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Portfolio manager Stephen Goddard has run one of the best performing U.S.<br>[http://www.Bing.com/search?q=mid-cap+funds&form=MSNNWS&mkt=en-us&pq=mid-cap+funds 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, 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 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  [http://tinyurl.com/ku6vjks ugg boots usa] 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 = Windmill graph
| image = [[Image:Windmill graph Wd(5,4).svg|220px]]
| image_caption = The Windmill graph Wd(5,4).
| vertices = ''(k-1)n+1''
| edges = ''nk(k−1)/2''
| automorphisms    =  
| girth = 3 if ''k > 2''
| diameter = 2
| radius = 1
| chromatic_number = ''k''
| chromatic_index = ''n(k-1)''
|notation = Wd(''k'',''n'')
| properties =
}}
 
In the [[mathematics|mathematical]] field of [[graph theory]], the '''windmill graph''' Wd(''k'',''n'') is an [[undirected graph]] constructed  for ''k'' ≥ 2 and ''n'' ≥ 2 by joining ''n'' copies of the [[complete graph]] ''K<sub>k</sub>'' at a shared vertex. That is, it is a [[clique-sum|1-clique-sum]] of these complete graphs.<ref>Gallian, J. A. "Dynamic Survey DS6: Graph Labeling." Electronic J. Combinatorics, DS6, 1-58, Jan. 3, 2007. [http://www.combinatorics.org/Surveys/ds6.pdf].</ref>
 
==Properties==
It has ''(k-1)n+1'' vertices and ''nk(k−1)/2'' edges,<ref>{{MathWorld|urlname=WindmillGraph|title=Windmill Graph}}</ref> girth 3 (if ''k > 2''), radius 1 and diameter 2.
It has [[k-vertex-connected graph|vertex connectivity]] 1 because its central vertex is an articulation point; however, like the complete graphs from which it is formed, it is ''(k-1)''-edge-connected. It is [[trivially perfect graph|trivially perfect]] and a [[block graph]].
 
==Special cases==
By construction, the windmill graph Wd(3,''n'') is the [[friendship graph]] ''F<sub>n</sub>'', the windmill graph Wd(2,''n'') is the [[Star (graph theory)|star graph]] ''S<sub>n</sub>'' and the windmill graph Wd(3,2) is the [[butterfly graph]].
 
==Labeling and colouring==
The windmill graph has [[chromatic number]] ''k'' and [[chromatic index]] ''n(k-1)''. Its [[chromatic polynomial]] can be deduced form the chromatic polynomial of the complete graph and is equal to
<math>\prod_{i=0}^{k-1}(x-i)^n.</math>
 
The windmill graph Wd(''k'',''n'') is proved not [[Graceful labeling|graceful]] if ''k'' > 5.<ref>K. M. Koh, D. G. Rogers, H. K. Teo, and K. Y. Yap, Graceful graphs: some further results and problems, Congr. Numer., 29 (1980) 559-571.</ref> In 1979, Bermond  has conjectured that Wd(4,''n'') is graceful for all ''n'' ≥ 4.<ref>J.C. Bermond, Graceful graphs, radio antennae and French windmills, Graph Theory and Combinatorics, Pitman, London (1979) 18-37.</ref> This is known to be true for ''n'' ≤ 22.<ref>J. Huang and S. Skiena, Gracefully labeling prisms, Ars Combin., 38 (1994) 225-
242.</ref> Bermond, Kotzig, and Turgeon proved that Wd(''k'',''n'') is not graceful when ''k'' = 4 and ''n'' = 2 or ''n'' = 3, and when ''k'' = 5 and ''m'' = 2.<ref>J. C. Bermond, A. Kotzig, and J. Turgeon, On a combinatorial problem of antennas in radioastronomy, in Combinatorics, A. Hajnal and V. T. Sos, eds., Colloq. Math. Soc. János Bolyai, 18, 2 vols. North-Holland, Amsterdam (1978) 135-149.</ref> The windmill Wd(3,''n'') is graceful if and only if ''n'' ≡ 0 (mod 4) or ''n'' ≡ 1 (mod 4).<ref>J.C. Bermond, A. E. Brouwer, and A. Germa, "Systèmes de triplets et différences associées", Problèmes Combinatoires et Théorie des Graphes, Colloq. Intern. du CNRS, 260, Editions du Centre Nationale de la Recherche Scientifique, Paris (1978) 35-38.</ref>
 
==Gallery==
 
[[Image:Windmill graphs.svg|thumb|550px|center|Small windmill graphs.]]
{{-}}
 
== References ==
{{reflist}}
 
[[Category:Parametric families of graphs]]
[[Category:Perfect graphs]]

Revision as of 10:50, 3 March 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, 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 ugg boots usa 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)