Final Project
FN 315 – Summer 2021
Due Date: Friday 2nd July
Portfolio Construction
The Case
My wife and I are 60 years old and plan to retire in 5 years.
At present, we have assets of $750,000 in stocks and bonds and retirement savings of $600,000.
We own our house and car and have no liabilities.
The clients are looking to grow their retirement savings by assuming risk more significant than the market β.
However, they want to take a more conservative position on their cu
ent cash and fixed income portfolio.
My wife and I would like you to construct two new portfolios meeting our risk profiles.
Assignment
· Construct the two portfolios per the clients' request showing the β of each. There are no more than ten stocks/ Bonds in each portfolio but must have four stocks and one bond.
· Explain to the client how the CAL works and how the client can increase and decrease risk and the CAL.
· Explain how the portfolio compares to the SML showing the Sharpe ratio. Of each portfolio.
· Based on five years of daily prices (15th June 2016 to 15th June 2021), calculate the ten-day 99% Var for each portfolio and explain the results to the client
Please use PowerPoint to explain your results and an excel spreadsheet to show me your workings.
Note that there is no right or wrong portfolio; it's how you make the case.
Sheet1
Stock Price % of portfolio Beta Portfolio B
IBM $ 145 10% 1.23 2.70 100%
OSTK $ 94 50% 4.46
C $ 80 10% 1.92
KHC $ 44 10% 1.10
20% 0.67
Stock Price % of portfolio Beta Portfolio B
IBM $ XXXXXXXXXX 30% 1.23 1.20
WMT $ XXXXXXXXXX 4% 0.48
AAPL $ XXXXXXXXXX 51% 1.27
KHC $ XXXXXXXXXX 15% 1.10
Example
Stock Price % of portfolio Beta Portfolio B
IBM $ 145 10% 1.23 2.70 100%
OSTK $ 94 50% 4.46
C $ 80 10% 1.92
KHC $ 44 10% 1.10
20% 0.67
Stock Price % of portfolio Beta Portfolio B
IBM $ XXXXXXXXXX 30% 1.23 1.20
WMT $ XXXXXXXXXX 4% 0.48
AAPL $ XXXXXXXXXX 51% 1.27
KHC $ XXXXXXXXXX 15% 1.10
Homework
Stock Price Beta (5yr) Dividend Yield OYTR Portfolio Weight Market Risk Premium Portfolio Beta
Dollar Gereral $206.76 0.51 0.82% 0.06% 10% 7.70% 1.211
Lowe's Inc $190.30 1.19 1.69% 20%
NVIDIA $703.67 1.58 0.09% 30%
Visa $230.50 1.12 0.56% 40%
Question 1
Single-index return
Dollar Gereral 3.96% Porfolio Return:
Lowe's Inc 9.15% 9.31%
NVIDIA 12.13%
Visa 8.62%
Question 2
Price Return
Dollar Gereral $206.76 $8.18 Portfolio Return
Lowe's Inc $190.30 $17.42 37.85
NVIDIA $703.67 $85.36
Visa $230.50 $19.86
Question 3 Risk adjusted return
m2= Rp-Rm
Risk Adjusted Return
Dollar Gereral -3.74% 1.61%
Lowe's Inc 1.45%
NVIDIA 4.43%
Visa 0.92%
Question 4
New Portfolios
Stock Price Beta (5yr) Dividend Yield OYTR Portfolio Weight Market Risk Premium Portfolio Beta
Dollar Gereral $206.76 0.51 0.82% 0.06% 10% 7.70% 1.211
Lowe's Inc $190.30 1.19 1.69% 20%
NVIDIA $703.67 1.58 0.09% 30%
Visa $230.50 1.12 0.56% 40%
Stock New Percents Beta Stock New Percents Beta
Dollar Gereral 29% 1.011 Dollar Gereral 7% 1.411
Lowe's Inc 30% Lowe's Inc 15%
NVIDIA 10% NVIDIA 68%
Visa 31% Visa 10%
1.010 Calculated 1.401 Calculated
Sheet1
Question 1: Using the annual return data provided in Exhibit 1 of the case for Lyxor ChinaH and Lyxor MSIndia, calculate their mean returns, standard deviations, covariance and co
elation. With these numbers, compute the standard deviation and return for Susie’s entire portfolio.
Lyxor ChinaH Square of Deviation From the Mean
2009 2.00% XXXXXXXXXX
2010 4.25% XXXXXXXXXX
2011 -29.40% XXXXXXXXXX
2012 13.23% XXXXXXXXXX
2013 8.86% XXXXXXXXXX
2014 2.31% XXXXXXXXXX
2015 -2.96% XXXXXXXXXX
Mean -0.24%
Variance XXXXXXXXXX
Standard Deviation 13.866%
Lyxor MSIndia Square of Deviation From the Mean
2009 5.86% XXXXXXXXXX
2010 22.40% XXXXXXXXXX
2011 -27.07% XXXXXXXXXX
2012 0.60% XXXXXXXXXX
2013 -6.84% XXXXXXXXXX
2014 33.87% XXXXXXXXXX
2015 -9.28% XXXXXXXXXX
Mean 2.79%
Variance XXXXXXXXXX
Standard Deviation 20.391%
Lyxor ChinaH Lyxor MSIndia Product of Deviation From the Mean
2009 2.00% 5.86% XXXXXXXXXX
2010 4.25% 22.40% XXXXXXXXXX
2011 -29.40% -27.07% XXXXXXXXXX
2012 13.23% 0.60% XXXXXXXXXX
2013 8.86% -6.84% XXXXXXXXXX
2014 2.31% 33.87% XXXXXXXXXX
2015 -2.96% -9.28% XXXXXXXXXX
Mean -0.24% 2.79%
Covariance 0.01601
Co
elation 0.56623
Existing Portfolio: 60% in Lyxor ChinaH and 40% in Lyxor MSIndia
Lyxor ChinaH Lyxor MSIndia Existing Portfolio Square of Deviation From the Mean
2009 2.00% 5.86% 3.54% XXXXXXXXXX
2010 4.25% 22.40% 11.51% XXXXXXXXXX
2011 -29.40% -27.07% -28.47% XXXXXXXXXX
2012 13.23% 0.60% 8.18% XXXXXXXXXX
2013 8.86% -6.84% 2.58% XXXXXXXXXX
2014 2.31% 33.87% 14.93% XXXXXXXXXX
2015 -2.96% -9.28% -5.49% XXXXXXXXXX
Mean -0.24% 2.79% 0.97%
Portfolio Variance XXXXXXXXXX
Portfolio Standard Deviation 14.581%
Alternative way of calculating standard deviation by using the formula
w2 0.36 0.16
Variance XXXXXXXXXX XXXXXXXXXX
Portfolio Variance XXXXXXXXXX
Portfolio Standard Deviation 14.581%
Question 2: After adding Lyxor USDJIA, what was the portfolio's standard deviation and return? How does the new portfolio compare with the calculation in Question 1?
Lyxor ChinaH Lyxor MSIndia Lyxor USDJIA New Portfolio Square of Deviation From the Mean
2009 2.00% 5.86% 5.56% 4.23% XXXXXXXXXX
2010 4.25% 22.40% 6.11% 10.25% XXXXXXXXXX
2011 -29.40% -27.07% 7.94% -17.50% XXXXXXXXXX
2012 13.23% 0.60% 18.29% 10.96% XXXXXXXXXX
2013 8.86% -6.84% 17.09% 6.62% XXXXXXXXXX
2014 2.31% 33.87% 14.20% 15.35% XXXXXXXXXX
2015 -2.96% -9.28% -4.71% -5.38% XXXXXXXXXX
Mean -0.24% 2.79% 9.21% 3.503%
Portfolio Variance XXXXXXXXXX
Portfolio Standard Deviation 11.341%
Question 3: Based on your data analysis, should Susie diversify her portfolio or remain invested in China and India only?
Lyxor USDJIA Square of Deviation From the Mean
2009 5.56% XXXXXXXXXX
2010 6.11% XXXXXXXXXX
2011 7.94% XXXXXXXXXX
2012 18.29% XXXXXXXXXX
2013 17.09% XXXXXXXXXX
2014 14.20% XXXXXXXXXX
2015 -4.71% XXXXXXXXXX
Mean 9.21%
Variance XXXXXXXXXX
Standard Deviation 8.039%
Lyxor ChinaH Lyxor USDJIA Product of Deviation From the Mean
2009 2.00% 5.56% XXXXXXXXXX
2010 4.25% 6.11% XXXXXXXXXX
2011 -29.40% 7.94% XXXXXXXXXX
2012 13.23% 18.29% XXXXXXXXXX
2013 8.86% 17.09% XXXXXXXXXX
2014 2.31% 14.20% XXXXXXXXXX
2015 -2.96% -4.71% XXXXXXXXXX
Mean -0.24% 9.21%
Covariance 0.00433
Co
elation 0.38822
Lyxor MSIndia Lyxor USDJIA Product of Deviation From the Mean
2009 5.86% 5.56% XXXXXXXXXX
2010 22.40% 6.11% XXXXXXXXXX
2011 -27.07% 7.94% XXXXXXXXXX
2012 0.60% 18.29% XXXXXXXXXX
2013 -6.84% 17.09% XXXXXXXXXX
2014 33.87% 14.20% XXXXXXXXXX
2015 -9.28% -4.71% XXXXXXXXXX
Mean 2.79% 9.21%
Covariance 0.00322
Co
elation 0.19643
Question 4: Calculate the betas of Lyxor ChinaH, Lyxor MSIndia, and Lyxor USDJIA. To calculate the covariance with the market proxy, use the Lyxor World return data shown in Exhibit 1 in the case. Assuming a risk-free rate of 2.5 per cent and a market risk premium of 5.5 per cent, what are the required returns for each of the three ETFs?
Lyxor World Square of Deviation From the Mean
2009 7.69% XXXXXXXXXX
2010 5.79% XXXXXXXXXX
2011 -3.28% XXXXXXXXXX
2012 20.75% XXXXXXXXXX
2013 14.14% XXXXXXXXXX
2014 15.06% XXXXXXXXXX
2015 -4.28% XXXXXXXXXX
Mean 7.98%
Variance XXXXXXXXXX
Standard Deviation 9.426%
Lyxor ChinaH Lyxor World Product of Deviation From the Mean Lyxor MSIndia Lyxor World Product of Deviation From the Mean Lyxor USDJIA Lyxor World product of deviation from mean
2009 2.00% 7.69% XXXXXXXXXX 2009 5.86% 7.69% XXXXXXXXXX 2009 5.56% 7.69% XXXXXXXXXX
2010 4.25% 5.79% XXXXXXXXXX 2010 22.40% 5.79% XXXXXXXXXX 2010 6.11% 5.79% XXXXXXXXXX
2011 -29.40% -3.28% XXXXXXXXXX 2011 -27.07% -3.28% XXXXXXXXXX 2011 7.94% -3.28% XXXXXXXXXX
2012 13.23% 20.75% XXXXXXXXXX 2012 0.60% 20.75% XXXXXXXXXX 2012 18.29% 20.75% XXXXXXXXXX
2013 8.86% 14.14% XXXXXXXXXX 2013 -6.84% 14.14% XXXXXXXXXX 2013 17.09% 14.14% XXXXXXXXXX
2014 2.31% 15.06% XXXXXXXXXX 2014 33.87% 15.06% XXXXXXXXXX 2014 14.20% 15.06% XXXXXXXXXX
2015 -2.96% -4.28% XXXXXXXXXX 2015 -9.28% -4.28% XXXXXXXXXX 2015 -4.71% -4.28% XXXXXXXXXX
Mean -0.24% 7.98% Mean 2.79% 7.98% Mean 9.21% 7.98%
Covariance With Market 0.00996 Covariance With Market 0.00955 covariance with market 0.00654
Beta of Lyxor ChinaH 1.12044 Beta of Lyxor MSIndia 1.07504 beta of Lyxor USDJIA 0.73655
Required Return 8.662% Required Return 8.413% required return 6.551%
Question 5: Calculate the existing portfolio’s beta and the new portfolio’s beta. Assuming a risk-free rate of 2.5 per cent and a market risk premium of 5.5 per cent, what are their required returns?
Beta Required Return Mean Historical Returns
Lyxor ChinaH 1.12044 8.662% -0.24%
Lyxor MSIndia 1.07504 8.413% 2.79%
Lyxor USDJIA 0.73655 6.551% 9.21%
Existing Portfolio: 60% Lyxor ChinaH, 40% Lyxor MSIndia 1.10228 8.563% 0.97%
New Portfolio: XXXXXXXXXX% Lyxor ChinaH, 30% Lyxor MSIndia, 30% Lyxor USDJIA 0.99165 7.954% 3.503%
The historical returns calculation for Lyxor USDJIA was higher than its required return after the CAPM calculation. This means that the Lyxor USDJIA ETF falls above the SML line, and is underpriced. Therefore, Susie should purchase this ETF.
Daily Prices London 10 am Fix
FRED Graph Observations SMA Daily Vol formula is per below
Federal Reserve Economic Data
Link: https:
fred.stlouisfed.org
Help: https:
fredhelp.stlouisfed.org
Economic Research Division
Federal Reserve Bank of St. Louis
5 Years
Frequency: Daily
observation_date GOLDAMGBD228NLBM Average Daily Returns Daily SMA Volatility
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XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX Daily Var 99% 1.9556%
XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX Holding Period ( days )
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