[SOLVED] Cqf exam one p0

InstructionsUpload two files: E1 YOURNAME REPORT.pdf and E1 YOURNAME CODE.zip. ZIP file to include source code, signed declaration (if not in PDF). Use YOURNAME as registered on CQF Portal.
You must prepare PDF REPORT that integrates workings, numerical answers and plots in the order ofquestions. Guide to report preparation:
1. If you draft the report from Python notebook – remove unnecessary output and unused code, add maths with Markdown TeX. Save IPYNB file to HTML first, then print PDF.
2. If you draft from Word/LaTeX – add maths requested, numerical solutions and plots. Here you can
insert code at your discretion, eg full/part code after each question or in an appendix.
4. ‘Code+output’ Python printouts (absent maths, explanation, issues with plots) or Excel printoutswill not be considered full reports.
Exam submissions and file names which do not follow these instructions will require extra processing time. Exam One computation in Excel is not recommended.
Marking Scheme: Q1 16% Q2 24% Q3 8% Q4 28% Q5 24%. Total is 100%.
An investment universe of the following risky assets with a dependence structure (correlation) applies to all questions below as relevant:
Asset µ σ w
0.4 0.3
A 0.05 0.07 w1 1 1 0.27 0.3
B 0.07 0.28 w2 0.4 0.27 1 0.42
C 0.15 0.25 w3
w4 0.42 0.5
D 0.22 0.31 0.5
Corr = 0.3
1
0.3
Question 1. Global Minimum Variance portfolio is obtained subject to the budget constraint:
argminw′ Σw s.t. w′1 = 1 w
• Derive the analytical solution for optimal allocations w∗. Provide full derivation workings.
• Compute optimal allocations (Global MV portfolio) for the given investment universe.
Question 2. Consider the optimization for a target return m. There is no risk-free asset.
argminw′ Σw
w
w′1 = 1 w′µ = m
• Compute correlation levels by stressing the matrix ×1, ×1.3, ×1.8, subject to the upper limit 0.99 for each cross-asset correlation. Diagonal elements stay equal to one.Add
√
• Compute w∗ and portfolio risk σΠ = w′Σw for m = 7% for three levels of correlation given.
Hints: it is possible to compute this kind of optimal allocation via analytical formula. Negative and nonrobust allocations (into ± 100s%) are possible, particularly for high correlation. Please do not reconfirm your numerical results via support.
Question 3. “Evaluating the P&L more frequently make it appear more risky than it actually is.” Make the following computations to demonstrate this statement.
• Write down the formula for Sharpe Ratio and note that σ is scaled with time.
• Compute Daily, Monthly, and Quarterly Sharpe Ratio, for Annualised SR of 0.53. Hint: this is an abstract computation, not related to Questions 1 and 2.
• Convert each Sharpe Ratio into Loss Probability (daily, monthly, quarterly, annual), using
Pr(P&L < 0) = Pr(x < −SR).
where x is a standard Normal random variable.
Assume you are an analyst concerned with how risky NASDAQ-100 became over S&P 500. Perform the backtesting of Analytical VaR (99%/10day) on the data provided in .csv files.
Question 4. The quick guide is given below, but please refer to the tutorial and CQF material.
√ VaR10D,t = Factor × σt × 10
• Compute the rolling standard deviation σt from 21 daily returns. Timescale of σt remains ‘daily’ regardless of how many returns are in the sample.• To make a projection over 10 days, we use the additivity of variance σ10D = pσt2× 10.
• A breach occurs when the forward realised 10-day return is below the VaRt quantity.
r10D,t+10 < VaR10D,t given both numbers are negative.
VaR is fixed at time t and compared to the return from t to t+10, computed ln(St+10/St). Alternatively, you can compare to ln(St+11/St+1) but state this assumption in your report upfront. Prepare and present the following deliverables in your report:
(a) The count and percentage of VaR breaches.with λ = 0.72 value set to minimise out of sample forecasting error.
Hint: use the variance for the entire dataset to initialise the computation.
(a-c) Provide the same deliverables (a), (b) and (c) as in the previous Question.
(d) Briefly discuss the impact of λ on smoothness of EWMA-predicted volatility (3-4 lines). Hint: you can discuss λ theoretically without recomputing EWMA-based backtest but, if you recompute for an extra illustration it is sufficient to do so for one market index only.
END OF EXAM