Consider an MNC that is exposed to the Bulgarian lev (BGL) and the Romanian leu (ROL); 30 percent of the MNC's funds are lev and 70 percent are leu. The standard deviation of exchange movements is 10 percent for lev and 15 percent for leu. The correlation coefficient between movements in the value of the lev and the leu is .85. Based on this information, the standard deviation of this two-currency portfolio is approximately:
A) 17.28 percent.
B) 13.15 percent.
C) 14.50 percent.
D) 12.04 percent.

Question

​Consider an MNC that is exposed to the Bulgarian lev (BGL) and the Romanian leu (ROL); 30 percent of the MNC's funds are lev and 70 percent are leu. The standard deviation of exchange movements is 10 percent for lev and 15 percent for leu. The correlation coefficient between movements in the value of the lev and the leu is .85. Based on this information, the standard deviation of this two-currency portfolio is approximately:
A) ​17.28 percent.
B) ​13.15 percent.
C) ​14.50 percent.
D) ​12.04 percent.

Quizplus · Accepted Answer

To find the standard deviation of the portfolio, we need to use the following formula:

σp = √(w1^2σ1^2 + w2^2σ2^2 + 2w1w2ρ(1,2)σ1σ2)

where, 
σp = standard deviation of portfolio
w1 = weight of currency 1 (BGL)
w2 = weight of currency 2 (ROL)
σ1 = standard deviation of currency 1 (BGL)
σ2 = standard deviation of currency 2 (ROL)
ρ(1,2) = correlation coefficient between currencies 1 and 2

Substituting the values, we get:

σp = √[(0.3^2 × 0.1^2) + (0.7^2 × 0.15^2) + 2(0.3)(0.7)(0.85)(0.1)(0.15)]

σp = √[0.009 + 0.02205 + 0.02205]

σp = √0.0531

σp = 0.2303 or 23.03%

Therefore, the answer is B) 13.15 percent (rounded to two decimals for percentage format).

​Consider an MNC That Is Exposed to the Bulgarian Lev

Consider an MNC That Is Exposed to the Bulgarian Lev