投機性商品需求探討-以台灣樂透彩為例

Investigating the Demand for Speculative Merchandises - A Study of Taiwan Lotto

田峻吉(JYUN-JI TIEN)

指導教授 ： 曾郁仁

國立臺灣大學/管理學院/財務金融學研究所/博士(2006年)

https://doi.org/10.6342/NTU.2006.01685

摘要

第一章 樂透需求與給付意願之探討

為何有許多人參與賭馬、樂透等不公平賭局，但同時購買保險。過去文獻提出這些人有可能為風險愛好者或是為了娛樂而參與賭局，然而這些理由無法充分闡釋上述現象。本文提出理論模型，將效用函數利用泰勒展開式延展到三階，可以解釋風險趨避者會參與不公平賭局的原因。結果顯示樂透購買者並非不理性，其效用函數有可能為局部風險趨避者，雖然不喜歡風險，但是為了追求極大的三階動差，仍會參與不公平賭局。
在實證方面，過去文獻只用有效價格去預測樂透銷售量，有可能產生估計參數偏誤與遺漏重要解釋變數等問題。本文將二階動差與三階動差加入模型中，可以更合理解釋人們會購買樂透的原因。本文研究對象為台北銀行所發行的樂透彩，樣本期間從民國九十一年一月至民國九十二年四月。實證結果發現樂透購買者為理性及局部風險趨避者，而且也支持本文所推導的理論結果。

第二章 投機性商品與金融資產之關係-以台灣樂透彩與股票市場為例

博奕事業如賭馬、樂透、職業運動彩券等，在全世界日益普及，銷售金額也十分可觀。過去探討投機性商品的時候，多半以效用函數的觀點，去研究為何參與者願意接受這種不公平賭局。然而投機性資產也是現實世界資產的其中一項，其報酬率有可能受到其他資產的影響。除此之外，投資者在賭博方面的行為也會反映到其他金融市場，例如購買垃圾債券或是財務重整的公司。因此投機性商品與其他財務資產應該存在某種程度的關係，如果明瞭此種關係，有助於我們了解投機性商品的風險與特性。然而這方面的議題，在從前的文獻卻極少被討論。
本篇文章希望利用樂透與股票市場作為探討投機性商品與金融資產之關係的起點。我們採用一個包含二階動差與三階動差的實證模型，不僅可以解釋風險趨避個體接受不公平賭局的原因，同時亦可釐清樂透銷售額與市場報酬率之間的關係。本文以台灣加權指數所計算的市場報酬與台北銀行所發行的樂透彩作為實證研究的對象，樣本期間為民國九十一年一月至民國九十二年十二月。實證結果發現市場報酬率與樂透彩各階動差呈反向關係，亦即樂透與股票市場的替代效果大於所得效果。然而在考慮樂透彩各階動差後，市場報酬率對於樂透銷售額有顯著的正向關係。代表投資人在排除對各階動差的理性預期後，其投資行為是在股市報酬較佳的時候，購買較多樂透彩。

關鍵字

樂透 ； 偏態 ； 有效價格 ； 投機性商品

並列摘要

Chapter1 Willingness to Pay and the Demand for lotto

Why do many bettors participate in an unfair gamble, in particular a lotto game, while at the same time purchase insurance? We analyze the willingness-to-pay for lotto to find a “rational” explanation for a (local) risk-avertor’s participation in an unfair bet. A reasonable case is found where bettors’ preference can be approximately characterized as a locally risk-averse and sufficiently prudent cubic function. Such bettors dislike risk but prefer standard third moment of the payoff. The result suggests that the traditional effective price for lotto demand may omit important explanatory variables. We thus propose an alternative method to examine the demand for lotto by incorporating the second and the third moments of lotto’s payoff. Evidence from Taiwan Lotto data supports that lotto bettors could be both (locally) risk-averse and rational.

Chapter2 The Relationship between Speculative Merchandises and Financial Assets - A Study of Lotto and the Stock Market

Gambling industries such as horse racing, lotto, and baseball betting are pervasive and popular worldwide. The speculative merchandises can be regarded as one kind of assets at financial market. People’s attitudes toward gambling are reflected in their stock investment choices and stock returns. Moreover, other financial assets could affect returns of speculative merchandises. However, little attention has been given to the link between gambling and other financial assets. This paper investigates the relationship between speculative merchandises and other assets, for example, lotto and stock market.

We propose an empirical model which incorporates the second and third moments of lotto payoff to examine how lotto sales are affected by market returns. This model not only explains why bettors accept an unfair lotto game but also estimates coefficients of regression more accurately. Evidence from Taiwan Lotto and stock market shows that the effect price (the second moment, the third moment) is increased (decreased, decreased) by market returns because the ‘Substitution Effect’ could be stronger than ’Wealth Effect’. A positive relationship exists between lotto sales and market return after controlling the estimated moment from rational expectations. It seems reasonable to conclude that investors will buy more lotto tickets while earning positive returns on stock market after expelling the effect from rational expectations.

並列關鍵字

Skewness ； Lotto ； Gambling ； Risk ； Effective Price

參考文獻

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