A VaR Investigation of Currency Composition In

International Research Journal of Finance and Economics ISSN 1450-2887 Issue 21 (2008) © EuroJournals Publishing, Inc. 2008 http://www.eurojournals.com/finance.htm A VaR Investigation of Currency Composition in Foreign Exchange Reserves Jer-Shiou Chiou Department of Finance and Banking, Shih-Chien University, Taipei, Taiwan E-mail: jschiou@mail.usc.edu.tw Tel: 886-2-25381111 ext. 8927 Jui-Cheng Hung Department of Finance and Banking Yuanpei Institute of Science and Technology, Taiwan E-mail: 89
of 17
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
  International Research Journal of Finance and EconomicsISSN 1450-2887 Issue 21 (2008)© EuroJournals Publishing, Inc. 2008http://www.eurojournals.com/finance.htm A VaR Investigation of Currency Composition inForeign Exchange Reserves Jer-Shiou Chiou Department of Finance and Banking, Shih-Chien University, Taipei, Taiwan E-mail: jschiou@mail.usc.edu.twTel: 886-2-25381111 ext. 8927 Jui-Cheng Hung Department of Finance and BankingYuanpei Institute of Science and Technology, Taiwan E-mail: 891490053@s91.tku.edu.tw Mei-Maun Hseu Department of Finance, Chihlee Institute of Techonology, Taipei,Taiwan E-mail: meimaun@mail.chihlee.edu.twTel: 886-2--2253-7240 ext. 347 Abstract In this study, Exponential Weighted Moving Average (EWMA), Bootstrapping, andMonte Carlo Simulation are used to calculate the VaRs for three groups’ foreign reservesportfolio from the year of 1995 to 2001.Empirically we find that EWMA finished relatively better than the other two. Basedon developing countries’ currency in 2001 if the other currencies’ holding ratio is fixed,reducing the U.S. dollar holding ratio while increasing the Euro holding ratio will makeVaR decrease in EWMA. However, if the Euro holding ratio is high, VaR increases. Thisimplies that despite the hedging effect of Euro, as its holding ratio increases, the marginaleffect decreases. The hedging effect of Euro is not persistent.In general, increase the holdings of the lowest-valued component VaR currencywhile decreases the holdings of the highest-valued component VaR currency can in factreduce the risk of the portfolio. Keywords: VaR, RMSE, RAPM, Marginal VaR, Component VaR  1. Introduction Experiencing from the Asian financial crisis of 1997-98, most developing Asian economies haverapidly increased their external surpluses and accumulated foreign reserves to reduce their vulnerabilityto future shocks; the expansion in US current account deficit is among the most. However, thecountries with largest reserves holdings were least affected by speculative pressures. But the recentincreasing oil prices and the foreign direct investment and portfolio inflows have begun to fade inseveral Asian countries, Asian governments suffer a sharp fall in the value of their dollar holdings and,more importantly, would see their export-dependent economies hit hard by a US slowdown. In this  International Research Journal of Finance and Economics - Issue 21 (2008) 77study, we seek to examine an alternative reserves management strategy in the level of internationalportfolio.There are three reasons make central banks keep certain amount of foreign exchanges. Thoseare liquidity needs for balance of trade, steady needs for government financing and interfering needsfor economy stability. Foreign exchanges have not only become a country’s key reserves assets butalso protect the country’s monetary interests. When the authority alters its portfolio holdings, thecontext of safety, liquidity, and profitability in foreign exchange reserves have always been taken intothe consideration. Due to the most international business and liability takes U.S. dollars as major means; the U.S. dollar inevitably acts an essential part in a country’s foreign exchange reserves.According to the IMF’s annual report, from 1995 to 2001, there is over 60% of developing countries’foreign exchange reserves were U.S. dollars.On April 29, 1999, the World Bank Annual Conference, Pam Greens suggested Value-at-Risk should be adopted when a country’s foreign reserves policies are under investigation. However, acountry’s actual reserves are usually confidential, not only retrieving truthful data becomes difficult,but the relative literatures are rare. Because the data retrieval difficulty, most studies focus on thedeterminants in foreign reserves management. Beschloss and Mendes (1999) considered liquidity asthe main concern for central banks in foreign reserves management. Dooley, Lizondo, and Mathieson(1989) found the fixed exchange policy, the major international competitors, and the foreign debts arethe key determinants in reserves management decision. Barry and Donald (2000) had shown that thestability of foreign reserves was resulted from the commodity trading, the capital flow, and the fixedexchange policy. While Kenen (2002) suggested that as Euro increases their influential on themembers in the European Union; Euro still can hardly replace the U.S. dollar as the major internationalcurrency.In terms of risk management, Winfried (1999) decomposes the portfolio total risks intoseparated Value-at-Risks in parts, while José, Carlos, and Juan (2001) take the conceptual Value-at-Risk in risk management practice. The study on center bank foreign reserves risk management onlyappears in Blejer and Schumacher (1998) who theoretically construct a center bank’s investmentportfolio VaR evaluation model and then analyze the associates policies implications, but unfortunatelyno empirical examinations were made.Departure from the existing literatures, in this study we take nine 1 regularly-taken reservescurrencies daily data, and the associates three major groups’ (that the IMF 2002 annual reportcategorized as the whole world, the industrial countries and the developing countries) reservesweighted information to study a central bank’s risk management strategy in terms of foreign reservesportfolio. We adopt models of the Exponential Weighted Moving Average (EWMA), Bootstrapping,and Monte Carlo Simulation to compute the VaR for these three groups’ foreign reserves portfoliofrom the year 1995 to 2001. Then, we take the best model to calculate and compare the risk-adjustedperformance measurement index (RAPM) for each group. At last, by adjusting each currenciesweighted importance, we analyze if the increasing Euro holdings was able to reduce the portfolio’srisks. 2. Methodology 2.1. Value at Risk In measuring variations, variance and standard error have often been taken to reveal the magnitude inthe changes of future asset prices. As the fluctuation in future prices is inherent, potential gains andlosses in assets holding become inevitable. But most investors seem concern losses more than gains;the variation criteria stated above is undesirable in describing this downside risks phenomenon. VaR isdefined as the worst expected loss over a great horizon within a given confidence level, Jorion (1996). 1 In practice, the IMF’s annual report presents 8 currencies and 1 unspecified currency. In this study we take the Australia dollar as the unspecifiedcurrency.  78 International Research Journal of Finance and Economics - Issue 21 (2008)  It not only provides an aggregate statistic of the order of magnitude of potential losses due to marketrisk, but also summarizes the effects of leverage, diversification, and probabilities of adverse pricemovements in a single dollar amount.Let’s define W 0 as the initial investment at the beginning, and R  * represents the estimateexpected returns, then VaR can be written as: mean VaR = ( ) *0 - W R - μ . (3)If defined VaR as the absolute loss that excludes the expected returns, then VaR can berewritten as: zero VaR = *0 - W R . (4)If we transform the probability distribution (W) f  into a standard normal distribution Ф ( ε ),where ε ~ N(0, 1). Then the probability of possible returns which is less than W * will be 1-C, and it canbe rewritten as: ε d) ε (dr )r (f dw)w(f C1 α R W ** ∫ ∫ ∫  −∞−−∞−∞− Φ===− , (5)wheret σ R t μα * Δ−Δ−=− , and t Δ is the time factor. After the value of  α is determined, Value at Risk can be written as: ( ) ttWVaR  0zero Δμ−Δσα= (6)tWVaR  0mean Δσα= . (7)In this study we take zero VaR as the measurement. That is, we take VaR as the absolute loss withoutconsidering the expected returns. 2.2. EWMA with Variance-Covariance consideration It had been shown in Jorion (2000) that when the returns are normally distributed, Value-at-Risk canbe expressed in two different forms depending on whether absolute returns or average returns weretaken. If foreign positions had been taken, the VaRs can be rewritten as ( ) tttzero,1t ZWVaR  μ−σ= α+ (8) ttmean,1t ZWVaR  σ= α+ , (9)where W t is the asset’s value at time t, μ t is the average returns at time t, σ t is the standard deviation attime t, and Z α represents the critical value with a confidence level of 1- α .Under the definition of absolute return and the assumption of W t =1, Z α , σ t and t μ can then beobtained. If a parametric model was taken to compute the VaR for a single asset, the variances multipleby a critical value at the confidence level of 1- α is necessary. While in computing the VaR for certainportfolios, the influential of covariance has to be considered, other than the variance.We therefore take EWMA as a mean to estimate the fluctuations of the portfolio. Their varianceand covariance can thus be rewritten as: 21t,i 21t,i 2t,i r )1( −− λ−+λσ=σ (10) 1t,j1t,i1t,ijt,ij r r )1( −−− λ−+λσ=σ , (11)whereji ≠ , 2, t i σ  and t ij , σ  are the variance of asset i and the covariance of asset i and j at time t. 1, − t i r   and 1, − t j r  are the return ratios of asset i and j at time t-1. λ  is the decay factor of which 0.94 for thedaily data and 0.97 for the monthly data. When EWMA is in use, the VaR for the next T days can bewritten as:TZWVaR  t,ptt σ= α , (12)  International Research Journal of Finance and Economics - Issue 21 (2008) 79where ∑ = ww t P ', σ  ,   NN2t,Nt,2Nt,1N t,N2 2t,2t,21 t,N1t,12 2t,1 × ⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡σσσσσσσσσ= ∑ LMOMM LK , 1NN21 wwww × ⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡= M ; i w is the weighted ratio of the i th foreign asset to the total portfolio, σ i,t , σ j,t , and σ ij,t are obtained byEWMA and they are the variance and covariance of the foreign asset, respectively. t P , σ  is the standarddeviation for the portfolio at time t, while T is the holding period for the foreign asset. Under theassumption of the holding period for the foreign asset is 1 day (T=1) and the confidence level is 99%,the daily VaR is obtained. 2.3. Bootstrapping It is not necessary to fully understand the distribution of the population when Bootstrapping is in usedto calculate the underlying VaR. The method takes the limited historical returns and go through theiterate sampling to construct the asset portfolio’s distribution for future returns. The VaR of an assetportfolio is then obtainable, whenever the confidence level and holding period are specified. Thedifference between Bootstrapping and Historical Simulation is that Historical Simulation directlyutilizes the future returns’ distribution that has only one price path, while Bootstrapping makes aniterate sampling from historical data to simulate the real return’s distribution to improve theshortcoming of a Historical Simulation.Assume it is known for each asset’s prices in a portfolio for the last 251 days. It would beattainable to get next day’s VaR for the portfolio by the Bootstrapping. The procedure can be describedas follows: Step 1 Convert the historical 251 days prices into 250 returns and perform 10000 repeated sampling from theunderlying returns. The same process can apply to any portfolio which contains N assets.)T(R  i , where i 1,2...,N =   T 1,2,...,10000 =   Step 2 Multiply the returns by the corresponding importance ratio, which is measured by any single asset tothe portfolio. Sorting the data in increasing order and sum together, the distribution of next day’s returncan therefore be obtained. Step 3 Using the above simulated future returns, VaR can be computed by a percentile criterion on theconfidence level of 1- α . 2.4. Monte Carlo Simulation Before applying the Monte Carlo Simulation, it is necessary to assume that the underlying portfolio’sreturn follows a certain random process. Usually, the Geometric Brownian Motion Model (GBM) isapplicable to the assets such as stocks and foreign exchange. It can be expressed as:dZdtR dR  tttt σ+μ= , (13)where R  t is the return of portfolio, t  is the drift term of the portfolio at time t, t  σ  is the standarddeviation at time t, and dZ is normally distributed with 0 mean and dt variance, whereby ( ) dt,0N~dZ . From (13) we found that if a portfolio’s return follows a multivariable normal distribution thatis ( ) NN1N ,N~R  ×× Σμ , then in order to simulate the return as an N N × normal distribution, a MonteCarlo process as be described as follows: Step 1
Similar documents
View more...
Related Search
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks