Compute the average excess return volatility pair wise

Question

Portfolio Management Final Homework

Exercise 1 -

For this exercise, you will have to use the data stored in the "EXE 1 Data & Returns" Worksheet of "Portfolio Final Homework.xls". It contains monthly data for four U.S. equity sectors as well as U.S. T-Bills (used as a proxy for the riskless asset).

1) Compute the average excess return, volatility, pair wise correlations and covariances of the four U.S. equity sectors. Comment on your results.

2) You are now asked to estimate various portfolios and analyse their properties:

a) Use the results from question 1) and construct a long-only MSR Portfolio that is invested in the four U.S. equity sectors.

b) Determine the optimal portfolio sector allocation of a risk-averse investor (coefficient of risk aversion of 7.93) and a risk-lover investor (coefficient of risk aversion of 1.19). Use the average return on the U.S. T-Bill as a proxy for the risk-free rate.

c) Let's now assume that the risk-lover investor faces some constraints that prevent him to use leverage. How could he proceed to nevertheless invest in a portfolio, which would be in-line with his level of risk aversion without using any leverage? What would be the implications on the performance of his portfolio? (No computations required)

3) Construct two portfolios, the first being equally-weighted in capital and the second equally weighted in risk. Compare the risk allocation of the two portfolios.

Exercise 2 -

For this exercise, you will have to use the data stored in the "EXE 2 Data & Returns" Worksheet of "Portfolio Final Homework.xls". It contains monthly data for seven US real-estate sectors and the FTSE EPRA/NAREIT North America Index, as well as U.S. T-Bills (used as a proxy for the riskless asset).

1) Forecast the one-month ahead volatility on the seven US real-estate sectors using an Exponentially Weighted Moving Average (EWMA) volatility estimator with a decay factor ???? = 0.90. Use the first 12 months of observations to compute the starting value for the volatility and then forecast the one-month ahead volatility for each month between Feb. 2007 and Feb. 2017.

2) Use the results from question 1) and estimate two risk-based portfolios (inverse-volatility):

a) An unlevered risk-based portfolio defined such as:

w^u_i,t = σ^{^-1}_i,t/_j=1∑ⁿσ^{^1}_j,t

where the individual asset volatilities σ^ˆ_i,t correspond to the EWMA estimates obtained in question 1).

b) A levered risk-based portfolio which is targeting a constant volatility of 40% on an ex-ante basis, with a maximum leverage level capped at 200%, such as:

w^l_i,t = l_tw^u_i,t

with:

l_t = (40%/σ^u_t, 200%)

where l_t is the leverage ratio required to match the target volatility and σ^u_t is the ex-ante volatility of the unlevered risk-based portfolio at time t.

3) Compare the historical performance and risk of the two risk-based portfolios and the FTSE EPRA/NAREIT North America Index (excess returns, volatility, skewness, excess kurtosis, Maximum Drawdown, Jensen-alpha, market beta, Sharpe ratio, Information ratio and Calmar ratio). What investment would you recommend to an investor? Justify your answer(s).

Exercise 3 -

For this exercise, you will have to use the data stored in the "EXE 3 Data & Returns" Worksheet of "Portfolio Final Homework.xls". It contains monthly data for Blackrock Global Allocation Fund and eight asset indices, as well as U.S. T-Bills (used as a proxy for the riskless asset).

1) Using stepwise regression approach with backward elimination, identify from the long list of asset indices the subset of risk factors that best explains the past returns of Blackrock Global Allocation fund. Use the excess returns on Blackrock Global Allocation and on the risk factors for your computations.

2) Using the risk factors identified in question 1), perform the systematic/specific portfolio return and risk decompositions for Blackrock Global Allocation Fund. Comment on your results.

3) Using the risk factors identified in question 1) and T-Bills, find a passive investable tracking fund that mimic the style risk exposures of Blackrock Global Allocation fund (Return-based Style Analysis). What is the quality of the fund replication? Justify your answer.

Attachment:- Assignment File.rar