Question

3. A-Z Corporation would like to borrow for 6 months in Yen and Euro. The following market information is available to the company.

            Mean effective 6-month rate on Yen = 4 %

            Mean effective 6- month rate on Euro = 10%

            Std. Dev for Yen effective rate = 0.10

            Std. Dev for Euro effective rate = 0.25

            Correlation of Yen and Euro effective rates = 0.35

A) What is the expected effective financing rate and the Std. Dev of effective financing if the portfolio contemplated by A-Z Corp consists of 35% Yen and 65% Euro?

[Ans: R_ip = 7.9%; ?_{i p} = 17.78% ]

B) Assume now that the Yen and the Euro are perfectly negatively correlated. Compute the relevant weights for the Yen and the Euro to construct a portfolio with zero risk and obtain the resultant effective financing rate.

[Ans: w₁ = 5/7; w₂ = 2/7; R_ip = 5.71%]

I know the answers, but I want to understand the work. Thank you.

Answer 1

A) Expected effective financing rate=4*35%+10*65%=7.9%

  

Now, variance=square of standard deviation'

So, variance for Yen=(10)²=100 since 0.1 means standard deviation of 10%.

So, variance for Euro=(25)²=625 since 0.25 means standard deviation of 25%.

Covariance= correlation between both*standard deviation of first*standard deviation of second

= 0.35*10*25

=87.5

Now we can put these in the standard deviation formula as follows:

  

B. For a zero risk portfolio where Yen and Euro are perfectly negatively correlated,

weight of Yen=standard deviation of second/(standard deviation of first+standard deviation of second)

=25/(10+25)

=5/7

weight of Euro=2/7

Expected effective financing rate=4*5/7+10*2/7

=40/7

=5.71%