1.35

Assume that when the stock price raise to $ x $, there will be no difference between two strategies. And we know:

$$
100 x - 9400 = ( x - 95 ) 2000 - 9400
\tag{1}
$$

Then $ x = 100 $, which means when the price raise above 100, the option strategy will be more profitable. So if the investor thought the price would exceed 100, he should choose the option strategy.

2.28

A increase of $ \$ 1000 $ will lead to a margin call. That means a price increase of:

$$
\frac{1000}{5000} = \$ 0.2 = 20 cents
\tag{2}
$$

That means there is a profit of $ \$ 1500 $. So the price will decrease by:

$$
\frac{1500}{5000} = \$ 0.3 = 30cents
\tag{3}
$$

3.27

Formula

$$
N = ( \beta_1 - \beta_2 ) * \frac{V_A}{V_F}
\tag{4}
$$

a

According to equation (4), we can get:

$$
N = ( 1.2 - 0.5 ) \frac{100,000,000}{2,000 250} = 140
\tag{5}
$$

So to decrease the beta, they should take a short position.

b

As the same:

$$
N = ( 1.2 - 1.5 ) \frac{100,000,000}{2,000 250} = -60
\tag{6}
$$

The value is negative, so they should take a long position.

4.28

Formula

$$
R_c = m * ln( 1 + \frac{R_m}{m} )
\tag{7}
$$

$$
R_F = \frac{R_2 T_2 - R_1 T_1}{T_2 - T_1}
\tag{8}
$$

a

According to the equation (7):

• For 6-month, $R_6 = 2 * ln(1 + \frac{0.04}{2}) = 3.96 \%$
• For 12-month, $R_{12} = 2 * ln(1 + \frac{0.045}{2}) = 4.45 \%$
• For 18-month, $R_{18} = 2 * ln(1 + \frac{0.0475}{2}) = 4.69 \%$
• For 24-month, $R_{24} = 2 * ln (1 + \frac{0.05}{2}) = 4.94 \%$

b

According to equation (8):

$$
R_F = \frac{0.0494 2 - 0.0469 1.5}{2 - 1.5} = 5.69 \%
\tag{9}
$$

4.29

$$
V_{FRA} = \frac{10,000,000 (0.07 - 0.06) 0.5}{1.025 ^ 4} = 45297.53
\tag{?}
$$

5.29

a

Present value of known cash flow:

$$
I = 1 e ^ {- 0.08 \frac{2}{12}} + 1 e ^ {- 0.08 \frac{5}{12}} = 1.9540
$$

Forward price:

$$
F_0 = (50 - 1.9540) e ^ {0.08 0.5} = 50.01
$$

Initial value is zero.

b

As the same:

Present value of cash flow:

$$
I = 1 e ^ {- 0.08 \frac{2}{12}} = 0.9868
$$

Forward price:

$$
F_1 = (48 - 0.9868) e ^ {0.08 \frac{3}{12}} = 47.96
$$

For short position, the value is:

$$
f = -(48 - 0.9868 - 50.01 e ^ {- 0.08 \frac{3}{12}}) = 2.01
$$