You have recently graduated with a major in finance and landed a financial plann

Question

You have recently graduated with a major in finance and landed a financial planner job with Barney Smith Inc., a large financial services corporation. Your first assignment is to invest $100,000 for a client. Because the funds will be invested in a new business the client plans to start at the end of the year, you have been instructed to plan for a 1-year holding period. Further, your boss has restricted you to the investment alternatives shown in Table 1 on the attached resource, "Topic 5 Assignment Graphic Tables." (Disregard for now the items at the bottom of the data; you will fill in the blanks later.) Note that the estimated returns of American Foam (Am. Foam), a bedding company, do not always move in the same direction as the overall economy. For example, when the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner-spring mattress may purchase a cheaper foam mattress instead. Under these circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average. Barney Smith’s economic forecasting staff has developed probability estimates for the state of the economy, and its security analysts have developed a sophisticated computer program that was used to estimate the rate of return on each alternative under several state of the economy scenarios. Alta Industries (Alta Inds) is an electronics firm; Repo Men collects past-due debts; and American Foam, as per above, manufactures mattresses and various other foam products. Barney Smith also maintains an "index fund" which owns a market-weighted fraction of all publicly traded stocks; you can invest in that fund, and thus obtain average stock market results. Given the situation as described, answer the following questions. 5. How does the risk of this two-stock portfolio compare with the risk of the individual stocks if those stocks were held in isolation? In what ways do "portfolio effects" impact how investors think about the risk of individual stocks? 6. If you decided to hold a simple one-stock 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? Explain. 7. Describe how market risk is measured for individual securities. How are beta coefficients calculated? Calculate beta using the following historical returns for the stock market and for another company, P.Q. Unlimited (PQU) as per Table 2 on the attached resource, "Topic 5 Assignment Graphic Tables." Note: Use the Excel formula function to calculate beta and interpret your results.

Table 1

Table 2

Returns on Alternative Investments Estimated Rate of Return Market portfolio 13.0% State of the 2-stock ortfolio 3.0% T. Repo Am. Alta Prob BillInds Me Foam 0.1 0.2 6.0% 6.0 Recession Below avg Average Above avg Boom r-hat r Std dev (o) Coef. of var. (cv) Beta (b) 22.0% 2.0 20.0 28.0% 14.7 10.0%" 10.0 15.0 29.0 43.0 15.0% 15.3 10.0 0.0 10.0 50.0 -20.0 1.7% 13.4 7.0 45.0 30.0 14.8% 18.8 1.6 0.93 0.2 0.1 35.0 15.0 6.0 6.0% 0.0 0.90

Explanation / Answer

5) The stock portfolio comprises of Alta Inds and Repo Man with equal weights to both the stocks in the portfolio.

Return of portfolio=0.5*Return of Alta Inds+ 0.5*Return of Repo Man

For e.g for recession ,Return of portfolio=0.5*(-22%)+ 0.5*(28%)=3%

Boom,Return of portfolio=0.5*(50%)+ 0.5*(-20%)=15%

Alternative method you can arrive at portfolio risk:

The Risk of portfolio(StdDev) at 3.34% is lesser than the risk of stock when held in isolation.Portfolio benefits from the diversification of the stocks that is the diversification decreases the risk of the overall portfolio.Investors benefits form holding the stocks in a portfolio ,stocks have a correlation that results in reduction in risk.

6)Yes the risk that have been eliminated results in lesser returns for the portfolio that is the investors reduces the idiosyncratic risk of the stock that would result in lesser return for the stock because the risk premiums is eliminated for the reduction of the risk taken.

7)

probability(pi) 2-stock portfolio(ri) pi*ri pi*(ri-r-hat)^2 Recession 0.1 3% 0.30% 0.000431649 BelowAvg 0.2 6.35% 1.27% 0.000207368 Avg 0.4 10% 4.00% 7.396E-06 AboveAvg. 0.2 12.50% 2.50% 0.000171698 Boom 0.1 15% 1.50% 0.000294849 r-hat 9.57% (=SUM(pi*ri)) StdDev() 3.34% (=sqrt(sum(pi*(ri-r-hat)^2))

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