Question

Assume that you recently graduated and landed a job as a financial planner with Cicero Services, an investment advisory company. Your first client recently inherited some assets and has asked you to evaluate them. The client has $2 million invested in the stock of Blandy, Inc., a company that produces meat-and-potatoes frozen dinners. Blandy’s slogan is “Solid food for shaky times.” Unfortunately, Congress and the president are engaged in an acrimonious dispute over the budget and the debt ceiling. The outcome of the dispute, which will not be resolved until the end of the year, will have a big impact on interest rates one year from now. You have also gathered historical returns as follows for the past 10 years for Blandy, Gourmange Corporation (a producer of gourmet specialty foods), and the stock market. The risk-free rate is 4% and the market risk premium is 5%.

	Historical Stock Returns
Year	Market	Blandy	Gourmange
1	30%	26%	47%
2	7	15	−54
3	18	−14	15
4	−22	−15	7
5	−14	2	−28
6	10	−18	40
7	26	42	17
8	−10	30	−23
9	−3	−32	−4
10	38	28	75
Average return:	8.00%	?	9.20%
Standard deviation:	20.10%	?	38.60%
Correlation with market:	1	?	0.678
Beta:	1	?	1.3

Based on the information provided above, complete the following:

QUESTION 1

• Suppose an investor starts with a portfolio consisting of one randomly selected stock. How to measure the risk and return given different scenarios for a particular stock?

• What are the criteria the investor should consider to choose a single stock to invest? As more and more randomly selected stocks are added to the portfolio, what happens to the portfolio’s risk?

• How does correlation affect your portfolio return and risk?

• Calculate the numbers with questions marks and the estimated correlation between Blandy and Gourmange using the data in the above Table. Does this explain why the portfolio standard deviation was less than Blandy’s standard deviation?

Answer 1

QUESTION 1

• Suppose an investor starts with a portfolio consisting of one randomly selected stock. How to measure the risk and return given different scenarios for a particular stock :

To measure Risk-adjusted return of the portfolio/stock a investors can use risk-reward ratio i.e Sharpe Ratio of each stock/asset. It measures a stock return against its volatility or risk.

Sharpe Ratio = (Asset Return - Risk-Free Rate) /  Standard deviation of the Stock

Now in Given example, Sharpe Ratio of Different Scenario are :

It shows the Risk-adjusted return of Market is much higher than each stock

Even if we have to choose between Blandy & Gourmange we should go for Gourmange because higher Sharpe ratio of Gourmange = 0.13

Market	Blandy	Gourmange
0.20	0.10	0.13

• What are the criteria the investor should consider to choose a single stock to invest? As more and more randomly selected stocks are added to the portfolio, what happens to the portfolio’s risk?

For selecting a  stock to invest an investor choosing for a stock majorly depends in many factors like what actually investors looking for Higher return while taking more and more risk or looking for diversification to reduce overall portfolio risk.

While looking for a Higher return an investor can go for stocks higher returns. But it will come at a cost of more volatility of the stock price lead to a loss in an economic downturn.

While looking for portfolio diversification an investor may look for correlation of the asset with its existing portfolio. Will look for Beta of the assets. And may prefer to construct beta neutral portfolio or Diversified portfolio for better return.

• How does correlation affect your portfolio return and risk?

Corelation is a great tool to manage a portfolio return and risk. Corelation can be two types Positively co-related or negaitively co-related.

When we add all positively co-related stocks to the portfolio expected return will increase but will increase risk of the portfolio.

While when we add few negaitively co-related stocks to the portfolio it will reduce risk of the portfolio but will reduce expected retun also.

• Calculate the numbers with questions marks and the estimated correlation between Blandy and Gourmange using the data in the above Table. Does this explain why the portfolio standard deviation was less than Blandy’s standard deviation?

Average return = Used AVERAGE Function in Excel = AVERAGE of last 10 Years return

Standard deviation = Used Std.Dev Function in Excel = STDEV(last 10 Years return)

Correlation with market = Used CORREL function in Excel =CORREL ( last 10 Years Stock return,  last 10 Years Market return)

Beta = Correlation * ( Standard deviation of Stock / Standard deviation of Market)

Answer :

Average return:	6.40%
Standard deviation:	25.19%
Correlation with market:	0.481
Beta:	0.60

Yes Portfolio Standard deviation will always be lesser than Individual stocks Standard deviation because of the diversification effect.