In this issue:

**1) Kelly Criterion**

**2) Portfolio Variance**

**3) Rules of Thumb**

4) Don't Diversify with Dutch Tulip Bulbs

4) Don't Diversify with Dutch Tulip Bulbs

*Dear Friends, Colleagues, and Investors,*

After identifying a variety of attractive investments, how much of our capital should we risk? Should we use leverage or hold cash in reserve? Should we invest all our money in our best idea or diversify broadly, even if that means devoting money to less attractive investments?

After identifying a variety of attractive investments, how much of our capital should we risk? Should we use leverage or hold cash in reserve? Should we invest all our money in our best idea or diversify broadly, even if that means devoting money to less attractive investments?

**1) The Kelly Criterion**

The scientist John Kelly created a simple formula that describes the optimal strategy for non-correlated bets. Before delving into the formula, let's look at a simple example. Let's say that you're going to make a series of 100 bets on a coin flip. The coin is weighted and thus lands on heads 60% of the time. You have $100. How much should you bet each time? It’s tempting to think that you should bet your entire bankroll every time to maximize your expected returns, but this is incorrect. While betting your bankroll does indeed maximize your expected value for any individual bet, it ignores the fact that you have a limited bankroll, and once you lose it, you also lose the opportunity to make future profitable bets. If you bet your entire bankroll each time, you will likely go bankrupt by the fourth bet, so you'll miss out on future advantageous bets.

Here's the Kelly Criterion formula:

Here's the Kelly Criterion formula:

where:

*f** is the fraction of the current bankroll to wager;*b*is the net odds received on the wager (that is, odds are usually quoted as "*b*to 1")*p*is the probability of winning;*q*is the probability of losing, which is 1 −*p*.

The most intuitive way to think about Kelly’s approach is to consider the outcome of a full “set” of bets. Let’s imagine that we bet our entire bankroll on that 60% weighted coin. If we bet 10 times, we can expect to double our portfolio 6 times, but then we will go bankrupt. If instead we only bet 20% of our portfolio, our bankroll will grow by a factor of 1.2 when we win, and shrink by a factor of 0.8 when we lose. The growth looks like this: 1.2*1.2*1.2*1.2*1.2*1.2*0.8*0.

While the Kelly Criterion is a good starting point, it has a lot of problems. First, it assumes that bets are uncorrelated. If I have 20 equities in my portfolio, their returns are certainly very correlated; a global depression will send all equities tanking. Even if we use Kelly for sequential bets, the correlation problem remains. In the real world, corporate earnings, GDP growth, and even stock market returns are not independent events each quarter; the current period impacts the next. Finally, the Kelly Criterion requires that we know the “edge” of any bet. We can never be sure of “edge”, and we are very likely to estimate it poorly. As with any formula, garbage in = garbage out.

The are numerous way to improve on Kelly for investors. First, we can adjust the Kelly weighting by the beta of the security to the rest of our portfolio; this will better take advantage of the benefits of diversification. For example, if Kelly recommends a weighting of 10% of our bankroll but the security has a negative beta to our portfolio, we will probably be happy with a higher weighting, since the security reduces our portfolio volatility. Second, we can recognize that the Kelly allocations will be too high because they fail to account for correlation and we can systematically reduce the allocations. Several prominent hedge fund managers routinely use the Kelly Criterion but divide the result by 2. Finally, we can use Kelly as a rough starting point for deciding how much capital to risk for a given amount of expected reward.

The greatest value of the Kelly Criterion is that it demonstrates that even when we’re sure we have found a great investment, we only want to commit a small portion of our portfolio.

**2) Portfolio Variance**

A complimentary approach to portfolio construction looks at the relative attractiveness of securities. Many fund managers feel more comfortable investing from the bottom up than trying to time the market. Mutual fund managers and pension managers are in the same boat because they generally prefer to be 100% long the market. To what extent should these managers concentrate their capital in their best idea? Even if you are a market timer, you must consider how to divide your capital between your best and second best investment ideas.

