17. A portfolio manager has a $50 million investment in a high-tech stock with a volatility of 50% and a CAPM beta of 1. The volatility of 50% and the CAPM beta are estimated using daily returns over the past 252 days. A firm's capital allocation allocates capital based on a 1% VaR with a one-year horizon. The capital allocation is USD 66 2/3 million and exceeds the initial market value of the stock. Which of the following statements about the firm's capital allocation scheme is correct?

A. Since a stock has limited liability, the capital allocation cannot exceed $50 million. The firm's mistake is simply to ignore the expected return on the stock

B. The firm made no mistake. The stock is simply very risky

C. The firm makes the mistake of assuming the normal distribution for a high tech stock. The firm should adjust the volatility to take into account the possibility of jumps and 2.33 times the adjusted volatility would produce the right capital allocation  

D. The firm should use the lognormal distribution for the stock price over a period of one year since the normal distribution for returns leads to a poor approximation of the distribution of the stock price a year hence

Correct answer is Dfficeffice" />

For long horizons, one should use the log normal distribution for the stock price.  For the period of year, the normal distribution for returns leads to a poor approximation of the distribution of the stock price one year out.  The difference between the two distributions is driven by the size of the volatility over the horizon.  Small values imply that the distributions are closely identical.  However, if the volatility is large, the difference between the normal distribution and lognormal is large.

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