Monday, 6 December 2021

D07完食感想

D系列終於完結了。

正確來說,天航老師在patreon上的連載早就結束了。實體書本我托人去書展買一本,至今仍末買得。加上疫情之下航運仍未恢復,我終於(暫時)斷了購買實體書的念頭而轉投電子書的懷抱。

說起來這也是我人生第一次購買電子書。我從來都是實體書的堅定擁護者,大概也只有我對D系列的牽掛加上這百年一遇的大環境才能逼我買那麼一本電子書吧?說起來Amazon居然沒有分辨不同地區帳號的功能有夠令人無言。我在網上找到的解答是當不同地區的帳號電郵和密碼俱同時系統會強制登入某一個帳號而使另一個沒法登入。我把密碼改了以後果然就沒有這個問題了。這個帳號→密碼→地區的樹型結構是那門子的大學生project啊?

回到D系列。

要我排名的話,D系列在我印象最深的系列小說裡不是第一也在三甲之列。原因與哈利那種對世界觀著迷的單一原因不同,應該說我對D系列的共嗚感已經超越了單純讀者與作品的關係吧。

(另一個不得不提的本土系列小說是同樣用英文字開頭--Q--的特工系列,不過人家也有自己的苦衷,我們苦苦強求結局也沒用。不知道如果當年乾脆利落地收尾的話大家的評價又會變成怎樣呢?)

我已經忘記了我買D01時候的場景--誰他媽會記得自己買幾千本書之一的場景啊?我買D02的時候倒是記得,因為第二集已成了大家奇待的暢銷作品。D03就更誇張了,書店的海報都要用搶的,我跟同學下課晚了十五分鐘就跟海報緣慳一面……嘛,扯遠了。

D01<<愛因斯坦被摑了一巴>>有著無數會被我銘記的元素。

首先主角很像我(被巴),尤其是外表,我跟D01再版封面的飯頭超像(再次被巴)。而且很重要很重要的一件事是這個封面的飯頭戴了個淺藍色吊墜,跟我的原創角色不謀而合。這……一定不是巧合吧!!

不過這點不是開玩笑的:那種對數字的狂熱跟他中學的成長軌跡都跟我十分相似,單是這點就注定這本小說會被我不停翻出來回味--翻看這本書就像翻看過去自己一樣,甜酸苦辣一次看完還能讓你感覺自己瞬間老了十歲。

D01的世界觀是一個很貼地的香港:舊式屋村、超任紅白機、在巴士上談情說愛(我好像在網誌裡寫過?快忘記了)、還有那個紙醉金迷的八九十年代香港。這些都比我所長大的年代要舊一些,但不妨礙我很早就對那個時代的香港有所向往,所以對這些文中這些描述並不陌生,甚至有點親切感。

我還記得,我把D01買回來後在班上傳了個遍。最後看那位同學過了暑假都沒還回來,我還差點被真的摑了一巴。不過至少我成功讓一堆同學成為了D系列的追隨者,這樣我買第二本收藏也算是值了。

D02緊接著第一集在翌年出版,在同學間依然掀起熱潮。無奈後天航瘋狂拖稿(這是事實),一直還在等的就剩下幾位書蟲。再到後來離開了校園,手上讀本的讀者就只剩我一個。但有些東西比如支持足球隊,當你開了個好頭它總是會吸引你支持下去,D系列就是其中之一。

必須承認我對第三四五六集的記憶遠不及前兩集來得高,排除老人癡呆症等因素後只能說前兩集在因緣際會下看完又看,對其印象當然比後面幾集各自相隔幾年的作品來得深。不過至少每一集的決鬥場景我都還記得:飯頭跟九歌在烏雲密佈的天空下對峙、阿紅作為演奏家在眾目葵葵之下動手竊物、賴飛雲與阿虎在碑林的決戰……天航筆下的高潮就是有這種魔力。這並不是D系列獨有的特質,包括三分球神射手甚至是五環戰士都在此之列。我會記住繼嗣在籃球場上燃盡生命的一戰,卻對同期出版之哈利波特四五六集裡三巫鬥法、決戰神祕部和老鄧之死的場景毫無興趣(就算加上電影改編同樣如此)。