Imagine we’re considering a simple portfolio with two assets, A and B. We believe that asset A will return 20% a year and asset B will return 15% a year, and they are uncorrelated. How should we distribute our funds? To maximize our expected value we would put all our money in Asset A, but we can earn almost as much with much lower risk through diversification. If we split our money evenly between the two assets we can expect a 17.5% return but we cut our portfolio’s variance in half! In the real world, very few assets are uncorrelated and managers face a more subtle decision. Calculating portfolio variance for a portfolio of 50 assets is hard by hand but easy with the proper software. The problem is that, as with any formula, garbage in = garbage out. If we make a poor estimation of the covariance of assets, we may end up with much more risk than we expected.

Imagine we’re considering a simple portfolio with two assets, A and B. We believe that asset A will return 20% a year and asset B will return 15% a year, and they are uncorrelated. How should we distribute our funds? To maximize our expected value we would put all our money in Asset A, but we can earn almost as much with much lower risk through diversification. If we split our money evenly between the two assets we can expect a 17.5% return but we cut our portfolio’s variance in half! In the real world, very few assets are uncorrelated and managers face a more subtle decision. Calculating portfolio variance for a portfolio of 50 assets is hard by hand but easy with the proper software. The problem is that, as with any formula, garbage in = garbage out. If we make a poor estimation of the covariance of assets, we may end up with much more risk than we expected.

**3) Rules of Thumb**

We can use a computer program to calculate the risk/return profiles of possible portfolios, but this is so imprecise as to be little better than simple rules of thumb in most cases.

Here's a very simple approach: Let’s start with the world of equities. Compared to holding just 1 stock, a portfolio of 4 stocks will have roughly 65% of the volatility, 12 will have 50%, and a portfolio of 60 stocks will have 40% of the volatility. As you can see, diversifying beyond 12 equities provides little benefit. We need to tweak this assumption when considering stocks that have very low correlation to our portfolio. For example, if you hold a dozen pro-cyclical stocks (like airplane and car makers), adding a couple counter-cyclical stocks (like an outplacement agency or fast food company) to your portfolio would provide significant diversification benefits.

In allocating capital between two stocks with average correlation (roughly 0.6), a useful rule of thumb is to adjust the capital allocation by the square root of the edge differential. This is a lot simpler than it sounds. For example, let’s say I have a portfolio consisting of only Apple and Caterpillar and I believe that Apple will appreciate by 20% next year and Caterpillar by only 10%. Since Apple has twice the edge of Caterpillar, I will devote sqrt(2) as much capital to Apple. If I had $100, I would put $58 into Apple and $42 into Caterpillar. This simplistic approach will generally deliver a happy medium between maximizing your returns and minimizing your portfolio’s risk. If the two stocks are very highly correlated, there is less benefit from diversification, so we might put $80 into stock A and only $20 into B. Alternatively, if the two assets are completely uncorrelated, the diversification benefits are greater so we should consider a 50/50 split.

If we’re building a long equity portfolio, we should aim for 6-20 stocks (depending on the prevalence of opportunities and our time available to analyze them), and overweight the most attractive investments by the square root of the extra edge they provide

.

When we include non-equity assets, the issue of correlation becomes much more difficult. Correlation deserves (and will get) it's own Risk over Reward essay, but I'll offer some simple ideas today. A very conservative approach is to assume that correlations will rise to their historic highs. For example, commodities and equities have at various times had very negative correlations, very positive correlations, and even been uncorrelated. If I have a portfolio that is long commodities and long equities, a very conservative measure of its risk assumes that the assets are very positively correlated. The absolute most conservative assumption is a correlation of 1. If I assumed a very negative correlation, the portfolio would look like it had very little risk; a poor assumption because even if correlations are negative today, they may become positive in the future.

In allocating capital between two stocks with average correlation (roughly 0.6), a useful rule of thumb is to adjust the capital allocation by the square root of the edge differential. This is a lot simpler than it sounds. For example, let’s say I have a portfolio consisting of only Apple and Caterpillar and I believe that Apple will appreciate by 20% next year and Caterpillar by only 10%. Since Apple has twice the edge of Caterpillar, I will devote sqrt(2) as much capital to Apple. If I had $100, I would put $58 into Apple and $42 into Caterpillar. This simplistic approach will generally deliver a happy medium between maximizing your returns and minimizing your portfolio’s risk. If the two stocks are very highly correlated, there is less benefit from diversification, so we might put $80 into stock A and only $20 into B. Alternatively, if the two assets are completely uncorrelated, the diversification benefits are greater so we should consider a 50/50 split.

