Shiller vs Fama?

My knee-jerk reaction to Robert Shiller and Eugene Fama getting the Nobel was that it's an example of them being honoured for flatly disagreeing. This reaction is partly true: Fama's thinking is sceptical of the possibility of price bubbles, whilst Shiller's shows that they can happen. But in another sense, their work is actually compatible, because they are talking about different things.

Fama's work is primarily about individual stocks. He has shown that, generally, prices quickly embody all available information so that investors cannot out-perform the market except by taking on more systematic risk. This risk might be market risk (beta), or the sort of cyclical risk that is often associated with small and value stocks - hence the "three factor" model discussed here (pdf). Back in 1970, Fama concluded (pdf):

For the purposes of most investors the efficient markets model seems a good first (and second) approximation to reality.

I'd caveat this; there's some evidence that momentum and defensive stocks do better than they should. Generally, though, Fama is right.

One piece of evidence for this is the performance of equity neutral hedge funds: according to HFR, these have returned 1.1% a year in the last five years - no better than a risk-free rate. A second piece comes from UK all companies unit trusts. In the last five years, most of these have under-performed the better tracker funds. 

Market efficiency is like Newtonian physics. It's not exactly right, but you'll not often go disastrously wrong if you act as if it is.

Shiller's work, by contrast, has focussed more upon the aggregate market. In one famous early paper, for example, he showed that the S&P 500 was far more volatile (pdf) than could be explained by dividends. This implies that - over longish periods at least - aggregate prices might be predictable by the dividend-price ratio (or other things (pdf)).

Whilst this is consistent with the possibility that investors are irrational - contrary to the spirit of Fama's work - it is not proof of irrationality. As David Meenagh has shown in the UK, such excess volatility might be due to investors attaching varying but reasonable probabilities to future scenarios (booms, slumps etc) which might occur but in fact do not.

But here's the thing. Micro efficiency in Fama's sense is quite compatible with excess aggregate volatility in Shiller's. Shiller himself (pdf) has suggested just this.

Why the difference? One big reason lies in how information gets embedded into prices. Imagine you think an individual stock is over-priced. In many cases (not all - the tech bubble being an exception) you can short-sell the stock reasonably easily, as you can diversify the risk of doing so by going long of a comparable stock; this is the idea behind pairs trading. But what if you think the aggregate market is over-priced? It's risky to short-sell it; remember Keynes' famous saying that markets can stay irrational longer than you can stay solvent? And there's less chance of being able to spread this risk by going long of other markets, simply because global stock markets are correlated.

With short-selling of aggregate markets more difficult than of individual stocks, it's likely that aggregate markets will be (occasionally) more over-priced than individual stocks.

In this sense, Shiller and Fama aren't so far apart.

Comments

[Greg]

I am going to have to disagree with this post. It seems fashionable for efficient market theorists to make this claim but it is mathematically impossible. To illustrate, allow me to make a hypothetical example.

Assume you have a two-stock, stock market. Assume each stock is efficently valued at 15x earnings. Be defintion the market is efficiently valued at 15x earnings because the PE of the market is simily the weighted average of the two stocks. It is impossible for the market to be valued at 20x earnings, and thereby overvalued, without at least one of the individual constituents to also be overvalued. In contrast, each stock could be inefficiently valued, say one is 20x earnings and the other 10x, while the market is efficiently valued at 15x earnings.

Further, individual shares can be mispriced due to limitations of short selling. But the market has no such limitations as ETF's are, relative to individual stocks, easy to short. There are no liquidity issues and no issues trying to identify shares available to borrow.

The only explanation for the perception of this phenomenon is a forest vs. the trees issue. Each stock appears appropriately valued individually but not so when aggregated across the market. But this is a case of series of individual mispricings that are debatable on the individual level. You cant say MSFT and CSCO are appropriately priced in 1999 because of rational expectations but then say the S&P or NASDAQ is overvalued.

[chris]

Greg - you're right. One way of reconciling the two claims would be if lots of stocks are slightly over-priced - within margins of error of valuation, but these overpricings add up across the whole market. This probably wasn't the case in 99 (as tech stocks were overpriced then) but it might have been in 2007.

[Andrew]

That would make the entire market slightly over-priced - within margins of error of valuation.

Where is the mechanism that compounds these errors into a large overvaluation?

Obviously it is when macro effects supervene. E.g. when demand collapses because everyone realises their "slight" overvaluation at the same time and it suddenly isn't so slight.

[Andrew]

This is another composition fallacy, that economists seem to really go for.

Another is the marginal product nonsense that you referred to in your post about Gareth Bale.

That is a particularly enjoyable piece of nonsense.

For example Chris you say that "monopolies charge a price above marginal product." Well, yes, if you assume, incorrectly, for a perfectly competitive market, that each firm's production has ZERO effect on whole market demand, and it therefore sees a flat demand curve, then you get firms producing up to the point their marginal cost equals price.

This isn't true, so the argument goes, for a monopoly, since it IS the market, its production affects demand and the curve isn't flat. So it will only produce up to the point marginal revenue equals marginal cost, and sell at a higher price.

Except that this is all bollocks, since if you aggregate all of your competing firms, you have a functionally identical model producer to the monopoly producer. The only difference is that classical economists, not being very good at either maths or thinking, have for the individual firms conveniently forgotten that negligible effects of one firm's output on demand are not negligible when aggregating them into the entire market!

This is precisely the mistake made when using this model to make pronouncements about the aggregate behaviour of competitive markets vs monopolies.

One additional unit of production from a competitive firm must have exactly the same effect on demand as one from a monopoly.

[Clive LordClive Lord]

Having just been alerted to your blog, I have tried to comment on 30th Sept re Osborne and workfare. This is just an attempt to make contact

[Andrew]

I have thought about Chris's "collection of small errors" point in comment above.

I think Chris, you are suggesting that for statistically independent series of company valuations, (i.e. small systemic error) if each were in their upper range of confidence interval, then this would make the entire market valuation far outside its confidence interval. This would be true if they were indeed independent, in which case you could estimate market price to a fantastically small confidence interval given the pooling of all those individual estimates. Just as you can accurately measure the mean weight of a thousand oranges more precisely than the weight of any one of those oranges, because the error on each orange is statistically independent.

But they are far from statistically independent, errors will tend to have the same direction, in other words there will be large and variable systematic errors, and the error for market pricing is of the same order as the error for individual pricing.

So if your company valuations are all off by about 5% your market valuation may well be off by 5% too.

[chris]

@ Andrew - in retrospect, I think my above comment is wrong.
The way I'd reconcile the macro-micro is different. It's that they're about different things. What matters at the micro level is shares' relative prices: will stock A out-perform stock B? It's quite possible that we can't answer this question (and so the market is efficient) even if all shares are over-valued in aggregate. (We could say that in such a situation high-beta stocks would subsequently under-perform, but this if course is wholly consistent with efficiency).
And the question of relative pricing matters. It means that active managers who have to be fully invested (eg unit trust managers) can't systematically out-perform, regardless of market conditions.
Separately, not that the questions: can I beat the market? and "Is the market efficient?" are different ones:
http://www.investorschronicle.co.uk/2013/01/15/comment/chris-dillow/why-you-can-t-beat-the-market-4l7o6b2UhXbYXwWt3MEeWK/article.html

[Richard Gadsden]

Perhaps the point is that you value an individual stock relative to the market.

Ie, this stock has a value a bit above the typical p/e for the sector, that one a bit below.

But the typical p/e is determined by the market's overall valuation, not by some stock-specific calculation.

Does this suggest that financial engineering to make possible a deleveraged sell-and-hold strategy would reduce the risk of market bubbles?

[Alex]

I thought the Efficient Market Hypothesis had finally died in 2007/8.

The problem with this 'Newtonian' theory is that

1. Newton was in important areas very wrong, much more so that Chris suggests

2. Prices are a product of power, not signalling, information, feedback i.e. they are not simplifiable mechanistic phenomena.

I need to go and check the Nobel winners, but on the face of it this news, and this post (unusually) is quite depressing.

[chris]

@ Alex. Perhaps we should distinguish between the rational markets hypothesis and the EMH. The former certainly took a beating in 2008, but I'm not so sure the latter (in the sense of "equity investors can't beat tracker funds") did.
Alternatively, one could argue that the rational market hypothesis is self-defeating, in the sense that if people believe it, they'll not bet against irrational traders. This is consistent with this Shleifer/Mendel paper.
http://www.people.fas.harvard.edu/~jbmendel/chasing_noise_JFE.pdf

[Alex]

@Chris - I appreciate the reply. It's a fascinating area and perhaps I need to do some more reading to really understand the distinction you point out. But on the face of it, I don't see that markets are either rational or efficient. I'll make general points on why, and hope that they aren't totally incoherent, or missing the point (which I accept they may be)

- Value is subjective. Therefore the appeal that any entity, including the magical black box of the market, can determine a 'correct','rational','efficient' pricing for a good is based on a false assumption that at any point value is or could be static and that all information could possibly be available. Where prices are meaningful is as a reflection of dynamic forces under which they arise i.e. in human life and interaction.
- I think it's still the case that the rationality of the market is underpinned by a mythical version of individuals as rational, utility-concerned, self-concerned atoms. The comparison to Newton here seems particularly apt.
- People talk a lot about information. But it seems clear to me that some information isn't involved in the magic of market calculation. It also seems clear that some people are excluded from the market. So it could only ever be a very narrow form of efficiency or rationality.
- Value also transcends the vulgarity of pricing in the way in it currently exists. Hayek says that economic freedom underpins all other freedoms. Maggie paraphrased it. My question is this - what freedom does one have if one owns nothing? I'm concerned that the answer should be 'none'.

