FIN 9852 Spring 2021 Homework #1
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Homework Assignment #1
Weight: 30%
Due on Tuesday, Fe
uary 16 via Blackboard
Only submit responses to the below questions in a MS Word or PDF format.
Do not include raw data (prices, returns, PnL vector).
Neatness of presentation will be factored in to your grade.
Part I [20 points]. Excel
1. Select any stock (e.g. MSFT, GM, JPM, etc.).
2. Go to Yahoo Finance (or any other source), and retrieve daily closing stock prices (adjusted for
dividends and splits) for the past 501 days. If Xi = price on day i, then series Xi should have 501
observations.
Specify the ticker of the stock you selected and the resultant date range that you used.
3. Compute the co
esponding 500 daily returns (arithmetic ?? =
??
??−1
− 1).
4. Assume you have a $10,000 portfolio consisting of the one stock you selected in step 1 (so P =
$10,000). Compute the PnL vector consisting of 500 daily PnL observations (PnLi = P ∙ Ri).
Note: Portfolio value P is constant, P = $10,000 for every Ri.
5. For the return series obtained in step 3 and the PnL vector from step 4, fill out the table:
Return PnL
Number of observations N
Average (mean) �̅� & ???̅̅ ̅̅ ̅
Median Median
Standard Deviation S
Maximum Max
Minimum Min
Range Max-Min
Skewness Skew
Excess Kurtosis Kurt
FIN 9852 Spring 2021 Homework #1
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6. Assume that tomo
ow’s expected return on your portfolio is normally distributed with ? = �̅�
and ? = ? from step 5 above. Compute the following parametric VaR estimates.
For h-day VaR, use the formula ???(ℎ, 1 − ?) = −(ℎ? − √ℎ??1−?)??−1
a. 1-day 90% VaR
. 1-day 95% VaR
c. 1-day 99% VaR
d. 5-day 95% VaR
e. 10-day 99% VaR
f. In your own words, describe the meaning of 1-day 95% VaR and the 10-day 99% VaR.
7. From the PnL vector in step 4, find the 10%-ile, 5%-ile, and 1%-ile of the data. Using these
values, compute the empirical (historical simulation) VaR estimates:
a. 1-day 90% VaR
. 1-day 95% VaR
c. 1-day 99% VaR
8. Compare the historical simulation VaR estimates from step 7 to the respective parametric
estimates from step 6. Interpret the difference (if any). Comment on whether the difference is
consistent with skewness, kurtosis, mean, and median calculated in step 5.
9. Using historical simulation approach, compute the below Expected Shortfall estimates. For
example, to estimate the 95% ES, take the negative average of 25 lowest PnL observations.
a. 1-day 90% ES
. 1-day 95% ES
c. 1-day 99% ES
d. In your own words, describe the meaning of the 1-day 95% ES.
10. Parametric Expected Shortfall
Assuming the return is normally distributed (similar to step 6), estimate the parametric ES:
a. 1-day 90% ES – use the formula: 90% ?? = −??−1(? − 1.755 ∙ ?)
. 1-day 95% ES – use the formula: 95% ?? = −??−1(? − 2.063 ∙ ?)
c. 1-day 99% ES – use the formula: 99% ?? = −??−1(? − 2.665 ∙ ?)
[*Note: 2.665 is calculated from
?(−??)
?(??)
=
1
√2?
?
−
?2
2
?
, ?â„Ž??? ? = 0.01 ]
FIN 9852 Spring 2021 Homework #1
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Part II [10 points]. Concepts/Definitions
1. Define Market Risk, Credit Risk, and Operational Risk.
2. Describe the three lines of defense as applied to financial risk management.
3. List at least 3 attractions of VaR as a risk measure.
4. List at least 3 limitations of VaR as a risk measure.
5. List at least 2 advantages of ES over VaR.
6. Name all four properties of a Coherent Risk Measure. Explain each one in words (using an
example is sufficient).
- Only have to do PART 1 .