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2011年6月23日 星期四

對外判軟件進行測試

數學是非常有趣的科目,而且應用非常廣泛,例如在建築、電子工程、電腦及金融行業等,每日的運作都必定離不開數學。以金融行業為例,由於近10年衍生工具、結構性產品的發展一日千里,愈趨複雜,投資機構面對的風險問題,亦成為投資部門、風險管理部門、監管機構以致政府高度關注的題目,特別是近年多次的金融事故多與衍生工具或結構性產品有關,風險管理不善,就會影響到個別金融機構的存亡,甚至可以動搖整個國家的根基。

要有效地管理衍生工具或結構性產品的風險,就必須要以客觀的方法,把風險量化(Quantify),例如監控承擔風險等值(Exposure)、對沖值(Delta)、對沖值變化值(Gamma)及波幅變化值(Vega)等。

數學與電腦 缺一不可

然而,量化這風險需要運用到大量的數學理論及複雜的財務方程式或模型(Financial Modeling),要懂得如何靈活及正確地運用這些理論或模型,一定要充分地掌握金融產品的特性,又必須要有深厚的數學/統計學的根基。在另一方面,數學模型裏面一定會牽涉到繁複的計算,非電腦不能應付。因此一定要將這些計算方法編成程式,才能便於應用。

軟件外判不等於責任外判

可是能夠同時擁有深厚的數學根基又精於電腦編程及對投資產品有深入認識的人才實在不多,根本不可能要求每一位同事都是數學家或財務工程師(Financial Engineer),所以很多機構都選擇把這方面的工作外判給顧問公司(Consultant)。但工作外判後也帶來很多問題,例如公司本身可能無法完全得知外判商是如何把這些數學理論及複雜的財務方程式轉成電腦程式,外判商亦不會把程式的原碼(Source Code)公開,公司本身很難對電腦程式及定價模型進行驗證(Model Validation)。

對外判軟件進行驗證

其實監管機構明確表明,受監管的金融機構在不洩漏機密資料的情況下可以外判工作,亦可以使用第三方軟件(Third Party Software),但外判工作的同時,不可把責任外判,即受監管的金融機構必須承擔自我監察的責任,仍然有責任確保所使用的財務方程式或第三方軟件準確性。

雖然在沒有原碼及程式的資料的情況下,要對第三方提供的軟件或財務方程式進行徹底的驗證不是一件易事,但並不表示毫無方法去估計其準確性,只要了解產品的特性並掌握其價格與其他因素之間的相互關係,就能作出有效的測試。這些測試方法不一定是直接的驗證,但如果多方面地進行旁敲側擊,也能起到測試的作用。

因素測試

什麽是因素測試呢?就以歐式認購期權作為一個簡單的例子,認購期權在到期前的理論價值(Theoretical Price, P)取決於以下的幾個因素:波幅(Volatility, v)、利率(Interest rates, r)、股息(Dividends, d)及到期時間(Time to maturity, T)。只要明白各因素對期權價值升跌的關係,就能對財務方程式或第三方軟件的準確性進行測試。

測試前需要在市場收集一些數據,如波幅(v)、利率(r)及股息(d)等。現時很多報價系統供應商都有提供波幅數據,如引伸波幅(由市場期權現價,利用期權計價程式逆向計算出來的波幅)及歷史波幅(等於現貨價格變動的標準差standard derivation)。利率可以參考銀行的同業拆息(Hong Kong Interbank Offered Rate)。股息可參考歷史股息率或分析員的估計。當有了以上的數據,就可以進行測試。

例如測試股價變動對期權價值升跌的關係(Moneyness testing):股價S比行駛價K少很多時(超價外期權deep out of the money),其價值應接近0,對沖值Delta亦應該接近0。當股價S開始接近行使價K時(價外期權Out of the money),期權的價值變動開始增加,對沖值亦開始增加,到股價S等於行駛價K時(現價期權At the money),期權的價值變動約為現貨價格變動的一半(對沖值大約0.5)。股價S再上升(價內期權In the money),期權的價值變動會進一步接近現貨價格變動。到股價進一步上升,期權變成超價內期權(deep in the money),期權價值的變動會與現貨價格變動相同(對沖值等於1)。

若外判軟件得出的結果未符合預期或與市場價格相差甚遠,則代表該系統未能通過測試,已毋須再進行其他測試。

如能成功通過以上測試,則可繼續進行其他測試──例如利用認沽認購期權等價理論(put-call parity)去進行套戥測試,也是一個常用的方法。

做一個數學的用家

作為一個金融業的工作者,當然不可以是一個數學盲,但也毋須要求他做一個數學專家。就以因素測試為例:我們當然可以用正規的數學方法──建立模型、推導公式、去證明【表】內的每一個關係。但數學證明並不重要,更重要的是用簡單、直覺的方法去理解這些關係,並收為己用。金融業的工作者無必要成為一個數學專家,只要能做一個數學的用家,那就足夠了。

作者李承諾任職於金融機構,派駐日本

林建教授為香港浸會大學榮休教授

2010年10月12日 星期二

Options Show No Black Swan in Emerging Markets as Stocks Surge

The smallest stock price swings and fastest economic growth in three years are convincing options traders that developing-nation equities are safer than ever relative to U.S. shares.

