| Course | FIN-3820 Risk Management |
|---|---|
| Module | Module 3 |
| Paper type | Written assignment 3: volatilities, correlations and value at risk |
| Length | About 593 words, 5 pages |
| Format | APA 7 student paper |
| School | Thomas Edison State University |
| Program | B.S.B.A. in Finance |
| Updated | October 2026 |
Free sample paper for FIN 3820 Module 3
One Bad Day in a Hundred: Estimating Volatility and Value at Risk for a Bank Portfolio
Student Name
B.S.B.A. in Finance, Thomas Edison State University
FIN-3820: Risk Management
Mentor Name
Month Day, Year
One Bad Day in a Hundred: Estimating Volatility and Value at Risk for a Bank Portfolio
Problem 1: Updating Volatility
An exponentially weighted moving average (EWMA) gives recent returns more weight than older ones. With a decay factor λ of 0.94, the RiskMetrics standard, the variance estimate updates as σ²n = λσ²n−1 + (1 − λ)u²n−1 (Hull, 2023). Yesterday's volatility estimate for the stock fund was 1.2 percent a day, and yesterday the fund fell 2.5 percent. Kupiec (1995) developed tests that compare the number of days losses exceed VaR with the number the model predicts, the basis of backtesting.
σ² = 0.94 × 0.012² + 0.06 × 0.025² = 0.000135 + 0.0000375 = 0.000173, so σ = 1.315 percent a day.
One large move raised the estimate by about a tenth. EWMA responds quickly to new information, which is useful in turbulent markets, though it also forgets old crises quickly.
Problem 2: Value at Risk for One Position
Value at risk answers the question: what loss will not be exceeded with a given probability over a given period? Assuming normally distributed returns, the 99 percent one-day VaR on $10 million is:
VaR = 2.326 × 0.01315 × $10,000,000 = $305,800.
On 99 days out of 100, the bank should not lose more than about $306,000 on the stock fund in a day. Scaling by the square root of time, which assumes independent daily returns, the ten-day VaR used in regulatory calculations is $305,800 × √10 = $967,100.
Problem 3: Portfolio VaR and Diversification
The bond fund has a daily volatility of 0.45 percent, and its returns have a correlation of −0.2 with the stock fund.
The portfolio's dollar standard deviation combines the two components with their correlation: √(131,476² + 22,500² + 2 × (−0.2) × 131,476 × 22,500) = $128,876. Because the funds move partly in opposite directions, the portfolio's VaR is lower than the stock fund's alone, and $58,400 less than the sum of the two.
| Component | Daily standard deviation in dollars | 99% one-day VaR |
|---|---|---|
| Stock fund, $10 million | $131,476 | $305,800 |
| Bond fund, $5 million | $22,500 | $52,300 |
| Sum of individual VaRs | | $358,100 | |
| Portfolio, correlation −0.2 | $128,876 | $299,800 |
| Diversification benefit | | $58,400 |
Problem 4: The Limits of VaR
VaR says nothing about how large losses can be on the worst day in a hundred. Two portfolios can have the same VaR but very different losses beyond it. VaR also need not be subadditive: Artzner et al. (1999) showed that VaR can, for some distributions, assign a combined portfolio more risk than the sum of its parts, violating a property a coherent risk measure should have. Normal-distribution VaR also understates the fat tails of real returns, and correlations tend to rise in crises, just when diversification is most needed.
Problem 5: Expected Shortfall
Expected shortfall, the average loss on days when losses exceed the VaR threshold, addresses the first two problems: it measures the size of tail losses and is subadditive. Basel's revised market risk framework replaced 99 percent VaR with 97.5 percent expected shortfall for regulatory capital. For the bank's portfolio, assuming normality, the 97.5 percent one-day expected shortfall is $128,876 × 0.05845 / 0.025 = $301,300, close to the 99 percent VaR under normality, but the two measures diverge sharply when returns have fat tails.
Conclusion
EWMA gives a responsive volatility estimate, VaR summarizes a portfolio's risk in one number and correlation determines how much diversification helps. The bank should report VaR and expected shortfall together and test both against stressed scenarios, since neither captures a crisis on its own.
References
Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203-228. https://doi.org/10.1111/1467-9965.00068
Hull, J. C. (2023). Risk management and financial institutions (6th ed.). Wiley.
Kupiec, P. H. (1995). Techniques for verifying the accuracy of risk measurement models. Journal of Derivatives, 3(2), 73-84. https://doi.org/10.3905/jod.1995.407942
FIN 3820 Module 3 instructions, in plain terms
Volatility, correlation and VaR here lead straight into the midterm, a 12- to 15-page paper that explains and judges VaR. Expect problems on volatility estimation, including EWMA or GARCH, correlation, one-day and multi-day VaR for single positions and portfolios and the comparison of VaR with expected shortfall. Kupiec's backtesting work shows how VaR models are checked. The portfolio figures here are composites. Expect EWMA or GARCH volatility updates, correlation estimates and a portfolio VaR calculation. Data are usually daily returns supplied in the assignment. Expect to report both daily and ten-day figures.
Inside the FIN 3820 Module 3 example
Problem 1 updates volatility with the EWMA formula and explains its responsiveness. Problem 2 computes one-day and ten-day VaR and translates the result into plain words. Problem 3 combines two positions with their correlation in a table and measures the diversification benefit. Problem 4 sets out VaR's limitations, citing research on coherent risk measures, and Problem 5 computes expected shortfall and explains why regulators adopted it. A short conclusion recommends reporting both measures with stress tests. Each estimate is followed by what it means for the portfolio's risk. The VaR result is compared with a simpler calculation that ignores correlation. A closing line states the VaR in dollars.
FIN 3820 Module 3 rubric: what earns full marks
Stating confidence, horizon and method for each VaR figure is graded closely. Mentors look for correct volatility, VaR and portfolio calculations and a clear explanation of what each number means and where it falls short. Explaining diversification through correlation, the square-root-of-time assumption and the reasons for expected shortfall shows the understanding the midterm project will build on. Showing formulas with inputs lets the mentor follow each step. Mentors check the volatility updating arithmetic and the use of correlation in portfolio VaR. Explaining why the EWMA estimate reacts faster than a simple average shows understanding. Results stated in dollars, not only percentages, help readers. VaR answers that state the confidence level, horizon and method, and that compare the result with actual losses, show a complete understanding of the measure.
FIN 3820 Module 3 help: mistakes that cost marks
VaR problems lose points for adding individual VaRs as if correlation were 1, for scaling one-day VaR to ten days without stating the independence assumption and for presenting VaR as the worst possible loss. Combine positions with their correlation. State each assumption. Explain what VaR does not tell you and how expected shortfall helps. Follow each figure with a sentence on what it means. A free first sample of your own FIN-3820 Module 3 problems is available on request. Show the weight on the latest return in each EWMA update, and convert daily figures to the horizon asked. Check that your correlation lies between minus one and one. Carry full precision until the last step.
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FIN 3820 Module 3 questions, answered
Where can I find a free FIN 3820 Module 3 sample paper?
The bank portfolio problem set above updates volatility with EWMA, computes one-day and ten-day VaR, measures diversification and compares VaR with expected shortfall.
What is value at risk?
The loss that will not be exceeded over a given period with a given probability, such as 99 percent over one day.
How does EWMA estimate volatility?
As a weighted average of past squared returns in which weights decline exponentially, so recent returns count most.
What is expected shortfall?
The average loss on the days when losses exceed the VaR threshold, a measure of tail risk.
Why is VaR criticized?
It ignores the size of losses beyond the threshold, can fail to reward diversification and often assumes returns are normal.