The Importance of Correlation

Earlier this week The Wall Street Journal ran a piece on, of all things, the importance of the correlation coefficients between the returns of investments. I have mixed feelings about it.

On the one hand, correlation between asset returns is a neglected subject of great importance. The mid-Twentieth Century realization of its central role was the start of modern financial theory as we now know it. A professional level understanding of risk begins and ends with correlations, so it would make some sense for amateur investors to know at least the basics.

On the other hand, the article serves as a good reminder of why they know so little. Despite being called Why the Math of Correlation Matters, it contains no math. This might be because the author worried that her readers would find the math scary and hard, but I fear it is because the author herself finds it scary and hard.

The correlation coefficient (known simply as correlation to his friends) is a basic statistical measure that gauges the relatedness of two sets of numbers. It ranges from –1 to 1. As the WSJ explains well, a correlation of 0 means that the two sets of numbers are unrelated, that knowing the values of set X gives you no information at all about set Y.

Positive values tell you that the numbers run together to some degree, with a perfect score of 1 meaning that they are in perfect lock step. Negative numbers denote an inverse relationship, with –1 meaning that they are perfectly counterbalanced.

However, perfect lockstep does not mean identical, only that knowing the value for one set of numbers is enough to work out the other. In algebraic terms, a correlation of 1 means that there exists an equation to calculate Y from X of the form:

Y = a + bX (or Y = a – bX when correlation is –1)

Where a and b (a.k.a the intercept and slope) are constants. So, for example, Fahrenheit and Celsius temperature readings are correlated at 1.0, with a = 32 and b = 1.8. The WSJ explains b, but forgets about a, which is a larger oversight than you might think.

The importance of correlation in the investing world comes from the simple (and Nobel Prize winning) insight that since investors naturally seek to minimize risk, what they should do is construct portfolios with assets that have as low a correlation with each other as possible. Buying two assets with a correlation of 1.0 is pointless. They will both do well or poorly at exactly the same time.

But buying assets with low correlations to each other makes you better off, since their returns will tend to balance each other out. That means that the portfolio of assets will have a lower volatility and/or a higher return than any individual asset within it. Thus the power of diversification, sometimes referred to as the only free lunch in investing.

The WSJ article provides an enlightening table of asset class correlations with the S&P 500 over the past ten years. The top three assets are non-US developed market stocks, US small cap stocks, and emerging market stocks, which come in at correlations to the S&P 500 of 0.89, 0.88, and 0.82 respectively.

Those numbers are likely a surprise to the many sophisticated investors who cleverly diversified themselves away from US large caps by shifting a little into small caps and non-US stocks. There is some diversification value to be had there, but not as much as was available in such things as real estate, commodities, and bonds. Stocks are stocks the world over, and a bad month on Wall Street is likely to be a bad month in Tokyo and Rio de Janeiro too.

Which is not to say that putting a chunk of your money in emerging markets ten years ago would not have been very clever. The MSCI EM index was up an average of 11% a year over that period while the S&P 500 was close to flat. Being highly (or even perfectly) correlated does not mean that one investment is not habitually better, just as Fahrenheit temperature readings are systematically higher than Celsius ones. This is the importance of the a (or alpha) part that the WSJ skipped over.

Overall, the article is an unsatisfying tease. It tells us that correlation is important, and hints at why, but never quite gets down to brass tacks. The last section, subtitled “Where can I find information on correlation?” is particularly disappointing.

Most online correlation calculators are available only for financial advisers. So, one option is to ask your financial planner.

Tools for individuals include assetcorrelation.com, which finds correlations between assets and between asset classes.

R-squared, a measure found on Morningstar.com, shows strength of correlations between funds and benchmark indexes, but not directions of movement. The scale ranges from 0 to 100.

If you get yourself lists of the returns from two assets, Excel will calculate the correlation. (=CORREL() ) It’s help function even has a decent explanation of how the calculation is performed. Assetcorrelation.com turns out to be a useful, if not very flexible, site.

R-squared is another statistical measure commonly used in finance. In the context of measuring the risk of a mutual fund, it is the square of the correlation between the fund and the benchmark. R is stats notation for an estimated correlation. R-squared runs from 0 to 1, not 0 to 100.

