a) The following predictions have been made regarding the economic states, share A and share B. Probability of the state Share A rate of return Share B rate of return State Recession 0.10 -0.20 0.30 Normal Boom 0.50 0.40 0.10 0.20 0.70 0.50 Calculate the expected return and standard deviation for share A Calculate the expected return and standard deviation for share B. b) Assume you observe the following situation: Security Beta Expected Return A 1.2 13% B 0.6 10% The Treasury Bill rate is 5 percent. Which one of the two securities is overvalued relative to the other? Show your working Which of these statements is false? Consider a stochastic block model on a directed simple random graph, with group sizes N1, ..., NK. The maximum number of edges that go from a node in block g to a node in block h g is (Ng 1)Nn - Consider a stochastic block model on a directed simple random graph, with group sizes N1, ..., NK. The maximum number of edges that go from a node in block g to a different node in block g is (Ng 1) Ng - The maximum likelihood estimator for the block connection probability of a stochastic block model with known labels corresponds to the density of edges within that block The maximum likelihood estimator for the connection probability of the G(n,p) model corresponds to the graph's density 1. Suppose the risk-free rate Rp is 3%, the expected return on the market portfolio RM is 8%, and the standard deviation of the return on the market portfolio M is 26%. (a) If you have 100% of your money in the risk-free asset, what is your portfolio expected return and standard deviation? (b) If you have 100% of your money in the market, what is your your portfolio expected return and standard deviation? (c) If you have 60% of your money in the market and 40% in the risk-free asset what is your your portfolio expected return and standard deviation?