The MSCI Emerging Markets Index’s historic volatility, a gauge of price swings during the past three months, fell to 12.1 last week, the lowest level since July 2007, according to data compiled by Bloomberg. The cost of options insuring against a drop in the iShares MSCI Emerging Markets Index exchange-traded fund has declined to a record versus those tied to the Standard & Poor’s 500 Index, the data show.

While the U.S. recession in 2008 helped spur the MSCI index’s worst-ever bear market, a 66 percent drop, Goldman Sachs Group Inc. says America’s slowing expansion now will force central banks to keep interest rates low and fuel gains in developing-nation stocks. The gauge rose an average 25 percent in the 12 months after the last 10 periods volatility sank to this level,beating the S&P 500 every time, data compiled by Bloomberg show.

“We’re probably going into a period of relatively low emerging-market volatility,” saidChristopher Palmer, who oversees about $6 billion as head of global emerging markets at Gartmore Investment Management. “The Black Swan way of looking at the world means that you have to take into account that there may be some things happening positively that are difficult to explain.”

Bull Rally

Nassim Nicholas Taleb, in his 2007 best-seller, “The Black Swan: The Impact of the Highly Improbable,” said most people underestimate the frequency of high-impact events. He has built strategies to protect investors from market swings using options, contracts that give the right to buy or sell assets at a set price by a specific date.

The MSCI emerging stock gauge has more than doubled from its bear-market nadir in October 2008 as the U.S. and Europe cut benchmark borrowing costs to all-time lows and developing-nation economic growth quickened to an annual rate of more than 7 percent this year, according to International Monetary Fund estimates. The index has climbed for six straight weeks and traded at 1,107 yesterday, the highest level on a closing basis since June 2008.

The three-month implied volatility for at-the-money options on the iShares MSCI Emerging Markets ETF was 25.92 on Oct. 8, compared with 20.65 for the SPDR S&P 500 ETF, according to data compiled by Bloomberg. The difference shrank to 3.72 on Oct. 4, the lowest since Bloomberg began compiling the data in March 2006. Implied volatility is the key factor in determining options prices.

Decoupling Bets

“People think there’s going to be a decoupling,” said Rebecca Cheong, an equity derivatives strategist at Societe Generale SA in New York. “There are a lot of people demanding downside protection in the S&P and there’s less demand for emerging-markets protection.”

Investors’ growing preference for developing nations is also reflected in relative equity valuationsand fund flows. The MSCI index trades for 2.06 times net assets, within 3 percent of the highest since March 2008 relative to the S&P 500, which is valued at 2.15 times, according to data compiled by Bloomberg. Emerging-market equity mutual funds lured $53.8 billion of net inflows this year, while U.S. funds had outflows of $65 billion, according to EPFR Global and Investment Company Institute data.

Rising valuations are leaving developing-nation stocks vulnerable to a renewed contraction in the U.S. economy, and investors should consider buying low-priced options that insure against equity losses, according to TCW Group Inc.’s Komal Sri- Kumar.

Bubble Risk

The Federal Reserve’s policy of cutting interest rates to a record low has had repercussions 彈回; 反衝 worldwide, including currency misalignments and the risk of asset price bubbles, Nobel Prize- winning economist Joseph Stiglitz said in a Bloomberg Television interview Oct. 6. Emerging-market policy makers from Brazilian central bank President Henrique Meirelles to Russian Deputy Finance Minister Dmitry Pankin warned last week that their markets may be forming bubbles as foreign investment pours into the nations’ assets.

The MSCI emerging gauge sank as much as 66 percent from its October 2007 high, nine percentage points more than the S&P 500’s peak-to-trough decline, after the U.S. recession and spiraling bank losses spurred the worst global financial crisis since the Great Depression. Profitsin the 21-country MSCI index dropped as much as 50 percent from their peak, compared with 47 percent for the S&P 500, data compiled by Bloomberg show.

Cheap Insurance

“The risk of a double-dip is still very much present,” Sri-Kumar, the Los Angeles-based chief global strategist for TCW Group, which oversees about $110 billion, said in an interview. “If you can get yourself cheap downside protection, that would be a better position to take in the short term, rather than be naked.”

Price swings increased prior to the end of the MSCI emerging index’s 2007 rally. The three-month volatility measure jumped to 27 just before stocks peaked in October 2007, more than double the level of 12.1 on Oct. 8, according to data compiled by Bloomberg.