If we’re building a long equity portfolio, we should aim for 6-20 stocks (depending on the prevalence of opportunities and our time available to analyze them), and overweight the most attractive investments by the square root of the extra edge they provide

.

When we include non-equity assets, the issue of correlation becomes much more difficult. Correlation deserves (and will get) it's own Risk over Reward essay, but I'll offer some simple ideas today. A very conservative approach is to assume that correlations will rise to their historic highs. For example, commodities and equities have at various times had very negative correlations, very positive correlations, and even been uncorrelated. If I have a portfolio that is long commodities and long equities, a very conservative measure of its risk assumes that the assets are very positively correlated. The absolute most conservative assumption is a correlation of 1. If I assumed a very negative correlation, the portfolio would look like it had very little risk; a poor assumption because even if correlations are negative today, they may become positive in the future.

**4. Don't Diversify with Dutch Tulip Bulbs**

**Most investment managers are chronic over-diversifiers. A portfolio of 20 stocks has almost the same risk as a portfolio of 100 stocks, so why dilute your best investment ideas? Warren Buffett wrote: "Many pundits would therefore say [that concentrating your capital] must be riskier than [diversifying like] more conventional investors. We disagree. We believe that a policy of portfolio concentration may well decrease risk if it raises, as it should, both the intensity with which an investor thinks about a business and the comfort-level he must feel with its economic characteristics before buying into it." Another great quote from the oracle, "Diversification is a protection against ignorance. It makes very little sense for those who know what they're doing."**

The very best investment managers like Warren Buffett and Seth Klarman usually have 70%+ of their capital in just 5 stocks! Diversification is a crutch used by managers who lack the confidence or will to perform deep due diligence on the companies in which they invest.

The modern twist on this fallacy is diversifying with asset classes. Funds are putting capital in commodities and real estate because those asset classes historically have a low correlation to equities...but that's not a good reason to put your money in an asset. No matter how uncorrelated a bad investment is to your portfolio, it's still a bad investment.

The very best investment managers like Warren Buffett and Seth Klarman usually have 70%+ of their capital in just 5 stocks! Diversification is a crutch used by managers who lack the confidence or will to perform deep due diligence on the companies in which they invest.

The modern twist on this fallacy is diversifying with asset classes. Funds are putting capital in commodities and real estate because those asset classes historically have a low correlation to equities...but that's not a good reason to put your money in an asset. No matter how uncorrelated a bad investment is to your portfolio, it's still a bad investment.

Any thoughts on opening a Chinese Bank account?

ReplyDeletehttp://online.wsj.com/article/SB10001424052748704307404576080222812076888.html?mod=rss_about_china

There's actually a game theory based equilibrium strategy well connected with the Kelly criterion regarding diversifying with multiples asset classes. The concept is you position evenly in all asset classes because capital has to go somewhere and you rebalance to take advantage of capital flow. That positions you to profit over time regardless of how unevenly capital is positioned provided there is movement and either no deflation or proportionally benefiting from inflation and deflation.

ReplyDeleteKelly criterion basically has you allocating proportional to the edge. There's a problem in the book fortune's formula that uses the example of horse betting and talks about risk management with multiple bets and the simple solution is to allocate proportional to the chances of winning... assuming your total edge is based upon having inside knowledge to more accurately handicap the horses then the crowd. In the market that would basically be like investing in the assets based upon probability of risk adjusted outperformance.

The permenant portfolio is actually very close to the GTO (game theory optimal) solution for 4 asset classes and avoids overdiversification as well.

