Review Questions 10
Textbook Page Questions
358 2, 3, 4, 5
361 12, 14, 16, 17, 20
362 21. 28, 29, 30
363 31, 32, 33, 34, 35
2. The risks of deaths of individual policyholders are largely independent, and therefore are
diversifiable. Therefore, the insurance company is satisfied to charge a premium that
reflects actuarial probabilities of death, without an additional risk premium. In contrast,
flood damage is not independent across policyholders. If my coastal home floods in a
storm, there is a greater chance that my neighbor's will too. Because flood risk is not
diversifiable, the insurance company may not be satisfied to charge a premium that reflects
only the expected value of payouts.
3. The actual returns on the Snake Oil fund exhibit considerable variation around the
regression line. This indicates that the fund is subject to diversifiable risk: it is not well
diversified. The variation in the fund's returns is influenced by more than just market-wide
4. Investors would buy shares of firms with high degrees of diversifiable risk, and earn high-
risk premiums. However, by holding these shares in diversified portfolios, they would not
necessarily bear a high degree of portfolio risk. This would represent a profit opportunity,
however. As investors seek these shares, we would expect their prices to rise, and the
expected rate of return to investors buying at these higher prices to fall. This process would
continue until the reward for bearing diversifiable risk dissipated.
5. a. Required return = r f (r m – rf) = 4% + .6 (11% – 4%) = 8.2%
With an IRR of 14%, the project is attractive.
b. If beta = 1.6, required return increases to:
4% + 1.6 (11% – 4%) = 15.2%
which is greater than the project IRR. You should now reject the project.
c. Given its IRR, the project is attractive when its risk and therefore its required return
are low. At a higher risk level, the IRR is no longer higher than the expected return on
comparable risk assets available elsewhere in the capital market. 12. Figure follows below.
Cost of capital = risk-free rate + beta × market risk premium
Since the risk-free rate is 4% and the market risk premium is 7%, we can write the cost of
Cost of capital = 4% + beta × 7%
Cost of capital (from CAPM)
Beta = 10% + beta × 8%
.75 4% + .75 7% = 9.25%
1.75 4% + 1.75 7% = 16.25%
7% = market risk
The cost of capital of each project is calculated using the above CAPM formula. Thus, for
Project P, its cost of capital is: 4% + 1.0 × 7% = 11%.
If the cost of capital is greater than IRR, then the NPV is negative. If the cost of capital
equals the IRR, then the NPV is zero. Otherwise, if the cost of capital is less than the IRR,
the NPV is positive.
Project Beta IRR NPV
Cost of capital
P 1.0 11.0% 11% 0
Q 0.0 4.0 6 +
R 2.0 18.0 17
S 0.4 6.8 7 +
T 1.6 15.2 16 +
- 2 - 14. We need to find the discount rate for which:
15 annuity factor(r, 10 years) = 100.
Solving this equation on the calculator, we find that the project IRR is 8.14%. The IRR is
less than the opportunity cost of capital, 13.8%. Therefore you should reject the project,
just as you found from the NPV rule.
16. If investors believe the year-end stock price will be $54, then the expected return on the
2 + (54 – 50)
50 = .12 = 12%,
which is greater than the opportunity cost of capital. Alternatively, the “fair” price of the
stock (that is, the present value of the investor's expected cash flows) is
(2 + 54)/1.0925 = $51.26, which is greater than the current price. Investors will want to buy
the stock, in the process bidding up its price until it reaches $51.26. At that point, the
expected return is a “fair” 9.25%:
2 + (54 – 51.26)
= .0925 = 9.25%.
17. a. The expected return of the portfolio is the weighted average of the returns on the
TSX and T-bills. Similarly, the beta of the portfolio is a weighted average of the beta of the
TSX (which is 1.0) and the beta of T-bills (which is zero).
(i) E(r) = 0 13% + 1.0 5% = 5% = 0 1 + 1 0 = 0
(ii) E(r) = .25 13% + .75 5% = 7% = .25 1 + .75 0 = .25
(iii) E(r) = .50 13% + .50 5% = 9% = .50 1 + .50 0 = .50
(iv) E(r) = .75 13% + .25 5% = 11% = .75 1 + .25 0 = .75
(v) E(r) = 1.00 13% + 0 5% = 13% = 1.0 1 + 0 0 = 1.0
b. For every increase of .25 in the of the portfolio, the expected return increases by
2%. The slope of the relationship (additional return per unit of additional risk) is
therefore 2%/.25 = 8%.
c. The slope of the return per unit of risk relationship is the market risk premium:
rM– r f 13% – 5% = 8%, which is exactly what the SML predicts. The SML says
that the risk premium equals beta times the market risk premium.
- 3 - 20. The CAPM states that r = r + f(r m – rf). If < 0, then r f r . Investors would invest in a
security with an expected return below the risk-free rate because of the hedging value such
a security provides for the rest of the portfolio. Investors get their “reward” in terms of risk
reduction rather than in the form of high expected return.
21. The historical risk premium on the market portfolio has been about 7%. Therefore, using
this value and the assumed risk-free rate of 3%, we can use the CAPM to derive the cost of
capital for these firms as 3% + 7%.
CHC Helicopter 1.34 12.38%
Open Text 1.52 13.64%
Loblaw Companies 0.71 7.97%
Tim Hortons 0.9 9.30%
28. a. False. The stock’s risk premium, not its expected rate of return, is twice as high as the
b. True. The stock’s unique risk does not affect its contribution to portfolio risk but its
market risk does.
c. False. A stock plotting below the SML offers too low an expected return relative to
the expected return indicated by th