EFB344 Risk Management and Derivatives: All answers Correct

Why might it be useful to assume that returns follow a particular statistical distribution when trying to think about risk? However, not all distributions are so simply summed up, so sometimes we need to think of different ways to summarise the risk of losses. If we have a random variable X that is Normally Distributed X ~ N(0, 1) with mean 0 and variance 1, what is the distribution of Y = μ σ X?. How does this enable us to make statements about any random variables with a random variable? Let’s say that the annual returns on Stock X are normally distributed with an average return of 10% and a standard deviation of 50% (which implies a variance of 0.25), such that X ~ N( 0.1 , 0.25). What is the probability that the stock return is between than -40% and 60% in the next year? Let’s say that the annual returns on Y are distributed Y ~ N( 0.05, 0.16). What is the probability that the stock return is less than -35% in the next year? Let’s say that the annual returns on Stock X are normally distributed with an average return of 10% and a standard deviation of 50% (which implies a variance of 0.25), such that X ~ N( 0.1 , 0.25) , and the returns on Stock Y are distributed Y ~ N( 0.05, 0.16). Let’s also say that the two sets of returns move together such that the correlation between them is ρ = 0.3. a) What is the distribution of the annual returns of a portfolio consisting of 40% in stock X and 60% in stock Y? b) What is the probability that the portfolio return is less than -29% in the next year? c) What is the probability that the portfolio return is less than -25% in the next year? What are some of the dangers associated with calculating a stock’s returns and their associated statistics straight from the stock’s historical closing price? Explain the EWMA model for estimating volatility from historical data.