Learning Objectives: Explain and give examples of linear and non-linear portfolios. Describe and explain the historical simulation approach for computing VaR and ES. Describe the delta-normal approach and use it to calculate VaR for non-linear derivatives.
24.3.1 Lenny runs a technology-focused hedge fund. The hedge fund is a long-only fund founded on 12/1/2023 that, prior to 1/1/2024, had never taken a short or derivative position. Here were the fund's major trades in January 2024:
a. 2nd
b. 12th
c. 24th
d. 27th
24.3.2 Scott is a risk manager for an investment manager. He is interested in estimating the potential loss the portfolio can expect over a specific time frame at a given confidence level (VaR) and the average of all potential losses beyond that potential loss (aka, expected shortfall, ES). Over the past 120 days, the portfolio's ten worst daily returns were the following:
View attachment 4193
Find the 1-day 5% VaR and ES for Scott (per Ch 2 Calculating and Applying VaR).
a. VaR 17.84%, ES 7.55%
b. VaR 7.43%, ES 16.12%
c. VaR 14.48%, ES 16.12%
d. VaR 14.48% ES 17.84%
24.3.3 A highly volatile car manufacturer has a share price of $485.00 and has annual volatility of 49.0% (252 trading days per year). A call option (on the stock) is near the money with a delta, Δ(call) of 0.450, and a gamma, Γ(call), of 0.00580. If share prices are normally distributed and there are 252 trading days in a year, what is closest to the one-month (21-day) 95% VaR of a long call option?
a. 68.60
b. 17.63
c. 112.85
d. 13.85
Answers here:
24.3.1 Lenny runs a technology-focused hedge fund. The hedge fund is a long-only fund founded on 12/1/2023 that, prior to 1/1/2024, had never taken a short or derivative position. Here were the fund's major trades in January 2024:
- On 1/2/2024, Lenny finds a good buy but is short on cash, so he purchases a forward contract.
- On 1/12/2024, Lenny believed the market was overvalued and thus wanted to remove market risk by adding a short position to hedge his market risk.
- On 1/24/2024, believing the market was still overvalued, Lenny began to sell call options.
- On 1/27/2024, Lenny began to buy put options on his portfolio.
a. 2nd
b. 12th
c. 24th
d. 27th
24.3.2 Scott is a risk manager for an investment manager. He is interested in estimating the potential loss the portfolio can expect over a specific time frame at a given confidence level (VaR) and the average of all potential losses beyond that potential loss (aka, expected shortfall, ES). Over the past 120 days, the portfolio's ten worst daily returns were the following:
View attachment 4193
Find the 1-day 5% VaR and ES for Scott (per Ch 2 Calculating and Applying VaR).
a. VaR 17.84%, ES 7.55%
b. VaR 7.43%, ES 16.12%
c. VaR 14.48%, ES 16.12%
d. VaR 14.48% ES 17.84%
24.3.3 A highly volatile car manufacturer has a share price of $485.00 and has annual volatility of 49.0% (252 trading days per year). A call option (on the stock) is near the money with a delta, Δ(call) of 0.450, and a gamma, Γ(call), of 0.00580. If share prices are normally distributed and there are 252 trading days in a year, what is closest to the one-month (21-day) 95% VaR of a long call option?
a. 68.60
b. 17.63
c. 112.85
d. 13.85
Answers here:
