Homework AD 717Week 10Unless stated otherwise, round your answers to threedecimals, and do not round intermediate calculations.Building an active portfolio.In this problem, we will build an active portfolio, that is, a portfolio consisting of individually selected stocks to complement our passive investments. To do this, create an Excel worksheet. Use the following instructions with a market risk premium𝑟”−𝑟$of 5%.Consider the following annualized information regarding a selection of six stocks (Apple Inc,Amazon.com Inc, Intuitive Surgical Inc, Target Corp, Walmart Inc, and Exxon Mobil Corp) and the S&P 500that we have obtained from a regression analysis:SD of Excess Return Beta SD of Systematic ComponentSD of ResidualS&P
5000.17011.000.17010.0000$AAPL0.28691.200.20410.2016$AMZN0.35541.600.27210.2286$ISRG0.34091.500.25510.2261$TGT0.27610.800.13610.2403$WMT0.22960.600.10200.2057$XOM0.21630.850.14460.1609•Find the covariance matrix according to the index model, where the covariance between two assets is defined as 𝐶𝑜𝑣(𝑟),𝑟+,=𝛽)𝛽+𝜎”1. [Hint: You can find the 𝜎”1from the above table if you compute the covariance of the index with itselfbecause 𝛽2&4566=1.]
Create a forecast of 𝛼)for each company, that is, the return in percent you anticipatein excess over the return expected through its 𝛽)in the coming year.[Example: If the 𝛽of the company were to be1, you’dexpect an excess return of 5%in the absence of 𝛼. However, if you anticipatedthat the company’s stock was going to realize an excess return of 4% or 6%, then its 𝛼would be -1% or +1%, respectively.] This forecast can just be a guess for this problem!
Construct the risky portfolio according to Table 27.1 in your book or according to “How to build your portfolio” in today’s lecture slides.Compute and report the following parameters for your portfolio:
1.Weights of the securities in your active portfolio and its 𝛼.
2.Weight of the active portfolio in the overall portfolio.
3.Aggregate alpha and beta of the active portfolio and of the overall portfolio.
4.Compare the Sharpe ratio of an investment in the market with the Sharpe ratio of the overall portfolio you have constructed!
You need to report answers with your own assumptions. But you can check your work with:AAPLAMZNISRGTGTWMTXOMAlpha0.5%0.5%1.0%-0.5%1.0%-0.8%Usingthese values for each stock, your active portfolio should have 𝛼4=3.263%,𝛽4=1.584. The overall portfolio should come out to 𝛼A=0.527%,𝛽A=1.094. The Sharpe ratio of this overall portfolio is 0.308, whereas the Sharpe ratio of the market portfolio is 0.294.