Investing, Media | Frank Curmudgeon | October 6, 2010 11:59 am

46 Comments

By Steve, October 6, 2010 @ 12:38 pm

Speaking of financial planners, I caught one just yesterday saying that a correlation of -1 means unrelated.
By jim, October 6, 2010 @ 1:45 pm

Correlation has been topic I don’t know much about myself. I don’t have a finance background and correlation is not something I’ve seen discussed in personal finance stuff at all. So its just something I haven’t learned yet.

I think the WSJ article was a pretty decent introduction to the topic. Its a pretty complex topic to cover in any detail and a newspaper article is limited in length and has to keep things appropriate for a broad audience.
By Stagflationary Mark, October 6, 2010 @ 2:15 pm

Steve,

That’s just sad.

I’d love to find a financial planner who offered financial advice with a perfect -1 correlation. He or she would be SO bad that you could actually make money off of the advice by *always* doing the exact opposite!

Perhaps you have stumbled upon such a person.
By Stagflationary Mark, October 6, 2010 @ 2:22 pm

One more thought on what a chart showing the lack of correlation looks like. I created the chart to make a point.

http://illusionofprosperity.blogspot.com/2010/09/failed-keynesian-phillips-curve.html

It shows the average unemployment over the previous 12 months vs. the year over year inflation rate (from 1948 to 2010). We’re told that inflation helps us all. I’m not seeing the correlation there. It looks more like an ink blot test to me.
By Stagflationary Mark, October 6, 2010 @ 2:29 pm

Out of curiosity, I just checked the r-squared value in the chart I just offered.

It was 0.02. On a scale of -1 to 1, that’s about as close to zero correlation as you can get.
By David Harper, October 6, 2010 @ 8:16 pm

The actual math is strangely always avoided, but any CFA/MBA knows: correlation = covariance(X,Y/[volatility X]*[volatility Y]; this allows such that correlation is a function of volatility and teases out the weakness of covariance/variance.

No two assets exhibit a “single correlation” as such; each sample produces a different historical correlation. Like volatility, current correlation is only an estimate of an unobserved relationship – going forward will time-vary.

(Also, correlation is a linear dependence; non-linear dependence may be more realistic, handled with copulas)
By bex, October 6, 2010 @ 11:08 pm

Another thing I wish the article talked about was the problem of herd mentality… Once too many people think two assets are not co-related, they sometimes BECOME correlated.

This was one of the downfalls of the “Long Term Capital Management” folks. Once some hedge fund starts making a lot of money, people (sometimes) try to deduce the pattern… the end result being that they all start to buy the same things, because they think they are hedged.

Now… assume asset A goes up, and asset B goes down… also assume that there’s suddenly a recession, or some other problem where these guys don’t have enough liquidity. What will happen?

Well, a lot of folks will start selling off asset A while it’s up to get some cash… which will probably make the price fall… just at the time that asset B is falling too.

Suddenly, all that fancy hedging ain’t worth squat if too many people think it’s a good idea
By Rob Bennett, October 7, 2010 @ 11:19 am

The importance of correlation in the investing world comes from the simple (and Nobel Prize winning) insight that since investors naturally seek to minimize risk

This is why things are such a mess today.

Investors seek to minimize risk? You could have fooled me.

A regression analysis of the historical data showed that the most likely 10-year return for stocks in 2000 was a negative 1 percent real. TIPS were paying a certain 4 percent real. Most investors (and most “experts”!) went with high stock allocations.

This is minimizing risk?

What most investors (and most “experts”!) do is construct convoluted theories for rationalizing their strong emotional preference for Get Rich Quick investing strategies.

I mean no personal insult with these words. My intent is to get some people to take a look at core flaws in the Modern Financial Theory mumbo jumbo that is in the process of eating us all alive (in my view!).

Rob
By Mt, October 7, 2010 @ 11:31 am

There is a person who made all these spreadsheets:

http://www.financialwebring.org/gummy-stuff/gummy_stuff.htm

In the list, there is one that I like called “Correlation” which pulls the information for 30 stocks from the internet and charts the correlations. There are others, too.

If you sift through the site, it is a treasure trove. I haven’t seen software available for purchase which can do everything he has done for free with spreadsheets.

The guy is like the Canadian Da Vinci of Excel investment data.
By Importing from china, July 16, 2013 @ 5:33 pm

Good day! Would you mind if I share your blog with my zynga group?
There’s a lot of folks that I think would really appreciate your content. Please let me know. Many thanks
By crade, April 25, 2023 @ 2:13 pm

With a free 60 MILLION coin welcome bonus, there has never been a better time to start spinning, so play Hit it Rich free online slots today! 1 2 3 iOS Link: https://itunes.apple.com/us/app/quick-hit-slots-spin-to-win/id945621521?mt=8 No. Quick Hit Slots – Casino Games does not seem legit based on our analysis. This conclusion was arrived at by running over 323,247 Quick Hit Slots – Casino Games User Reviews through our NLP machine learning process to determine if users believe the app is legitimate or not. Based on this, Justuseapp Legitimacy Score for Quick Hit Slots Is 34.8/100.. OOFOS | mOOvers | Alex Smith :15 You should boot up the game on a desktop or mobile device, choosing whether to use real or demo money to start with. If you have played the game or similar ones before, start with real money. However, we recommend trying the demo version first to get a feel for it. In Quick Hit slot free you can change the value of each coin depending on how much you wish to wager, with the minimum value set at 0.01 and the maximum at 15.00. This will allow you to adjust your stake according to how much you want to gamble with. Though, the higher your stake the higher your potential to win. Remember to ensure that it remains fun and never bet what you cannot afford to lose. Clicking ‘spin’ will start the round.
http://www.np-ubora.com/apt/board/bbs/board.php?bo_table=free&wr_id=79117
100 Burning Hot is a retro-themed real money slot created by developer EGT for its Burning Hot series. With a big win potential (10,000x stake on a single spin) and a progressive jackpot, 100 Burning Hot offers players some seriously entertaining spins. The slot has 5 columns. All payments in the “Burning Hot” gambling machine are formed as a result of the formation of combinations of identical symbols. They are located one after the other on the neighboring sectors of the drums and always left to right. In one chain can be from three to five pictures. The more valuable the pictogram, the higher the prize coefficients. The multiplier is multiplied by the actual amount at stake and forms the final cash prize for the current spin. All symbols and multiplication factors are indicated in a special table in the information section. The prize multipliers are dynamic and change depending on the change of settings. With minimal investment by the player, they can be as follows:
By mynames, April 29, 2023 @ 7:47 pm

I have read so many content concerning the blogger lovers except this piece of writing isin fact a pleasant article, keep it up.
By kax, May 1, 2023 @ 11:40 am

After the Christmas break, the action returns to the Indian Super League (ISL) 2022-23. Kerala Blasters FC will be locking horns with Odisha FC. The match will be taking place at the Jawaharlal Nehru Stadium in Kochi and is slated to begin at 7:30 PM (IST). The first half ended without goals, but it was a feisty period. Five yellow cards were brandished before the break, with the Blasters picking up four of them. At half-time, Odisha FC had eight attempts, out of which three were on target, while the hosts only managed one wayward shot from Carneiro. ISL 2021-22 live telecast will be available on the Star Sports 2, Star Sports 2 HD, and Star Sports 3 TV channels. ISL telecast in Hindi commentary will be on the Star Sports 1 Hindi and Star Sports 1 HD Hindi TV channels.
https://www.club4g.com/index.php?topic=173637.150
Football tipster Today’s Match Prediction of VLD vs RM Dream11 Fantasy Football, La Liga 2022. The Real Valladolid vs Real Madrid, La Liga 2022-23 will be played at the Estadio Municipal José Zorrilla in Valladolid. The game will be held on December 31, 2022 (Saturday) and the match is scheduled to begin at 2:00 AM IST (Indian Standard Time). Laporte: City will be ready for Real Madrid decider Match Logs (Champions League) Real Madrid will be disappointed that they let Barcelona get a two-point lead over them. They might have a slightly depleted side, owing to the fact that some of their WC superstars are not ready to be back in action yet. The good news is that Benzema is back to full fitness and he is expected to start this game. Real Valladolid vs Real Madrid LIVE Streaming: Madrid look to CUT GAP at the top by winning against Valladolid, Check preview, Predicted XI, Team News – Follow LIVEReal Valladolid Team News: Jawad El Yamiq picked up a hamstring injury for Morocco in the World Cup and is not expected to play a part in this game.
By Doups, May 18, 2023 @ 10:58 am

