FIN609A – CASE STUDY (Risk & Return)
FIN609A – CASE STUDY (Risk & Return)
Question 1 – Case Study One
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 owns a bond portfolio with $1 million invested in zero coupon Treasury bonds that mature in 10 years.47 The client also has $2 million invested in the stock of Blandy, Inc., a company that produces meatandpotatoes 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. Your first task is to determine the risk of the client’s bond portfolio. After consulting with the economists at your firm, you have specified five possible scenarios for the resolution of the dispute at the end of the year. For each scenario, you have estimated the probability of the scenario occurring and the impact on interest rates and bond prices if the scenario occurs. Given this information, you have
Note. (The total par value at maturity is $1.79 million and yield to maturity is about 6%, but that information not important for this case)
calculated the rate of return on 10year zero coupon Treasury bonds for each scenario. The probabilities and returns are shown here:
The riskfree rate is 4%, and the market risk premium is 5%.
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. Graph the probability distribution for the bond returns based on the 5 scenarios. What might the graph of the probability distribution look like if there were an infinite number of scenarios (i.e., if it were a continuous distribution and not a discrete distribution)?
c. Use the scenario data to calculate the expected rate of return for the 10year zero coupon Treasury bonds during the next year.
d. What is the standalone risk? Use the scenario data to calculate the standard deviation of the bond’s return for the next year.
e. Your client has decided that the risk of the bond portfolio is acceptable and wishes to leave it as it is. Now your client has asked you to use historical returns to estimate the standard deviation of Blandy’s stock returns. (Note: Many analysts use 4 to 5 years of monthly returns to estimate risk, and many use 52 weeks of weekly returns; some even use a year or less of daily returns. For the sake of simplicity, use Blandy’s 10 annual returns.)
f. Your client is shocked at how much risk Blandy stock has and would like to reduce the level of risk. You suggest that the client sell 25% of the Blandy stock and create a portfolio with 75% Blandy stock and 25% in the highrisk Gourmange stock. How do you suppose the client will react to replacing some of the Blandy stock with highrisk stock? Show the client what the proposed portfolio return would have been in each year of the sample. Then calculate the average return and standard deviation using the portfolio’s annual returns. How does the risk of this twostock portfolio compare with the risk of the individual stocks if they were held in isolation?
g. Explain correlation to your client. Calculate the estimated correlation between Blandy and Gourmange. Does this explain why the portfolio standard deviation was less than Blandy’s standard deviation?
h. Suppose an investor starts with a portfolio consisting of one randomly selected stock. As more and more randomly selected stocks are added to the portfolio, what happens to the portfolio’s risk?
i. (1) Should portfolio effects influence how investors think about the risk of individual stocks?
(2) If you decided to hold a onestock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all of your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying?
j. According to the Capital Asset Pricing Model, what measures the amount of risk that an individual stock contributes to a welldiversified portfolio? Define this measurement.
k. What is the Security Market Line (SML)? How is beta related to a stock’s required rate of return?
Question 2. – Case Study 2: FIN609A
Assume that you have just been hired as a financial analyst by Triple Play Inc., a midsized California company that specializes in creating highfashion clothing. Because no one at Triple Play is familiar with the basics of financial options, you have been asked to prepare a brief report that the firm’s executives can use to gain a cursory understanding of the topic. To begin, you gathered some outside materials on the subject and used these materials to draft a list of pertinent questions that need to be answered. In fact, one possible approach to the report is to use a questionandanswer format. Now that the questions have been drafted, you have to develop the answers.
a. What is a financial option? What is the single most important characteristic of an option?
b. Options have a unique set of terminology. Define the following terms:
(1) Call option
(2) Put option
(3) Strike price or exercise price
(4) Expiration date
(5) Exercise value
(6) Option price
(7) Time value
(8) Writing an option
(9) Covered option
(10) Naked option
(11) Inthemoney call
(12) Outofthemoney call
(13) LEAP
. Consider Triple Play’s call option with a $25 strike price. The following table contains historical values for this option at different stock prices:
Stock Price Call Option Price
$25 $3
30 7.5
35 12
40 16
45 21
50 25.5
(1) Create a table that shows
(a) stock price,
(b) strike price,
(c) exercise value,
(d) option price, and
(e) the time value, which is the option’s price less its exercise value.
(2) What happens to the time value as the stock price rises? Why?
d. Consider a stock with a current price of P $27. Suppose that over the next 6 months the stock price will either go up by a factor of 1.41 or down by a factor of 0.71. Consider a call option on the stock with a strike price of $25 that expires in 6 months. The riskfree rate is 6%.
(1) Using the binomial model, what are the ending values of the stock price? What are the payoffs of the call option?
(2) Suppose you write one call option and buy Ns shares of stock. How many shares
must you buy to create a portfolio with a riskless payoff (i.e., a hedge portfolio)? What is the payoff of the portfolio?
(3) What is the present value of the hedge portfolio? What is the value of the call option?
(4) What is a replicating portfolio? What is arbitrage?
e. In 1973, Fischer Black and Myron Scholes developed the BlackScholes option pricing model (OPM).
(1) What assumptions underlie the OPM?
(2) Write out the three equations that constitute the model.
(3) According to the OPM, what is the value of a call option with the following characteristics?
Stock price= $27.00.
Strike price =$25.00.
Time to expiration = 6 months = 0.5 years
Riskfree rate = 6.0%
Stock return standard deviation = 0.49
f. What impact does each of the following parameters have on the value of a call option?
(1) Current stock price
(2) Strike price
(3) Option’s term to maturity
(4) Riskfree rate
(5) Variability of the stock price g. What is put–call parity

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Solution: FIN609A – CASE STUDY (Risk & Return)