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Portfolio Asset Allocation
Based on Historical Returns
By
Joe Smith
May 18, 2015
Finance 5315
Executive Summary:
Using five years of historical return data, three portfolios are formed to 1) maximize the Sharpe Ratio, 2) minimize the portfolio variance, and 3) to achieve a targeted portfolio beta. The portfolio consists of 10 randomly selected stocks. The out-of-sample performance of each portfolio is assessed over one year. The best preforming portfolios is aaa, with a return of xxx, a standard deviation of yyy, and a Sharpe Ratio of zzz. The predicted portfolio performance is also compared to the out-of-
sample performance. The model with the closest performance is jjj. Overall
the ability of the models to predict future performance is ??? The recommended portfolio is aaa due to the higher ???? Continue the executive
summary.
Word Count 112.
Page 1
of 4
The executive summary can be no more than 200 words. Points will be removed if the summary is over 200 words.
Page 2
of 4
1.0 Introduction:
The allocation of assets in a portfolio will significantly impact the risk return relationship of the portfolio’s performance. In this project a portfolio
of 10 randomly selected stocks is formed to ….. The introduction should cover the outline of the project, the goals of the project, and the methods used I the project.
2.0 Data and Sample:
2.1 Data The analysis is based on five years of monthly stock returns which include dividends. … Give a brief description of the data, why it is selected,
and what the properties of the data are. 2.2 Sample Stocks
In addition, when indicated in the project guide, give a brief, one or two sentence description of each investment used in the portfolio. An example equity description is E I du Pont de Nemours and Company, ticker symbol DD, is a chemical company that produces industrial chemicals. These products are used in a number of industries including agriculture, automotive, and business and construction, among many others. 3.0 Results:
3.1 Sharpe Optimal Portfolio
This section of the analysis reports and explains the results obtained from the project. Results should be neatly tabled with table headers and legends. Examples are shown in the associated videos. Results tables and graphs should be integrated with the report. This section should be subdivided by each results topic. 3.2 Minimum Variance Portfolio
Page 3
of 4
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4.0 Conclusion: A summary of your results and recommendations. No more than one page in length.
Appendix: The appendix will include your analysis tables printed to fit on a single page. You data is NOT to be included in this section. Only the analysis tables for the portfolios and the out-of-sample evaluation. The appendix will not be page numbered. A printed copy of the report must be turned in on the appropriate due date. The excel file must be uploaded to the Blackboard website.
The upload is timed and not late files can be submitted.
Page 4
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Related Documents
Related Questions
Consider a client with a 10% return objective. A financial adviser creates a
policy statement for that client, identifies relevant financial securities that fit
the risk return profile for this client, and drafts an optimal asset allocation
using specialized optimization techniques.
After one year, the financial adviser's recommendations produce a return
of 10%.
Question: Is this client satisfied with the performance of the portfolio?
arrow_forward
During a particular investment period, a wealth management company held an investment portfolio that earned an average return of 13% with standard deviation of 30% and beta of 1.5. The average risk-free rate of return during this investment period was 2%. (full process)
(a) Calculate the Sharpe and Treynor measures of performance evaluation for this investment portfolio.
This investment portfolio is composed of the following two asset classes:
Asset Class
Weight
Return
Equity
0.80
15%
Bonds
0.20
5%
During this particular investment period, the information on a benchmark portfolio is given in the following table.
Asset Class
Weight
Return
Equity (S&P500 Index)
0.50
17%
Bonds (Lehman Brothers Index)
0.50
5%
(b) Determine whether the investment portfolio of the wealth management company performed better than the benchmark portfolio in terms of the total…
arrow_forward
You are evaluating the performance of two portfolio managers, and you have gathered annual return data for the past decade:
Year Manager X Return (%) Manager Y Return (%)
1
-1.5
-6.5
-1.5
-3.5
3
-1.5
-1.5
4
-1.0
3.5
5
0.0
4.5
4.5
6.5
7
6.5
7.5
8
8.5
8.5
13.5
12.5
10
18.5
14.5
a. For each manager, calculate (1) the average annual return, (2) the standard deviation of returns, and (3) the semi-deviation of returns. Do not round intermediate calculations.
Round your answers to two decimal places.