Delete(25% gold, 25% cash, 25%stocks, 25% bonds)

Find the best Dice Games with the lowest house edges. All reviewed by Bitcoin Chaser, the authority onBitcoin gambling. freebitcoin

ReplyDeleteEvery online casino offers bonuses. Every online casino bonus comes with its own terms and conditions, but many players have no clue what it takes to redeem them. In this article readers will see exactly what the advantages and disadvantages found with online casino bonuses. Learn how to avoid ruining online casino promotions and discover what it takes to cash out free casino bonuses. Monopoly Casino Game

ReplyDeleteGiven all these properties of spread betting, it should be pretty easy to make a fair bit of money without too much effort. If only.

ReplyDeleteguarantor loans

If you decide that you will bet on the team that is expected to win, they will have to win by more than the spread number and cover the spread before you are considered to have chosen correctly. agen piala dunia

ReplyDeleteThis comment has been removed by the author.

ReplyDeleteWow, it's really hard. My dad used to make investments, but I don't get a think about it. Too hard. But I think it's fair. It's hard, but it can bring you a lot of money. I saw at the review of kingessays that people earn a lot of money doing good investments

ReplyDeleteThis comment has been removed by the author.

ReplyDeleteYou people have actually provided the best blogs that are easy to understand for the folks

ReplyDeleteJudi Online

I have read all the articles .. I really enjoy this article in this blog Poker Online

ReplyDeletegood article well hopefully useful. Situs Poker Online

ReplyDeleteFind the best Dice Games with the lowest house edges. All reviewed by Bitcoin Chaser, the authority onBitcoin gambling.

ReplyDeleteSbobetthis article is very interesting. judi online terpercaya

ReplyDeleteWoow, that's awesome!

ReplyDeleteDont forget to visit our site

agen pokerif u want to know more aboutsitus poker onlineThanks Dude!

nice article... allow me to share it

ReplyDeleteAgen Togel

ReplyDeleteamazing article,thank you very much for the article and the information.. maybe if you can please visit our website

judi online terpercayaThanks for your excellent posting! I quite enjoyed reading it, you happen to be a great author. I will remember to bookmark your blog and will eventually come back very soon. casino online

ReplyDeleteThanks for your excellent posting! I quite enjoyed reading it, you happen to be a great author. I will remember to bookmark your blog and will eventually come back very soon. casino online

ReplyDeleteArticles on good and interesting Visit my website if you want to know more about

ReplyDeleteSitus Judi OnlineThanks for your excellent posting! I quite enjoyed reading it, you happen to be a great author. I will remember to bookmark your blog and will eventually come back very soon. situs judi online

ReplyDeleteThanks for your excellent posting! I quite enjoyed reading it, you happen to be a great author. I will remember to bookmark your blog and will eventually come back very soon. live casino

ReplyDeleteThanks for your excellent posting! I quite enjoyed reading it, you happen to be a great author. I will remember to bookmark your blog and will eventually come back very soon. sicbo

ReplyDeletethis article is very interesting. togel online

ReplyDeleteGood Article very interesting Dont forget to visit my site

ReplyDeleteBandar Pokerif you want to know more about

ReplyDeleteplaying poker it is a pleasure to waste time and relieve stress on the head go visit my website

TaktikQQ

Articles on good and interesting Visit my website if you want to know more about

ReplyDeleteagen poker

ReplyDeleteplaying poker it is a pleasure to waste time and relieve stress on the head go visit my website

TaktikQQ

Thanks for your excellent posting! I quite enjoyed reading it, you happen to be a great author. I will remember to bookmark your blog and will eventually come back very soon. LIVE CASINO

ReplyDeleteThanks for your information so useful for me.

ReplyDeleteThanks for sharing

Domino QQThis article is interesting if you want to know more visit our website. slot online

ReplyDeleteThe more they play utilizing these guides, the better understanding they will create. slot online

ReplyDeleteThanks for your excellent posting! I quite enjoyed reading it, you happen to be a great author. I will remember to bookmark your blog and will eventually come back very soon. SITUS JUDI ONLINE

ReplyDeleteThis information is very useful and interesting. Thank you for sharing and do not forget to visit our website to

ReplyDeletebandar togelif you want to know more about

This article gives me a new experience thanks, visit also my website if you want to know more

