Paul Dennon is senior manager at Apple Markets Associates, an investment advisory firm. Dennon has been examining portfolio risk using traditional methods such as the portfolio variance and beta. He has ranked portfolios from least risky to most risky using traditional methods.
Recently, Dennon has become more interested in employing value at risk (VAR) to determine the amount of money clients could potentially lose under various scenarios. To examine VAR, Paul selects a fund run solely for Apple's largest client, the Jude Fund. The client has $100 million invested in the portfolio. Using the variance-covariance method, the mean return on the portfolio is expected to be 10% and the standard deviation is expected to be 10%. Over the past 100 days, daily losses to the Jude Fund on its 10 worst days were (in millions): 20, 18, 16, 15, 12, 11, 10, 9, 6, and 5. Dennon also ran a Monte Carlo simulation (over 10,000 scenarios). The following table provides the results of the simulation:
Figure 1: Monte Carlo Simulation Data
The top row (Percentile) of the table reports the percentage of simulations that had returns below those reported in the second row (Return). For example, 95% of the simulations provided a return of 15% or less, and 97.5% of the simulations provided a return of 20% or less.
Dennon's supervisor, Peggy Lane, has become concerned that Dennon's use of VAR in his portfolio management practice is inappropriate and has called for a meeting with him. Lane begins by asking Dennon to justify his use of VAR methodology and explain why the estimated VAR varies depending on the method used to calculate it. Dennon presents Lane with the following table detailing VAR estimates for another Apple client, the York Pension Plan.
To round out the analytical process. Lane suggests that Dennon also incorporate a system for evaluating portfolio performance. Dennon agrees to the suggestion and computes several performance ratios on the York Pension Plan portfolio to discuss with Lane. The performance figures are included in the following table. Note that the minimum acceptable return is the risk-free rate.
Figure 3: Performance Ratios for the York Pension Plan
Using the variance/covariance method, the value at risk in the Jude Fund with 97.5% probability will be closest to:
- $10 million.
- $20 million.
- $90 million.
Answer(s): A
Explanation:
The variance/covariance method relies on the assumption of a normal distribution. With a 97.5% probability, the lower bound on the distribution is the mean less two standard deviations which equals 10% - 2(10%) = -10%.
On a $100 million investment, therefore, the VAR using the variance/covariance method is $100 million times 10% or $10 million. (Study Session 14, LOS 40.e,f)
Professor's Note: Remember that for a 97.5% (2.5%) VAR you use the z-score for a 95% confidence interval (- 2.00), because 2.5% of the distribution falls in each tail. For a 95% (5%) VAR, you use the z-score for a 90% confidence interval, because 5% of the distribution falls in each tail. The VAR significance, in this case either 2.5% or 5%, is the proportion of the distribution in the lower tail. In computing VAR, we ignore the upper tail.