我真的不是想寫D系列的書評,因為那樣我可能得重看整個系列,不過還是容我簡單說個兩點吧。

D系列從一開始就是神祕學大雜燴,卻又能揉合現代科學的觀點加以詮釋(當然經不起嚴謹科學的推敲但這不重要--發射劍氣又可能跟弱核力扯上關係呢?)這種有趣而不覺尷尬的筆觸一直都是這系列的亮點。正如倪匡先生所言,這是難得雜燴起來還好吃的作品,即使拿掉神怪還是好看(具體字眼忘了)。明明不是推理小說,文中卻是伏筆處處,在決戰前夕一次過unwind給你看的爽度甚至不比決戰本身差。你以為「只要我不尷尬,那尷尬的就會是你們」是最高境界嗎?不,最高境界是「你以為會很尷尬,但一下場你除了鼓掌甚麼也記不得了」。

數字貫穿了整部作品,尤其是一頭(D01)一尾(D07)。天航雖不是理科出身但我還是能感受到他找數字fit進去的努力。D01那個四位密碼真的很有趣,長大以後才發現符合文中條件的四位數字其實有兩個,多虧那道密碼門錯誤三次才發警報設定(笑)。D07裡的六位密碼有點掉漆就是,因為那串數字在普通的小童向數學讀物中就很容易接觸到了,我當初就是從麥兜系列那邊看回來的。

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看到D07後記的一句感觸很深:「如果連屬於香港人的純文字創作也消失的話,香港的文化還剩下甚麼?」

後半句當然有問題:香港那種華洋之交匯的生活方式本身就是一種不可磨滅的文化,即使在2019之後受到催殘稀釋,這種文化卻依然隨香港人漂流到世界不同角落。就算只談創作好了,在本土電影業末落的今天那些拍香港過去三兩年點點滴滴的小本電影依然在金馬獎大有斬獲,不就是香港文化頑強地活著的證明嗎?

他的前半句倒是真的:我無聊上天航的官網一看,除了發現三分球神射手被移出首頁(太偏心了吧,阿米巴系列都還在)以外,還發現原來從D03開始這系列就佔據暢銷書榜,第四五六集甚至分別霸佔了12、15和18年的第一位。我就挺納悶了,前面兩集怎可能沒上榜?

結合前兩本的銷量來看的話,合理解釋就只有一個:書本的市場大不如前,不論是作者的質與量跟讀者的消費意欲兩邊都一直往下。

這不單是「文化沙漠」的問題,也是繁體中文甚至全世界書市都遇到的問題。單看台灣在鮮鮮、冒天相繼倒下後實體書的廣度大不如前;日本的文本銷量也是一路往下,倒是輕小說市場抓住毒物這個財富密碼一路狂推,在市場夠大(別忘了海外的會看日文的人說不定不比日本本土少)的情況下還是活得還可以。

這種問題太艱深,不是我們這種小蝦米可以解決的。我們唯一可以做的就是繼續支持本土創作--支持本土電影製作、支持本土同人、當然也要支持香港的純文字創作者。

天航是我印象中最後一位可以吸引全城追捧的本土作家,單這一點就值得我們支持下去了。

等航運恢復後我一定要買D07實體版,希望到時還沒賣光吧?

Monday, 15 November 2021

Short comments on CTWC2021

 

Both entering level 29 (aka the kill screen...or the second transition) with 1.15m, Richy proceeded and scored another 200k using the rolling technique. (Source: CTWC Twitch stream)

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CTWC2021 has just concluded. Pretty low profile comparing to to last year. Although admittedly I had time last year to watch the whole tourney due to some coincidences.

Still I got the chance to have a quick glance on some of the group stage fights of those veterans, and of course caught the live stream for the finals today. Dog performed so consistently that although we found his opponents sometimes outperforming him he met no real troubles in overall. Now a reigning champion, but it's hard to tell whether he will win as well next year, and the 7 times champions Jonas will always be the legend to be remembered.

So, anything special about CTWC2021 comparing with the 2020 ones?

Many focused on how rolling would destroy hypertappers (the era of DAS is for sure gone forever), but the tournament showed that rolling has a long way to go before such style starts to outperform in general.

The output of rolling has been inconsistent, as shown by the performance of rollers in their daily practices or even during the qualifiers. At best you see Richy scoring another 200k+ post level 29 and at worst you see others topping out at 100k. The aggressiveness brings you survivability in the worst condition, but they do not always bring you the cleanest of the boards.

