Question

who can give me the example like this:(also give me the answer,Tell me what formula should use to calculate and how to use those formulas.)thank you

Known:

risk profolio.

expect return and variance of stock A.

expect return and variance of stock B.

The yield correlation coefficient of two stocks.

Risk combination characteristics

Question:

expect return.

variance.

Build a complete portfolio according to the investor's requirements.

How many should investors invest in risk portfolios and security assets(T-bill).

Calculating the sharp ratio of complete profolio.

Draw the capital allocation line.

the varience of profolio B.

Answer 1

Problem

The expected return on Stock A is 12.5%, the expected return on Stock B is 20%, the variance on Stock A is .00263, the variance on Stock B is .04200, the standard deviation on Stock S is 5.12%, and the standard deviation on Stock B is 20.49%. and Correlation Coefficient is -1

Solution:

1.Expected Return on a Portfolio of Stocks A and B

Note: E[RA] = 12.5% and E[RB] = 20%

Portfolio consisting of 50% Stock A and 50% Stock B

So Expected Return = 50%*12.5% + (1-50%)*20% = 16.25%

2.Variance of the portfolio

Variance and Standard Deviation on a Portfolio of Stocks A and B

Note: E[RA] = 12.5%, E[RB] = 20%, sA = 5.12%, sB = 20.49%, and rAB = -1.

Using either the correlation coefficient or the covariance, the Variance on a Two-Asset Portfolio can be calculated as follows:

= (0.5)²(0.0512)² + (1-0.5)²(0.2049)²+2(0.5)(-1)(0.512)(0.2049)

=0.00591

3.Standard Deviation of the portfolio

Standard Deviation = Square root of variance = square root of 0.00591 = 7.68%

4.Sharpe Ratio of the portfolio

Sharpe ratio = (Average Portfolio Returns – Risk-Free rate)/Standard Deviation of Portfolio

=(16.25%-2.44%)/7.68% = 1.72