Measuring Long-Term Tail Risk: Evaluating the Performance of the Square-Root-of-Time Rule

2018 ◽  
Author(s):  
Jying-Nan Wang ◽  
Jiangze Du ◽  
Yuan-Teng Hsu
Keyword(s):  
Square Root ◽  
Tail Risk

Measuring long-term tail risk: Evaluating the performance of the square-root-of-time rule

2018 ◽  
Vol 47 ◽  
pp. 120-138
Author(s):  
Jying-Nan Wang ◽  
Jiangze Du ◽  
Yuan-Teng Hsu
Keyword(s):  
Square Root ◽  
Tail Risk

How Accurate is the Square-Root-Of-Time Rule at Scaling Tail Risk: A Global Study

2010 ◽  
Author(s):  
Jying-Nan Wang ◽  
Jin-Huei Yeh ◽  
Nick Ying-Pin Cheng
Keyword(s):  
Square Root ◽  
Tail Risk ◽  
Global Study

Use of various functions to analyse the fertiliser responses of maize ( Zea mays L.) hybrids in long-term experiments

2006 ◽  
Vol 54 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Z. Berzsenyi ◽  
Q. L. Dang
Keyword(s):  
Analysis Of Variance ◽  
Response Pattern ◽  
Root Function ◽  
Quadratic Function ◽  
Maize Yield ◽  
Maximum Point ◽  
Square Root ◽  
Maize Hybrids ◽  
Year Effect

The effect of various fertiliser treatments on the yield of maize hybrids was studied on the basis of 26 years of data obtained in a long-term bifactorial split-plot experiment set up in 1967. The seven treatments (NPK ratio 2:1:1) applied were as follows (rates per hectare): 1. Control (no fertiliser), 2. 100 kg NPK, 3. 200 kg NPK, 4. 300 kg NPK, 5. 400 kg NPK, 6. 600 kg NPK, 7. 800 kg NPK. The maize was grown with the conventional cultivation techniques in continuous cropping. The results of analyses carried out with three different methods (analysis of variance, cumulative yield analysis and regression analysis) all indicated that under the given conditions the yield of maize hybrids was highest at an NPK fertiliser rate of 200-400 kg ha -1 . The effect of fertilisation on the maize yield was significant in 21 of the 26 years. Combined analysis of variance for the years showed that the year effect (quantity of rainfall) had the greatest effect on the maize yield, but although the year effect had a fundamental effect on the yield level it did not influence the fertiliser response pattern. The fertiliser responses of the maize hybrids were described by fitting four types of functions (quadratic, square root, inverse exponential, linear-plateau) to the yield data. It was found that when selecting the best function a consideration of the regression deviations (measured yield - calculated yield) was just as important as the coefficient of determination (R 2 ). In 12 of the 26 years the fitting of the quadratic function was not significant and overestimated the fertilisation optimum. The fertiliser response curve generally has a broad maximum which is far better described by the square root function than by the quadratic. If the fertiliser response pattern includes a depressive phase, a square root function should definitely be used in place of the quadratic function. If the maximum of the response surface forms a plateau (as opposed to a maximum point) a linear-plateau function or an inverse exponential function can be recommended. In the present work the linear-plateau function gave the best results.

The Response of Tail Risk Perceptions to Unconventional Monetary Policy

2016 ◽  
Vol 8 (2) ◽  
pp. 111-136 ◽  
Author(s):  
Masazumi Hattori ◽  
Andreas Schrimpf ◽  
Vladyslav Sushko
Keyword(s):  
Monetary Policy ◽  
Interest Rate ◽  
Risk Perceptions ◽  
Equity Market ◽  
Unconventional Monetary Policy ◽  
Tail Risk ◽  
Forward Guidance ◽  
The Impact ◽  
Future Path

We examine the impact of unconventional monetary policy (UMP) on stock market tail risk and risks of extreme interest rate movements. We find that UMP announcements substantially reduced option-implied equity market tail risks and interest rate risks. Most of the impact derives from forward guidance rather than asset purchase announcements. Communication about the future path of policy rates reduced volatility expectations of long-term rates and the associated risk premia. The reaction of equity market tail risk, in turn, points to the risk-taking channel of monetary policy, as the commitment to low funding rates may have relaxed financial intermediaries’ risk-bearing constraints. (JEL E52, E58, G12, G13, G14)

