B. Assume there are only two assets in a portfolio. If this portfolio has a positive weight for each asset, can its (portfolio.s) variance be greater than the variance of returns on the asset in the portfolio that has the higher variance of the two? Explain. Can the variance of the portfolio be smaller than the variance of returns on the asset in the portfolio that has the smaller variance? Explain.

I'm looking for a mathematical proof along with theory to explain
thanks!

Solution Preview

Assuming the two assets are A and B, then
Asset A has a variance of Va, a standard deviation of SDa and a share of Wa;
Asset B has a variance of Vb, a standard deviation of SDb and a share of Wb;
Let Va > Vb,
and since SD = SQRT(V),
SDa > SDb
Also, by definition, Wa+Wb = 1

The variance of the portfolio is:
Variance (P) = Variance(A) * (Wa)^2 + Variance(B) * (Wb)^2 +2(Wa)*(Wb)*Covariance(A,B)
Variance (P)= Va* (Wa)^2 + Vb * (Wb)^2 +2 Wa * Wb* SDa * SDb) *Corr(A,B)
(* where "^2" means "squared", and Corr(A,B) is the Correlation ...

3. Consider two securities with expected return of 16% and 20% and standard deviation of 25% and 40%, respectively.
a. If the returns of the two assets are perfectly correlated, create a portfolio with an expected return of 24%. Find the standard deviation of that portfolio.
b. Create a portfolio with a standard deviation o

Question: A portfolio is made up of 75% of stock 1, and 25% of stock 2. Stock 1 has a variance of .08, and stock 2 has a variance of .035. The covariance between the stocks is -.001. Calculate both the variance and the standard deviation of the portfolio.

Given the following expected return vector and variance-covariance matrix for three assets:
ER= 10.1
7.8
5.0
VC= 210 60 0
60 90 0
0 0 0
and given the fact that Pie Traynor's risky portfolio is split 50-50 between the two risky asets:
a) Which security of the thre

Your Company has a portfolio made up of 2 assets, One from the USA and the other from Swaziland. Their information is as follows:
USA Swaziland
Return 12.2% 18.4%
Deviation 10.5%

1. What is the correlation coefficient?
2. What is the amount to put in the bond fund to achieve the minimum variance portfolio?
3. What is the expected return, variance, and standard deviation on this portfolio?
4. What is the slope of a line going from Rf through this portfolio?
5. What is the utility of this portfolio?
6

Case Study #2
Listed below are the annual rates of return on the stocks for companies A, B, C, ..., G for each year 1975-2004.
(1) Determine the efficient frontier using portfolios generated from combining just these seven risky assets. Graph the results. In listing the results in tabular form, show the weights for each le

See attached spreadsheet.
Problem 1
a. Your portfolio is invested 28 percent each in A and C, and 44 percent in B. The expected return of the portfolio is_______% (Input answer as a percent rounded to 2 decimal places).
b. The variance of this portfolio is________ (Round answer to 6 decimal places) and standard dev

Consider the following information about three stocks:
State of Economy
Probability of State of Economy Rate of Return if State Occurs
Stock A Stock B Stock C
Boom .4 .20 .35 .60 .4 .20 .35 .60
Normal .4 .15 .12 .05 .4 .15 .12 .05
Bust .2 .01 -.25 -.50 .2 .01 -.25 -.50
a. If your portfolio is invested 40% each in A a

1. Supposed you invest $400,000 in government bonds and $ 600,000 in the market portfolio. what is the return on your portfolio if bonds yield 6 percent and the market risk premium is 8.6 percent? what does the return on this portfolio imply for the expected return on individual shares with betas of 0.6?
(The step of calculat