EBK ESSENTIALS OF INVESTMENTS
EBK ESSENTIALS OF INVESTMENTS
10th Edition
ISBN: 8220102800267
Author: Bodie
Publisher: YUZU
Question
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Chapter 19, Problem 13PS
Summary Introduction

(A)

  1. According to the given result, he should lend in the UK market.
  2. According to the explanation, he should borrow in the US market.

Expert Solution
Check Mark

Answer to Problem 13PS

  • Hence, in total, the cash flow today would be nullified, but would give a profit of 0.0079 at the time when this swap would be made.
  • Explanation of Solution

    Given Information:

    Rus = 5%

    rUK = 7%

    E0 = 2.0 dollars per pound

    F0 = $1.97/E (one-year delivery)

    Data can be summarized as follows:

    Risk free rate of USrUS=5%

    Risk free rate of UKrUK=7%

    Original exchange rateEo=$2/£

    Forward exchange rateFo=$1.97/£

    Determine where to Lend:

    Suppose an investor lends $10,000 in the UK market. Thus, according to the exchange rate, he will give £5,000, calculated by multiplying with the current exchange rate, that is,Eo=$2/£ the risk free rate in UK is 7%, so the interest payment he receives in one year would be as follows:

    Interestamount=£5,000×7%=£350

    Hence, the amount he gets after one year, which includes the total interest and the principle amount, is£5,350£5,000+£350=£5,350.

    The exchange rate after one year is,Fo=$1.97/£. Hence, to obtain the return in dollar, multiply£5,350 with the exchange rate as follows:

      £5,350×$1.97=$10,539.50

    Thus, it can be seen that initially, he had $10,000 to invest in return, and later, he gets total of $10,593.50 as returns. Therefore, his net profit is $539.50.

    $10,539.50$10,000=$539.50

    If he would have lent the same amount in the US market, he would have got interest according to the rate of 5%, which is the risk free rate in US market as follows:

    Interestamount=$10,000×5%=$500

    Thus, in total, he would have got $10,500 by the year end, which is less than what he is getting in the UK market, that is, $10,539.50.

    Thus, according to the above result, he should lend in the UK market.

    Conclusion

    Thus, according to the above result, he should lend in the UK market.

    Summary Introduction

    (B)

    Adequate information:

      rus = 5%rUK = 7%E0 = 2.0 dollars per poundF0 = $1.97/E oneyear delivery

    To compute:

    Where would you borrow?

    Introduction:

    Expert Solution
    Check Mark

    Answer to Problem 13PS

    According to the explanation, he should borrow in the US market.

    Explanation of Solution

    Determine where to borrow from:

    Suppose an investor borrows £10,000 in the US market. According to the exchange rate, he will get $20,000, which is calculated by multiplying with the current exchange rate, that is,

    E0=$2/£.

    The risk free rate in US is 5%. Hence, the interest payment for one year is as follows:

    Interestamount=$20,000×5%=$1,000

    After one year, the total amount including the principle that he gives, in addition to the interest, is $21,000. However, the exchange rate after one year is,F0=$1.97/£. Hence, in pounds, the amount payable would be $21,000 divided by the exchange rate as follows:

    $21,0001.97=£10,659

    If he would have borrowed the same amount in the UK market, he would have paid interest according to the rate of 7%, that is, the risk free rate in UK market. The interest is calculated as follows:

    Interestamount=£10,000×7%=£700

    Hence, he would have paid £10,700 in total by the year end, which is more that what is more that what he is paying in the US market.

    Thus, according to the explanation, he should borrow in the US market.

    Conclusion

    Thus, according to the explanation, he should borrow in the US market.

    Summary Introduction

    (C)

    Adequate information:

      rus = 5%rUK = 7%E0 = 2.0 dollars per poundF0 = $1.97/E oneyear delivery

    To compute:

    How could you arbitrage?

    Introduction:

    Expert Solution
    Check Mark

    Answer to Problem 13PS

    According to the explanation, he should borrow in the US market.

    Explanation of Solution

    Calculate the forward rate according to the interest rate parity relationship.

    Interest rate parity relationship: It is the relation between the forward exchange rate and spot exchange rate that do not allow arbitrage to take place. Forward price can be calculated using the formula as follows:

    F0E0=1+rfUS1+rfUK

    Here,

    Original exchange rate =Eo

    Forward rate =Fo

    Risk free rate of US=rUS

    Risk free rate of UK=rUK

    Calculate forward rate as follows:

    F02=1+0.051+0.07F0=2×1.051.07F0=1.9626

    The following steps can be taken to take advantage of the arbitrage position:

      ActionInitial cash flowCash flow at Time T
      Enter a contract to sell

        £1.07

      at a (future price) ofF0=$1.97

      0.0
      1.07×1.97E1
      Borrow $2.00 in the US
      2.00
      2.00×1.05
      Convert the borrowed dollars to pounds, and lend the UK at a 7% interest rate
      -2.00
      1.07×E1
      Total
      0
      0.0079

    Enter into a contract to sell £1.071+rfUK at a future price of 1.96 as calculated. At this time, the initial cash flow would be nil. At the future date, the cash flow would be

    1.07×1.97E1

    Here,E1 is the forward exchange rate.

    The borrowed dollars are converted to pounds and given in the UK market at 7% interest rate thus, initial cash flow here would be -2.00, but in future, the cash flow would become1.07×E1 .

    Hence, in total, the cash flow today would be nullified, but would give a profit of 0.0079 at the time when this swap would be made.

    Conclusion

    Hence, in total, the cash flow today would be nullified, but would give a profit of 0.0079 at the time when this swap would be made.

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