ANALISIS RISIKO PORTOFOLIO LQ45 MENGGUNAKAN PENDEKATAN VALUE AT RISK BLOCK MAXIMA-GENERALIZED EXTREME VALUE

Setiap bentuk investasi memiliki risiko yang dapat menyebabkan kerugian bagi investor. Semakin tinggi hasil yang diharapkan dari investasi tersebut, maka semakin tinggi juga tingkat risikonya. Dengan demikian, investor perlu mengetahui besar risiko yang akan dihadapinya, sehingga dapat melakukan tindakan pencegahan agar bisa mengantisipasi risiko tersebut. Metode yang dapat digunakan untuk mengukur risiko adalah value at risk (VaR). Extreme value theory (EVT) merupakan metode yang digunakan untuk mengukur risiko pada data runtun waktu yang memiliki distribusi ekor gemuk. Distribusi ekor gemuk memiliki kecenderungan lebih besar terjadinya kejadian ekstrem dibandingkan dengan distribusi normal. Umumnya, hal ini ditandai oleh nilai kurtosis yang positif. Salah satu metode EVT adalah block maxima yang mengikuti distribusi GEV (generalized extreme value). Perhitungan VaR yang akurat pada data runtun waktu finansial dapat menggunakan VaR dengan metode block maxima-GEV. Penelitian ini menggunakan data harga saham penutupan harian pada indeks LQ45 periode 1 Januari sampai 31 Desember 2018. Saham yang digunakan untuk pembentukan portofolio ada lima yaitu PTBA, ANTM, PGAS, BBCA, dan ICBP, yang mana saham-saham tersebut dipilih berdasarkan nilai mean return tertinggi. Berdasarkan hasil analisis, diperoleh nilai VaR dengan metode block maxima-GEV dengan tingkat kesalahan 5% adalah sebesar 2,555% dari total nilai investasinya. Misalnya, jika investor berinvestasi sebesar Rp100.000.000,00,- maka investor tersebut mempunyai risiko sebesar Rp2.555.000,00. Kata Kunci : investasi, VaR, extreme value theory, heavy tail

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Extreme value theory in emerging markets: Evidence from the Montenegrin stock exchange

Economic Annals ◽

10.2298/eka1506087c ◽

2015 ◽

Vol 60 (206) ◽

pp. 87-116 ◽

Cited By ~ 1

Author(s):

Julija Cerovic ◽

Vesna Karadzic

Keyword(s):

At Risk ◽

Stock Market ◽

Extreme Value Theory ◽

Value At Risk ◽

Emerging Market ◽

Value Theory ◽

Extreme Value ◽

Peaks Over Threshold ◽

Threshold Method ◽

Block Maxima

The concept of Value at Risk(VaR) estimates the maximum loss of a financial position at a given time for a given probability. This paper considers the adequacy of the methods that are the basis of extreme value theory in the Montenegrin emerging market before and during the global financial crisis. In particular, the purpose of the paper is to investigate whether the peaks-over-threshold method outperforms the block maxima method in evaluation of Value at Risk in emerging stock markets such as the Montenegrin market. The daily return of the Montenegrin stock market index MONEX20 is analyzed for the period January 2004 - February 2014. Results of the Kupiec test show that the peaks-over-threshold method is significantly better than the block maxima method, but both methods fail to pass the Christoffersen independence test and joint test due to the lack of accuracy in exception clustering when measuring Value at Risk. Although better, the peaks-over-threshold method still cannot be treated as an accurate VaR model for the Montenegrin frontier stock market.

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A COMPARISON OF SOME UNIVARIATE MODELS FOR VALUE-AT-RISK AND EXPECTED SHORTFALL

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024907004548 ◽

2007 ◽

Vol 10 (06) ◽

pp. 1043-1075 ◽

Cited By ~ 17

Author(s):

CARLO MARINELLI ◽

STEFANO D'ADDONA ◽

SVETLOZAR T. RACHEV

Keyword(s):

At Risk ◽

Extreme Value Theory ◽

Value At Risk ◽

Value Theory ◽

Extreme Value ◽

Expected Shortfall ◽

Stable Laws ◽

Peaks Over Threshold ◽

Threshold Method ◽

Block Maxima

We compare in a backtesting study the performance of univariate models for Value-at-Risk (VaR) and expected shortfall based on stable laws and on extreme value theory (EVT). Analyzing these different approaches, we test whether the sum–stability assumption or the max–stability assumption, that respectively imply α–stable laws and Generalized Extreme Value (GEV) distributions, is more suitable for risk management based on VaR and expected shortfall. Our numerical results indicate that α–stable models tend to outperform pure EVT-based methods (especially those obtained by the so-called block maxima method) in the estimation of Value-at-Risk, while a peaks-over-threshold method turns out to be preferable for the estimation of expected shortfall. We also find empirical evidence that some simple semiparametric EVT-based methods perform well in the estimation of VaR.

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