10 Investment Portfolio Choice II: …
higher expected return, you should of course choose B-PORT (the optimal
portfolio).
10.8 The first thing we do is to use the SML to get the market discount rate, k. Since
the β-value of Ingerzoll Raand is 1.15 the discount rate is
k = rf + β(μmarket – rf ) = 0.03 + 1.15 · 0.06 = 0.099 = 9.9%
The constant growth rate DDM is given by equation (6.7) and today’s stock price
is therefore
D
1. 5
P0 = 1 =
≈ $25.4
k − g 0. 099 − 0. 04
10.9(i) 12%
(ii)3.5%
(iii) 0.10 = w · 0.12 + (1 – w) · 0.035 → 0.10 = (0.12 – 0.035) · w + 0.035 → 0.065 = 0.085 · w → w ≈ 0.76 = 76%
(iv) β = 0.76 · 1 = 0.76
(v) You should borrow, instead of deposit, money from the bank. If you want an
expected return equal to 120%, then you should borrow 900000 euro and
invest the total 1 million euro in the market portfolio. The expected return on
your initial investment (100000 euro) will be a whopping 120% but the risk
will be huge as well.
10.10 Since Biimoto is twice as risky as the market, it has to have a β-value equal to 2
and a market discount rate, k, equal to
k = rf + β(μmarket – rf ) = 0.04 + 2 · 0.06 = 0.16 = 16%
Then we solve for g in the constant growth rate DDM model
DO · (1 + g)
→
k–g
0.5 · (1 + g)
12 =
→
0.16 – g
P0 =
12(0.16 – g) = 0.5 · (1 + g) →
1.92 – 12g = 0.5 + 0.5g →
1.42 = 12.5g →
1. 42
g=
≈ 0. 11 = 11%
12. 5
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2014-10-06 08.48