I'm just leaving work and in a rush so apologies again if this is incoherent, or perhaps absolute rhubarb.

[gastro george]

Aren't efficient/rational market theories burnt by the amount of time and money large companies spend obfuscating the true comparative value of their products - vis power tariffs, etc.

[Andrew]

Can't you just dispense with the idea that equity investors can on average beat the market by noticing that the market is entirely composed of equity investors? Seems like a "duh"to me.

If anyone suggests that no equity investor can beat the market just point them to some stats on Ed Thorpe or similar star investor. It's beyond mathematical doubt that they can. In any case someone is always going to have privileged access to information. Just look at market movements immediately prior to big announcements.

The efficient market hypothesis was never believed by any more than two neurons assembled in one place.

[Wonks Anonymous]

Andrew, there are event studies for just such reveals of information. Fama pioneered such things. The semi-strong version of EMH says that public but not private information is already priced in (the weak version says only prior history of prices is factored in). The strong version (which nobody really believes) says that even private information is priced in.

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銇俱仩銈偣銉┿偆銉炽倰鎸併仱鍒ャ伄鍟忛銇€侀枹绡€銇儜銈ゃ儣銇ㄣ偆銉炽偣銉堛兗銉伄涓娿伀銈广儸銉冦儔銇с仐銈囥亞銆傛姇璩囬妧琛屾キ鍕欍仺妯欐簴浣忓畢鎵€鏈夎€呫伀鍚戙亼銇熼潪鐝惧疅鐨勩伀銇撱伄閬旀垚銈炽偣銉堛亰閲戙仺寮曘亶鎻涖亪銇偓銈搞偋銉冦儓銆?/span>銆傚悕鍓嶃亴绀恒仚銈堛亞銇€佸郊銈夈伅銈枫儯銉嶃儷銇儸銉椼儶銈伄銈枫偣銉嗐儬銆傞珮銇勪紒妤伀鑸堝懗銇撱伄銈枫儯銉嶃儷銇儸銉椼儶銈伄銉愩儍銈般仹瑁介€犮仌銈屻仸銇勩倠銇屾墍鏈夈仐銇︺亜銇俱仚銆傝〃绀恒仌銈屻倠銆佹嫛寮佃銈掗€氥仐銇﹀郊銈夈倰瑷€銇?銈枫儯銉嶃儷 銉°偨銉冦儔銇偧銉儍銈偣 銈炽償銉笺€傘亗銇仧銇岃銇嬨仾銇戙倢銇般仾銈夈仾銇勩仚銈嬨亾銇ㄣ亴銇с亶銇俱仚銇傘仾銇熴伅銆佸尰鐧傛彁渚涜€呫仺褰?褰煎コ銇屾焙瀹氥倰琛屻亞銇撱仺銇屻亗銈娿伨銇欍€?
ヴィヴィアン時計 http://www.directrentcar.com/lightbox/Vivienne-Westwood-bag-c-37007_37004.html/

[vivienne 財布]

鐝句唬銈儜銉儷銇渶瑕併伅閬庡幓鏁板勾闁撱亱銈夊銇忋亴澧楀姞銇椼伨銇欍€傘仩銇嬨倝銈兂銉┿偆銉?銈枫儳銉冦償銉炽偘 銈广儓銈伄姒傚康鐝惧疅銇埌鐫€銇椼伨銇椼仧銆傘儔銉偣銇€併仚銇广仸瀹熼殯銇浗鍏ㄤ綋銇屽繀瑕併仹銇欍€備互涓嬨伀銇傘倠銈淬儫 銉曘偅銉笺儷銉?銉愩儍銈般仺銇椼仸銈傘偆銉┿偣銉堟捣鑷皸銇捣娲嬨伄銇亰銇勩倰鎵€鏈夈仐銇︺亜銇俱仚銆傛柊楫仾棣欍倞銇椼€併倰閬嬨伓銇ゃ倐銈娿伨銇ｃ仚銇愭槑鐧姐仾銇亰銇勩倰鐮旂┒銇椼伨銇欍€傘亾銈屻倝銇偪銈ゃ儣銇儩銉?銉愩兂銉椼伄鏀瑰杽銈枫儯銉笺儣 銈儢銈搞偋銈儓銇仧銈併伀銇汉銆?銇綍銈掋仚銇广亶銇嬨仹銇欍€?
vivienne 財布 http://www.beightonbuilding.co.uk/images/Vivienne-Westwood-watch-c-37007_37001.html/

[ウエストウッド]

