實務上常以夏普比率評估基金的績效表現,但該統計量的精確度與財務報酬率的統計性質有關,不正確的統計量可能導致錯誤的推論與決策。當投資人欲以夏普比率比較投資組合與標的市場組合績效時,必須確認標的市場夏普比率的統計性質,因此,依據標的市場報酬率的特質,推導其漸近分配則有其必要性。本論文共分三部分,第一篇研究為Ho (2006)的延伸,假設標的市場報酬率遵循廣義隨機波動率模型(generalized stochastic volatility model),本研究証明以√n和非√n 收斂速度收斂至常態極限分配都是可能成立,該收斂速度則由報酬率的波動性之參數所決定。 第二篇研究主要在從投資者結構、績效、風險偏好及產業競爭程度的觀點,探討過去十年(1994-2004)避險基金產業的發展與變革。本研究發現投資者結構的改變是引導該產業各階段的主流投資型態及風險偏好轉趨保守的因子。各種策略基金的產業環境,會因投資者偏好改變造成不同投資型態基金間的競爭與消長,進而影響其生存空間。再者,投資者因避險基金產業的蓬勃發展,有更多投資標的可供選擇,相對在績效表現與風險的要求上,遠比產業初期嚴苛,且大量資金的流入及新設基金的成立,都促使避險基金產業環境更趨競爭。因此,新基金必須具備快速適應環境,滿足投資者要求的能力,才不致於被市場淘汰。此外,整體避險基金產業對風險的控制也較初期重視,其在股市下跌時的連動性,隨時間呈逐步降低的趨勢。 第三篇研究主要從適者生存的角度,分析經歷產業競爭、金融市場衝擊及投資者考驗而存活的成功基金群,與其他失敗或小規模基金群行為及特質的差異,藉以發現影響避險基金存活的關鍵因素。考量資料具右設限存活的特質(right censoring for survival data),我們採用存活模型- Kaplan-Meier model, Cox proportional hazard model探討上述關鍵因素對避險基金存活函數的影響。利用驗證後的攸關變數,建構一綜合評比的指標進行基金的篩選,並與夏普比率的篩選績效及折損率予以比較。本研究發現影響基金存活的因素包含絕對及相對績效、報酬波動率、管理資產規模、現金流量、產業被偏好程度、恢復損失能力、槓桿、高水位機制(high water mark)、提供審計財報、閉鎖時間及管理費率,但各因素對趨勢交易策略基金(directional fund)與非趨勢交易策略基金的影響程度有所不同。利用攸關資訊所建構的綜合評比指標的確能降低被挑選基金的折損率,尤其在小型基金上的效果最為顯著。其中夏普比率較適合挑選風險屬性較高的投資標的,而恢復損失比率則適合風險屬性較低的標的。
Sharpe ratio is a simple instrument of evaluation for funds in practice, but the accuracy of its estimator depends on the statistical properties of financial returns, thus measurement inaccuracy for the Sharpe ratio can lead to make wrong inference and decision. It is a constant task for both researchers and practitioners to use Sharpe ratio to evaluate whether a portfolio performs better than a certain benchmark index. In order to achieve this based on sound and statistical justification, it is necessary to derive the asymptotic distribution of the Sharpe ratio statistics of the benchmark of interest. Essay 1 of this study aims to extend the work of Ho (2006) by assuming that the return series follows a generalized stochastic volatility model in which the volatility component is formed by a general functional of a linear process. The study shows that both the and non- asymptotic normality are possible and the normalization constants are determined by the decay rate of the coefficients of the linear process that governs the volatility behavior of the returns. Essay 2 of this study provides some evidences about the development in the hedge fund industry over the past decade, focusing on the change in the composition of investors, preference for risk and reward, and the degree of competition. The change of hedge fund is closely related to the current industrial environment and its evolution, our findings include: (1).The change in the structure of the investors drives the result of the fact that the risk preference of the industry tends to be more conservative and affects the mainstream style of strategy during each phase in industrial development. (2).The dynamic competition effect for hedge funds across each strategy affect the fund survival and main strategy varied over competition and market condition. (3).The profit-making space of hedge funds is being gradually compressed due to more intense competition, besides; investors would have the benefit of industrial contest, which have wider and more flexible choice of target investments. Therefore, investors are more rigorous for required returns and less patient to undertake a loss than before. (4).Young hedge funds face harder survival environment than before and have great difficulty to survive during elimination. (5).The overall hedge funds abandoned upside gains in the terminal bull market to reduce the reversal loss, and raised a tendency towards risk control. Essay 3 of this study first investigates the key to the survival of the fittest by way of analyzing the difference between groups of the successful funds and other live or defunct funds. Next, in consideration of the right censoring for survival data, we use the survival models such as the Kaplan-Meier model, Cox proportional hazard model to confirm whether these factors are good predictor variables related to hedge funds’ survival and estimate the survival function and time of the hedge fund. Lastly, we construct a composite filter, which make use of the relevant covariates of hazard rate, to select funds and compare the out-of-sample performance and attrition rate with the Sharpe ratio. The findings include: (1).The poor absolute, relative performance and high volatility increase the risk of failure, however, the no effect of the standard deviation of relative performance. (2).Different initial sizes lead to different investment philosophies as young age. The successful funds with an initial small size will dynamically adjust their risk/reward relationship during the lifecycle phase. (3).Directional funds are more sensitive to size than non-directional funds. The stability of the flows is the key to survival for small funds and change of favorite by investors is one factor which leads large funds to close. (4).The recovering ability of maximum loss during the tolerant period given by investors becomes a necessary condition of survival. (5).The characteristics of high water mark and providing audited reports are important factors of hedge funds’ survival. The funds that do not pay attention investor’s right and have the potential agency conflicts will be eliminated from competition. (6).The composite filter indeed provides the function of decreasing the attrition rate, especially, the effect for small fund selection is significant (7).Using the recovery rate to screen non-directional targets performs well and the Sharpe ratio is properly to select more volatile large targets.