In order to withdraw any winnings resulting from this welcome deposit bonus from SilverSands Casino, you must fulfill the wagering requirements of 10x bonus + deposit. In other words, you must wager 10-times the value of the bonus and your deposit to successfully withdraw any bonus-related winnings from the casino. Taking a look at an example, depositing R1,500 will get you a match deposit bonus worth R1,125 in bonus money. To be able to withdraw the bonus funds and any associated winnings, you will need to wager R26,250. Sitemap Please Get no deposit bonus at Silver Sands Casino Posts by date Fairspin Casino200 TFS Tokens No Deposit Does SilverSands Casino offer a welcome bonus?SilverSands Casino is proud to offer new players who sign-up a truly massive Welcome Bonus of R8,888! This bonus is available to all new players at SilverSands Mobile Casino as well as the SilverSands Desktop Casino.
https://delta-wiki.win/index.php?title=Crypto_poker_jackpots
It’s simple enough, but for children playing the game, the long-term outcome could be more complicated. A professor from the United Kingdom says that games played on social networks can be addicting and possibly lead to bad habits later in life. Pragmatic Play merupakan perusahaan penyedia game online yang berfokus pada pengembangan slot mobile dan juga aplikasi slot online. Dengan bermain menggunakan taruhan uang asli, game slot demo ini sangat banyak menjadi pencarian pemain yang bermain game online. Terdapat banyak permainan slot dan juga live casino yang bisa kamu mainkan hanya dengan menggunakan ponsel pintar milikmu. Game slot demo gratis yang ini pun bisa kamu mainkan sebagai pengisi waktu hiburan karena tidak menggunakan deposit. Banyak permainan game slot demo gratis yang disediakan, di mana semua itu juga bisa membantu pemain mendapatkan pengetahuan cara bermain slot yang aman.
By nug, May 23, 2023 @ 2:32 pm

Además, en William Hill podrás crear tus apuestas personalizadas gracias a la función Crear #MiApuesta. También te ofrecemos la posibilidad de jugar a tu manera con nuestra CombiPLUS+ donde podrás atacar o defender con tu combinada. Y eso no es todo, porque esta temporada te traemos nuevos mercados como Apuestas estadísticas, Tricombinazos, Trending de la semana, We love Sundays, MiApuesta+ o Boombets. La sección William Hill Apuestas es sin duda la más famosa de este operador, aunque en esta reseña nos hemos centrado principalmente en su oferta de casino online. Las William Hill Apuestas en directo son de hecho dos de los menús principales de su sitio web, y contemplan prácticamente todas las apuestas deportivas disponibles. William Hill ofrece cuotas inmejorables (un 30% más que en plataformas similares…), entre las que destacan las de los partidos de las distintas ligas. Además, los William Hill codigos promocionales se aplican a una enorme variedad de juegos de azar y eventos deportivos.
https://stephenggdz630629.losblogos.com/21030983/casinosaga
Las tragaperras más populares Estas son algunas de las tragaperras online con bote que atraen a más jugadores: Además, que diga. Casino móvil sin depósito de 20 euros 2023 según la ley estatal, qué casinos están representados oficialmente en el territorio del país. Si desea obtener más información sobre Inspired, especialmente cuando puede multiplicar ese pago del premio hasta 6 veces con la ayuda de wilds y la función de bonificación Police Chase. Si está pensando en agregar más mesas, más del 75% de los residentes de las regiones administrativas defienden la prohibición total de fumar en los lugares de juego. Se habla mucho de tragamonedas sueltas o máquinas tragamonedas que probablemente golpeen, depositar en Parimatch será rápido. El paquete de depósito debe desbloquearse en la configuración de su cuenta antes de poder reclamarlo, fácil y barato.
By Paito, May 25, 2023 @ 3:21 pm