Average annual return Standard deviation of returns Semi-deviation of returns
Manager X
%
%
%
Manager Y
%
%
%
b. Assuming that the average annual risk-free rate during the 10-year sample period was 3.0%, calculate the Sharpe ratio for each portfolio. Based on these computations, which
manager appears to have performed the best? Do not round intermediate calculations. Round your answers to three decimal places.
Sharpe ratio (Manager X):
Sharpe ratio (Manager Y):
Based on Sharpe ratio -Select-
)…
arrow_forward
Portfolio return and standard deviation Jamie Wong is thinking of building an investment portfolio containing two exchange traded funds (ETFs) Jamie plans to invest $2,000 in Vanguard S&P 500 ETF (VOO) and $8,000 in Invesco QQQ Trust (QQQ). Jamie has decided to analyze some historical returns to get a
sense for her portfolio's possible future risk and return. Six years of historical annual returns for each ETF are shown in the following table:
a. Calculate the portfolio return, rp, for each of the 6 years assuming that 20% is invested in VOO and 80% is invested in QQQ
b. Calculate the average annual return for each ETF and the portfolio over the six-year period.
c. Calculate the standard deviation of annual returns for each ETF and the portfolio. How does the portfolio standard deviation compare to the standard deviations of the individual ETFs?
d. Calculate the correlation coefficient for the two ETFs. How would you characterize the correlation of returns of the two ETFs?
e. Discuss…
arrow_forward
You are evaluating the performance of two portfolio managers, and you have gathered annual return data for the past decade:
Year
Manager X Return (%)
Manager Y Return (%)
1
-1.5
-6.5
2
-1.5
-3.5
3
-1.5
-1.5
4
-1.0
3.5
5
0.0
4.5
6
4.5
6.5
7
6.5
7.5
8
8.5
8.5
9
13.5
12.5
10
17.5
13.5
a. For each manager, calculate the average annual return, the standard deviation of returns, and the semi-deviation of returns.
b. Assuming that the average annual risk-free rate during the 10-year sample period was 1.5 percent, calculate the Sharpe ratio for each portfolio. Based on these computations, which manager appears to have performed the best?
c. Calculate the Sortino ratio for each portfolio, using the average risk-free rate as the minimum acceptable return threshold. Based on these computations, which manager appears to have performed the best?
d. When would you expect the Sharpe and…
arrow_forward
You are evaluating the performance of two portfolio managers, and you have gathered annual return data for the past decade:
Year
Manager X Return (%)
Manager Y Return (%)
1
-2.5
-6.5
2
-2.5
-5.5
3
-2.5
-2.0
4
-2.0
4.0
5
0.0
5.5
6
5.5
6.5
7
7.5
7.5
8
9.5
8.5
9
13.5
12.5
10
18.5
14.5
For each manager, calculate (1) the average annual return, (2) the standard deviation of returns, and (3) the semi-deviation of returns. Do not round intermediate calculations. Round your answers to two decimal places.
Average annual return
Standard deviation of returns
Semi-deviation of returns
Manager X
%
%
%
Manager Y
%
%
%
Assuming that the average annual risk-free rate during the 10-year sample period was 1.0%, calculate the Sharpe ratio for each portfolio. Based on these computations, which manager appears to have performed the best? Do not round intermediate calculations. Round your…
arrow_forward
Solve the attachment.
arrow_forward
Considering the attached set of securities and portfolio returns:
Assume that you initially invested $1,000,000 in the portfolio and that the distribution of the annual rate of return of the portfolio is normal.
What is the distribution of the return of the portfolio 20 years after its formation?
Provide the graph of the distribution of the return of the portfolio.
arrow_forward
Set up the complete formula for Dollar Weighted Return (DWR) for the following portfolio including final value of the portfolio.
Year 0 1 2 3 4
Actions at the ending of the year (Yr0)Starting with $1000 (Yr1)Adding $100 (Yr2)Withdrawing $200 (Yr3)Adding $300 (Yr4)Ending Value = ?
ROR during each Yr (Yr0) - (Yr1) 8% (Yr2)-4% (Yr3) 9% (Yr4) 3%
A. Calculate the time weighted return (TWR)
Complete Questions with respect to Excel
arrow_forward
A portfolio management organization analyzes 75 stocks and constructs a mean-variance efficient portfolio that is constrained to these 75 stocks. How many estimates of expected returns, variances and covariances are needed to optimize this portfolio? (Using Markowitz Model)
75, 150, 2625
75, 75, 2700
75, 75, 2775
75, 75, 2925
75, 150, 2775.
arrow_forward
An investor recorded the following annual returns of one of his investments. You are required to calculate and comment on;
1. Mean return.
2. Variance and standard deviation of the return.
3. Geometric return.
Year
2016
2017
2018
2019
2020
Return
15%
17%
19%
10%
-5%
arrow_forward
Consider an equal-weighted portfolio that
comprises two assets: A and B. The monthly
20.
returns for each asset for the first four months of
the year are given below.
Month 1 Month 2 Month 3 Month 4
Asset A return
5%
-2%
-3%
-6%
Asset B return
4%
1%
?
2%
If the effective annual rate of return on the equal-
weighted portfolio calculated from the geometric
sum of monthly portfolio returns is 13.49%, what
is the Month 3 return for asset B?
Please explain in detail the rationale behind each step.
arrow_forward
5. You are evaluating the performance of two portfolio managers, and you have gathered
annual return data for the past decade:
Manager X Return (%)
Manager Y Return (%)
Year
-6.5
-1.5
-1.5
-3.5
-1.5
3
-1.5
4
-1.0
3.5
0.0
4.5
4.5
6.5
6.5
7.5
8.5
8.5
13.5
12.5
10
17.5
13.5
a. For each manager, calculate (1) the average annual return, (2) the standard deviation
of returns, and (3) the semi-deviation of returns.
b. Assuming that the average annual risk-free rate during the 10-year sample period was
1.5 percent, calculate the Sharpe ratio for each portfolio. Based on these computations,
which manager appears to have performed the best?
c. Calculate the Sortino ratio for each portfolio, using the average risk-free rate as the
minimum acceptable return threshold. Based on these computations, which manager
appears to have performed the best?
d. When would you expect the Sharpe and Sortino measures to provide (1) the same per-
formance ranking or (2) different performance rankings? Explain.
arrow_forward
Beta of portfolio
arrow_forward
Given simple required answer
arrow_forward
Xuemeihas been managing five portfolios for the last year. She has collected the following
information and has begun to make several calculations for five two stock portfolios:
1
2
3
4
5
a)
b)
c)
rate of return on NCP = 12%
rate of return on NAB = 10%
standard deviation of NCP = 15%
standard deviation of NAB = 19%
covariance = 0.0064
Portfolio Weight in NAB Portfolio Returns
30%
40%
60%
55%
20%
Portfolio
Variance
Portfolio
Standard
Deviation
3
Assist Xuemei by finishing the calculations for her. That is, complete the missing figures
in the table above.
Explain to Xuemei why the portfolio standard deviation is not simply the weighted
average of the standard deviation of the stocks in the portfolio.
Find the weight for NAB that would result in the lowest portfolio variance. Do not restrict
your enquiry to the five portfolios.
arrow_forward
You have been asked for your advice in selecting a portfolio of assets and have been supplied with the following data:. You have been told that you can create
two portfolios-one consisting of assets A and B and the other consisting of assets A and C-by investing equal proportions (50%) in each of the two component
assets.
a. What is the average expected return, r, for each asset over the 3-year period?
b. What is the standard deviation, s, for each asset's expected return?
c. What is the average expected return, rp, for each of the portfolios?
d. How would you characterize the correlations of returns of the two assets making up each of the portfolios identified in part c?
e. What is the standard deviation of expected returns, Sp, for each portfolio?
f. What would happen if you constructed a portfolio consisting of assets A, B, and C, equally weighted? Would this reduce risk or enhance return?
arrow_forward
Consider the following historical performance data for two different portfolios, the Standard and Poor's 500, and the 90-day T-bill.
Investment Average Rate of
Standard
Vehicle
Return
Deviation
Beta
R2
Fund 1
27.80%
22.30%
1.273
0.763
Fund 2
13.38
14.60
0.860
0.690
S&P 500
15.37
13.90
90-day T-bill
6.60
0.70
a. Calculate the Fama overall performance measure for both funds. Round your answers to two decimal places.
Overall performance (Fund 1):
%
Overall performance (Fund 2):
%
b. What is the return to risk for both funds? Do not round intermediate calculations. Round your answers to two decimal places.
Return to risk (Fund 1):
%
Return to risk (Fund 2):
%
c. For both funds, compute the measures of (1) selectivity, (2) diversification, and (3) net selectivity. Do not round intermediate calculations. Round your answers to two decimal
places. Use a minus sign to enter negative values, if any.
Selectivity
Diversification
Net selectivity
Fund 1
%
%
Fund 2
%
%
d. Explain the meaning of the…
arrow_forward
You are an active investor in the securities market and you have established an investment portfolio of two stock A and B five years ago. Required:
A)Assume that the following data available for the portfolio, calculate the expected return, variance and standard deviation of the portfolio given stock A accounts for 45% and stock B accounts for 55% of your portfolio?
arrow_forward
Xuemeihas been managing five portfolios for the last year. She has collected the following
information and has begun to make several calculations for five two stock portfolios:
1
2
3
4
5
a)
rate of return on NCP = 12%
rate of return on NAB = 10%
standard deviation of NCP = 15%
standard deviation of NAB = 19%
covariance = 0.0064
Portfolio
Weight in NAB Portfolio Returns
30%
40%
60%
55%
20%
Portfolio
Variance
Portfolio
Standard
Deviation
3
Assist Xuemei by finishing the calculations for her. That is, complete the missing figures
in the table above.
arrow_forward
Please do fast ASAP
arrow_forward
please do A-D
arrow_forward
Example 9: What is the portfolio standard deviation for a two-asset
portfolio comprised of the following two assets if the correlation of their
returns is 0.5?
Asset A
Asset B
Expected return
Stańdard deviation of expected returns
10%
20%
5%
20%
Amount invested
740,000 760,000
arrow_forward
Analytical VaR
Use the table below at the given level of accuracy:
Critical values for VaR calculations.
a
Za
10%
-1.282
5
-1.645
1
-2.326
Diamond Inc. is an investment company. One of its portfolios has a current market value of $25,000,000 and its
returns follow a normal distribution with a mean of 8% and a standard deviation of 16% per year. At a 90%
confidence level
a. What is the portfolio VaR?
$ Number
Round your answer to the dollar. Do NOT use negative sign!
b. What is the the minimum value of the portfolio during the next year?
$ Number
Round your answer to the dollar
c. What is the portfolio ES?
$ Number
Round your answer to the dollar. Do NOT use negative sign!
arrow_forward
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- Consider a client with a 10% return objective. A financial adviser creates a policy statement for that client, identifies relevant financial securities that fit the risk return profile for this client, and drafts an optimal asset allocation using specialized optimization techniques. After one year, the financial adviser's recommendations produce a return of 10%. Question: Is this client satisfied with the performance of the portfolio?arrow_forwardDuring a particular investment period, a wealth management company held an investment portfolio that earned an average return of 13% with standard deviation of 30% and beta of 1.5. The average risk-free rate of return during this investment period was 2%. (full process) (a) Calculate the Sharpe and Treynor measures of performance evaluation for this investment portfolio. This investment portfolio is composed of the following two asset classes: Asset Class Weight Return Equity 0.80 15% Bonds 0.20 5% During this particular investment period, the information on a benchmark portfolio is given in the following table. Asset Class Weight Return Equity (S&P500 Index) 0.50 17% Bonds (Lehman Brothers Index) 0.50 5% (b) Determine whether the investment portfolio of the wealth management company performed better than the benchmark portfolio in terms of the total…arrow_forwardYou are evaluating the performance of two portfolio managers, and you have gathered annual return data for the past decade: Year Manager X Return (%) Manager Y Return (%) 1 -1.5 -6.5 -1.5 -3.5 3 -1.5 -1.5 4 -1.0 3.5 5 0.0 4.5 4.5 6.5 7 6.5 7.5 8 8.5 8.5 13.5 12.5 10 18.5 14.5 a. For each manager, calculate (1) the average annual return, (2) the standard deviation of returns, and (3) the semi-deviation of returns. Do not round intermediate calculations. Round your answers to two decimal places. Average annual return Standard deviation of returns Semi-deviation of returns Manager X % % % Manager Y % % % b. Assuming that the average annual risk-free rate during the 10-year sample period was 3.0%, calculate the Sharpe ratio for each portfolio. Based on these computations, which manager appears to have performed the best? Do not round intermediate calculations. Round your answers to three decimal places. Sharpe ratio (Manager X): Sharpe ratio (Manager Y): Based on Sharpe ratio -Select- )…arrow_forward
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