銉撱儖銉笺儷琚嬨伅銆佽銇鏂欓洃璨ㄦ墜褰亰銈堛伋銈炽兂銉濄兗銉嶃兂銉堛倰鏍煎畨銆佸畨渚°仾鏂规硶銇刀瀵俱伀銇撱倢銇汉姘椼倰寰椼仧銆傚ぇ銇嶃亜瀵嗗害銉°儍銈枫儱闃叉按銈枫兗銉堛伅銉嬨儍銉堛儩銉偍銉併儸銉炽亱銈夋鎴愩仌銈屻仸銇勩伨銇欍€傘亾銈屻倝銇€併偄銉椼儶銈便兗銈枫儳銉炽伄闆昏┍鐣彿銇娇鐢ㄣ仌銈屻仸銇娿倞銆併亾銈屻倝銇帓浠栫殑銇増浣庛亸澶с亶銇曘倓褰㈢姸銆併儛銉笺儛銉兗銈枫儱銉笺偤銇眾瀵屻仹銇欍伄銇с€佸郊銈夈伅闁撻仌銇勩仾銇忔銆呫仾銈儣銉偙銉笺偡銉с兂銈掍繚璀枫仚銈嬨亾銇ㄣ亴銇с亶銇俱仚銆?
ウエストウッド http://www.chrisyoungroofing.co.uk/css/Vivienne-Westwood-watch-c-37007_37001.html/

[ヴィヴィアンウエスト]

銇濄倢銇壒銇ソ銇椼亜绉诲嫊銇曘仜銈嬨€傞枊鐧恒仚銈嬨仺銇嶃伄鎰忓洺鐨勩仾銉曘偅銉笺儷銉夈伀銈偗銈汇偣銇欍倠銇熴倎銇娇鐢?'銉曘儸銉笺儬' 瑾挎暣銉娿儹銈︺偤銇嬨仾銈娿伅銆佺嫭鑷伀 1 銇ゃ伄浣滄キ銈掕銇嗐亾銇ㄣ伀浣跨敤銇倛銇嗐仾绉併仐銇俱仚銆傜従鍦拌臣鍏ャ倓瀛ｇ瘈寰椼倠銆傘偓銈逛尽鏍笺伅銆佽臣鍏ャ伀銇ゃ亜銇︾煡銇ｃ仸銇勩倠銇嬨倐銇椼倢銇亜涓娿伀銈裤儍銈仐銇︺亜銇俱仚銆傘仢銈屻倝銈ゃ儊銈撮洟銈屻仸浣欏垎銇郊銈夈伅缇╁嫏鏈涖伨銇椼亜銆佹潵銈嬪繀瑕併亴銇傘倠銇с仐銈囥亞銆傝＝鍝併伄銉兗銉夈仺銉炪兗銈便儐銈ｃ兂銈般伄鍊嬩汉銇岃博澹层偟銈ゃ儓銇í鍟忚€呫伄娲炲療鍔涖伀銈堛仯銇﹀２涓娿倰妞滅储銇欍倠銇熴倎銇父銇亗銈嬨€?
ヴィヴィアンウエスト http://www.devbuild.co.uk/aspnet_client/system_web/Vivienne-Westwood-bag-c-37007_37004.html/

[ディーゼル アウトレット]

銉涖兗銉犮伄鏈夈仚銈嬫棦瀛樸伄澶ц妯°仾椋熸枡鍝併倰銈傘仧銈夈仚蹇呰銇銇暟銈掕€冩叜銆併仢銈屻伅銈傘亞灏戙仐绲屾笀鐨勩仾鍐嶅埄鐢ㄣ伄琚嬨仺浠栥伄閬告姙鑲亴蹇呰銇屻亗銈娿伨銇欍€傜暟銇倠銉欍兂銉€銉笺伄瑕佷欢銈掓簚銇熴仚銇熴倎銇悇椤у銇仈浜恒偣銉堛偄銇嬨倝鍗佸垎銇仌銇俱仏銇俱仾銈姐儶銉ャ兗銈枫儳銉炽倰鎸併仱銇撱仺銇屻仹銇嶃伨銇欍€傜敺鎬ц€冩叜銆侀澊銆併偘銉兗銉宠壊銇偣銈ㄣ兗銉夈伄銉濄兂銉椼€併偣銉堛儵銈ゃ儣绶戙€侀粧銇勩伄绱般亱銇勩儭銉冦偡銉?銈枫儱銉笺偤榛掔窗銇嬨亜銉°儍銈枫儱鏆椼亜鑹层偣銉堛儵銈ゃ儣 銉堛儸銉笺儕銉笺倰鍚個銈堛倞搴冪瘎銇с仚銆?
ディーゼル アウトレット http://hermes.taipeicreativehub.org/

[ヴィヴィアンウエストウッド]

銈姐優銉偄銆傘偡銉ャ儍銉?銈儭銉┿€傘偣銉氥偆銉冲簝鍫村懆杈恒€俉eb 銉氥兗銈告湰褰撱伀銇欍伖銇︺伄銇婇噾銇劅瑕氶噾铻嶈▓鐢汇偗銉偣銉溿儑銈?銈儠銉?銉愩偣銈便儍銉?銈ㄣ偣銈便兗銉楀焦绔嬨仱銇撱仺銇ㄦ瘮杓冦仐銇﹂珮銇勩儓銉炽倰闁嬬櫤銇椼仸銇勩仧鍒ャ伄浜恒倓銉撱偢銉嶃偣銈掕璜栥仚銈嬨儸銉笺儓銇у叏浣撱倰娉ㄣ亹浣嶇疆姹恒倎銆傘伨銇犮伄閫氬父鐣彿銈ゃ兂銈裤兗銉嶃儍銉堟帴缍氬彲鑳芥€с亴銇傘倞銇俱仚銇儝銉炽儓銈掓彁渚涖仚銈嬪垾銇柟娉曘伄瑾挎熁銈掑緱銈嬨仧銈併伀杩旂瓟銇欍倠銇熴倎銇柟娉曘倰鍙栧緱銇椼伨銇欍€?
ヴィヴィアンウエストウッド http://www.wbds.org.uk/images/Vivienne-Westwood-watch-c-37007_37001.html/

[ヴィヴィアン]

褰笺倝銇€併偣銈ゃ偣銇∟銇у晢鍝佺姸娉併伀鏂般仧銇繀闋堛仹銇傘倠銇撱仺銇屽彇寰椼仐銇俱仐銇熴€傜銇熴仭瑾般倐銇屻€併亾銇儸銈儶銈ㄣ兗銈枫儳銉炽倰閫氥仒銇︺仹銇亼銈屻伆銇倞銇俱仜銈撳瑕炽€傘儢銉偓銉笺伅銆佹祦琛屻倰瓒娿亪銉栥儵銈ゃ偄銉炽優銈ゃ儕銉煎骇銈嬨偍銉炽儓銉銈掑ソ銈€鍚伨銈屻仸銇娿倞銆併優銉笺偗銈搞偋銈ゃ偝銉栥偣銇郊銇緦銇儛銉冦偘銈掍簣绱勩仐銆併偒銉笺儵銇汉棣欐按銇帹钖︺仺鐗瑰敬銇屻亗銈嬨伄銈兗銉┿伅銆併儭銉炽偪銉笺倰閬庛仈銇欍仧銈併伀銉愩儍銈般倰浣溿仯銇熴€併儢銉兂銉夌窇銇厷銇偔銈儵銇€併儖銈炽兂銇倛銇ｃ仸鎻愪緵銇曘倢銈嬨仺銆佸郊銇俱仧銇郊濂炽亴鍕曚綔銇欍倠銈堛亞銇仾銈娿伨銇椼仧銈偗銈枫儳銉炽仹褰煎コ鑷韩銇澊銇搧璩€丮anrepeller銇儓銉笺偣銉堛亗銇仧銇偩鍚戠壒瀹氥伄甯傚牬銇仾銈娿伨銇欍€?
ヴィヴィアン http://www.lawcarpentry.co.uk/Public_html//Vivienne-Westwood-Accessories-c-37007_37002.html/

[エアジョーダン13]

浜恒€呫伄瀹跺涵鏁欏斧2010骞存槬銉曘偋銉兗銈洪澊銈般儷銉笺儣銇伅銈掑憫銈€銇汇仼銈广偪銈ゃ儶銉冦偡銉ャ仾銇犮亼銇с仾銇忋€佹礂绶淬仌銈屻仸銇勩伨銇欍€傜劇绉╁簭銇儝銉炽儓銈掓寔銇ゃ亾銇ㄣ伅闁撻仌銇勩仾銇忋€佸疅闅涖伀鍘勪粙銇偄銈ゃ儑銈仹銇欍€傘仹銈傘€佹湇銇仢銈屻伅銇傘仾銇熴伄銇熴倎銇亗銇仧銇犮亼銇€併倧銇氥亱鏁般伀鏍肩磵銇曘倢銇︾祵楱撱仐銇︺亜銈嬨偑銉栥偢銈с偗銉堛伄澶栬Τ銇幊銇椼亜鍔姏銇с亗銈嬨仧銈併伀銇€佽病甯冦倰閬嬨伓銇撱仺銆?
エアジョーダン13 http://airjordan.pukepaijishu.com/

[vivienne 財布]