Sportsbooks have started offering more and more bet types across all events. You can bet the Super Bowl winner, conference winners, exact Super Bowl matchups, and more. Last year the AFC was the weaker conference. The seven AFC playoff teams averaged 10.6 wins, while the seven NFC teams averaged only 11.4 wins. However, the AFC became the superior conference during the offseason. Russell Wilson got traded from the Seattle Seahawks to the Denver Broncos, and Davante Adams got traded from the Green Bay Packers to the Raiders. Even if Watson plays the entire year, the Browns have very little chance of winning the conference. Below we’ve listed all the Super Bowl winners since 2000 and their reason odds. July 11: The last few months haven’t shaken up the Super Bowl odds board too much — the Panthers didn’t make much of a move following the Baker Mayfield trade. The biggest moves came earlier in the offseason with all the quarterback shuffles.
https://jasperabyw529528.onzeblog.com/19405117/biggest-bet-on-the-super-bowl
He was the first man out of the Tour Championship last month but finished T-12 at the BMW Championship the week before. Why he’ll win: Schauffele has always been an elite performer at major championships. He has finished in the top 10 in nine of 20 majors he has played and has been T-3 or better four times. His form did not look promising until the Byron Nelson this past weekend. At 22-1, there is some betting value on Schauffele to finally break through and win his first career major. The AT&T Pebble Beach Pro Am in one of the events of the PGA season, and this weekend the golf’s best tee off with sports and entertainment A-Listers. While Abraham Ancer and Tommy Fleetwood have games that should suit the narrow fairways at TPC Harding Park, we’re going to make another form pick and run with Tyrrell Hatton. While he may have had a tough week at the WGC Fedex St. Jude Invitational (69th in a field of 78), his play leading into that event had been exceptional. He finished in the top-six (including a win) at the two events going into the COVID pause and then backed that up with a third at the RBC Heritage and a fourth at the Rocket Mortgage Invitational. Tough courses seem like they should suit him and if the notorious hothead can keep his wits about him he may find himself contending for his first major championship on Sunday.
By Cib, May 25, 2023 @ 9:20 pm

Dieser Töffli-Event war einfach super genial und hat uns allen riesig gefallen! Es hat alles geklappt und wir wurden vom Team Wermelinger wunderbar betreut und beraten. Der Rückzug von PayPal schmerzt zwar, aber zum Glück gibt es zum PayPal Casino Alternativen. Im Kassenbereich der Casinos tummeln sich immer noch genügend hochkarätige Bezahloptionen. Auch wenn du aktuell keine PayPal Erfahrungen machen kannst, die Möglichkeit einer Rückkehr von PayPal in die Casinos ist durchaus gegeben. Die Beliebtheit von PayPal kommt nicht von ungefähr, denn der Zahlungsanbieter bietet zahlreiche Vorteile. Insbesondere im Vergleich zu traditionelleren Zahlungsmethoden wie der Banküberweisung oder Kreditkartenzahlung kann das E-Wallet punkten, denn anstatt sensible Daten angeben zu müssen, reicht bei PayPal eine Anmeldung mit der eigenen E-Mail-Adresse und dem selbst festgelegten Passwort völlig aus. Auf diese Weise kann man es verhindern, seine Bankinformationen auf verschiedenen Seiten zu hinterlegen; diese geben Sie nur einmal bei PayPal selbst an und schon können Sie problemlos überall Zahlungen durchführen, was natürlich auch im Online Casino einen riesigen Vorteil darstellt.
http://www.dae-gyeong.com/bbs/board.php?bo_table=free&wr_id=20459
You’ve landed on $translations $translations Online-Sportwetten haben einen klaren Vorteil: Man bequem von zuhause aus oder auch unterwegs wetten. Im Gegensatz zum klassischen Wettbüro kann man seine Wetten nämlich vom heimischen Computer aus genauso abgeben wie auch vom Smartphone. Online-Sportwetten gelten daher als äußerst unkompliziert. Nichtsdestotrotz genießen Wettbüros und Wettlokale in Österreich bis heute eine große Beliebtheit. mga casino trustlyDiese solle aus leitenden Angestellten und externen Experten bestehen.Euro.Eine solche hatten britische Parlamentarier und Spielerschützer bereits seit Jahren von der Glücksspielbranche gefordert.Gemeinsam mit G4 habe der Glücksspielriese eine „kulturelle Bewertung“ seines Geschäfts auf verschiedenen Ebenen durchgeführt.Kooperation mit ExpertenUm eine noch sicherere Umgebung für Spieler in Großbritannien zu realisieren, habe Gauselmann mit der Global Gambling Guidance Group (G4) aus Amsterdam zusammengearbeitet, einem Unternehmen zur Zertifizierung von Glücksspielprodukten.Im Vergleich zum zweiten Quartal 2019 sind die Einnahmen aber um 17,71 % gestiegen.spinit casino bonus codes 2019
By ingem, May 26, 2023 @ 3:54 am

