1
$\begingroup$

I am struggling trying to find out where they get the $8$% interest rate for the loan you make to purchase the Sterling Bond in the following strategy:

Problem:

Suppose that $A(0)$ = $100$ and $A(1)$ = $105$ dollars, the present price of pound sterling is $S(0)$ = $1.6$ dollars, and the forward price is $F = 1.50$ dollars to a pound with delivery date $1$. How much should a sterling bond cost today if it promises to pay $£100$ at time $1$? Hint: The forward contract is based on an asset involving negative carrying costs (the interest earned by investing in sterling bonds).

Strategy:

Suppose that a sterling bond promising to pay $£100$ at time $1$ is selling for $x$ pounds at time $0$. To find $x$ consider the following strategy.

At time $0$:

• Borrow $1.6x$ dollars and change the sum into $x$ pounds.

• Purchase a sterling bond for $x$ pounds.

• Take a short forward position to sell $£100$ for $\$1.50$ to a pound with delivery date $1$.

Then, at time $1$:

• Cash the bond, collecting $£100$.

• Close the short forward position by selling $£100$ for $\$150$.

• Repay the cash loan with interest, that is, $1.68x$ dollars in total.

$\endgroup$
1
$\begingroup$

First, it's not a 8% loan. The .08 interest on 1.6 is 5%. It appears that it is coming from the $A (1) = 105$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.