An investment in company A has an expected return of $\$ 30,000$ with a standard deviation of $\$ 4000$. An investment in company B has an expected return of $\$ 45,000$ with a standard deviation of $\$ 3000$. If investments are made in both companies, what are the expectation and standard deviation of the total return?

Security $F$ has an expected return of 10 percent and a standard deviation of 43 percent per year. Security $G$ has an expected return of 15 percent and a standard deviation of 62 percent per year.
a. What is the expected return on a portfolio composed of 30 percent of Security $F$ and 70 percent of Security $G$ ?
b. If the correlation between the returns of Security $F$ and Security $G$ is .25 , what is the standard deviation of the portfolio described in part (a)?

An investment in company A has an expected return of $\$ 30,000$ with a standard deviation of $\$4000$. An investment in company B has an expected return of $\$ 45,000$ with a standard deviation of $\$3000$. If the returns are normally distributed and independent, what is the probability that the total return from both investments will be at least $\$85,000$?

Create a truth table for the logical statement. ~(~p→~q)

Solve the equation algebraically and graphically. Check for extraneous solutions.

$$x+2=\dfrac{15}{x}$$

write the partial fraction decomposition of the rational expression. Check your result algebraically.

$$3x^2+4x/(x^2+1)^2$$

An investment in company A has an expected return of $\$ 30,000$ with a standard deviation of $\$ 4000$. What is the probability that the return will be at least $\$ 25,000$ if it has a normal distribution?

Mabel Cousino has $35,000 to invest in a certificate of deposit for 4 years. The certificate of deposit earns interest at 4.75% compounded daily. What is the annual percentage yield to the nearest thousandth of a percent?

Jacob Hernandez invests $25,000 in a CD for 5 years. The CD earns interest at an annual rate of 5.5% compounded quarterly. What is the annual percentage yield to the nearest hundredth of a percent?

In addition to the information in previous exercise on the S&P 500 and core bonds, J.P. Morgan Asset Management reported that the expected return for real estate investment trusts (REITs) was 13.07% with a standard deviation of 23.17% (J.P. Morgan Asset Management, Guide to the Markets, 1st Quarter, 2012). The correlation between the S&P 500 and REITs is . 74 and the correlation between core bonds and REITs is -.04 . You are considering portfolio investments that are composed of an S&P 500 index fund and REITs as well as portfolio investments composed of a core bonds fund and REITs.

a. Using the information provided here and in earlier exercise , determine the covariance between the S&P 500 and REITs and between core bonds and REITs.

b. Construct a portfolio that is 50% invested in an S&P 500 fund and 50% invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio?

c. Construct a portfolio that is 50% invested in a core bonds fund and 50% invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio?

d. Construct a portfolio that is 80% invested in a core bonds fund and 20% invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio?

e. Which of the portfolios in parts (b), (c), and (d) would you recommend to an aggressive investor? Which would you recommend to a conservative investor? Why?

Simplify: (62 1/2)/100

In addition to the information in above exercise on the S&P $500$ and core bonds, J.P. Morgan Asset Management reported that the expected return for real estate investment trusts ( REITs) during the same time period was $13.07\%$ with a standard deviation of $23.17\%$ (J.P. Morgan Asset Management, Guide to the Markets). The correlation between the S&P $500$ and REITs is $.74$ and the correlation between core bonds and REITs is −$.04$. You are considering portfolio investments that are composed of an S&P $500$ index fund and REITs as well as portfolio investments composed of a core bonds fund and REITs.

a. Using the information provided here and in above exercise, determine the covariance between the S&P $500$ and REITs and between core bonds and REITs.
b. Construct a portfolio that is $50\%$ invested in an S&P $500$ fund and $50\%$ invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio?
c. Construct a portfolio that is $50\%$ invested in a core bonds fund and $50\%$ invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio?
d. Construct a portfolio that is $80\%$ invested in a core bonds fund and $20\%$ invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio?
e. Which of the portfolios in parts (b), (c), and (d) would you recommend to an aggressive investor? Which would you recommend to a conservative investor? Why?

J.P. Morgan Asset Management publishes information about financial investments. Over a 10-year period, the expected return for the S&P 500 was $5.04 \%$ with a standard deviation of $19.45 \%$, and the expected return over that same period for a core bonds fund was $5.78 \%$ with a standard deviation of $2.13 \%$ (J.P. Morgan Asset Management, Guide to the Markets, 1st Quarter, 2012). The publication also reported that the correlation between the S&P 500 and core bonds is $-.32$. You are considering portfolio investments that are composed of an S&P 500 index fund and a core bonds fund.

a. Using the information provided, decide the covariance between the S&P 500 and core bonds.

Determine whether ΔSTU ≅ ΔXYZ. Explain. S (2, 2). T (4, 6), U (3, 1), X (-2, -2), Y (-4, 6), Z (-3, 1)