Looks like you haven’t added anything to your cart yet. Let’s put something in there. FREE STANDARD SHIPPING ON ALL U.S ORDERS $50 OR MORE (EXCLUDES HAWAII AND ALASKA) Looks like you haven’t added anything to your cart yet. Let’s put something in there. Opened in 2010 to bring a new boutique experience to skincare & cosmetics retail in the Cayman Islands, we offer exclusive products and deliver world-class customer service. From shop MyMakeupBrushes Available with a rose gold handle, this Luxie brush will help transform your average makeup set to an Insta-worthy professional studio. Pretty in pink, the 231 Small Tapered Blending Brush costs a cool $14. Please double check the email you have entered! To take advantage of all HSN has to offer, please upgrade your browser to a newer version. You may get the latest here: browsehappy.
https://nyx-waterline-eyeliner.bloggersdelight.dk/2023/03/17/clio-black-eyeliner/
If dark circles and under-eye bags are your biggest concern, this eye treatment will perk up your skin in no time. Formulated with licorice water and extract (another K-beauty favorite ingredient) and caffeine, the cream helps brighten dark areas, tighten skin, and reduce puffiness. In other words, it’s your best bet for an awakened appearance. The less expensive products that are suitable for your skin type will certainly be better. Now that you know all of this, it’s time to choose the best Korean moisturizer for you. That said, navigating the K-beauty world can be tricky, but we made the work easy for you with all the best Korean skincare products that deserve a spot in your 10-step skincare routine, below. We love the Belif Moisturizing Eye Cream so much that we added it to our 2021 Allure Beauty Box lineup. You can score the Allure Beauty Box here for access to even more editor favorites — for just $23.
By Строительная чешуя, June 26, 2023 @ 3:32 am

Wow, awesome blog layout! How long have you been blogging for? you make blogging glance easy. The whole glance of your site is great, let alonewell as the content!
By vammebel.ru, June 26, 2023 @ 8:09 am

This piece of writing offers clear idea designed for the new people of blogging, that truly how to do blogging and site-building.
By spravki-kupit.ru, June 26, 2023 @ 3:45 pm

где купить справку
By bub, June 26, 2023 @ 10:55 pm

But that’s not all we have to offer. To find more types of Vegas slots to play online, head over to Mr Green’s casino page. Mr. Vegas is the luckiest man in town. No one takes as many chances as he does, nobody wins as much either. Women surround him and everybody wants to meet him and catch some of his luck. This is your chance, you are invited to become part of his inner circle, why not? give yourself some luck. Mammoth Peak: Hold and Win is a prehistoric animal slot filled with exciting features. You will play Mammoth Peak: Hold… We’ll start with the Mr Vegas welcome bonus. An effective tool used to attract new members is to offer an enticing new customer offer. As a new player you will be offered a really nice Mr. Vegas Casino bonus, in conjunction with more bonus opportunities.
http://megaplant.co.kr/bch/bbs/board.php?bo_table=free&wr_id=1698
In such a way, all knowing Bugs are fixed. Best aussie online casinos casino bonuses can be a wonderful thing for players from Great Britain but we need to sort through all the different types, funny sound effects. Par conséquent, and smooth touch screen controls. Unlike most 3 pay-line games, I’d love to hear from you in the comment section below. Each step is taken with those old rogueish concerns in tow: can I avoid a hit, three. Camp grounds or sites are yet another ideal location to install a vending machine, and four. The IGT S2000 slot machine is probably the most recognizable slot machine in the world due to its wide distribution and the movie industry. Most casinos today will have these on the game floor. The IGT S2000 remains a favorite of “reel machine” enthusiast worldwide. IGT S2000 slot machines are a must have for any floor and are also one of the lowest cost slots available now.
By Professor Smith, June 27, 2023 @ 10:56 am

Informative article, exactly what I needed.
By купить диплом специальном образовании, June 27, 2023 @ 11:59 am

Appreciating the time and energy you put into your website and in depth information you present. It’s good to come across a blog every once in a while that isn’t the same outdated rehashed material. Excellent read! I’ve saved your site and I’m including your RSS feeds to my Google account.
By накрутка подписчиков в яппи, July 30, 2023 @ 7:13 am

I must thank you for the efforts you have put in writing this website. I am hoping to view the same high-grade blog posts from you in the future as well. In fact, your creative writing abilities has motivated me to get my own website now
By smartremstroy.ru, July 31, 2023 @ 7:59 pm

I love your blog.. very nice colors & theme. Did you design this website yourself or did you hire someone to do it for you? Plz reply as I’m looking to design my own blog and would like to know where u got this from. cheers
By химчистка дивана на дому борисов, September 2, 2023 @ 7:04 am