That leads to our second observation: hypertappers are still evolving in consistency. When hypertapping was first introduced it was sought as a way to handle bad situations from level 19. Then it was used to grind a little more from level 29. But people realized the most efficient way of hypertapping is to get aggressive in regular (level 1-28) gameplay for more Tetrises -- but not overly aggressive. What we observed this year is a big step by hypertappers edging closer to optimal efficiency, a balance between scoring and consistency. Dog in particular showed that top level hypertapping could reach 1.1-1.2m regularly which would always give you at least a 3-1 if not 3-0.

We would expect the same development trail for rollers. In the experimenting stage they get to solve bad situations from level 19, then the second step is to grind a hell lot more from level 29. Rollers this year already grind quite a lot out there but it's just not consistent enough. The same goes for rolling at lower levels. They have not been able to control as precise as hypertappers so their Tetris efficiency is dragging them down, so they need to devise a way to score properly as well. The strategy could be completely different from hypertapping strategies though -- the frequency and accuracy of making inputs makes the crucial difference. 

As an intermediate solution, some rollers took a hybrid approach using hypertappings before level 29. This is a sensible way of playing considering that hypertapping could probably perform close to optimal with hypertapping already so there is no need to take the risk. The only problem is to transform into the rolling stance during the light speed gameplay.

How long would it take before rollers start to boss over hypertapping in both the pre-29 and post-29 phase? This is hard to tell. It took hypertappers a few years before it finally sentenced the death of DAS, and the improvement made these two years after Joseph first won the tourney, is still significant. It may not take as long for rollers due to higher exposure to public, higher attention as a game and more top level fights held regularly and so on, but it will take some time for sure.

Rollers or not, the overall performance still improved by a lot. Remember what I describe the Koryan match as the most epic ever game with 1.1m each? Well, we have 1.2m each games this year and a hell load of 1.1m each games. Still I think that battle last year remains as the more dramatic ones, but higher scores are higher scores. We observed a major performance boost this year, and I expect the same to happen next year. The only uncertainty is that when lockdown is over for major countries, will the tournament be held completely online anymore? Does that affect out-of-America players? This is even a harder question to answer, but we will see next year.

Tuesday, 9 November 2021

Exposure of LETFs and why we don't need cash in the portfolio

Since when did I last wrote financial/stock market stuffs? Probably not since 2008. That doesn't mean I stopped interacting with the market though.

One major change is that ETFs (exchange traded funds) have been much more popular since 10 or 20 years ago instead of ETNs or traditional mutual funds. Simple index funds like SPY and QQQ started around 2000 and we now see similar products all over the world: 2800 (tracker fund) in Hong Kong is nothing new, 0050 (TW top 50 tracker) in Taiwan proved more efficient than most investors, and we even find these products in Tokyo, a traditionally conservative place (they just set up more regulations this year on ETFs!).

But what I wanted to cover today isn't really about index funds, but those leveraged ones (LETFs). No words are needed to describe how they separate themselves from other leveraging methods: they automatically leverages/deleverages themselves on a daily basis. Since their introduction around 2010s, leaders like TQQQ (3x Nasdaq100) has accumulated much popularity, gaining even more attention on every major drawdown.

The ups and downs of LETFs are apparent: you are under leveraged gains (the gains themselves are compounded which magnifies with time), but are also under leveraged risk. Due to volatility decay and the asymmetry of the rise and fall, the return (per unit time) multiplier is always below the leverage ratio and the risk (sd p.a.) is always above the leverage ratio. That gives a lower Sharpe ratio. Of course this is to be expected -- it is impossible for us to leverage a certain portfolio at risk free rate.

Facing these elevated risks are two kinds of people: the yolo apes who are happy to take the risk and went all in TQQQ, and the boogleheads who try to take advantage of the LETFs but also maintaining efficiency in overall. For those who are going all in there isn't much to say -- you probably don't have many alternatives with similar return, and TQQQ is probably one of the best choices. But for those boogleheads the strategy can be extremely diversified.

In light of the classic 60% equity - 40% bond combination, people seem to be applying the same ratio for their leveraged portfolio, and it seemed to work: if you consider TQQQ and TMF (3x 20yr bond) only, max Sharpe occurred at a 55/45 ratio but 60/40 gives almost the same ratio. If you backtest the thing since the beginning of the Nasdaq index, a 60/40 portfolio would beat any other portfolio, including the all in strategy (this is mainly due to 2000 and 2008, admittedly. But who can assure that it won't happen again?). It is also noteworthy that similar conclusion applies if we replace TQQQ by UPRO, the 3x S&P LETF. 

