Calculating Volatility-Adjusted Historical VaR and Expected Shortfall

Summary

The document presents an exam-style portfolio risk problem. It supplies a current portfolio value, a sequence of ten daily log returns, an initial variance forecast, and an exponential moving volatility parameter. The requested outputs are one-day historical Value at Risk adjusted for volatility and Expected Shortfall, with a specified confidence level. This frames the task as applying a volatility scaling procedure to historical returns before deriving tail risk measures.

No worked solution or answer is included, so the text provides inputs and an objective rather than evidence about a particular computed VaR or Expected Shortfall. To solve it, a reader must establish the variance update and scaling convention, apply the adjusted historical observations consistently, and identify the relevant loss tail and quantile or tail average. The prompt does not spell out conventions for finite-sample quantiles, tail averaging, or converting log returns into portfolio currency losses, so those choices should be stated when presenting a numerical result.

Key ideas

• The example asks for one-day volatility-adjusted historical VaR and Expected Shortfall for a portfolio.
• It provides ten daily log returns, a starting variance forecast, and an exponential volatility decay parameter.
• The volatility model is intended to rescale historical observations before assessing the loss distribution.
• Expected Shortfall summarizes losses in the tail beyond the VaR threshold.
• The prompt supplies no solution and leaves quantile, tail-average, and currency-loss conventions unstated.

Tags

# Value at Risk of a Portfolio


# Value at Risk of a Portfolio












I am currently practicing for my Risk Management exam in July but my lecturer is of no help and my colleagues and I have no idea on how to proceed with this question. The past exam papers have similar questions so I would appreciate any advice on how to proceed with such a question. In so doing, I would be able to follow similar logic in attempting questions like these. Thanks in advance

Consider the following historical information on a portfolio currently valued at USD 100 million:

```
                 Log Returns

02/01/2004       -0.20%
05/01/2004       -0.15%
06/01/2004        0.14%
07/01/2004        0.30%
08/01/2004       -1.43%
09/01/2004       -0.79%
12/01/2004        0.55%
13/01/2004       -0.53%
14/01/2004        0.80%
15/01/2004        0.13%
```

Compute a one-day, 20% volatility-adjusted historical VaR and the Expected Shortfall of the portfolio. The volatility is to be estimated using an exponential moving volatility model with 𝜆 = 0.96. As at 01/01/2004 the variance forecast is 0.0000053%.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.