市場風險衡量的財務計量新方法

Abstract

財務風險管理是財務金融的一個核心領域, 而風險的衡量更為其中的關鍵。 各式的風險指標經常被廣泛地應用於定價、避險、投資組合的優化、資本的配置, 或投資成效的評估中。 數十年來, 風險的測度與衡量, 一直是財金學界、業界以及管理者最關心的議題。 本論文考慮三個新的衡量系統性市場風險的財務計量方法, 包括高頻率的市場貝他係數 (market beta)、實現的波動性 (realized volatility), 以及金融資產的極值風險 (tail risks)等。 眾所皆知高頻的資產報酬常混雜著諸如缺乏交易 (notrade), 買賣價差反彈 (bid-ask bounce) 等市場微結構效應; 尤其當所考量的一組資產發生因為非同步交易 (non-synchronous trading) 而造成資產報酬序列為非同期 (asynchronous) 時, 直接使用這樣的報酬資料於風險管理中, 很可能導致獲利/損失被誤導, 或避險策略被扭曲等系統性的失誤。 論文的前兩章即在探討利用高頻資料估計市場貝他與實現的共變異矩陣時, 市場微結構的效果和處理的方法。 為了正式地探討這個議題, 我們在第一章介紹一個新的隨機時序加總 (stochastic temporal aggregation) 時間數列模型, 以呈現非同步交易的現象; 我們發現隨機時序加總會干擾或遮蔽 (mask) 一些常見定態 (stationary) 時間數列所原有的相依性。 據此, 我們建議透過 MCMC 法復原出 (recover) 真實的報酬數列來解決非同步交易所造成的偏誤, 並進一步應用於高頻市場貝他係數的推論。 理論推導的結果顯示, 不考慮非同步交易而任意設算的貝他係數嚴重低估真實的高頻市場貝他。 應用前述方法於 NYSE 若干中小型股的實證結果中, 我們發現和理論結果一致的低估現象; 高頻市場貝他也顯著地異於低頻的日貝他。 此外, 所建議的還原法能夠校正高頻市場貝他中高達 $60\%$ 因非同步交易所致的誤差。 因此, 輕忽非同步交易可能所導致的問題是危險的。 實現的波動性, 透過加總極小區間所抽樣的日內報酬率平方以逼近不可見的日波動性, 已從連續時間的觀點被證實。 然而迄今為止, 建構實現的指標, 諸如波動或相關性等, 都仍侷限於交易頻繁的金融資產。 本文的第二章即嘗試著透過第一章的方法, 從一組包含不同交易頻率的證券報酬中, 去建構一個不受非同步交易偏誤以及其他市場微結構效應影響的實現共變異矩陣, 以供投資成效評估或策略性資產配置所需。 我們利用同步化過後的真實報酬序列去算實現的波動性與相關。 實證結果發現, 還原法併同濾過相依性的步驟, 的確能有效地調整來自非同步交易與其他市場微結構的效應; 而且對一些非交易頻繁的股票而言, 受非同步交易的影響遠甚於其他市場微結構。 在控制了非同步交易的效果之後, 源於其他市場微結構的效應仍明顯存在, 但幾乎可以被忽略。 因此, 還原法併同濾過相依性的程序可以讓我們得到更精確的實現波動性與相關性, 以作為更進一步的財務應用。

尾端或極值風險在風險管理扮演著顯著而重要的角色。 在第三章, 我們提出一個根據 expectile 所設算的新涉險值指標 -- 稱作 EVaR, 以適當地將金融資產潛藏於分配尾端的災難性風險納入考量, 彌補常用的根據分量 (quantile) 所計算出來的涉險值的不足。 因為 EVaR 是透過極小化一個非對稱加權的均方變異而得, 因此它能夠反映出分配尾端的型態, 像是異常極端的損失。 文中討論了 expectile 的統計性質, 以及它與分量之間的關係。 為了反映實際上對極端風險管理的考量, 我們繼而提出一個可以用非對稱最小平方法估計的 CARE (Conditional AutoRegressive Expectile) 模型, 以計算條件 EVaR; 我們將 Newey 與 Powell (1987) 的結果推廣到適用於弱相依隨機過程。 在對六個國家匯率報酬的實證中發現, 以 rate of exceedance 為準則, 透過 CARE 設算的新涉險值 EVaR 的確在 Mexico Peso 與 Thai Baht 這兩個遭遇過金融危機的通貨中, 同時在樣本內與樣本外優於 QVaR。 此外, 若結合這兩個涉險值指標的訊息, 將有助於同時在樣本內與樣本外進一步降低 rate of exceedance。

