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A recent retiree and avid reader of Reddit forums is inspired to invest their 401(k) entirely in GameStop shares and Bitcoin. We can write the return on their portfolio over the next year, R, as the weighted average of the returns on GameStop shares, Rg, and bitcoin, Rb: R = wRg + (1 1 w)Rb, where w is the proportion invested in GameStop shares. Suppose the expected return on GameStop and Bitcoin over the next year are E[Rg] = =0.15 (i.e, -15%) and E[Rn] = .05 (i.e., 5%) respectively and that the investor has put 20% of their 401(k) assets into GameStop (so w = 0.2) and the remaining 80% in Bitcoin. Suppose also that the variance of the returns on GameStop and Bitcoin over the next year are Var[Rg] = 0.7 and Var[Rb] = 0.4 and that the correlation between Rg and Rb is s0.6.
(a) Calculate the expected value of the return on the investor's portfolio.
(b) Calculate the covariance of the returns on GameStop shares and Bitcoin.
(c) Calculate the variance of the return on the investor's portfolio.
(d) Suppose the investor wanted to choose the fraction w invested in GameStop shares to minimize the variance of the return on their 401(k) over the next year. What value of w
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