Certainly! Below is a **step-by-step breakdown** (in two steps) for solving the Value at Risk (VaR) problem described in your prompt. Since the daily returns data file is not attached, I’ll **explain the process and formulas** you should use, so you can apply them with your actual data. --- # **Step 1: Delta-Normal VaR Calculation** ### **1.1 Calculate Mean and Standard Deviation** - **Mean (μ):** Use Excel: `=AVERAGE(range_of_returns)` - **Standard Deviation (σ):** Use Excel: `=STDEV.S(range_of_returns)` **Explanation:** The mean gives the average daily return, and the standard deviation measures the volatility of returns. These are required for the normal VaR calculation. --- ### **1.2 Compute 1-Day VaR at 95% and 99% Confidence** - **Critical Z-values:** - 95% confidence: -1.645 - 99% confidence: -2.326 (Alternatively, use in Excel: `=NORM.INV(1-confidence_level, , 1)`) - **VaR Formula:** \[ \text{VaR} = -\left(\mu + Z \cdot \sigma\right) \] (Negative sign because VaR is a loss measure) - **Dollar VaR:** \[ \text{Dollar VaR} = \text{VaR} \times \text{Portfolio Value} \] For a $1,000,000 portfolio, multiply calculated VaR by $1,000,000. **Explanation:** This step estimates the maximum expected loss over one day with a given confidence level, assuming returns are normally distributed. --- # **Step 2: Historical Simulation VaR Calculation** ### **2.1 Sort Returns** - Sort the 60 daily returns from worst (lowest) to best (highest). **Explanation:** Sorting helps identify the cutoff points for the required percentiles (5th and 1st). --- ### **2.2 Find 5th and 1st Percentile Returns** - **5th percentile (for 95% VaR):** Use Excel: `=PERCENTILE.INC(range_of_returns, .05)` - **1st percentile (for 99% VaR):** Use Excel: `=PERCENTILE.INC(range_of_returns, .01)` ### **2.3 Calculate Dollar VaR** - Multiply the identified percentile returns by the portfolio value: \[ \text{Dollar VaR}_{95\%} = |\text{5th Percentile Return}| \times \$1,000,000 \] \[ \text{Dollar VaR}_{99\%} = |\text{1st Percentile Return}| \times \$1,000,000 \] **Explanation:** This step uses actual historical returns to estimate possible losses, avoiding distribution assumptions. --- # **Final Answer Structure** - **Step 1:** - Mean and std dev calculated, use normal distribution to find VaR at 95% and 99%, multiply by portfolio value for dollar VaR. - **Step 2:** - Sort data, find 5th and 1st percentiles, multiply by portfolio value for dollar VaR. --- ### **Final Answer:** - Calculate dollar VaR using **both Delta-Normal** and **Historical Simulation** methods as explained. - **Compare** the results and discuss which is more conservative, and the pros/cons of each method. --- **You can now apply these steps to your data in Excel to get the exact numbers!**