Question

On May 22, 2012, The Wall Street Journal reported the following (for May 21):

Prime interest rates:              United States 3.25 percent;

Switzerland 0.52 percent;

Japan 1.475 percent.

Spot rates:                             $1.0670 = 1 Swiss franc;

                                                79.31 Japanese yen = $1

3-month forward rates:        $1.0685 = 1 Swiss franc

79.24 Japanese yen = $1

1. In terms of the dollar, was the Swiss franc at a forward discount or a forward premium? By what percent? Looking at the prime rates of the United States and Switzerland, is your calculated percentage discount/premium reasonably consistent with covered interest parity? Why or why not?
2. In terms of the Japanese yen, was the U.S. dollar at a forward discount or a forward premium? By what percent? Looking at the prime rates of Japan and the United States, is your calculated percentage discount/premium reasonably consistent with covered interest parity? Why or why not?

I need a clear explanation on this question. Thanks so much!

Answer 1

Prime interest rates:              

United States 3.25 percent;

Switzerland 0.52 percent;

Japan 1.475 percent.

Spot rates: $1.0670 = 1 Swiss franc;

   79.31 Japanese yen = $1

3-month forward rates:     

$1.0685 = 1 Swiss franc

79.24 Japanese yen = $1

A) The Swiss Franc was at premium with dollar

Forward rate is greater than spot ($/Franc)

% Premium is equal to (Forward/spot) - 1

= [($1.0685 $/Franc /$1.0670 $/Franc) - 1] = 0. 1406%  --------(2)

{2} Premium is reasonably consistent with covered interest parity

Interest parity comparision = (interest of usd - interest of swiss franc) / 4

= (Forward rate of ($/Franc) / spot rate ($/Franc))-1

(3 month forward rate is used so it is divided by 4)

[(0.0325 - 0.0052)/4] = 0.006825 or 0.6825% -------(1)

[($1.0685/$1.0670) - 1] = 0. 1406% --------(2)

Here Investment should move to the United States till the interest parity condition is realized.

[1-2] 0.5419‬% percent (or 54 basis points)

It have the arbitrage equilibrium already because the transaction cost is near ~50 basis points

B) The interest rate difference

= [interest of yen - int of dollar]/4

= [(0.01475 - 0.0325)/4] =-0.0044375‬ --------- [1]

Please note three months fwd rate so/4

In Terms of the Japanese yen

The dollar is at discount relative to the yen (the yen is at premium relative to the dollar)

because the forward rate on the dollar is less than spot rate

% Discount is equal to (Forward / spot)-1

= [ 79.24 / 79.31 ] -1 =-.0008822~ -.009 ------------[2]

[1-2] The difference between the forward discount and the interest rate difference
= -.0035553 = .355% OR 35 basis points

There is little incentive to move funds between the two countries.

In the absence of transactions costs funds should move to New York from Japan until the parity condition is realized.

Please note : In negative numbers largest value is smallest