ITs calculation Assignment. All the calculation need to shown in word file .All the instruction are in the attached file please.Thank you

Topic: Portfolio Investment Management Calculations and their Application to Decision-making
Solution 1:
(a)
    Equal weighted method
    Company
    No. of Shares
    Beginning Price per share
    End Price per share
    % Change
    Good Ltd
    800
    12.00
    12.48
    4.00%
    Better Ltd
    1000
    8.00
    8.80
    10.00%
    Best Ltd
    2000
    30.00
    34.20
    14.00%
     
     
     
     Total % Change
    28.00%
     
     
     
     Equal Weighted Return
    9.33%
Good Ltd % Change = (End price per share – Beginning price per share) ÷ Beginning price per share
= (12.48 – 12.00) ÷ 12.00 = 4%
Better Ltd % Change = (End price per share – Beginning price per share) ÷ Beginning price per share
= (8.80 – 8.00) ÷ 8.00 = 10%
Best Ltd % Change = (End price per share – Beginning price per share) ÷ Beginning price per share
= (34.20 – 30.00) ÷ 30.00 = 14%
Equal weighted return = 4% + 10% + 14% = 28% ÷ 3 = 9.33%
    Price Weighted method
    Company
    No. of Shares
    Beginning Price per share
    End Price per share
    % Change
    Good Ltd
    800
    12.00
    12.48
    
    Better Ltd
    1000
    8.00
    8.80
    
    Best Ltd
    2000
    30.00
    34.2
    
     
     
    50.00
    55.48
    10.96%
     
     
    16.67
    18.49
    10.96%
Beginning price per share of three companies = 12 + 8 + 30 = 50 ÷ 3 = 16.67
End price per share of three companies = 12.48 + 8.80 + 34.20 = 55.48 ÷ 3 = 18.49
% Change as per Price Weighted Method = (18.49 -16.67) ÷ 16.67 = 10.96%
    Value Weighted Index
    Company
    No. of Shares
    Beginning Price per share
    End Price per share
    Total Amount Beg
    Total Amount End
    % Change
    Good Ltd
    800
    12.00
    12.48
    9600
    9984
     
    Better Ltd
    1000
    8.00
    8.80
    8000
    8800
     
    Best Ltd
    2000
    30.00
    34.20
    60000
    68400
     
     
     
     
     
    77600
    87184
    12.35%
Good Ltd = (No. of shares x Beg price per share) = 800 * 12 = 9600
(No. of shares x End price per share) = 800 * 12.48 = 9984
Better Ltd = No. of shares x Beg price per share) = 1000 * 8 = 8000
(No. of shares x End price per share) = 1000 * 8.80 = 8800
Best Ltd = No. of shares x Beg price per share) = 2000 * 30 = 60000
(No. of shares x End price per share) = 2000 * 34.20 = 68400
Total Amount of Beginning price per share = 9600 + 8000 + 60000 = 77600
Total Amount of End price per share = 9984 + 8800 + 68400 = 87184
% Change as per Value weighted Index = (87184 – 77600) ÷ 77600 = 12.35%
(b)
    Method
    Returns
    Explanation/ Comments
    Equal Weighted
    9.33%
    Equal weighted method assumes equal weights of investment in each security. It does not represent a signal to buy or hold a security unless the portfolio is rebalanced in each period.
     
    
    
    
    Price Weighted
    10.96%
    Price weighted indices method gives a greater than proportional weight for the equity shares with smaller capital. Since there is downward biases the high growth companies with stock split lose relative importance as it reflects downward bias.
     
    
    
    
    Value Weighted
    12.35%
    Value weighted method is the best suited method as it mimics the returns so that one can buy or hold the stock or a portfolio. Also, as per this method Sadie can also earn more and the highest returns compared to the other methods.
     
    
    
    
Solution 2:
    Average Risk Free Rate (90 Days T-Bill)
    4%
     
     
     
     
    Annual Returns
    Yield Square
    Deviation from mean
    Square of deviation
     
    12%
    0.2%
    0.05
    0.002
     
    7%
    0.0%
    0.00
    0.000
     
    -4%
    1.3%
    -0.11
    0.013
     
    9%
    0.0%
    0.02
    0.000
     
    13%
    0.3%
    0.06
    0.003
    Arithmetic average annual return
    7.40%
    0.46%
    Sum
    0.019
     
     
     
    Variance
    0.004
    Standard Deviation Calculation
    6.09%
     
    
    
    
    
    
    Geometric average annual return
     
    -0.72
    
    
     
     
     
    
    
    Sharpe Ratio
     
    0.56
    
    
Arithmetic average annual return
= 12% + 7% + (-4%) + 9% + 13% = 37% ÷ 5 = 7.40%
Standard Deviation Calculation
Deviation from mean = (Annual returns – Arithmetic average annual returns) = (12% - 7.40%) + (7% - 7.40%) + (-4% - 7.40%) + (9% - 7.40%) + (13% - 7.40%) = 0.05 + 0.00 + (-0.11) + 0.02 + 0.06
Square of deviation (Variance) = (0.05)^2 + (0.00)^2 + (-0.11)^2 + (0.02)^2 + (0.06)^2 = 0.002 + 0.000 + 0.013 + 0.000 + 0.003 = 0.019 ÷ 5 = 0.004
Standard Deviation SD_A = 〖VAR_A〗^0.5 = 0.004^0.5 = 6.09%
Geometric average annual return
= (1 + Annual Return) x (1 + Annual Return) + (1 + Annual Return) + (1 + Annual Return) + (1 + Annual Return)^1/n - 1
= (((1.12)*(1.07)*(0.96)*(1.09)*(1.13))^1/5) – 1
= -0.72
Sharpe Ratio = Sharpe Ratio = (Average fund returns − Riskfree Rate) / Standard Deviation of fund returns
Sa = E [Ra-Rb] ÷ σa
= (7.40% - 4%) ÷ 6.09% = 0.56
Here, Risk Free Rate is 4%, Arithmetic average annual return = 7.40% and Standard Deviation (σ) = 6.09%
(e) Risk aversion inventors will tend to make an investment in an asset with lower standard deviation. This is because a lower standard deviation will mean that the asset prices will experience less volatility and there will be very less probability for making major losses.     
    Risk aversion degree on a scale of 1 to 5
    1
    Risk free interest rate (T-bill)
    4%
    Expected return of the portfolio
    7%
    Volatility of security returns
    6.09%
     
     
    Optimal percentage allocations to risky V. risk-free asset
    7.21%
Calculation of Optimal percentage allocations to risky V. risk free asset = Expected return on portfolio – 0.5 x Degree of Risk aversion x volatility of security returns^2
= 7% - 0.5 x 1 x 6.09%^2
= 7.21%
(f) If the degree of risk aversion is 5, the utility score is 5.72% which is more than the risk free rate of 4%. Thus, the investors will choose to invest in Tasty Food Ltd which is known as 'A'. Also, even if the degree of risk aversion is 1, the utility score is 7.21% which is also more...