財務危機預警模型之研究－以台灣地區上市公司為例

Abstract

長久以來許多經濟及財務學家僅使用公司一期之觀察資料來預測公司發生財務危機之機率，例如 Altman (1968) 使用多變量區別分析、Ohlson (1980) 使用 Logit 模型及 Zmijewski (1984) 使用 Probit 模型等，Shumway (2001) 將這些模型稱之為靜態模型。有別於靜態模型，Shumway 提出一個離散型倖存模型，該模型之優點係能夠有效地使用公司所有之歷史資料來分析，所以可預測取樣公司在樣本期間內每一個時間點發生財務危機之機率；再者，其參數估計式具有一致性及不偏性之性質，且無靜態模型中所存在之樣本選擇偏誤之問題，因此 Shumway 推論出離散型倖存模型其參數之估計與樣本外時間點公司發生財務危機之預測能力，均較靜態模型有較佳之表現。 Shumway 在其實證研究中係將離散型倖存模型定義為多期 Logit 模型，然而，其所定義之多期 Logit 模型之概似函數忽略了樣本公司在 時仍存活之機率，因此本研究將其概似函數加以修正，進一步使修正後之離散型倖存模型之概似函數完全考慮所有取樣公司在 及 時之存活機率與發生財務危機之機率，故對修正後之離散型倖存模型、 Logit 模型、Probit 模型及多變量區別分析進行實證研究，採用二組解釋變數組合，分別係 Altman 變數組合及 Zmijewski 變數組合，以比較各模型對公司發生財務危機之預測能力，並研究在何種模型下，使用何種解釋變數組合可以得到公司發生財務危機之最佳預測效果。 實證結果顯示，公司年齡取自然對數後，其參數值之檢定結果在各模型中均不顯著，顯示出公司之存續期間與公司是否發生財務危機之關聯性很小，在 Altman 變數組合中，僅有 RE/TA 變數其參數值之檢定結果在四種模型中均係顯著，表示公司累積獲利之能力愈強，愈不易發生財務危機；至於在 Zmijewski 變數組合中，僅有 NI/TA 變數其參數值之檢定結果在四種模型中均係顯著，表示公司之總資產報酬率愈高，獲利能力愈強，愈不易發生財務危機。 在 Altman 與 Zmijewski 變數組合之解釋能力方面，給定樣本外型 II 誤差率，四種模型分別使用 Altman 變數組合比使用 Zmijewski 變數組合可得到較大之樣本外檢定力函數值，因而採用 Altman 變數組合作為解釋變數來進行公司發生財務危機之預測，其正確率會高於使用 Zmijewski 變數組合。 雖然理論上離散型倖存模型會比 Logit 模型、Probit 模型及多變量區別分析有較佳之表現，然而實證結果卻與理論有些出入，但是若排除多變量區別分析，僅比較離散型倖存模型、Logit 模型及 Probit 模型，則結果係使用離散型倖存模型，再搭配 Altman 變數組合，其預測公司發生財務危機之準確率最高。

For a long time many economists and accountants have been forecasting bankruptcy by single-period classification models, one set of independent variables for each firm, which Shumway (2001) refers to as static models, with multiple-period bankruptcy data. Shumway develops a discrete-time survival model that uses all available information to produce bankruptcy probability estimates for all firms at each point in time. By using all the available data, it avoids the selection biases inherent in static models. While static models produce biased and inconsistent bankruptcy probability estimates, the discrete-time survival model proposed here is consistent in general and unbiased in some cases. Shumway interprets it outperforms static models in out-of-sample forecasts. Shumway estimates a multi-period logit models that can be interpreted as discrete-time survival model. A logit estimation program can be used to calculate maximum likelihood estimates. I modify the discrete-time survival model’s likelihood function because it ignores the probability of surviving at time t. This idea completely considers the probability of failure at time t, surviving up to and at time t for all firms. I estimate discrete-time survival model, logit model, probit model, and multivariate discriminant analysis with two different sets of independent variables that incorporate Altman’s (1968) 5 variables and Zmijewski’s (1984) 3 variables, as well as Shumway’s (2001) variable of the log of firm age. I find that the log of firm age is not statistically significant in the all models. There appears to be little duration dependence in bankruptcy probability. According to the set of Altman’s variables, the only statistically significant variable is RE/TA. While according to the set of Zmijewski’s variables only NI/TA is excellent bankruptcy predictor. Both of them represent the higher the (cumulative) profitability the lower the financial distress. Because all models use the set of Altman’s variables can get larger power given the type II error rate out-of-sample, so the out-of-sample accuracy of the set of Altman’s variables is higher than the set of Zmijewski’s variables. Although discrete-time survival model is preferable to static models theoretically, empirical result produces contradictory. If I exclude MDA, combining the discrete-time survival model with the set of Altman’s variables, then I estimate it is quite accurate in out-of-sample test.