ReplyDeletedewa pokerThis information is very useful and interesting. Thank you for sharing and do not forget to visit our website to

ReplyDeletejudi onlineif you want to know more about

Articles on good and interesting Visit my website if you want to know more about

ReplyDeleteJudi OnlineTogel OnlineGame Online TerbaikCasino OnlineTaruhan BolaThe information you provide is perfect thank you very much

ReplyDeletedominoqqWWW.ERADOMINOQQ.COM

Thank you for allow me to comment in here

ReplyDeleteAgen Poker

Situs Poker

Dominoqq

Domino99

Bandarq

amazing article,thank you very much for the article and the information.. maybe if you can please visit our website to

ReplyDeletetogel onlineif you want to know more aboutThank you for allow me to comment in here

ReplyDeleteAgen Poker

Situs Poker

Dominoqq

Domino99

Bandarq

This article gives me a new experience thanks, visit also my website if you want to know more

ReplyDeleteSitus Judi OnlineJudi CasinoPrediksi BolaLive CasinoThank you for allow me to comment in here

ReplyDeleteAgen Poker

Situs Poker

Dominoqq

Domino99

Bandarq

Thank you for allow me to comment in here

ReplyDeleteAgen Poker

Situs Poker

Dominoqq

Domino99

Bandarq

TOYOTAQUIQUI.COM

Thank you for allow me to comment in here

ReplyDeleteAgen Poker

Situs Poker

Dominoqq

Domino99

Bandarq

"Thank you for allow me to comment in here

ReplyDeleteAgen Poker

Situs Poker

Dominoqq

Domino99

Bandarq"

"Thank you for allow me to comment in here

ReplyDeleteAgen Poker

Situs Poker

Dominoqq

Domino99

Bandarq"

Articles that are very good and interesting thanks

ReplyDeletepoker online terpercayadominoqqdomino99agen poker terbaikbandarqsitus poker tercepatjoin sekarang di taktikqq.net mudah menang dan banyak bonus nya ao buruan gabung sekrang

ReplyDeleteTaktikQQ

"Thank you for allow me to comment in here

ReplyDeleteAgen Poker Terpercaya

Situs Poker Terpercaya

Dominoqq Online

Domino99 Online

Bandarq"

Articles on good and interesting Visit my website if you want to know more about

ReplyDeletejudi onlineArticles on good and interesting Visit my website if you want to know more about

ReplyDeletebandar togel online indonesiaBandar togel singapura terpercayaBandar togel hongkong terpercayabandar judi togel onlinebandar judi singapura terbaikbandar judi hongkong terbaikThank you for allow me to comment in here

ReplyDeletesitus baccarat online terpercaya

situs slot online terpercaya

situs judi sic bo terpercaya

situs slot online terpercaya

situs roulette online terpercaya

Thank you for allow me to comment in here

ReplyDeletesitus baccarat online terpercaya

situs slot online terpercaya

situs judi sic bo terpercaya

situs slot online terpercaya

situs roulette online terpercaya

ReplyDeleteThank you for allow me to comment in here

situs baccarat online terpercaya

judi rolet indonesia

situs judi sic bo terpercaya

situs slot online terpercaya

situs roulette online terpercaya

Articles that are very good and interesting thanks

ReplyDeletepoker online terpercayaagen poker onlinedominoqq onlinedomino99bandarqsitus poker terbesarqiu qiukiu kiuThanks for your awesome post

ReplyDeletepoker online

daftar poker online

panduan poker online

Good Article Well Do Not Forget Visit Our Website

ReplyDeleteJudi OnlineTogel SingapuraTogel HongkongThis comment has been removed by the author.

ReplyDeleteThis is very educating post, thanks for sharing with us.

ReplyDeletetogeltogel onlinetogel singapuratogel hongkongArticles that are very good and interesting thanks

ReplyDeletepoker onlinedominoqqdomino99bandarqArticles on good and interesting Visit my website if you want to know more about

ReplyDeletetogel onlinetogel hkgtogel sgppengeluaran togeljudi onlineslot onlinecasino onlinebandar bolaagen pokerdewa pokerArticles that are very good and interesting thanks

ReplyDeletepoker onlinesitus poker onlinedominoqqdomino99bandarqqiu qiukiu kiuArticles that are very good and interesting thanks

ReplyDeletecasino online

This article is interesting, if you want to know more visit our website.