Thank you a bunch for sharing this with all people you really recognise what you are talking approximately! Bookmarked. Please also discuss with my web site =). We may have a link exchange agreement among us
By чистка диванов в смолевичах, September 2, 2023 @ 9:25 am

This article will help the internet viewers for creating new website or even a blog from start to end.
By Fernando Touchstone, September 6, 2023 @ 12:31 pm

Your blog is refreshing. The standard of your writing makes visiting a delight.
By sadovoe-tut.ru, September 6, 2023 @ 10:39 pm

Hi there mates, good article and pleasant arguments commented here, I am actually enjoying by these.
By agrosadovnik.ru, September 6, 2023 @ 11:22 pm

I’ve read some just right stuff here. Definitely worth bookmarking for revisiting. I wonder how much attempt you set to create any such magnificent informative web site.
By loan places near me, October 7, 2023 @ 9:46 am

Usually I do not read article on blogs, however I wish to say that this write-up very forced me to take a look at and do so! Your writing taste has been amazed me. Thank you, quite great article.
By online television, October 9, 2023 @ 7:19 am

Today, I went to the beach with my kids. I found a sea shell and gave it to my 4 year old daughter and said “You can hear the ocean if you put this to your ear.” She put the shell to her ear and screamed. There was a hermit crab inside and it pinched her ear. She never wants to go back! LoL I know this is entirely off topic but I had to tell someone!
By online television, October 11, 2023 @ 12:36 am

obviously like your web-site however you need to test the spelling on quite a few of your posts. A number of them are rife with spelling problems and I in finding it very bothersome to tell the truth then again I will certainly come back again.
By гостиничные чеки москва купить с подтверждением, October 15, 2023 @ 5:47 pm

Hi everybody, here every one is sharing these knowledge, so it’s good to read this weblog, and I used to visit this webpage everyday.
By чеки на гостиницу в москве с подтверждением, October 16, 2023 @ 3:30 pm

Hi there! Do you know if they make any plugins to help with SEO? I’m trying to get my blog to rank for some targeted keywords but I’m not seeing very good results. If you know of any please share. Appreciate it!
By online television, October 18, 2023 @ 1:42 am

Magnificent web site. A lot of useful information here. I’m sending it to some buddies ans also sharing in delicious. And obviously, thank you for your effort!
By Онлайн казино, October 21, 2023 @ 7:08 pm

I’ve been exploring for a little bit for any high-quality articles or blog posts in this kind of area . Exploring in Yahoo I eventually stumbled upon this site. Reading this info So i’m satisfied to express that I have a very good uncanny feeling I came upon exactly what I needed. I such a lot definitely will make certain to don?t overlook this site and give it a look on a constant basis.
By стяжка, October 23, 2023 @ 3:44 am

Хотите получить идеально ровный пол в своей квартире или офисе? Обратитесь к профессионалам на сайте styazhka-pola24.ru! Мы предоставляем услуги по устройству стяжки пола в Москве и области, а также гарантируем качество работ и доступные цены.
By snabzhenie-obektov.ru, October 24, 2023 @ 3:53 pm

снабжение строительства
By гостиничные чеки купить в москве, October 25, 2023 @ 10:56 pm

Hi, i think that i saw you visited my blog so i came to ?return the favor?.I am trying to find things to improve my website!I suppose its ok to use some of your ideas!!
By оштукатуривание стен, October 26, 2023 @ 7:57 pm

Хотите получить идеально ровные стены в своем доме или офисе? Обратитесь к профессионалам на сайте mehanizirovannaya-shtukaturka-moscow.ru! Мы предлагаем услуги по механизированной штукатурке стен любой сложности и площади, а также гарантируем качество работ и доступные цены.
By гостиничные чеки купить в москве, October 29, 2023 @ 10:25 am

Hi everyone, it’s my first pay a visit at this website, and post is really fruitful in favor of me, keep up posting such posts.
By spourry, July 25, 2024 @ 5:31 am

real cialis no generic In addition, strong amide and water absorbance bands are found in region of 1, 500 1, 700 and 3, 000 3, 600 cm 1, respectively
By сервис центры в москве, September 9, 2024 @ 6:41 pm

Профессиональный сервисный центр по ремонту бытовой техники с выездом на дом.
Мы предлагаем: сервис центры бытовой техники москва
Наши мастера оперативно устранят неисправности вашего устройства в сервисе или с выездом на дом!