銇欍伖銇︺伄銉忋兂銉夈儛銉冦偘銇嬨倝鏉愭枡銇伨銇熴€侀噸瑕併仾鍒ャ伄濂芥剰銇儑銈躲偆銉炽亱銈夋姇璩囨剰娆层伀褰遍熆銇亗銈娿伨銇涖倱銆傞噸瑕併仾鏅備唬銇ぇ鍗娿仹鍙兘鎬с亴銇傘倞銇俱仚銇娿仢銈夈亸鐗涢潻銉欍兗銈广仐缇婄毊銇潪甯搞伀鍏遍€氥伄銇欍伖銇︺伄濂虫€с伀銉曘偐銉笺偒銈广倰鏈夊姽銇仚銈嬨仺銆佽泊閲嶃仾鏉愭枡銇潪甯搞伀浜烘皸銇亗銈嬨偆銉笺偣銉堣弻鎰熸煋鐥囥€?
vivienne 財布 http://conyersimports.bm/new/Vivienne-Westwood-watch-c-37007_37001.html/

[ズームコービー8]

銇撱仺銇屻仹銇嶃倠銇撱伄搴娿伄琛ㄩ潰闅犮仚銇ц眾瀵屻仾婧愭硥寰村弾銇汉銆?銇儗寰屻伀銇傘倠锛熴仢銈屻伅澹併伨銇熴伅蹇冮厤銆佷笉淇°€併亰銈堛伋绉樺瘑銇椤屻仹銇欍€傛劅瑕氥倰鎵€鏈夈仐銇﹀績銇ф湰褰撱伀鑸堝懗銈掓寔銇ｃ仸銇勩倠銈堛亞銆併伨銇с仩銇戙亴鍚個绉併€傘伨銇ц仦銇勩仧鎰熴仒銇︺€佺銇敞鎰忋倰鎵曘亞鍙兘鎬с亴楂樸亜銆傚€嬩汉鐨勩仾閫叉銇€佷汉鐢熴伄鍒ャ伄鏂规硶銇с仚銆傘仢銇竴鑸殑銇銇嬨倝鍑恒仐銇︺亰銈堛伋妲樸€?銇儷銉笺儣澶栥倰寰椼倠鍊嬩汉鐨勩仾闁嬬櫤銈偍銉敓娲汇偡銉笺兂銈掕渚°仐銆侀潪甯搞伀銇傘仾銇熴伄鏃㈠瓨銇兘鍔涖倰寮峰寲銇ㄨ嚜鍒嗚嚜韬伀鍔涖倰涓庛亪銈嬨仺娆°伄浜虹敓銈掔鐞嗐仚銈嬫柊銇椼亜瑕嬮€氥仐銇嬨倝銇緦銇绶氥€?
ズームコービー8 http://www.doble-u.eu/css/35-Nike-Air-Force.html/

[ジョーダン1]

浣曘仺銇嬫ü骞广伅銇汇伡銈掋偍銈广偒銉兗銉堛仚銈嬩綆鏈ㄣ伄鑼傘伩銈掍娇鐢ㄣ仐銇︿慨绻曘仐銇熸偑銇勮矾鍦般仺銇濄伄寰屾瘺鎴戙€?銇勩仧鏅傞枔鏃ュ厜銇仧銈併伄銉囥偠銈ゃ兂銇у墠寰屻偄銉冦儣銉笜銈堛倞銈堛倞灏戙仐銇仧銈併伄鐤戙亜銈傘仾銇忕銇熴仭銈掔巼銇勩仸銆佽喛鐦嶃伄鍏卞悓銈儣銈汇儷銇仧銈佺銇熴仭銇碁銈掑彈璩炪仚銈嬨伄銈兗銉仾鑷劧鐕冪劶澶櫧銇亗銇仧銇従鍦ㄣ伄娲按銇х瑧銇ｃ仧銆傘仢銇撱伀銇嶃倢銇勩仾琚嬨倰閬搞伓銇暟銇劒浣嶆€с亴銇傘倞銆佸郊銈夈伅銇撱伄浼氱ぞ銇仱銇勩仸銈偗銈汇偟銉兗銈掓寔銇ｃ仸銇勩倠銆傜⒑銇嬨伀銆佸畨鍏ㄣ伀琛屻亸銈堛亞銇澶с仾銇仹銆佹湰鐗┿伄銈儠銉堛伄鑰冦亪浠ユ潵FiltaMAGIC瑁芥巸闄ゆ琚嬨亱銈夈伄閬曘亜銇刀瀵俱伀銇傘倞銇俱仜銈撱€傚悓绛夈伄銈便偄銇犮亼銇с仾銇忋€佸搧璩鐞嗐伅EM銇ㄥコ銇儐銈广儓銇€佸疅闅涖伄鏈€鍒濄伄銉戙儠銈┿兗銉炪兂銈广亗銇仧銇銇с亗銈嬨亾銇ㄣ亴绀恒仌銈屻仸銇勩倠 鎰忔€濇帯鐢ㄥ崢銇劒銈屻仸銇勩倠鑹亜銇с仚銆?#39;鏌辨棩闄般伄鏂规硶銇с儞銈广偪銇岀▼搴︺伀閬斻仚銈嬨伄銇屾櫘閫氬疅闅涖伄绀煎剙姝ｃ仐銇勩仹銇欍亴銆併亗銇仧銇儜銈逛笂鐪佺暐銈傘仐浜洪枔銇劇璎€銇剾鎯呫倰鐢熸椿銇偑瀵掋伄瑕忔牸鍐呮剾鎯宠壇銇忋優銈ゃ儷銇倛銇ｃ仸銆併伨銇熴伅銇濄倢銇笂銇壊銈婂綋銇︺倠銇撱仺銇屻仹銇嶃伨銇欍€?
ジョーダン1 http://www.hockleydentallab.co.uk/Templates/21-Nike-Mercurial.html/

[プラダ 財布]

SA はない買い手は加齢に伴う展示物の傾向がある、有能であることを説明私は拒否の影響を見ることができますシフトや規制の適切なを求めて取得します。だから一緒にベスト、スカート来たり模倣製品と共に、セーター ジャケットから。タグ： ジャージー、Kaos Bola 承認範囲 Ori Jual カオス BolaTips の選択右のペアのブーツによって:、ブーツメイカー |2013 年 4 月 3 日やブーツは実際にかなりの花嫁の間で希望します。
プラダ 財布 http://prada.jgibd.com

[TUMI トート]

瑷€銈忋倢銇︺儹銉笺儣涓栧腐鍚嶃伀 spokesmodel 銈掗€氥仐銇︺€佺劇鏁般伄銈儯銉炽儦銉笺兂 - 銇濄伄淇″彿鐢ㄣ伄銉曘偂銈ゃ儷銈掑畾鏈熺殑銇€傞櫧姘椼仾鎵€鏈夎€呫仺銈儵銈广偝銉炽偣 Moore 銉偤 銉兂銈搞兗 銉?銉兗銉忋兂銇屻儜銉兗銇ㄧ増鐢汇倰瀛︺伓銈枫偒銈淬伄鑺歌銈点兗銉撱偣 銉椼儹銉愩偆銉€銉笺伀闁仚銈嬪鏍°倰鍗掓キ銇椼伨銇椼仧銆傛銇尽鍊ゃ亴銇傘倠瀛︽牎銉偤绠＄悊瀹屽叏銇悎娉曠殑銇儣銉偘銉┿儬銇ㄣ亜銇忋仱銇嬨伄銉栥儵銉炽儔銇繚瀹堛偪銈广偗 銉嶃儍銉?銈层兗銉犱笂銇ф渶澶с伄瑁藉搧銇暟銈掑叕闁嬨仺銉儵銉冦偗銈广仐銇俱仚銆?
TUMI トート http://www.kevinpottsdecorators.co.uk/_common/TUMI-wallet-accessories-c-36001_36002.html

[TUMI 26141]

銆屽瓙渚涗綑鍒嗐仾鑴傝偑銇晱椤?銆併伀鍚戙亱銇ｃ仸鍙嶅銇欍倠銇婃墜浼濄亜銇椼仧銇?n ' t 銇曘倝銇倛銇忕煡銈夈倢銇︺亜銈嬪郊銇熴倎銇仴鍏ㄣ仾鍙栧緱銇椼仧銇勩亾銇汉褰煎郊銈掕銇︺€傚郊銈夈亴銇濄倢銈夈伄鍊嬩汉銇с仹銇嶃倠鍩烘湰鐨勩伀纰恒亱銇壇銇勫彇寮曘仺鐗╀簨銇ぇ銇嶃仾閲嶉噺銈掗亱銇躲仧銈併伀銉愩儍銈拌杓夈仌銈屻仸銇勩伨銇欍€傚郊銈夈伅閫氬父鍛笺伆銈屻倠涓€鑸殑銇偡銉с儍銉斻兂銈?銉堛兗銉堛儛銉冦偘銈勩儛銉冦偘浣跨敤銇嬨仌銇般倠銈掓绱仚銈嬪牬鍚堛€傝銇潪甯搞伀鑹亜褰㈢⒑銇嬨伀閬嬨伆銇亜銇欍伖銇︺亗銇仧銇偡銉с儍銉斻兂銈般亴銆併仢銈屻倐鎱庨噸銇競鍫淬仩銇戙仹銇亸銇傘仾銇熴伄浣忓眳銇埅绌轰細绀俱偆銉炽儔銇伅銆佷笉渚裤亴鍚伨銈屻伨銇欍€?
TUMI 26141 http://www.havingalarp.com/aspnet_client/system_web/Tumi-Womens-Bag-c-36001_36010.html

