低偏動差與變異數之遠期外匯避險績效比較

Comparison of Hedging Performance by the Lower Partial Moment and Variance of Forward Exchanges

高麗琪(Li-Chi Kao)

指導教授 ： 楊奕農

中原大學/商學院/國際貿易研究所/碩士(2004年)

https://doi.org/10.6840/cycu200400580

摘要

金融資產報酬風險之衡量，傳統上多數之文獻以變異數作為風險衡量指標。然而，在運用變異數來進行風險之估計與衡量時，由於變異數計算式的主要部份，是以樣本觀察值與其平均數離差之平方和來計算之。因此，對於所衡量出來之風險，無法區分其資產價值變動之方向性，也就是說，以變異數作為風險衡量指標，其實是將價格之上漲與下跌均視為同樣的風險。然而，持有資產之價格升高，使得效用增加，乃是投資人所樂見的；而持有資產價格之下跌，造成效用降低，才應該是投資人所認為的損失風險。因此，本研究欲運用低偏動差僅考量損失風險之特性，針對遠期外匯市場進行實證分析。並且比較在不同的目標報酬率、持有期間與歷史資料期間之下，以低偏動差與變異數為基礎所計算之資產組合，何者之避險績效較佳。
本研究乃針對美元兌英鎊、德國馬克、瑞士法郎、日圓以及台幣等遠期匯率來進行分析。資料期間為1998年1月1日到1999年12月31日。資料來源取自教育部AREMOS資料庫。本研究之實證結果顯示，在相同歷史資料期間，不同的目標報酬率之下，馬克、瑞士法郎以及日圓，這三種幣別以低偏動差為風險衡量指標，所計算出來之資產組合避險績效，大致上都優於以變異數為基礎所求算的；而英鎊與台幣之避險績效優劣，則視目標報酬率之不同而改變。另外，在目標報酬率的設定上，本研究分別選用零以及即期匯率之平均報酬率，兩種不同的基準來進行比較。其原因在於，若單單以目標報酬率為零之情況下來進行分析，如果資料期間所求得之即期與遠期匯率平均報酬率皆大於（小於）零，則會造成所衡量出來之低偏動差值低估（高估），進而使得最適避險比率高估（低估）。而實證發現，若單從英鎊在不同風險衡量指標為基礎下之避險績效優劣來看，在相同的歷史資料期間下，以即期匯率報酬率之平均數為目標報酬率所求得之資產組合避險績效，優於目標報酬率設定為零下所求得之資產組合。而在持有期間方面，由實證結果亦可看出，若該種貨幣以LPM為基礎下能求得風險與報酬間之最適比例，則不論持有期間之長短為何，以LPM為基礎所求算之投資組合避險績效皆優於變異數所求算的。而在不同的歷史資料期間下，本研究發現，歷史資料期間設定為6個月的情況下，以低偏動差為基礎所求算之資產組合，其避險績效優於變異數的比例最高。

關鍵字

避險績效 ； 最適避險率 ； 低偏動差 ； 遠期外匯 ； 匯率

並列摘要

Traditional hedging analysis adopts variance of financial assets return as the risk measure. However, variance by the definition is based on the difference between each sample value and the mean. The downside and upside risks are implicitly regarded as the same according to the definition. Utility of financial asset holders increases as the price of the assets increases. The realized risk occurs when the price of financial assets goes down to decrease the value of the assets that lead to a decline in the utility of assets holder. This paper applies the lower partial moments that only consider the downside risk to construct the hedging portfolios of foreign exchange to assess the portfolio’s performance. Meanwhile, this paper also compares the hedging performance of asset portfolios constructed by the LPM and variance under different target rates, lengths of holding period and historical sample.
The sample data we study here include British pounds, Deutsche marks, Swiss Francs, Japanese yens and Taiwanese which are based on the US dollar as a numeriare. The data used in this study are daily exchange rates ranging from January 1998 to December 1999. The data source is the AREMOS database.
Under the same lengths of historical sample and different target rates, it is found that Deutsche marks, Swiss Francs and Japanese yens have better hedging performance of asset portfolios constructed by the LPM risk measurement. Otherwise, the British pounds and Taiwan dollars present a different case under different target rates. This paper chooses zero and the mean return of spot exchange rate as the target rate to compare the hedging performance. The rationale is as follows. If we only consider the zero of target rate to analyze, the LPM would be underestimated (overestimated) and optimal hedging ratio would also be overestimated (underestimated) while the average of spot rates and forward rates both are above (below) zero. Here we focus on the hedging performance of British pounds. If lengths of historical samples are the same, the hedging performance of portfolio by the LPM with mean returns of spot exchange rate as the target rate is better than the one by the LPM with zero as the target rate. For comparisons of different lengths of holding periods, the empirical result also shows that if the currency can find out the optimal hedging ratio by the LPM, regardless of which criterion is applied, the assets portfolio by the LPM will get better hedging performance than the one by variance. Comparing the hedging performance between different lengths of historical samples, our study found that the hedging performance of assets portfolio by the LPM is better than the one by variance if the historical sample’s length were six months.

並列關鍵字

forward exchange rate ； hedging performance ； optimal hedge ratio ； lower partial moment ； exchange rate

參考文獻

Bawa, V.S. (1975) “Optimal Rules for Ordering Uncertain Prospects” Journal of Financial Economics 2,95-121

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