You are a new financial analyst for an actively managed mutual fund and need to analyse the following funds: Variance-Covariance Matrix Fund Expected Return (%) S&P 500 Lion Fund Capital Fund S&P 500 12% 0.0325 0.0420 0.0300 Lion Fund ? 0.0300 0.1225 0.0260 Capital Fund ? 0.0420 0.0260 ? Note that the Variance-Covariance matrix tells you the variance and covariance of S&P500, Lion Fund, and Capital Fund. The variances are the diagonal elements and the covariances are the off-diagonal elements. For instance, the variance of the Lion Fund is 0.1225 and the covariance of S&P500 and Capital Fund is 0.0420. You have also found the following probabilities for Capital Fund's returns in the next year: Probability Returns State (%) (%) Good 25% 45% Average 50% 18% Bad 25% -20% The actual average annual returns for the last 10 years for Lion Fund was 12% and the actual average annual returns of the S&P500 was also 12%. The risk- free rate over the period is 3%. All rates given are annual. a) Assuming that your probabilities are correct, what are the expected return and standard deviation for Capital Fund next year? [3 marks) b) Assuming that the S&P 500 is a good proxy for the market portfolio, what is the beta for Capital Fund? Using this beta, what is the expected return for Capital Fund according to CAPM? [2 marks] c) Assuming that the S&P 500 is a good proxy for the market portfolio and that the CAPM is correct, what is the expected return for Lion Fund? (2 marks] d) Suppose that your probabilities in part (a) are the best proxy for average annual returns for Capital Fund. Combining your answers from parts (o) - (c), what are the alphas for Capital Fund and Lion Fund with respect to the CAPM? (2 marks) e) What is your interpretation of the alphas of both Capital Fund and Lion Fund? [2 marks] f) Using the predicted expected returns from CAPM in parts (b) and (c), which of the three funds would you invest in based on their Sharpe ratios? Explain. [2 marks) g) Using the actual returns of the Lion Fund and the S&P 500 index as well as the probabilities of returns for Capital Fund, which of the three funds would you now choose based on their Sharpe ratios? Explain. [2 marks]