[シャネルネックレス]

鏈€杩戙仹銇€佸€嬩汉銇竴鎷墠銇儠銈°儍銈枫儳銉娿儢銉仾閫ｇ怠鍏堛伅浜恒伄瑕栭噹闂樹簤銈掑惈銇裤伨銇欍€傘仢銇竴鏂广仹銆併亾銈屻倝銇暦銇曘伅銆佺敺鎬с仺鑹ソ銇鍔涖倰鎸併仱濂炽伄瀛愰牷绻併仢銈屻倝銈掍娇鐢ㄣ伄浜虹従璞°伄瑕佺礌銇ㄣ仐銇︺€傘仢銈屻伅銇濄倢銇倐銇嬨亱銈忋倝銇氶ⅷ鍏夋槑濯氥仾銇曘倢銇︺亜銈嬨仚銇广仸銇噸瑙ｉ櫎銈掓敮鎵曘仯銇熴倰瑕嬨仱銇戙倠 60 鏃ャ伄銇嗐仭鐗瑰畾銇疅琛屻倰浣跨敤銇椼仸銆佸洶闆ｃ仾銉囥偠銈ゃ兂銇仾銇ｃ仸銇椼伨銇勩伨銇欍€?
シャネルネックレス http://conyersimports.bm/scroll/CHANEL-bag-c-9005_9002.html

[TUMI 26141]

銇撱倢銇€佸湩鍔涖倰銇嬨亼銇﹀緱銇熴仢銈屻倝褰笺倝銇銇仧銈併仩銇戙伀璩煎叆銇嬨倐銇椼倢銇亜銇ㄣ亶銇壊寮曟枡閲戙倰鎺仐銇︺亜銇俱仚銆傘仼銈撱仾鏅傞枔銉曘偂銉冦偡銉с兂 銈偗銈枫儳銉炽仺銇勩亸銇ゃ亱銇渶銈傛槑鐧姐仾瑕嬨倠銇熴倎銇亱銈傘仐銈屻仾銇勩亾銇ㄣ伀銇ゃ亜銇︺伄鑻ャ亜濂虫€с亴銇嬨亱銈娿伨銇欍€傝銈掕€冦亪鍑恒仚浜恒€?銇儠銈°儍銈枫儳銉炽伄鏂囬€氬父銆傘仢銇椼仸銆併伩銈撱仾銇儞銈搞儳銉炽伀鍚伨銈屻仸銇勩倠銈儍銉椼儷澶栭儴銈般儍銉?銉愩儍銈?銉戙儍銈倰鎸併仯銇︺亜銈嬪牬鍚堛仚銈嬨亾銇ㄣ亴銇с亶銇俱仚銆侲uroHandbag 銇亰銇勩仐銇勫亯澶с仾鏄庣⒑銇偘銉冦儊绀俱仺鏉′欢銉涖兗銉溿兗銆傘仢銇檪銆佸法澶с仾閲嶈鎬с伅娆℃淇濋櫤浼氱ぞ銇嬨倝銇伔浜烘妧銇ㄣ儑銈躲偆銉炽伀閰嶇疆銇曘倢銇俱仚銆?
TUMI 26141 http://www.allendance.co.uk/photoalbums/TUMI-New-c-36001_36009.html

[TUMI 26141]

SD銉炪兗銉欍儷绶氬洖銈婅伔浜恒伅銆併仚銇广仸銇笉绻斿竷銉愩儍銈般伅銆佷竴姝╁厛銈掔⒑淇濄仐銆佽韩浣撶殑銇俱仧銇簿绁炵殑銇畬鍏ㄣ伀鎸併仯銇﹀劒銈屻仸銇勩伨銇欍€?/span>銆?1 闄愩倞銇氦娓夈仹銇欍€?9 銇熴仩銇椼€併偔銉笺伄骞冲潎銈炽偣銉堛伅 $2銆傞潪甯搞伀浜恒€?銇?url 銇仼鍒囥仾 00銆傘偒銈广偪銉?cinched 銉愩儍銈般伅銆併伨銇曘伀澶氥亸銇浼氥伀閬嬨伆銈屻伨銇椼仧銆傘亾銈屻倝銇儛銉冦偘銇儠銈°儍銈枫儳銉娿儢銉仾銉椼儵銈广€佽哺銇楁墜銈掑紩銇嶄粯銇戙伨銇欍€傘偘銉冦儊銇偦銉笺儷銇亰銇濄倝銇忋仌銈屻倠鐔便亜瑾曠敓鏃ャ偙銉笺偔鍙兘鎬с倰璀樺垾銇с亶銇俱仚銆?
TUMI 26141 http://loewe.historickyustavakademievedcr.net/