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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.
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Related Questions
What is portfolio A's CAPM beta based on your analysis? Round off your answer to three digits after the decimal points. State your answer as a percentage point as 1.234.
Compute the Treynor measure for portfolio B. Round off your answer to three digits after the decimal point. State your answer as 1.234
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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…
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Consider the following bootstrapped 3-year performance of an actively managed investor's portfolio
and a relevant benchmark:
Investor's Portfolio
Benchmark Portfolio
Iteration
Portfolio Value
Portfolio
Portfolio Value Portfolio Return
t=3
Return p.a.
t=3
р.а.
1
1.3
9.1%
1.2
6.3%
0.9
-3.5%
0.9
-3.5%
3
0.9
-3.5%
0.8
-7.2%
4
1.2
6.3%
1.1
3.2%
5
1.3
9.1%
1.2
6.3%
What is the tracking error of investor's portfolio relative to the benchmark (compounded
outperformance) over 3 years (rounded to one decimal place)?
Select one:
O a. 1.4%
ОБ. 2.7%
O. 4.5%
O d. 4.6%
O e. None of the above
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Be fast
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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-
)…
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Question One
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.
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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…
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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…
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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…
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Solve the attachment.
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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
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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.
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Beta of portfolio
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Given simple required answer
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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?
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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…
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Asset
A
B
C
Cost
$35,000
$36,000
$39,000
$10,000
Beta at purchase
0.79
0.96
1.49
1.32
Yearly income
$1,600
$1,500
SO
$250
Value today
$35,000
$37,000
$45,500
$10,500
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This question requires you to consider a three-asset portfolio valued at 10 million AUD. The portfolio
consists of the following assets: AMP, Commonwealth Bank (CBA) and QBE. The variance covariance
matrix of 5 day continuously compounded returns is equal to
(a) Define the Value at Risk (VAR) for a portfolio.
(b) Assuming portfolio weights of AMP (40%), CBA (30%), QBE (30%), calculate the 99 % 5 day
relative
VaR estimate (employ a z score measured to 2 decimal places)
(c) Calculate the VaR diversification benefit of the portfolio.
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please do A-D
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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
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Remember, the expected value of a probability distribution is a statistical measure of the average (mean) value expected to occur during all possible
circumstances. To compute an asset's expected return under a range of possible circumstances (or states of nature), multiply the anticipated return
expected to result during each state of nature by its probability of occurrence.
Consider the following case:
Aaron owns a two-stock portfolio that invests in Happy Dog Soap Company (HDS) and Black Sheep Broadcasting (BSB). Three-quarters
of Aaron's portfolio value consists of HDS's shares, and the balance consists of BSB's shares.
Each stock's expected return for the next year will depend on forecasted market conditions. The expected returns from the stocks in
different market conditions are detailed in the following table:
Market Condition Probability of Occurrence
0.20
0.35
0.45
Strong
Normal
Weak
Happy Dog Soap
17.5%
10.5%
-14%
• The expected rate of return on Happy Dog Soap's stock over…
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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!
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uppose the average return on Asset A is 7.1 percent and the standard deviation is 8.3 percent, and the average return and standard deviation on Asset B are 4.2 percent and 3.6 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions.
a.
What is the probability that in any given year, the return on Asset A will be greater than 12 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
b.
What is the probability that in any given year, the return on Asset B will be greater than 12 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
c-1.
In a particular year, the return on Asset A was −4.38 percent. How likely is it that such a low return will recur at some point in the future? (Do not round…
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Consider the following two assets:
Asset Expected return Standard deviation of returns
1 18% 30%
2 8% 10%
The returns on the two assets are perfectly negatively correlated (i.e. coefficient of -1).
Calculate the proportions of assets 1 and 2 that generate a portfolio with a standard deviation of zero.
What is the expected return of that portfolio
Calculate the expected returns and standard deviations of three other portfolios with weightingsof your choice. Present a graph of your results.
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Give typing answer with explanation and conclusion
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Please solve all parts very soon
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You are going to invest $20,000 in a portfolio consisting of assets X, Y, and Z, as follows:
Asset Annual Return Probability Beta Proportion
X 10% 0.50 1.2 0.333
Y 8% 0.25 1.6 0.333
Z 16% 0.25 2.0 0.333
Given the information in Table 5.2, The beta of the portfolio in Table 8.2, containing assets X, Y, and Z is ________.
Select one:
a. 1.6
b. 2.0
c. 1.5
d. 2.4
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OA
Graphical derivation of beta A firm wishes to estimate graphically the betas for two assets, A and B. It has gathered the return data shown in the following table for the market portfolio and for both assets over the last 10 years, 2009-2018:
a. Which of the following graphs represents the graphical derivation of beta for assets A and B?
b. Use the characteristic lines from part a to estimate the betas for assets A and B.
c. Use the betas found in part b to comment on the relative risks of assets A and B.
a. Which of the following graphs represents the graphical derivation of beta for assets A and B? (Select the best answer below.)
Asset Return (%
Beta Derivation
20
15
20-150
540 15 20
-10-
--15-
Asset A
Asset B
20
OC.
Market Retum (%)
Beta Derivation
20-
15
Asset Return (%)
10-
15 20
5
-10
-15
G
-20
Asset A
Asset B
Market Return (%)
b. Using the characteristic lines from part a, which of the following pairs of data represents the beta estimates for assets A and B? (Select the best…
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An investment banker has recommended a $100,000 portfolio containing assets B, D, and F. $30,000 will be
invested in asset B, with a beta of 1.5; $50,000 will be invested in asset D, with a beta of 2.0; and $20,000
will be invested in asset F, with a beta of 0.5. The beta of the portfolio is
1.37
1.61
1,55
1.43
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Karen Kay, a portfolio manager at Collins Asset Management, is using thecapital asset pricing model (CAPM) for making recommendations to her clients.Her research department has developed the information shown in the followingexhibit.Forecast Returns, Standard Deviations, and BetasForecast Return Standard Deviation BetaLow β stock (X) 14.0% 36% 0.8High β stock (Y) 17.0% 25% 1.5Market index 14.0% 15% 1.0Risk-free rate 5.0%(a) Calculate expected return and alpha for each stock.(b) Identify and justify which stock would be more appropriate for an investorwho wants to add this stock to a well-diversified equity portfolio.(c) Now consider Karen employs the “Betting Against Beta” strategy and let, , and denote the portfolio weights of the investmentin each of the asset classes (e.g. risk-free asset, low beta stock, market index,high beta stock, respectively) such that .According to its investment mandate, Collins Asset Management shouldtarget a gross leverage of 2.3. How much does she have to…
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- What is portfolio A's CAPM beta based on your analysis? Round off your answer to three digits after the decimal points. State your answer as a percentage point as 1.234. Compute the Treynor measure for portfolio B. Round off your answer to three digits after the decimal point. State your answer as 1.234arrow_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_forwardConsider the following bootstrapped 3-year performance of an actively managed investor's portfolio and a relevant benchmark: Investor's Portfolio Benchmark Portfolio Iteration Portfolio Value Portfolio Portfolio Value Portfolio Return t=3 Return p.a. t=3 р.а. 1 1.3 9.1% 1.2 6.3% 0.9 -3.5% 0.9 -3.5% 3 0.9 -3.5% 0.8 -7.2% 4 1.2 6.3% 1.1 3.2% 5 1.3 9.1% 1.2 6.3% What is the tracking error of investor's portfolio relative to the benchmark (compounded outperformance) over 3 years (rounded to one decimal place)? Select one: O a. 1.4% ОБ. 2.7% O. 4.5% O d. 4.6% O e. None of the abovearrow_forward
- Be fastarrow_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_forwardQuestion One 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
- 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_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 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_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 -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_forwardSet 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 Excelarrow_forwardA 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
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