Before implementing risk management techniques, Smitherspoon expresses confusion regarding some measures of risk management. "I know beta and standard deviation, but what is all this stuff about convexity, delta, gamma, and vega?

Mark Stober, William Robertson, and James McGuire are consultants for a regional pension consultancy. One of their clients, Richard Smitherspoon, chief investment officer of Quality Car Part Manufacturing, recently attended a conference on risk management topics for pension plans. Smitherspoon is a conservative manager who prefers to follow a long-term investment strategy with little portfolio turnover. Smitherspoon has substantial experience in managing a defined benefit plan but has little experience with risk management issues. Smitherspoon decides to discuss how Quality can begin implementing risk management techniques with Stober, Robertson, and McGuire. Quality’s risk exposure is evaluated on a quarterly basis.

Before implementing risk management techniques, Smitherspoon expresses confusion regarding some measures of risk management. "I know beta and standard deviation, but what is all this stuff about convexity, delta, gamma, and vega?" Stober informs Smitherspoon that delta is the first derivative of the call-stock price curve, and Robertson adds that gamma is the relationship between how bond prices change with changing time to maturity.

Smitherspoon is still curious about risk management techniques, and in particular the concept of VAR. He asks, "What does a daily 5% VAR of $5 million mean? I just get so confused with whether VAR is a measure of maximum or minimum loss. Just last month, the consultant from MinRisk, a competing consulting firm, told me it was ‘a measure of maximum loss, which in your case means we are 95% confident that the maximum 1-day loss is $5.0 million." McGuire states that his definition of VAR is that "VAR is a measure that combines probabilities over a certain time horizon with dollar amounts, which in your case means that one expects to lose a minimum $5 million five trading days out of every 100." Smitherspoon expresses bewilderment at the different methods for determining VAR. "Can’t you risk management types formulate a method that works like calculating a beta? It would be so easy if there were a method that allowed one to just use mean and standard deviation. I need a VAR that I can get my arms around."

The next week, Stober visits the headquarters of TopTech, a communications firm. Their CFO is Ralph Long, who prefers to manage the firm’s pension himself because he believes he can time the market and spot upcoming trends before analysts can. Long also believes that risk measurement for TopTech can be evaluated annually because of his close attention to the portfolio. Stober calculates TopTech’s 95% surplus at risk to be S500 million for an annual horizon. The expected return on TopTech’s asset base (currently at S2 billion) is 5%. The plan has a surplus of $100 million. Stober uses a 5% probability level to calculate the minimum amount by which the plan will be underfunded next year.

Of the following VAR calculation methods, the measure that would most likely suit Smitherspoon is the:
A . variance-covariance method.
B . historical simulation method.
C . Monte Carlo simulation method.

View Answer

Answer: A

Explanation:

Variance-covariance method

The variancc-covariance method, also known as the delta-normal method, only requires estimates of mean and standard deviation of returns to estimate VAR. This is the closest method to which Smicherspoon refers. (Study Session 14, LOS 40.f)