Empirical Dissolution Rate Law for the Glass R7T7 Contacting Halite- and Silica-Saturated Brines

1991 ◽  
Vol 257 ◽  
Author(s):  
B. Grambow ◽  
W. Lutze ◽  
R. Müller
Keyword(s):  
Time Dependence ◽  
Dissolution Rate ◽  
Diffusion Coefficients ◽  
Water Diffusion ◽  
Square Root ◽  
Borosilicate Glasses ◽  
Rate Law ◽  
Apparent Diffusion Coefficients ◽  
Apparent Diffusion

ABSTRACTWe report on the time dependence of release of glass constituents during static dissolution experiments with the COGEMA glass R7T7 in saline MgCl2 and NaCl dominated solutions at temperatures between 110 and 190°C. The experiments were performed at high S/V values to ensure silica saturation almost from the start of the tests. The results show a square root of time dependence indicating diffusion as rate-controlling with apparent diffusion coefficients similar to that of water diffusion in alkali silicate, borosilicate glasses or long-term weathered obsidians.

MODELING THE VOLATILITY AND EXPECTED VALUE OF A DIVERSIFIED WORLD INDEX

2004 ◽  
Vol 07 (04) ◽  
pp. 511-529 ◽  
Author(s):  
ECKHARD PLATEN
Keyword(s):  
Stock Market ◽  
Financial Market ◽  
Expected Value ◽  
Quadratic Variation ◽  
Stock Index ◽  
Square Root ◽  
Growth Optimal Portfolio ◽  
World Stock Index ◽  
Diversified World Stock Index

This paper considers a diversified world stock index in a continuous financial market with the growth optimal portfolio (GOP) as reference unit or benchmark. Diversified broadly based indices and portfolios, which include major world stock market indices, are shown to approximate the GOP. It is demonstrated that a key financial quantity is the trend of a world index. It turns out that it can be directly observed since the expected increments of the index equal four times those of the quadratic variation of its square root. Using a world stock index as approximation of the discounted GOP it is shown that, in reality, the trend of the discounted GOP does not vary greatly in the long term. This leads for a diversified world index to a natural model, where the index is a transformed square root process of dimension four. The squared index volatility appears then as the inverse of the square root process. This feature explains most of the properties of an index and its volatility.

How accurate is the square-root-of-time rule in scaling tail risk: A global study

2011 ◽  
Vol 35 (5) ◽  
pp. 1158-1169 ◽  
Author(s):  
Jying-Nan Wang ◽  
Jin-Huei Yeh ◽  
Nick Ying-Pin Cheng
Keyword(s):  
Square Root ◽  
Tail Risk ◽  
Global Study

scholarly journals A Million Metaorder Analysis of Market Impact on the Bitcoin

2015 ◽  
Vol 01 (02) ◽  
pp. 1550008 ◽  
Author(s):  
J. Donier ◽  
J. Bonart
Keyword(s):  
Price Impact ◽  
Square Root ◽  
Market Impact ◽  
Exchange Market ◽  
Heterogeneous Agent ◽  
Statistical Arbitrage ◽  
Complete Dataset ◽  
Heterogeneous Agent Models ◽  
Impact Models

We present a thorough empirical analysis of market impact on the Bitcoin/USD exchange market using a complete dataset that allows us to reconstruct more than one million metaorders. We empirically confirm the “square-root law” for market impact, which holds on four decades in spite of the quasi-absence of statistical arbitrage and market marking strategies. We show that the square-root impact holds during the whole trajectory of a metaorder and not only for the final execution price. We also attempt to decompose the order flow into an “informed” and “uninformed” component, the latter leading to an almost complete long-term decay of impact. This study sheds light on the hypotheses and predictions of several market impact models recently proposed in the literature and promotes heterogeneous agent models as promising candidates to explain price impact on the Bitcoin market — and, we believe, on other markets as well.

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