$5.$ You are an analyst at Merrill Finch, Inc. and your first $$150,000$ bonus rides on your handling of your first client, who is a wealthy individual and whose parents and grandparents have been clients of Merrill Finch for a very long time. Your client asked you to evaluate a portfolio she inherited from her grandfather. The portfolio is a bond portfolio valued at $$1$ million and is invested in zero coupon Treasury bonds. The client also inherited a stock portfolio valued at $$2$ million, which is invested in two stocks, Swag, Inc. and NoSwag, Inc.

As it stands right now, the interest rate environment is very uncertain as the Federal Reserve is not showing its hand as to when or how much the next rate hike will be$.$ This uncertainty has significantly affected bond yields. However, the economist at Merrill Finch has provided you with some interest rate scenarios for bond returns and the probability of each. The scenarios and the probabilities are listed below.

Scenarios Probability of Scenario Return on $10-$Yr Zero Coupon Bonds

Worst Case $10\%-14\%$

Poor Case $20\%-4\%$

Most Likely $40\%6\%$

Good Case $20\%16\%$

Best Case $10\%26\%$

$100\%$

Additionally, your due diligence allowed you to gather historical returns on the stocks noted above.

Also, you are given the fact that the risk$-$free rate is $4\%$ and the market risk premium is $5\%.$

Year Market Swag, Inc No$-$Swag, Inc

$130\%26\%47\%$

$27\%15\%-54\%$

$318\%-14\%15\%$

$4-22\%-15\%7\%$

$5-14\%2\%-28\%$

$610\%-18\%40\%$

$726\%42\%17\%$

$8-10\%30\%-23\%$

$9-3\%-32\%-4\%$

$1038\%28\%75\%$

Average Return $8\%??9\mathrm{.}2\%$

Std$.$ Deviation $20\mathrm{.}1\%??38\mathrm{.}6\%$

Correl.with Mkt $1\mathrm{.}00??0\mathrm{.}678$

Beta $1\mathrm{.}00??1\mathrm{.}30$

Answer the following questions.

a$)$ What are investment returns? What is the return on an investment that costs $$1,000$ and is sold after $1$ year for $$1,060.?$

b$)$ Use a clearly labeled and neat graph, show the probability distribution of the bond returns based on the scenarios noted above.

c$)$ Use the scenario data to compute expected rate of return for the $10-$year zero coupon bond.

d$)$ What is stand$-$alone risk? Use the scenario data to calculate the standard deviation of the bond$$s return.

e$)$ Your client has decided that the risk of the bond portfolio is acceptable and wishes to leave it as it is$.$ However, she asks you compute the standard deviation of Swag$$s stock returns.

f$)$ Based on the riskiness of Swag, Inc. stock you recommend that she sell $25\%$ of Swag and create a portfolio of $75\%$ in Swag, Inc and $25\%$ in No$-$Swag, Inc. What is the return of such a portfolio, each year of the sample.

g$)$ Then compute the average return and standard deviation of the portfolio$$s return.

h$)$ Calculate the estimated correlation coefficient between Swag, Inc and No$-$Swag stocks.

i$)$ Explain what happens to a portfolio$$s risk when randomly selected stocks are added to the portfolio. Show this result is a neat and well labelled diagram.

j$)$ What does market equilibrium mean?