You are hired to evaluate an active equity portfolio XYZ investing totally in UK common stocks. The following table shows the average annual return for the portfolio, the passive equity portfolio FTSE 100 ETF and the UK Treasury bills: Beta Average Return 10% Standard Deviation 18% Tracking error 13% 0.6 Equity Portfolio XYZ FTSE 100 ETF UK Treasury Bills 13% 1 12% 6% (a) The passive fund FTSE 100 ETF charges an annual fee of 0.12%, the active equity fund XYZ charges a fee of 0.2% per year. Calculate the Jensen's alpha, the Treynor, Sharpe measures, and the information ratio for the equity portfolio XYZ. Briefly explain whether the portfolio XYZ underperformed, equalled or outperformed the FTSE 100 ETF on a risk- adjusted basis using both the Treynor measure and the Sharpe measure. (40% weighting) (o) A hedge fund uses the same strategy as the equity portfolio XYZ to identify "good" and "bad" stocks, but implements the strategy as a long-short hedge fund, applying 5/3 times leverage. The risk-free interest rate is rf= 6% and the financing spread is zero (meaning that borrowing and lending rates are equal). The hedge fund's return before fees is given as: 5 phedge fund before fees FTSE 100 XYZ = 6% + 3" (1) Calculate the hedge fund's volatility, its beta and its alpha before fees (20% weighting) (ii) Suppose that an investor has 70% allocation in the active fund XYZ and 30% allocation in cash. What are the investments in the passive ETF fund, the hedge fund and cash (the risk-free asset) that generate the same market exposure, alpha? As a result, what is the fair management fee for the hedge fund that would make the investor indifferent between two allocations? (40% weighting) You are hired to evaluate an active equity portfolio XYZ investing totally in UK common stocks. The following table shows the average annual return for the portfolio, the passive equity portfolio FTSE 100 ETF and the UK Treasury bills: Beta Average Return 10% Standard Deviation 18% Tracking error 13% 0.6 Equity Portfolio XYZ FTSE 100 ETF UK Treasury Bills 13% 1 12% 6% (a) The passive fund FTSE 100 ETF charges an annual fee of 0.12%, the active equity fund XYZ charges a fee of 0.2% per year. Calculate the Jensen's alpha, the Treynor, Sharpe measures, and the information ratio for the equity portfolio XYZ. Briefly explain whether the portfolio XYZ underperformed, equalled or outperformed the FTSE 100 ETF on a risk- adjusted basis using both the Treynor measure and the Sharpe measure. (40% weighting) (o) A hedge fund uses the same strategy as the equity portfolio XYZ to identify "good" and "bad" stocks, but implements the strategy as a long-short hedge fund, applying 5/3 times leverage. The risk-free interest rate is rf= 6% and the financing spread is zero (meaning that borrowing and lending rates are equal). The hedge fund's return before fees is given as: 5 phedge fund before fees FTSE 100 XYZ = 6% + 3" (1) Calculate the hedge fund's volatility, its beta and its alpha before fees (20% weighting) (ii) Suppose that an investor has 70% allocation in the active fund XYZ and 30% allocation in cash. What are the investments in the passive ETF fund, the hedge fund and cash (the risk-free asset) that generate the same market exposure, alpha? As a result, what is the fair management fee for the hedge fund that would make the investor indifferent between two allocations? (40% weighting)