Q 18) Sarah is a risk manager responsible for the fixed income portfolio of a large insurance company. The portfolio contains a 30-year zero coupon bond issued by the US Treasury (STRIPS) with a 5% yield. What is the bond’s DV01?
Q 19)Suppose you simulate the price path of stock HHF using a geometric Brownian motion model with drift µ=0.02, volatility σ = 0.18and time step ∆t=0.5. Let St be the price of the stock at tme t. If So = 100, and the first two simulated (randomly selected) standard normal variables are ∑1=0.253, ∑2 = -0.675, what is the simulated stock price after the second step?
Q 34) In country X the probability that a letter sent through the postal system reaches its destination is 2/3. Assume that each postal delivery is independent of every other postal delivery, and assume that if a wife receives a letter from her husband, she will certainfy mail a response to her husband. Suppose a man in country X mails a letter to his wife (also in country X) through the postal system. If the man does not receive a response letter from his wife, what is the probability that his wife received his letter?
Q 36) An asset manager analyzes a position consisting of a put option sold on an underlying asset, which is a hedge fund pursuing a fixed income strategy. This hedge fund, which the asset manager does not own, reports daily returns to the asset manager. Due to the credit crisis, return volatility of the hedge fund has been increasing, which makes the manager nervous about the short option position. When the asset manager entered this trade, he set a guideline limiting the 95% 1-day VaR exposure of this trade to 1.0% of the fund’s NAV. Assuming the hedge fund returns are normally distributed and that there are 250 trading days per year, what is the lowest level of annualized return volatility that exceeds the guideline?
Q 41) John Flag, the manager of a USD 150 million distressed bond portfolio, conducts stress tests on the portfolio. The portfolio’s annualized return is 12%, with an annualized return volatility of 25%. In the last two years, the portfolio encountered several days when the daily value change of the portfolio was more than 3 standard deviations. If the portfolio suffered a 4-sigma daily event, which of the following is the best estimate of the change in the value of this portfolio? Assume that there are 250 trading days in a year.
Q42) A risk analyst seeks to find out the credit-linked yield spread on a BB-rated 2-year zero coupon bond issued by a multinational petroleum company. It the prevailing annual risk-free rate is 3%, the default rate for BB-rated bonds is 7% per year, and the loss given default is 60%, then the yield-to-maturity of the bond is:
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