Financial risk management is a core field in finance in which risk assessment plays a key role. Risk measures have been widely applied to pricing, hedging, portfolio optimization, capital allocation and performance evaluation. Over decades, the measurement of risks has long been a primary concern for both practitioners and regulators in the sector of financial industries. This dissertation considers three new econometric recipes for assessing systematic market risks, including high frequency market beta, realized volatility, and tail risks for financial assets. The first two chapters focus on market microstructure effects on estimating market beta and constructing realized covariance matrix based on high frequency data. It is well known that returns sampled at high frequency are contaminated by market frictions, such as nontrade, bid-ask bounce, among others. When considering a basket of assets, asynchronous financial return series due to non-synchronous trading complicate or bias many tasks of financial management. Profit and losses can be biased and the hedging strategy may be distorted. Hence, using non-synchronous returns is likely to result in systematic errors. To formally address this issue, in Chapter 1, we investigate the effect of Stochastic Temporal Aggregation (STA) of time series that exhibits non-synchronous trading. For various time series models, we observe that stochastic temporal aggregation will mask the dependence structure or the uncorrelated nature of the original process. We thus propose to resolve the non-synchronous trading problem by recovering the virtual return processes via the Markov chain Monte Carlo method utilizing information hinged upon the stochastically aggregated returns. We consider estimating high-frequency beta among several asynchronously traded asset returns. Theoretical results on auto-covariance and cross covariances derived for non-synchronously traded returns show that arbitrarily computed beta without considering the non-synchronous trading effect seriously underestimate the true beta. Applying the proposed recovering method to some mid- or small-cap NYSE equities in TAQ data, we found the empirical results are in line with our theoretical results. High frequency beta also differs substantially from low frequency estimates like daily beta. Furthermore, the recovering procedure can correct up to $60\%$ biases in beta due to non-synchronous trading, depending on the informational content of the observed returns. Hence overlooking non-synchronous trading bias can be dangerous.

Realized volatility, summation over finely sampled intraday squared returns to approximate the latent time-varying daily volatility, has been justified by standard continuous time arguments. Nonetheless, so far the construction of realized measures for both volatility and correlation are restricted to those actively traded financial assets. The second chapter aims at constructing a bias-free realized covariance matrix among a group of assets including both liquid and illiquid equities using high frequency data, either to monitor the performance of a chosen portfolio or for strategic asset allocation in timing the market. The difficulty on how to deal with a set of non-synchronously traded intra-daily returns while at the same time correcting for the other market microstructure noises can be solved through the proposed synchronizing procedure in Chapter 1. We use the synchronized set of recovered return values to construct realized volatility and correlations. Our empirical results show the proposed method is effective in correcting for both non-synchronous trading and other market friction effects. We also found that non-synchronous trading bias plays a dominant role among the other market microstructure effects for less actively traded equities. After controlling the effect from non-synchronous trading, the effect from the other microstructure is evident but negligible in the context of realized measures construction. The new recovering and filtering procedures allow one to get more precise realized measures for volatilities and correlations that are applicable to further financial applications. Tail risks plays a prominent role in risk management. In the third chapter, we propose a new measure for Value at Risk based on expectile, EVaR, to properly account for the potential risk in the extreme tail, complementary to the commonly used quantile-based VaR (QVaR). Obtained from minimizing an asymmetrically weighted mean quadratic variations, EVaR is capable of incorporating the tail shape information, such as influential extreme risks. The statistical properties of expectile and its relationship with quantile are discussed. To allow for practical considerations in tail risk management, Conditional EVaR via a Conditional AutoRegressive Expectile (CARE) model is proposed and estimated by the method of asymmetric least squares. We generalize the results of Newey and Powell (1987) to encompass the class of weakly dependent processes. The empirical studies are conducted for six foreign exchange rate returns. Our results show that EVaR through CARE does outperform QVaR both in-sample and out-of sample in terms of rate of exceedance for exchange rates that experienced crises, such as Mexico Peso and Thai Baht. Moreover, combining the information from both measures further reduces the rate of exceedance both in-sample and out-of-sample.