While the U.S. will probably grow at a 1.5 percent to 2 percent rate through the middle of next year, there’s a chance the world’s largest economy will fall back into recession, according to Jan Hatzius, Goldman Sachs’s New York-based chief U.S. economist. The Fed, which has already bought $1.7 trillion of debt to bolster economic growth, may take additional measures in its next meeting at the start of November, Hatzius said in an e-mail to clients last week.

‘Silly Valuations’

The biggest emerging-market economies will probably expand more than 8 percent as a group next year, according to forecasts in September from Goldman Sachs. Earnings in the MSCI emerging gauge will increase 28 percent in the next 12 months, topping the 22 percent growth for the S&P 500, analysts’ estimates compiled by Bloomberg show.

The slowing U.S. economy “may be one of the better scenarios” for emerging-market equities because it will ensure interest rates stay low without sparking another crisis, according to Goldman Sachs strategists including Kamakshya Trivedi in London. The iShares MSCI Emerging Markets ETF will probably outperform the S&P 500, the strategists said in an Oct. 8 e-mail.

The iShares ETF has climbed 11 percent this year, compared with a 4.5 percent gain in the S&P 500. The MSCI All-Country World Index of shares in emerging and developed nations has advanced 4.5 percent.

Plamen Monovski, the London-based chief investment officer at Renaissance Asset Managers, said developing-nation stocks may continue to climb because some of the biggest industries were left behind in the rally. The MSCI Emerging Markets Energy Index is little changed this year.

“To get to a widespread bubble, you need to see silly valuations across the markets and the sectors,” said Monovski, who helps oversee about $2 billion. “We haven’t reached insanity levels. Volatility can stay low for some time.”

2010年10月3日 星期日

此時此景,擁有更多現金、房產?

錢志健

在過去十.一長周末,我如以往一樣繼續工作。蘭桂坊整個大「block」大變天。蘭桂坊之父Alan Zeman把他的物業商廈大做翻新工程(facelift), location, location, location,作為「蚊型」(LKF)地產投資者的我,實在也變得歡喜若狂,但地產泡沫又何時完結?是否先爆後狂瀉?

文章出版的今天已是第四季的開始。在絕對回報的領域,只有年尾才會收基金獎勵費(incentive fee)的操盤人實在心情矛盾,今年8月是美國道指自2001年來最差的月份,不少人做短倉看淡,9月份各大指數又強力急升。有位在第三季過後有錢賺的操盤人,在上周四的happy hour「吹水」時段對我說:「Ed,頭三季度真難捱。一上一落難以掌握,到現在已有利潤,不想第四季亂『操』而失去利潤,最重要還是要日曆年力保不失!」

操盤人愈來愈審慎

不知何時開始,可能自2008年金融海嘯後,很多操盤人也變得愈來愈審慎。去到第三季尾,又有正回報的操作者,在以往,只會更加想「挑戰自我」,甚至想「超越自我」為大前提。絕對回報的世界便是這樣:Best Hedge Fund of the Year, Best China Fund of the Year, Best Sector Fund ... 差不多每個類別也有良性競爭。到現在,當盤路及行情去到某一關鍵時刻,操盤人也會想多了,槓桿多一些,博什麼?Stupid move!

有位已與時代「脫節」的老行尊在北美時曾對我說:「去到最後,投資是要緊抱更多現金及磚頭,不是更多股票!」在我人生上半場當中,見到跌到變「零」的股票不下十隻:Lehman、Nortel、Etoys、Bre-X ...,除非我手頭擁有的全是津巴布韋(Zimbabwe)紙幣,我的地產投資也是「豆腐」房子,擁有更多現金及磚頭,做錯的機會比較細。

在文章的下半部分,我會和大家分享一位投機者(草蜢仔)的獨白。

先談地產。在super asset class的慨念中,不可能不投資房地產!讓我找家族資產執行人Rudy和我們繼續上周還未說完的話,(Rudy的家族資產投資本身基地在香港以外)。他主管的家族資產極為低調,以下是兩周多前拜訪他,可「出街」的部分內容:

Ed:有super asset class的概念,這才不會有任何資產有機會弄到你一敗塗地。

Rudy:我們這裏也看到華文報紙及網上《信報》新聞,你也有引用過,「你要把資產分為七份或八份,因為你不知道將來會有什麼災禍發生」。這句話從哪裏來?

Ed:《傳道書》十一章二節。這是說到所羅門王受上帝啟示後,獲得的一套治家治國的大智慧。

Rudy:我比你現代化。我還是相信Harry Markowitz所說的有效率邊際(efficient frontier),適度的資產分散。

Ed:家族資產,永遠離不開地產投資。你們是實業起家,又不是地產發展商,如何決定投資在哪一個地區及領域?

Rudy:首先,我們這裏差不多人人可以置業。這可以說是我們這地方公民的基本權利。你們香港人的欲望,就是股市、地產及賭博,並不健康。你們所謂的香港精神,就是以累積財富為人生目標……。

Ed:Rudy,可否入正題?

Rudy:香港五十年不變,countdown餘下只有三十多年,你曾和我說過,香港高地價政策難以改變,所以香港地產投資風險極高。

Ed:你所指是接火棒,一下子升得太急?如果高地價政策不變,樓價只可能大漲小回,難以大跌。再說,香港不同美國,基本上現在已沒有什麼no money down的怪招,遊戲規則便是這樣。

Rudy:我們家族資產的投資,在房地產方面,最重要是先了解當地稅制及法例。我們的六人投資團隊還不足夠,需要有country specialist,這是和股票及其他liquid strategies的最大分別。

對香港地產投資有保留

Ed:看來你對香港地產行情有所保留?

Rudy:並不,你們是1998年買樓的香港負資產一族,不需要「十年抗戰」才變正資產,但三十多年後香港只是大陸其中一個城市而已,坦白說,看淡的人永遠是不受歡迎的。我們做的項目,當「下注」每個國家時也要drill deeper,像你們香港人買樓一樣,會研究土地政策、潛在風險等。

Ed:你以旁觀及投資產者看香港地產,你認為最大風險在哪裏?

Rudy:你們香港是一個怪異的地方,八十、九十後,no jobs、no equity,變相一些父母可能會送一層樓給二十多歲的子女,或最少送首期;父母不僅負擔兒女完成大學及碩士的費用,還要幫助他們置業,too bad,so sad ...。

(後感:在liquid strategies上,我極同意Rudy的投資理念。Rudy看淡香港地產,我可以理解。我也明白當他說下一代no jobs,no equity,是指父母如何節衣縮食,如果無父母「發功」,籌集首期也是考工夫的事情,沒有對與錯。)

另一話題。一位投機者的獨白。

「草蜢仔」在投機市場數十個交易月,有賺有蝕。在「金融圈內」專欄中,除了Rambo已選擇離場外,「草蜢仔」還是在槓桿市場上掙扎。我無法盡錄和他的對話,但在此想,對他說一段心底話:

利用Credit Spread期權的特性,特別是時間值損耗法去尋找獲利機會,可行性是有的。看北美洲模擬組合【表】,有十五隻股票及ETF。如果由2006年中buy & hold,股票帶來的利潤可能是負或打和。利用bear call及bull put的特性,實在是千變萬化的策略,非筆墨一般可以形容。沒有人有水晶球,但像CME、芝加哥衍生及商品交易所,金融海嘯後不對沖基金倒閉,有立場後做dedicated bear call看淡,比做Iron Condor(bear call + bull put)可能更加有效。但世事無絕對,CME成交量增加後行情可能大變。還有,在2010年中Apple已取代Microsoft,成為全世界最大市值公司,但十年前,我也眼見Apple曾經有接近九成的跌幅,後來「復活」,波幅極大,小心!

草蜢仔「投機者獨白」

以下是「草蜢仔」的背景,因內容太長,只可摘錄:

草:我在2008年年初,向財務公司借了55萬元,加上自己5萬元,以十一倍槓桿,每月建立一個期權盤來操作。因每月必須結算,不論輸贏,都必須了結。

Ed:你是否有點兒在賭運氣?絕對投機?

草:我認為這只是實驗,你可說是wealth lab吧。實驗結果,由2008年初60萬元本金,曾累積至290萬元,當中已扣除每月的還款及不定期的提款作開支。雖然,今年7月及9月,輸掉及用去了150萬元,本月戶口還有150萬元來操作,成績相當滿意。

Ed:九十日內,drawdown有五成,如果是基金,去到四成已停止所有操作。你這兩年第三四季這樣的roller coaster ride,值得嗎?

草:很高風險,是不是?我這種破斧沉舟的感覺,我很享受……。

(後感:普通人操盤最難的地方,是太輕易加碼。「草」的position sizing,只有他自己才知道。如無意外,「草」是操恒指期權在9月份出錯。2000多點恒指的上落,大漲小回,只要bear call那一邊張數太多,損耗可以很大,但風險是預知的。)

坦白說,沒有人能百分百掌握每個asset class的起落,每個人財力及能力也不一樣。Rudy是另一個層次的「守業」執行人,「草蜢」是投機者。正如我所說,把投資上的損耗降至最低,equity curve才有潛在機會上升,達至複息增長,這才是最高境界!

最後,Option Theory & Trading, A Practial Step by Step Guide:「期權實戰室」於11月13日星期六下午,在香港證券學會舉行。有興趣了解,可用電郵聯絡我。祝大家平安,下周一見!

mdehedgecenter@gmail.com