Thread starter
#1

*Learning objectives: Estimate VaR using a historical simulation approach. Estimate VaR using a parametric approach for both normal and lognormal return distributions.*

**Questions:**

707.1. A mutual fund's daily returns for the last 300 trading days is plotted on this histogram. Additionally, the worst 20 daily returns are sorted explicitly below the histogram:

Under the basic historical simulation approach, which of the following is the

**BEST**one-day 99.0% value at risk (VaR)?

a. 0.710

b. 0.840

c. 0.800

d. 0.900

707.2. Consider the following asset over three periods that starts with an initial price of $20.00 and pays a $2.00 dividend each period. In addition to the asset's price and dividends over three periods, we also show its per-period arithmetic (aka, simple) return:

About this asset's performance, each of the following statements is true

**EXCEPT**which is not accurate?

a. Geometric returns cannot be greater than arithmetic returns

b. The geometric returns in each period are approximately +22.31%, -9.10% and 35.14%

c. If the asset instead paid zero dividends, then the geometric return would equal the arithmetic return

d. The three-period geometric return is conveniently the sum of per-period geometric returns which, in this case, is about +22.31% -9.10% +35.14% = 48.36%

707.3. A risk manager is estimating the market risk of a portfolio using both the normal distribution and the lognormal distribution assumptions. The manager gathers the following data on the portfolio:

- Annual mean: 12.0%
- Annual volatility: 37.0%
- Current portfolio value: USD $1.1 million due to 12,500 shares at a current price of $80.00 per share
- Trading days in a year: 250

**correct**? (This question inspired by GARP's 2017 Practice Exam Part 2, Question #2 despite its tedious nature)

a. Lognormal 95% VaR is greater than than normal 95% VaR at the one-day holding period by about 2.43%

b. Lognormal 95% VaR is less than than normal 95% VaR at the one-year (250 days) holding period by about 3.90%

c. Lognormal 99% VaR is greater than normal 99% VaR at the one-day holding period by about 4.04%

d. Lognormal 99% VaR is less than normal 99% VaR at the one-year (252 days) holding period by about 21.75%

**Answers here:**

Last edited by a moderator:

## Stay connected