20.5 percent since 2010, a performance that puts it in the top five percent among the 334 funds in the mid-cap blend category, according to fund tracker Morningstar. Goddard, who runs the fund through the London Company, a sub-adviser, credits the gains to his focus [http://tinyurl.com/ku6vjks uggs on sale] companies he deems safe; those with high margins, large amounts of free cash and low-priced valuations.<br><br>"It's easier to minimize downside loss than it is to find the next big winner. It's like winning by default," Goddard said.<br>Goddard's strong performance has come amid a two-year stock rally. Soon, he may have to prove that he can continue to find stable companies even when the market is not, said Todd Rosenbluth, [http://tinyurl.com/ku6vjks http://tinyurl.com/ku6vjks] director of mutual fund research at S&P Capital IQ.<br><br>A pullback [http://tinyurl.com/ku6vjks uggs on sale] the Federal Reserve's bond-buying stimulus program, a possible showdown over the U.S. debt ceiling and mounting tensions in Syria could all pull down the benchmark Standard and Poor's 500 index, which has gained nearly 18 percent for the year to date.<br><br>"We just don't have a history with how management will do in down markets," Rosebluth said. Goddard has only run the fund since 2011, though the fund outperformed its category in each of those years.<br><br>For his part, Goddard said that a volatile market would have little effect [http://tinyurl.com/ku6vjks uggs on sale] his strategy.<br>"It's like playing a good prevent defense," he said, in reference to the American football defensive alignment designed to stop a big loss of ground or a touchdown.<br>He runs a concentrated portfolio of 30 to 35 companies, with close to half of his fund's assets invested in the 10 largest positions. Top-holdings M&T Bank and deepwater rig operator Atwood Oceanics each make up approximately 4.4 percent of assets, followed by uniform maker Cintas at 4.3 percent.<br><br><br>He's owned Whirlpool since late 2011, for example, because the lack of aggressive competition in the appliance market allows the company to have higher margins, he said. A rebound in the U.S. housing market and strong demand from China also made the company attractive, Goddard added.<br>Whirlpool is up 73 percent over the last 12 months, and pays a dividend of 1.8 percent.<br><br>"This is a company that's considered mature, but it throws off loads of cash," he said.<br>More recently, Goddard has been buying specialty shoe retailer Deckers Outdoor Company and mattress-maker Tempur Sealy International.<br>Deckers Outdoor, which has a market cap of $2.5 billion, is best known as the maker of the [http://imageshack.us/photos/popular+Ugg popular Ugg] line of boots and shoes.<br><br>"Everybody thinks this is a fashionable item, but actually it is a steady high margin product which may have seen better growth days but the company has ample amounts of cash flow," Goddard said.<br>The company's shares peaked at nearly $118 in October 2011 and fell to a low of just under $30 in late 2012 because of slow sales during a warm winter and higher costs of sheepskin. Now selling slightly above $60, shares are up 54 percent for the year.<br><br>Approximately 85 percent of the company's revenue comes from sales of [http://tinyurl.com/ku6vjks uggs on sale], Goddard said, but it is expanding into sandals and men's shoes too.<br>In its July earnings call, Decker said it expects its margins to increase to approximately 46.8 percent, slightly above the median of 46 percent among peers such as Crocs, Steve Madden and Skechers USA, according to Thomson Reuters data. The company, which does not pay a dividend, trades at a price to forward cash flow of 11.8, well below the median of 27.8 among its competitors.<br><br>Goddard said that he is still buying Decker because he believes in "letting his winners run" and typically only sells when a company starts to significantly underperform, he said.<br>Goddard has also been buying shares of Tempur Sealy International, which was formed from the merger of the two largest U.S. mattress companies in late 2012. Goddard began buying into Tempur-Pedic, the larger company of the two before the merger, in June 2012 when the shares hit $23.<br><br>They have since rebounded to approximately $41, giving him a gain of 78 percent.<br>"The mattress business is not going away," he said.<br>The fund charges an annual fee of 92 cents per $100 invested, a level that Morningstar considers below average for an actively managed fund. It pays a dividend yield of 1.5 percent.<br><br>(Reporting by David Randall; editing by Linda Stern and Andrew Hay)
| name = Tutte 12-cage
| image = [[Image:Tutte 12-cage.svg|240px]]
| image_caption = The Tutte 12-cage
| namesake = [[W. T. Tutte]]
| vertices = 126
| edges = 189
| automorphisms = 12096
| girth = 12
| diameter = 6
| chromatic_number = 2
| chromatic_index = 3
| properties = [[Cubic graph|Cubic]]<br>[[Cage (graph theory)|Cage]]<br>[[Hamiltonian graph|Hamiltonian]]<br>[[Semi-symmetric graph|Semi-symmetric]]<br>[[Bipartite graph|Bipartite]]
}}
In the [[mathematics|mathematical]] field of [[graph theory]], the '''Tutte 12-cage''' or '''Benson graph'''<ref name="SURV"/> is a 3-[[regular graph]] with 126 vertices and 189 edges named after [[W. T. Tutte]].<ref>{{MathWorld|urlname=Tutte12-Cage|title=Tutte 12-cage}}</ref>
 
The Tutte 12-cage is the unique (3-12)-[[cage graph|cage]] {{OEIS|A052453}}. It was discovered by C. T. Benson in 1966.<ref>Benson, C. T. "Minimal Regular Graphs of Girth 8 and 12." Canad. J. Math. 18, 1091&ndash;1094, 1966.</ref> It has [[chromatic number]] 2 ([[Bipartite graph|bipartite]]), [[chromatic index]] 3, girth 12 (as a 12-cage) and diameter 6. Its [[Crossing number (graph theory)|crossing number]] is 170 and has been conjectured to be the smallest cubic graph with this crossing number.<ref>Exoo, G. [http://isu.indstate.edu/ge/COMBIN/RECTILINEAR/ "Rectilinear Drawings of Famous Graphs"].</ref><ref>Pegg, E. T. and Exoo, G. "Crossing Number Graphs." Mathematica J. 11, 2009.</ref>
 
==Construction==
The Tutte 12-cage is a [[cubic graph|cubic]] [[Hamiltonian graph]] and can be defined by the [[LCF notation]] [17, 27, &ndash;13, &ndash;59, &ndash;35, 35, &ndash;11, 13, &ndash;53, 53, &ndash;27, 21, 57, 11, &ndash;21, &ndash;57, 59, &ndash;17]<sup>7</sup>.<ref>Polster, B. A Geometrical Picture Book. New York: Springer, p. 179, 1998.</ref>
 
It is the incidence graph of the generalized hexagon GH(2,2) with 63 points and 63 lines.<ref name="SURV"/>
 
The [[Balaban 11-cage]] can be constructed by excision from the Tutte 12-cage by removing a small subtree and suppressing the resulting vertices of degree two.<ref>Balaban, A. T. "Trivalent Graphs of Girth Nine and Eleven and Relationships Among the Cages." Rev. Roumaine Math 18, 1033&ndash;1043, 1973.</ref>
 
==Algebraic properties==
The automorphism group of the Tutte 12-cage is of order {{formatnum:12096}} and is a [[semi-direct product]] of the [[projective special unitary group]] PSU(3,3) with the [[cyclic group]] '''Z'''/2'''Z'''.<ref name="SURV">Geoffrey Exoo & Robert Jajcay, Dynamic cage survey, Electr. J. Combin. 15 (2008).</ref> Its acts transitively on its edges but not on its vertices, making it a [[semi-symmetric graph]], a regular graph that is [[edge-transitive graph|edge-transitive]] but not [[vertex-transitive graph|vertex-transitive]]. In fact, the automorphism group of the Tutte 12-cage preserves the bipartite parts and acts primitively on each part. Such graphs are called bi-primitive graphs and only five cubic bi-primitive graphs exist; they are named the Iofinova-Ivanov graphs and are of order 110, 126, 182, 506 and 990.<ref>Iofinova, M. E. and Ivanov, A. A. "Bi-Primitive Cubic Graphs." In Investigations in the Algebraic Theory of Combinatorial Objects. pp. 123&ndash;134, 2002. (Vsesoyuz. Nauchno-Issled. Inst. Sistem. Issled., Moscow, pp. 137&ndash;152, 1985.)</ref>  
 
All the cubic semi-symmetric graphs on up to 768 vertices are known. According to [[Marston Conder|Conder]], Malnič, Marušič and Potočnik, the Tutte 12-cage is the unique cubic semi-symmetric graph on 126 vertices and is the fifth smallest possible cubic semi-symmetric graph after the [[Gray graph]], the Iofinova&ndash;Ivanov graph on 110 vertices, the [[Ljubljana graph]] and a graph on 120 vertices with girth 8.<ref>{{citation
| last1 = Conder | first1 = Marston | author1-link = Marston Conder
| last2 = Malnič | first2 = Aleksander
| last3 = Marušič | first3 = Dragan | authorlink3 = Dragan Marušič
| last4 = Potočnik | first4 = Primož
| title = A census of semisymmetric cubic graphs on up to 768 vertices
| journal = Journal of Algebraic Combinatorics
| volume = 23 | year = 2006 | pages = 255–294
| doi = 10.1007/s10801-006-7397-3}}.</ref>
 
The [[characteristic polynomial]] of the Tutte 12-cage is
 
: <math>(x-3)x^{28}(x+3)(x^2-6)^{21}(x^2-2)^{27}.\ </math>
 
It is the only graph with this characteristic polynomial; therefore, the 12-cage is determined by its [[Spectral graph theory|spectrum]].
 
