CFA Level IPortfolio ManagementHard
A portfolio manager estimates that portfolio returns are normally distributed with an expected annual return of 8% and a standard deviation of 15%. The portfolio's current market value is $10 million. Using a 95% confidence level (z = 1.65), what is the one-year Value at Risk (VaR) in dollar terms?
- A$1,500,000
- B$800,000
- C$2,475,000
- D$1,675,000
Show answer & explanationAnswer & explanation
Correct answer: D. $1,675,000
VaR at 95% confidence = (μ − z×σ) × Portfolio Value, when the result is negative it represents the loss threshold: (8% − 1.65×15%) = 8% − 24.75% = −16.75%. Dollar VaR = 16.75% × $10,000,000 = $1,675,000, meaning there is a 5% chance the portfolio loses more than $1,675,000 over the year.
Why the other options are wrong
- A. This only uses z×σ without netting the expected return, giving an inaccurate cutoff.
- B. This roughly represents just the expected return in dollars, not the risk-adjusted threshold.
- C. This uses z×σ alone without subtracting the expected return, overstating potential loss.
Value at Risk (VaR)
VaR estimates the minimum loss expected to be exceeded with a given probability over a specified time period, often assuming a normal distribution of returns.
- Formula: VaR = (μ − zσ) × Portfolio Value (loss magnitude is the negative of this)
- Common confidence levels: 95% (z=1.65) and 99% (z=2.33)
- VaR does not indicate the potential magnitude of losses beyond the threshold
Memory trick: Mean minus z times sigma tells you the danger zone