Chapter 2 - Problems

Expected returns 1 Calculate returns 2 Required returns Return and risk 3 Return variation 4 Risk/return comparison Portfolio volatility 5 Calculate beta 6 Risk/return comparison Using beta 7 Calculate E(r) 8 With CAPM Combining returns and risk 9 Problem Solutions   Attached spreadsheet

1 - Calculate returns

Your client is interested in buying a business. You help structure the transaction and draw up the appropriate dcouments. The client has been offered to ways to pay the $400,000 purchase price. One is for cash, which your client could finance by borrowing from the bank with a 9% loan payable over 10 years -- annuial payments due on December 31 of each year. THe other is a strcutrued purchase as follows:  $40,000.00/yr. for 10 years, payable by December 31 of each year, beginning next year plus each year accrued interest on the outstanding balance at an interest rate of 6%/year for the first five years, then 10% for years 6 through 10.

Which is the better deal for your client?

Assuming that past returns predict future returns, what is the expected return for the following investments?

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2 - Required returns

You are considering buying a car for $8,500. You live in the city and taking the bus costs you $1,700 in fares and aggravation. You expect the car will cost about $1,950 in annual maintenance and insurance costs. After five years you expect to sell the car for $5,000. To buy the car, you will dip into your savings account, which earns 4.5% after taxes. You ask yourself whether you should buy the car or keep on taking the bus.

• What are the cash flows and expected return applicable to buying the car?
• Which is a better choice - buying the car (with attendant costs and benefits) or keep on riding the bus and investing the money?
• What if you plan to use money from your tax-free municipal bond mutual fund, which has had steady after-tax returns of 7.8%. How much should you spend on the car given your alternative use of the purchase price?

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3 - Return variation

You are considering three stock investments. You have studied the stocks' historical returns over the last five years.

Assuming that historical returns are a measure of future returns --

• Calculate the expected return, the standard deviation (s) and coefficient of variation for each stock.
• Which stock has the highest expected return? the highest risk?
• Which is the best combination of risk and return?

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4 - Risk/return comparison

Portfolio A has an expected return of 8.4% and a standard deviation of 12.1%. Portfolio B has an expected return of 10.7% and a standard deviation of 15.8%. The risk free rate of return is 5.1%.

• Assuming CAPM, what is the slope of the market line if Portfolio A lies on the line? What about Portfolio B?
• What do these slopes tell you? Which is the better portfolio -- that is, the better combination of risk and return?

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5 - Calculate beta

You want to calculate the betas for two companies. You have the following return data:

• How might you compute beta?
  • Draw the characteristic line for each stock and estimate slope.
  • Use regression analysis to compute the line's slope.
• Are the stocks riskier, less risky than the market?
• What is the beta of a portfolio containting with equal amounts of Stock X and Stock Y? Is this portfolio riskier than the market?
• You're not sure if the market will be up or down. What will be the return on Stock X and Stock Y, assuming either an up market next year with returns of +20.0% or a down market with returns of -6.0%?

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6 - Risk/return comparison

Assume the risk-free rate of return is 10%, and the expected return on the market is 16%. An investment manager can choose between two portfolios, A and B, having the following properties:

Under the CAPM, which portfolio should the investment manager choose?

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7 - Calculate E(r)

You compute the historical betas for various investments and assume they are good predictors of expected volatility -- thus risk. You also assume various risk-free rates and expected market returns. In each case calculate the expected return for the investment.

If the expected return is greater than the promised return - what should you do? Buy or sell?

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8 - With CAPM

Use the CAPM equation to compute the unknown variable --

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9 - Problem

You compare two stocks, both traded on the stock exchange. You are thinking of selling one. Which investment is a better combination of risk and return? You look at returns (cash flow and market appreciation) over the last ten years. You predict that future returns will be comparable.

• Calculate the annual rate of return for each asset for each year, and then compute the average return.
• Use these results to find standard deviation and coefficient of variation for each investment.
• Based on these results, which investment offers a better mix of risk and return?
• Assuming betas (X = 1.60, Y = .85) and a risk-free rate of 4.8% and an expected market return of 14.2%, use the CAPM to find the required return for each investment.
• Using these CAPM results and comparing them to past returns, which investment seems to offer a better mix of risk and returns?

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