Graphing the Mean-Variance Efficient Frontier Assignment Help
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An efficient frontier is a group of portfolios that give the best-expected return or in other words the lowest risk for the expected return. Portfolios below the efficient frontier are not optimal as they don’t compensate for the risk incurred. It is a curved graph plotting average return with standard deviation (the level of risk) the portfolios to the right are also not optimal as they have a higher risk than return.
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Need for mean-variance efficient frontier?
It is the process in which risk is plotted against expected return. With the help of mean-variance investors chooses the lowest variance of expected return or in other words, pick the investment with the lowest risk and highest profitability. For a better graphing the Mean-Variance Efficient Frontier Homework help, let us consider there are two investments in the portfolio as follows:
- Investment X: Value-$50,000 expected return-10%
- Investment Y: Value-$1,00,000 expected return-20%
Therefore the total weight of each asset is
Inv X Weight=$50,000/$150000=33.33%
Inv Y Weight=$1,00,000/$150000=66.66%
Then the total expected return is
(33.33%*10%) + (66.66%*20%)= 4.5%
Portfolio variance can be calculated using the formula
Portfolio variance = m(1) ^2 x O(1) ^ 2 + n(2) ^ 2 x O(2) ^ 2 + (2 x m(1) x n(2) x 0(1) x 0(2) x p),where
m1=the weight of investment X
n2=the weight of investment Y
0(1)=the standard deviation of Inv X
0(2)=the standard deviation of Inv Y
p=correlation coefficient between Inv X and Inv Y.
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How to build the mean-variance efficient frontier?
- Collect the data on the average return of the assets that is the average monthly return with standard deviation.
- Construct a covariance table which tells us with precision how prices of assets move with each other.
- Discover the portfolio with the lowest risk (standard deviation) which include statistics like the average return of assets, standard deviation and capital allocation line.
- Create the portfolio with the highest Sharpe Ratio (A measure for calculating return by adjusting risk)
- Plot the efficient frontier after completing the construction of the portfolio.
Disadvantages of Graphing Mean Variance Efficient Frontier:
- The assumptions while plotting an efficient frontier like assets is distributed normally are not true in reality. Assets follow a distribution pattern that is 0.03% of assumed values.
- It assumes that all investors will avoid risks but in the real market scenario who could influence market prices by taking risks and following no rationale.
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