Question

Consider the following hypothetical facts about Mexico: The peso recently lost over 40% of its value relative to the dollar. Over the course of the next 90 days, there is a 25% chance that the Mexican government will lose control of the economy. If it does, the peso will lose 20% of its value relative to the dollar, and the Mexican stock market will fall by 10%. Alternatively, the U.S. Congress may vote to help Mexico by offering collateral for Mexican government loans. In that case, the peso will appreciate 10% relative to the dollar, and the Mexican stock market will rise by 5%. As a U.S. investor with no current assets or liabilities in Mexico, you have decided to speculate. Calculate your expected dollar return from investing dollars in the Mexican stock market for the next 90 days. Express the return in annualized terms.

Answer 1

Answer:

The annualized return of the investment is R=0.286 or 28.6%.

Explanation:

The expected value takes into account all the possible outcomes and their probabilities. In this case, there are only 2 possible outcomes:

1) Mexican government lose control of the economy. Probability: 25%.

2) The Mexican government don't lose contol of the economy. Probability: 75%

In the Case 1, the local stock market will fall by 10% and the peso will lose 20%.

The return in dollars can be calculated as:

$R=(1+\Delta SM)/(1-\Delta P)-1=(1-0.10)/(1+0.2)-1\\\\R=0.90/1.20-1=0.75-1=-0.25$

being ΔSM the return of the stock market and ΔP the apreciation of the peso.

For the Case 2, we have that the local stock market will rise by 5% and the peso will appreciate by 5%.

The return in this case is

$R=(1+\Delta SM)/(1-\Delta P)-1=(1+0.05)/(1-0.10)-1\\\\R=1.05/0.90-1=1.17-1=0.17$

Then, the expected value is:

$E(R)=\sum p_iR_i=p_1R_1+p_2R_2=0.25*(-0.25)+0.75*(0.17)\\\\ E(X)=-0.0625+0.1275=0.065$

The expected dollar return in the 90 days is R=0.065.

If we annualized, the annual rate of return of this investment is:

$R_a=(1+R)^{N/n}-1=1.065^{360/90}-1\\\\R_a=1.065^4-1=1.286-1=0.286$