ReplyDeletedadu online

Articles on good and interesting thanks for sharing with us, Visit my website if you want to know more about.

ReplyDeletejudi onlinejudi togelsitus judi onlinetogel212togel singapuratogel hongkongslot onlinecasino onlinebandar bolaagen pokerdewa poker

ReplyDeleteThis article is interesting, if you want to know more visit our website.

situs judi online

Articles that are very good and interesting thanks

ReplyDeletepoker onlinesitus poker onlinedominoqqdomino99bandarqqiu qiukiu kiudemonstrate the extent of the blinds and even give a planning capacity to keep play moving.Book of Ra 6 kostenlos spielen ohne anmeldung

ReplyDeleteThank you for allow me to comment in here

ReplyDeleteAgen Bola

thanks for sharing this www.eradominoqq.com

ReplyDeletebandarq

Thank you for allow me to comment in here

ReplyDeleteBandar Bola

Thank you for allow me to comment in here, YOUR ARITKEL IS VERY NICE

ReplyDeleteAgen Poker

poker online

Dominoqq

Domino99

Bandarq

kiu kiu

qiu qiu

situs poker

pokerqq

This article is interesting, if you want to know more visit our website.

ReplyDeletecasino online

ReplyDeleteThis article is interesting, if you want to know more visit our website.

roulette online

situs judi online

casino online

live casino

dadu online

ReplyDeleteThis article is interesting, if you want to know more visit our website.

roulette online

Thank you for allow me to comment in here, YOUR ARITKEL IS VERY NICE

ReplyDeleteBandarq

ReplyDeleteThis article is interesting, if you want to know more visit our website.

roulette online

situs judi online

casino online

live casino

dadu online

good article, hopefully this article useful for us, do not forget also through our web

ReplyDeleteJudi OnlineTogel SingapuraTogel HongkongTogel Online

ReplyDeleteThis article is interesting, if you want to know more visit our website.

roulette online

this interesting article may be useful and do not forget to visit our website

ReplyDeleteTogel HongkongThank you for allow me to comment in here

ReplyDeleteAgen Judi Online

Thanks for posting this info. I just want to let you know that I just check out your site and I find it very interesting and informative

ReplyDeleteBandar Bola

Thanks for posting this info. I just want to let you know that I just check out your site and I find it very interesting and informative

ReplyDeleteBandar Bola

This article is interesting, if you want to know more visit our website.

ReplyDeleteJudi BolaBandar BolaTaruhan BolaThis article is interesting, if you want to know more visit our website.

ReplyDeletejudi onlinetogel212togel singapuratogel hongkong212togel onlineslot onlinebandar bolacasino onlinedewa pokerThis article is interesting, if you want to know more visit our website.

ReplyDeletelive casino

ReplyDeleteThis article is interesting, if you want to know more visit our website.

live casino

This article is interesting, if you want to know more visit our website.

ReplyDeletejudi onlinetogel212togel singapuratogel hongkong212togel onlineslot onlinebandar bolacasino onlinedewa pokerThank you for allow me to comment in here

ReplyDeleteJudi Online

Articles that are very good and interesting thanks

ReplyDeletepoker onlinesitus poker onlinedominoqqdomino99bandarqqiu qiukiu kiu

ReplyDeleteThis article is interesting, if you want to know more visit our website.

casino online

Thank you for allow me to comment in here, YOUR ARITKEL IS VERY NICE

ReplyDeletepoker online

ReplyDeleteThis article is interesting, if you want to know more visit our website.

live casino

This article is interesting, if you want to know more visit our website.

ReplyDeletejudi onlinetogel212togel singapuratogel hongkong212togel onlineslot onlinebandar bolacasino onlinedewa poker

ReplyDeleteThis article is interesting, if you want to know more visit our website.

dadu online

ReplyDeleteThis article is interesting, if you want to know more visit our website.

casino online

This article is interesting, if you want to know more visit our website.