The question is, why? Why does the ratio carries through upon leveraging?

To answer this allow me to introduce exposure, another keyword from the title.

Exposure is a fancy word of leverage ratio, but also applies to a specific component of the portfolio rather than the whole thing. To be precise, a certain portfolio's exposure on a product X is the movement per X's unit price change while leaving all others constant.

For example, QQQ has about 10% of MSFT. That means if MSFT rises by 1% then we would expect a 0.1% corresponding change in QQQ. In a similar way, since TQQQ is leveraged by 3 times, it has a 30% MSFT exposure. A 1% change in MSFT would lead to a 0.3% change in TQQQ.

Amazingly, exposure adds up even among independent tickers. Continuing from the above example let us also introduce SPY which holds approximately 5% of MSFT. If your portfolio consists of 50% TQQQ and 50% SPY, then you will have a 10%*3*0.5+5%*0.5 = 17.5% exposure of MSFT.

And now here is the main principle: portfolio with equal exposure (in all assets) would act identically upon tracking errors due to expense ratio, compounding effect and volatility decays.

The error are all long term tracking errors so the statement holds if it holds in a daily basis which is apparent: if two portfolios have equal exposure in every asset, each of the asset would contribute equal influence to the two portfolios.

Still, the difference between two portfolio with identical exposure due to the above errors are minimal. Given a portfolio suppose we up-leverage part of it and de-leverage another part of it to achieve the same exposure. The elevated risk and decayed return of the up-leveraged part is offset by the opposed effect from the de-leveraged part. 

Let us consider the following two portfolios:

1) 50% TQQQ and 50% QQQ
2) 100% QLD

Both portfolio have 200% QQQ exposure so we expect them to act almost the same, and we now calculate the effect of decay on the two profiles.

Suppose QQQ rises by $x$ one day and drops by $x$ on the next day. Then QQQ drops by $x^2$ in overall. On the other hand, the first portfolio takes a drop of $5x^2$ while the second one takes a drop of $4x^2$. We can see that their decays are really close to each other only differing by $x^2$. Sure this is still the same order as the ordinary decay, but the coefficient is greatly compressed. You can argue the same for expense fees as well as the compounded return.

(Note that the above example shouldn't be interpreted as "the decay of a 2x ETF is 4 or 5 times the underlying ETF" because you are not comparing when underlying ETF is at the original price, so it is natural for the LETF to drop more to reflect such shift. If we alter our method, either by boosting the up-day or to give it another day to rise back to the original price level we will get a much smaller decay. Take the above example again: the first portfolio will suffer a decay of $3x^2+O(x^3)$ and the second is of $2x^2+O(x^3)$ when QQQ is at 100%. This is the truly decayed part.)

Due to convexity and Jensen's inequality, the above always holds when comparing portfolios with identical exposures but distinct leverage irregularities. On the other hand using the same argument, we can see that the compounding effect favors portfolio with higher leverage irregularities. 

In practice however, it is more often to see that portfolios with less leverage irregularities perform better. A possible explanation is the asymmetry of the rise and fall again. A decay lost of $-x^2$ and a compounded gain of $+x^2$ gives a net gain of $-x^4$. Small but accumulate over time.

As a result, even though portfolio of identical exposure behaves almost the same, it's still desirable to reform the portfolio to achieve a homogeneous leverage ratio.

If we treat cash as a 0x etf, then we shouldn't hold cash at all -- instead, spend these cash to deleverage the rest of your portfolio for that extra bit of return.

For example consider a 40% TQQQ 40% SPY 20% cash portfolio. If we are to deleverage it using the 20% cash it could become 60% QLD 40% SPY. Backtest shows that the altered portfolio gives 0.5% more return per year with a drop of 0.6% in risk. Note that TQQQ and QLD has the same expense ratio so the altered portfolio is winning even with higher fees!

Three possible portfolio with identical exposures but different cash levels (0, 20%, 30%). 
Taken from portfolio visualizer.

Now if we operate the other way round: we up-leverage the portfolio to free more cash, what can we do? We are certainly not leaving these cash alone because we know that would leave the portfolio inefficient. Instead we can buy something else using these cash.

Something important that solves our question at the beginning: why does the 60/40 ratio carries through?

(Cont.)