==Gallery==
<gallery>
Image:Tutte 12-cage 2COL.svg|The [[chromatic number]] of the Tutte 12-cage is 2.
Image:Tutte 12-cage 3color edge.svg|The [[chromatic index]] of the Tutte 12-cage is 3.
</gallery>
 
== References ==
{{reflist}}
 
[[Category:Individual graphs]]
[[Category:Regular graphs]]

Latest revision as of 12:44, 6 September 2014

Portfolio manager Stephen Goddard has run one of the best performing U.S.
mid-cap funds over the last three years by focusing uggs on sale deeply discounted companies rather than the next great growth story.
The $322 million Touchstone Mid-Cap Fund has returned an annualized 20.5 percent since 2010, a performance that puts it in the top five percent among the 334 funds in the mid-cap blend category, according to fund tracker Morningstar. Goddard, who runs the fund through the London Company, a sub-adviser, credits the gains to his focus uggs on sale companies he deems safe; those with high margins, large amounts of free cash and low-priced valuations.

"It's easier to minimize downside loss than it is to find the next big winner. It's like winning by default," Goddard said.
Goddard's strong performance has come amid a two-year stock rally. Soon, he may have to prove that he can continue to find stable companies even when the market is not, said Todd Rosenbluth, http://tinyurl.com/ku6vjks director of mutual fund research at S&P Capital IQ.

A pullback uggs on sale the Federal Reserve's bond-buying stimulus program, a possible showdown over the U.S. debt ceiling and mounting tensions in Syria could all pull down the benchmark Standard and Poor's 500 index, which has gained nearly 18 percent for the year to date.

"We just don't have a history with how management will do in down markets," Rosebluth said. Goddard has only run the fund since 2011, though the fund outperformed its category in each of those years.

For his part, Goddard said that a volatile market would have little effect uggs on sale his strategy.
"It's like playing a good prevent defense," he said, in reference to the American football defensive alignment designed to stop a big loss of ground or a touchdown.
He runs a concentrated portfolio of 30 to 35 companies, with close to half of his fund's assets invested in the 10 largest positions. Top-holdings M&T Bank and deepwater rig operator Atwood Oceanics each make up approximately 4.4 percent of assets, followed by uniform maker Cintas at 4.3 percent.


He's owned Whirlpool since late 2011, for example, because the lack of aggressive competition in the appliance market allows the company to have higher margins, he said. A rebound in the U.S. housing market and strong demand from China also made the company attractive, Goddard added.
Whirlpool is up 73 percent over the last 12 months, and pays a dividend of 1.8 percent.

"This is a company that's considered mature, but it throws off loads of cash," he said.
More recently, Goddard has been buying specialty shoe retailer Deckers Outdoor Company and mattress-maker Tempur Sealy International.
Deckers Outdoor, which has a market cap of $2.5 billion, is best known as the maker of the popular Ugg line of boots and shoes.

"Everybody thinks this is a fashionable item, but actually it is a steady high margin product which may have seen better growth days but the company has ample amounts of cash flow," Goddard said.
The company's shares peaked at nearly $118 in October 2011 and fell to a low of just under $30 in late 2012 because of slow sales during a warm winter and higher costs of sheepskin. Now selling slightly above $60, shares are up 54 percent for the year.

Approximately 85 percent of the company's revenue comes from sales of uggs on sale, Goddard said, but it is expanding into sandals and men's shoes too.
In its July earnings call, Decker said it expects its margins to increase to approximately 46.8 percent, slightly above the median of 46 percent among peers such as Crocs, Steve Madden and Skechers USA, according to Thomson Reuters data. The company, which does not pay a dividend, trades at a price to forward cash flow of 11.8, well below the median of 27.8 among its competitors.

Goddard said that he is still buying Decker because he believes in "letting his winners run" and typically only sells when a company starts to significantly underperform, he said.
Goddard has also been buying shares of Tempur Sealy International, which was formed from the merger of the two largest U.S. mattress companies in late 2012. Goddard began buying into Tempur-Pedic, the larger company of the two before the merger, in June 2012 when the shares hit $23.

They have since rebounded to approximately $41, giving him a gain of 78 percent.
"The mattress business is not going away," he said.
The fund charges an annual fee of 92 cents per $100 invested, a level that Morningstar considers below average for an actively managed fund. It pays a dividend yield of 1.5 percent.

(Reporting by David Randall; editing by Linda Stern and Andrew Hay)