ReplyDeletecasino online

ReplyDeleteThis article is interesting, if you want to know more visit our website.

dadu online

ReplyDeleteThis article is interesting, if you want to know more visit our website.

baccarat online

Thank you for allow me to comment in here

ReplyDeleteBola Online

Articles on good and interesting thanks for sharing with us, Visit my website if you want to know more about.

ReplyDeletejudi onlinesitus judi onlinerouletteroulette onlinebaccaratbaccarat onlinecasino onlinelive casinoagen casinojudi casino

ReplyDeleteThis article is interesting, if you want to know more visit our website.

baccarat online

Thank you for allow me to comment in here

ReplyDeleteAgen Judi

Thank you for allow me to comment in here, YOUR ARITKEL IS VERY NICE

ReplyDeleteDominoqq

Domino99

Domino 99

This article is interesting, if you want to know more visit our website.

ReplyDeletecasino online

Articles that are very good and interesting thanks

ReplyDeletedomino qqdomino 99dominoqqdomino99

ReplyDeleteThis article is interesting, if you want to know more visit our website.

dadu online

ReplyDeleteThank you for allow me to comment in here, YOUR ARITKEL IS VERY NICE

Dominoqq

Domino99

This article is interesting, if you want to know more visit our website.

ReplyDeletelive casino online

Thank you for allow me to comment in here, YOUR ARTIKEL IS VERY NICE

ReplyDeleteroulette online indonesia

This article is very interesting , come and visit our website at here

ReplyDeletejudi onlinesitus judi onlineslotslot onlineslot online uang aslimain slot onlinemain slot gameslot online androidslot online terpercayapoker onlinesitus poker onlinedominoqqdomino99bandarqqiu qiukiu kiuThank you for allow me to comment in here

ReplyDeleteJudi Bola

Taking in the when and how of settling on these choices is a more elevated amount ability that is basic for reliable poker achievement. poker qq

ReplyDeleteThank you for allow me to comment in here

ReplyDeletedadu online

ReplyDeleteThank you for allow me to comment in here, YOUR ARTIKEL IS VERY NICE

casino online indonesia

This article is interesting, if you want to know more visit our website.

ReplyDeletebaccarat online

poker onlinesitus poker onlinedominoqqdomino99bandarqqiu qiukiu kiu

ReplyDeleteThis article is interesting, if you want to know more visit our website.

baccarat online

ReplyDeleteThis article is interesting, if you want to know more visit our website.

dadu online

ReplyDeleteThank you for allow me to comment in here

dadu online

Have you at any point acquired cash to fund gambling? Odds are whether you have, things are not looking so great.lottery website

ReplyDeleteThank you for allow me to comment in here

ReplyDeleteSitus Judi Online

Thank you for allow me to comment in here

ReplyDeletedadu online

Thank you for allow me to comment in here

ReplyDeletedadu online

This article is interesting, if you want to know more visit our website.

ReplyDeletelive casino

ReplyDeleteThank you for allow me to comment in here, YOUR ARTIKEL IS VERY NICE

roulette online indonesia

poker onlinesitus poker onlinedominoqqdomino99bandarqqiu qiukiu kiuArticles that are very good and interesting thanks

ReplyDeleteLive Poker IndonesiaAgen PokerPoker OnlineJudi Online Terpercaya Di IndonesiaBandar Ceme KelilingBandar DominoAgen Dominothank you for being given the opportunity to read this very perfect article. please visit the best sports betting around the world.

ReplyDeleteSitus Judi Online

ReplyDeleteThis article is interesting, if you want to know more visit our website.

live casino

Thank you for allow me to comment in here, YOUR ARITKEL IS VERY NICE

ReplyDeleteDominoqq

thank you for allow me to comment here , your article is very good . please come and visit our website at here

ReplyDeletejudi onlinesitus judi onlineslotslot onlineslot online uang aslimain slot onlinemain slot gameslot online androidslot online terpercayaExtremely pleasant article, I appreciated perusing your post, exceptionally decent share, I need to twit this to my adherents. Much appreciated!. free betting offers

ReplyDelete