Mathematics · Statistics
Expected-Shortfall-to-VaR Ratio Calculator
Calculate tail-loss severity ratio from expected shortfall magnitude and value-at-risk magnitude at same level.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=a/b with expected shortfall magnitude=18 and value-at-risk magnitude at same level=12.
- tail-loss severity ratio=1.5.
Understand Expected-Shortfall-to-VaR Ratio
One idea, three depths
Choose how deeply to explain Expected-Shortfall-to-VaR Ratio
Expected-Shortfall-to-VaR Ratio: Calculate tail-loss severity ratio from expected shortfall magnitude and value-at-risk magnitude at same level.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Expected-Shortfall-to-VaR Ratio to answer this question: calculate tail-loss severity ratio from expected shortfall magnitude and value-at-risk magnitude at same level? Enter expected shortfall magnitude and value-at-risk magnitude at same level; the calculator shows tail-loss severity ratio. For example: expected shortfall magnitude=18 and value-at-risk magnitude at same level=12 produce tail-loss severity ratio=1.5. The answer tells you tail-loss severity ratio.
Age 15Explain it to a 15-year-oldConnect it to the formula
Expected-shortfall-to-VaR ratio compares average loss beyond the quantile with the quantile loss threshold. This page evaluates the relationship directly. The rule is c=a/b. Its input values are expected shortfall magnitude, value-at-risk magnitude at same level, and the main result is tail-loss severity ratio. For example: expected shortfall magnitude=18 and value-at-risk magnitude at same level=12 produce tail-loss severity ratio=1.5.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated expected-shortfall-to-var ratio relation over the valid real-number domain stated below. The implemented relation is c=a/b, evaluated from expected shortfall magnitude, value-at-risk magnitude at same level to produce tail-loss severity ratio. Expected-shortfall-to-VaR ratio compares average loss beyond the quantile with the quantile loss threshold. This page evaluates the relationship directly. Both measures must use the same tail, confidence level, horizon, and loss sign convention.
Inputs and valid domain
- expected shortfall magnitude must be a finite real number.
- value-at-risk magnitude at same level must be a finite real number.
Important boundary: Both measures must use the same tail, confidence level, horizon, and loss sign convention.
The formula
c=a/b
How the calculator works through it
It substitutes expected shortfall magnitude, value-at-risk magnitude at same level into the formula and exposes every numerical step above. The main output is tail-loss severity ratio.
Read the result correctly
The tail-loss severity ratio is the direct answer to “calculate tail-loss severity ratio from expected shortfall magnitude and value-at-risk magnitude at same level.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
expected shortfall magnitude=18 and value-at-risk magnitude at same level=12 produce tail-loss severity ratio=1.5.
Where this model stops being reliable
Both measures must use the same tail, confidence level, horizon, and loss sign convention.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Expected-Shortfall-to-VaR Ratio works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Expected-Shortfall-to-VaR Ratio uses c=a/b. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Averages and representative values
Representative values help you judge what the Expected-Shortfall-to-VaR Ratio inputs summarise and what the result can legitimately describe.
Review this foundation about 5 min
Optional enrichment
- Spread and measurement variation
Variation is not always part of the Expected-Shortfall-to-VaR Ratio formula, but it helps you judge how stable a reported result may be.
Review this foundation about 6 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read expected shortfall magnitude, value-at-risk magnitude at same level.
- Evaluate the principal relationship: c=a/b.
- Return tail-loss severity ratio and check the domain conditions described above.
Python
from math import *
def expected_shortfall_var_ratio_calculator(a, b) -> float:
return (a / b)
assert abs(expected_shortfall_var_ratio_calculator(18, 12) - 1.5) < 1e-6 * max(1.0, abs(1.5))
C
#include <assert.h>
#include <math.h>
double expected_shortfall_var_ratio_calculator(double a, double b) {
return (a / b);
}
int main(void) {
const double expected = 1.5;
const double actual = expected_shortfall_var_ratio_calculator(18, 12);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double expected_shortfall_var_ratio_calculator(double a, double b) {
return (a / b);
}
int main() {
constexpr double expected = 1.5;
const double actual = expected_shortfall_var_ratio_calculator(18, 12);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double expected_shortfall_var_ratio_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global expected_shortfall_var_ratio_calculator
section .text
expected_shortfall_var_ratio_calculator:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
divsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = expected_shortfall_var_ratio_calculator(a, b)
result = (a / b);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a / b);
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Introductory Statistics 2e
Read the free OpenStax statistics textbookCite this book
- APA 7
- Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
- MLA 9
- Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
- Chicago author-date
- Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Expected-Shortfall-to-VaR Ratio Calculator. MW SysArc Tools. https://math.mwsysarc.com/statistics/expected-shortfall-var-ratio-calculator
MLA 9
MW SysArc. “Expected-Shortfall-to-VaR Ratio Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/expected-shortfall-var-ratio-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Expected-Shortfall-to-VaR Ratio Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/expected-shortfall-var-ratio-calculator.
Harvard
MW SysArc (2026) ‘Expected-Shortfall-to-VaR Ratio Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/expected-shortfall-var-ratio-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_expected_shortfall_var_ratio_calculator_2026,
author = {{MW SysArc}},
title = {Expected-Shortfall-to-VaR Ratio Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/statistics/expected-shortfall-var-ratio-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Expected-Shortfall-to-VaR Ratio Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/statistics/expected-shortfall-var-ratio-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Expected-Shortfall-to-VaR Ratio do?
Calculate tail-loss severity ratio from expected shortfall magnitude and value-at-risk magnitude at same level.
How does the Expected-Shortfall-to-VaR Ratio work?
The calculator applies c=a/b. Expected-shortfall-to-VaR ratio compares average loss beyond the quantile with the quantile loss threshold. This page evaluates the relationship directly.
What can I learn from the Expected-Shortfall-to-VaR Ratio?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .