ease of comparison and discussion.Use the data provided on HW1_data19 to work on the following questions. The data include monthlyreturns of the following 8 asset classes from Jan 1990 to Dec 2019: 30-day T-bill (T-bill), value weightedUS total stock market (US Equity), the Barclays aggregate bond index (US Bond), MSCI developedmarket (Foreign Equity), MCSI Emerging market (Emerging Equity), Goldman Sachs aggregatecommodity index (Commodity), Equity REITs index (Real Estate), HRI aggregate hedge fund index(Hedge Fund).1. Understand Returns and Risks(1.1) Calculate the average monthly returns (arithmetic mean) and standard deviations for all the 8 assetsfor the full sample period of 1990-2019, and for the three 10-year sub-periods: 1990-1999, 2000-2009,and 2010-2019. Examine how different the returns and risks of the sub-periods are from each other andfrom the overall sample period.(1.2) Assuming an investor invested $1000 each in the 8 assets from 1990, how much will the investmentin each asset be at the end of 2019? If a 401(K) plan participant invested in the safest asset for hisretirement throughout this period, how does the investment fare?(1.3) Estimate the correlation between US Equity and the other 7 asset classes, and the correlationsbetween US bonds and the other 6 assets classes. Obtain the estimates for the full 30-year period.2. Forming Risky PortfoliosFor this question, use historic returns, risks and the correlations of the assets from the full sample period.(2.1) Form the optimal risky portfolio using the two risky assets, US Equity and US Bonds based on thehistorical information over the 30-year period. Determine the weights of the two assets and compute theSharpe Ratio of this portfolio.(2.2) Using the estimates from the sample period, form the risky portfolio using US Equity and ForeignEquity. What do we learn about the benefit of international diversification based on the actual data?(2.3) Bonus Question: Form the optimal risky portfolio using the four risky assets: US Equity, US Bond,and Real Estate.3. Returns and Risks of Investment StrategiesConsider the following strategies using US equity and US bonds. For all the calculations, you can assumethat the initial investment is $1000. You can compute the portfolio value at the end of each month, thenyou can obtain the monthly returns.(3.1) “Buy and Hold” with and without rebalancing. For this question, compute the returns of theportfolios for the full sample period.A. Buy and hold: with an initial allocation of 60/40 mix (60% in stock, 40% in bond), no rebalancing.B. Constant 60/40 mix: 60% in stock, 40% in bond at the beginning of each month.Calculate the average monthly returns and standard deviations for the portfolios constructed from thestrategies (A) and (B). Compare the returns and risks of the two strategies for the full sample period.(3.2) Market Timing:Assuming one investor can perfectly forecast the relative return of US Bond vs. US Equity for the nextmonth and will switch between bond and equity based on the forecast. The investor will allocate 100% ofthe portfolio in the higher return asset for the subsequent month. How much is the initial $1000investment worth at the end of 2019? Compare the dollar value of investment following such a strategywith investing only in US stocks or US bonds.(3.3) “Stop-loss”Assuming you make asset allocation decisions based on the relative return of bond vs. equity in theprevious month and switch between bond and stock market based on the past relative performance. Theinvestor will allocate 100% of the portfolio in the higher return asset of the past month for the subsequentmonth (this can be termed as a “stop-loss” strategy in asset allocation). How much is the $1000 initialinvestment worth at the end of 2019? Compute the return and risk of this strategy and discuss whetherthis strategy outperform the simple strategy of investing in stocks or bonds alone? What are the possiblereasons of the different performance?(3.4) “Target-date”Start with 80% in stock, 20% in bond, and at the beginning of each subsequent year, reduce the weight ofstock by 1% while increasing the weight on bond by 1%. For example, at the beginning of 1991, theweight of stock drops to 79% and the weight of bond is 21%. Compute the returns and risks of the targetdate portfolio for the full sample period. Compare the results with “buy and hold” and “constant mix” forthe full sample period in (3.1).4. Leveraged PortfoliosAssume we have ultra portfolios that are similar to the ProShares ETFs but are based on monthly returns.Four ETF portfolios are based on US Equity and US Bond monthly returns: Ultra (2×) and Ultrashort (-2×).(4.1) Compute the cumulative returns of the four portfolios from 1990 to 2019. Show that the long termreturns (the cumulative returns) for the leveraged portfolios are not (2×) or (-2×) of the long term returnsof the underlying index.(4.2) How much are your $1000 initial investments worth at the end of 2019 if you invested in the ultra-equity and ultra-bond respectively in 1990 respectively? Compare with the results in (1.2) for US Equityand US Bonds. How are the Ultra ETF investments different from the results in 1.2.Verify and explain.(4.3) You are considering forming your overall portfolio using either Ultra-US equity or US equity tocombine with T-bill, would your allocation decisions be different for the two cases? Based on what wehave learned and the return and risk characteristics of the two risky assets, which one would you choose?Explain