Question 2 (10 marks) You are evaluating two passive equity funds Vanguard Small-growth ETF (VBK) and Invesco Trust (QQQ). Both funds' objective is to track the performance of small and growth firms. The information about the two funds are provided below. Multi-factor regression model estimates are based on monthly excess returns and shown below: VBK QQQ 0.056 0.076 Standard deviation of excess returns Residual standard deviation Multi-factor model regression 0.03 0.04 0.001 +0.974 X MRP + 0.428 X SMB -0.177 X HML +0.01 X MOM + 0.200 X BAB -0.257 x QMJ 69% 0.003 + 1.125 X MRP +0.117 XSMB -0.612 X HML -0.018 X MOM - 0.212 X BAB + 0.109 x QMJ 63% R2 Further information about factor returns (monthly frequency): Standard deviation of returns Factor Market excess return (MRP) Small minus big (SMB) High minus low (HML) Winner minus loser (MOM) Low-beta-bias (BAB) Quality minus Junk (QMJ) Average Return 0.005 0.002 0.001 0.003 0.04 0.03 0.03 0.05 0.04 0.006 0.005 0.03 Assuming all the factors are uncorrelated. A. Calculate the funds' annual excess returns. (2.5 marks) B. Calculate the funds' annual Sharpe and Treynor ratios. (2.5 marks) C. Calculate the funds' annual Jensen alpha and information ratios using the multi-factor model as the benchmark. (2.5 marks) D. Do the funds achieve their objective of tracking the performance of small and growth firms? Explain your answer. (2.5 marks) Question 2 (10 marks) You are evaluating two passive equity funds Vanguard Small-growth ETF (VBK) and Invesco Trust (QQQ). Both funds' objective is to track the performance of small and growth firms. The information about the two funds are provided below. Multi-factor regression model estimates are based on monthly excess returns and shown below: VBK QQQ 0.056 0.076 Standard deviation of excess returns Residual standard deviation Multi-factor model regression 0.03 0.04 0.001 +0.974 X MRP + 0.428 X SMB -0.177 X HML +0.01 X MOM + 0.200 X BAB -0.257 x QMJ 69% 0.003 + 1.125 X MRP +0.117 XSMB -0.612 X HML -0.018 X MOM - 0.212 X BAB + 0.109 x QMJ 63% R2 Further information about factor returns (monthly frequency): Standard deviation of returns Factor Market excess return (MRP) Small minus big (SMB) High minus low (HML) Winner minus loser (MOM) Low-beta-bias (BAB) Quality minus Junk (QMJ) Average Return 0.005 0.002 0.001 0.003 0.04 0.03 0.03 0.05 0.04 0.006 0.005 0.03 Assuming all the factors are uncorrelated. A. Calculate the funds' annual excess returns. (2.5 marks) B. Calculate the funds' annual Sharpe and Treynor ratios. (2.5 marks) C. Calculate the funds' annual Jensen alpha and information ratios using the multi-factor model as the benchmark. (2.5 marks) D. Do the funds achieve their objective of tracking the performance of small and growth firms? Explain your answer. (2.5 marks)