Learning objectives: Describe and calculate LVaR using .... the exogenous spread approach. Describe endogenous price approaches to LVaR, their motivation and limitations, and calculate the elasticity-based liquidity adjustment to VaR. Describe liquidity at risk (LaR) and compare it to LVaR and VaR, describe the factors that affect future cash flows, and explain challenges in estimating and modeling LaR. Describe approaches to estimate liquidity risk during crisis situations and challenges which can arise during this process
Questions:
808.1. Ralph the risk analyst is evaluating a $1.8 million equity position that consists of 10,000 shares when the price per share of the stock is $180.00. The stock's volatility is 20.0% per annum. Ralph's estimate of the stock's one-day 99.0% value at risk (VaR) includes the following calculations, where he assumes the expected return, µ, over the short period of one day is zero:
a. $900.00
b. $5,380.00
c. $7,180.00
d. $14,360.00
808.2. Patricia's fund contains a very large position in a micro-capitalization stock: her position is worth 15.0% of the market. She estimates the price elasticity of demand, η = -0.60. She has already determined the position's value at risk (VaR). Under the endogenous price approach, what is the liquidity adjustment to the VaR?
a. Increase by 9.0%
b. Increase by 15.0%
c. Increase by 30.0%
d. Increase by 45.0%
808.3. In regard to liquidity at risk (LaR), EACH of the following statements is true EXCEPT which is false?
a. The value at risk (VaR) of a portfolio of long European put options is greater than its liquidity at risk (LaR)
b. The value at risk (VaR) of a net position hedged with futures contracts (and low basis risk) is less than its liquidity at risk (LaR)
c. Because liquidity at risk (LaR) does not require a confidence level and horizon, the estimation of LaR should utilize different methods than those used to estimate VaR
d. Factors that affect liquidity at risk (LaR) include borrowing/lending, margin requirements, collateral obligations, unexpected cash flows, and changes in risk management policy
Answers:
Questions:
808.1. Ralph the risk analyst is evaluating a $1.8 million equity position that consists of 10,000 shares when the price per share of the stock is $180.00. The stock's volatility is 20.0% per annum. Ralph's estimate of the stock's one-day 99.0% value at risk (VaR) includes the following calculations, where he assumes the expected return, µ, over the short period of one day is zero:
- 99.0% one-day normal VaR = $1.8 million * [-0 + 0.20 * 2.326 * sqrt(1/250)] = $52,959
- 99.0% one-day lognormal VaR = $1.8 million * (1 - exp[0 - 0.20 * 2.326 *sqrt(1/250)]) = $52,188
a. $900.00
b. $5,380.00
c. $7,180.00
d. $14,360.00
808.2. Patricia's fund contains a very large position in a micro-capitalization stock: her position is worth 15.0% of the market. She estimates the price elasticity of demand, η = -0.60. She has already determined the position's value at risk (VaR). Under the endogenous price approach, what is the liquidity adjustment to the VaR?
a. Increase by 9.0%
b. Increase by 15.0%
c. Increase by 30.0%
d. Increase by 45.0%
808.3. In regard to liquidity at risk (LaR), EACH of the following statements is true EXCEPT which is false?
a. The value at risk (VaR) of a portfolio of long European put options is greater than its liquidity at risk (LaR)
b. The value at risk (VaR) of a net position hedged with futures contracts (and low basis risk) is less than its liquidity at risk (LaR)
c. Because liquidity at risk (LaR) does not require a confidence level and horizon, the estimation of LaR should utilize different methods than those used to estimate VaR
d. Factors that affect liquidity at risk (LaR) include borrowing/lending, margin requirements, collateral obligations, unexpected cash flows, and changes in risk management policy
Answers:
