Question

A. (Beta) Classify the following stocks as aggressive, average, or defensive and identify if its beta is less than 1, equal to 1, or greater than 1:

a. Stock rises by 30% in response to a market rise of 20%.

b. Stock rises 10% in response to a market rise of 10%.

c. Stock falls 15% in response to a market decline of 20%.

d. Stock falls 10% in response to a market decline of 10%.

B. (Beta of a portfolio) A portfolio manager currently holds a diversified portfolio of 30 stocks. The amount invested in each stock is $10,000, and the portfolio beta is 1.05. What would happen to the portfolio beta under each of the following scenarios?

a. Another stock is added to the portfolio: amount $10,000, beta 1.05.

b. One of the stocks with beta 1.05 is sold.

c. Another stock is added to the portfolio: amount $10,000, beta 1.50.

d. One of the stocks with beta 0.75 is sold.

C. (The security market line) The pure rate of interest is 3%, investors demand a 5% inflation premium on long-term investments, and the risk premium for a stock with beta of 1 is 7%. ZZZ stock has a beta of 1.35.

b. Suppose investors increase their inflation premium to 6%. What is the new required rate of return from ZZZ stock?

c. Now suppose investors increase their risk premium for a stock with beta of 1 to 8% (the inflation premium is still 5%). What is the new required rate of return from ZZZ stock?

d. Now suppose investors decrease their estimate of ZZZ’s beta to 1.25 (the inflation premium is still 5%, and the risk premium is still 7%). What is the new required rate of return from ZZZ stock?

D. . (Yield-to-maturity) Proctor & Gamble has outstanding an issue of $1,000 face value, 12 5/8% coupon bonds that mature in 14 years. Calculate the bond’s yield-to-maturity if its current market price is:

a. $ 875

b. $ 950

E. (Bond price over time) General Electric Corporation has outstanding an issue of $1,000 face value, 11 3/4% coupon bonds that mature in 20 years. Today investors require a 10.5% rate of return.

a. Calculate the price of these bonds today.

b. Calculate the price of these bonds 7 years from now if market interest rates do not change.

c. Calculate the price of these bonds 14 years from now if market interest rates do not change.

d. Calculate the price

Answer 1

Answer- A:

1. If the stock rise by 30% as compare to a market rise of 20% (variation more than market), it means the Beta of the stock is greater than 1 and it’s a aggressive stock.
2. If the stock rise by 10% as compare to a market rise of 10% (variation equal to the market), it means the Beta of the stock is equal to 1 and it’s a average stock
3. If the stock falls by 15% in response to a market decline of 20% (variation less than market), it means the Beta of stock is less than 1 and it’s a defensive stock.
4. If the stock falls by 10% as compare to a market decline of 10% (variation equal to market), it means the Beta of stock is equal to 1 and it’s a average stock.

Answer- C:

Required Rate of Return = (1 + pure rate) * (1 + inflation premium) * (1 + risk premium) - 1

Risk Premium = Beta of Stock * Market Risk Premium

a)

Pure Rate = 3%

Inflation Premium = 5%

Risk Premium = (1.35 * 7) = 9.45

Required Rate of Return = (1 + 0.03) * (1 + 0.05) * (1 + 0.0945) – 1 = 18.37%

b)

If inflation premium = 6%

Risk Premium = (1.35 * 7) = 9.45

Required rate of Return = (1 + 0.03) * (1 + 0.06) * (1 + 0.0945) - 1 = 19.497 or 19.50

c)

Inflation Premium = 5%

Risk Premium = (1.35 * 8) = 10.8%

Required Rate of Return = (1 + 0.03) + (1 + 0.05) (1 + 0.108) – 1 = 19.83%

d)

Inflation Premium = 5%

Risk Premium = (1.25 * 7) = 8.75

Required Rate of Return = (1 + 0.03) + (1 + 0.05) (1 + 0.0875) – 1 = 17.61%