2. Portfolio Returns and Risk Targeting Consider a portfolio of futures positions with weights w, to asset i. Each asset has a mean of , and standard deviation of o. The correlation between different assets is pij. Consider a simple cash asset we which we will assume to have no risk over short horizons and deterministic return e. For a futures portfolio, this return is the return of the funding cash portfolio. (a) Consider a portfolio with n assets, write an expression for the expected value and variance of the portfolio. (b) Consider the scenario that an investor wants to own this portfolio but at higher risk, oT, demonstrate how to adjust the portfolio to get a target at higher risk (Hint: in practice different portfolio may target higher or lower risk but adjusting the cash versus non cash weights). = (c) If there are only three assets stocks bonds and cash, with weights {ws = 0.2, wb = 0.2, we 0.6} with og = 0.16, 0B = 0.04, 0 = 0 and PSB = -0.1, what is the standard deviation (risk targeted) for this portfolio? If the investor wants to target 5% risk what would the new weights of this portfolio need to be?