Liu2020-08-16 21:51:35

there is a question and hope you can explain. Consider a trader with an investment in a corporate bond with face value of $100,000 and default of 0.5%. Over the next period, we can either have no default, with a return of zeroor default with a loss of $100,000. The payoffs are thus -$100,000 with probability of 0.5% and $0 with a probability of 99.5%. Since the probability of getting %0 is greater than 99%, the VaR at the 99% confidence level is $0 without taking the mean into account. This is consistent with the definition that VaR is the smallest loss, such that the right tail probability is at least 99%. Now consider a portfolio invested in 3 bonds A,B and C with same characters and independent payoffs. The portfolio var at the 99% is A 0. B. $100,000 C. $200,000 D. 300,000. Why the answer is B ? 1. the information already tells us that 99% VaR is $0. So why not $0? 2. as they are independent and undiversified, why not $100,000 ＋ $100,000 ＋100,000 = $300,000?