5) Suppose that there is a bank that is ordering to lend and/or borrow money at an interest rate of 8% (regardless of the time-to-maturity of the loan). Further suppose that there is a two-year coupon bond trading with a face value of $100 and a coupon rate of 5% trading in the market. Price the bond using an explicit no-arbitrage argument. Answer: =$5/(1+0.08)^1+($5+$100)/(1+0.08)^2 =$94.65 The price of the bond using an explicit no-arbitrage argument is $94.65 6) Suppose that the bond in the previous question is actually trading for $92. Show how you could exploit the mispricing to make an arbitrage profit. Answer: As we know that if trading price 92 is lower and current price is higher 94.65 as per calculation then there is a chance to increase the trading price therefore investor can make arbitrage profit. 7) produce annual cash flows of $100 (with certainty) for five years starting in two years, i.e, from t= 2 tot = 6. What is the arbitrage-free price of the gold mine? Suppose that the bank from the previous question is still around. Consider a gold mine that will Present Value Year Cash Flow Present Value factor @ 8% 1. 0.9259 100.00 0.8573 85.73 100.00 0.7938 79.38 4. 100.00 0.7350 73.50 100.00 0.6806 68.06 6 100.00 0.6302 63.02 Price of Gold mine 369.70 8) Now suppose that the cash flows from the mine in the previous question are risky with a standard deviation of = $50. How would your answer change? 2. 3.
5) Suppose that there is a bank that is ordering to lend and/or borrow money at an interest rate of 8% (regardless of the time-to-maturity of the loan). Further suppose that there is a two-year coupon bond trading with a face value of $100 and a coupon rate of 5% trading in the market. Price the bond using an explicit no-arbitrage argument. Answer: =$5/(1+0.08)^1+($5+$100)/(1+0.08)^2 =$94.65 The price of the bond using an explicit no-arbitrage argument is $94.65 6) Suppose that the bond in the previous question is actually trading for $92. Show how you could exploit the mispricing to make an arbitrage profit. Answer: As we know that if trading price 92 is lower and current price is higher 94.65 as per calculation then there is a chance to increase the trading price therefore investor can make arbitrage profit. 7) produce annual cash flows of $100 (with certainty) for five years starting in two years, i.e, from t= 2 tot = 6. What is the arbitrage-free price of the gold mine? Suppose that the bank from the previous question is still around. Consider a gold mine that will Present Value Year Cash Flow Present Value factor @ 8% 1. 0.9259 100.00 0.8573 85.73 100.00 0.7938 79.38 4. 100.00 0.7350 73.50 100.00 0.6806 68.06 6 100.00 0.6302 63.02 Price of Gold mine 369.70 8) Now suppose that the cash flows from the mine in the previous question are risky with a standard deviation of = $50. How would your answer change? 2. 3.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
I need help with question 8 but is related to the other ones
Transcribed Image Text:Suppose that there is a bank that is ordering to lend and/or borrow money at an interest rate of
5)
8% (regardless of the time-to-maturity of the loan). Further suppose that there is a two-year coupon
bond trading with a face value of $100 and a coupon rate of 5% trading in the market. Price the bond
using an explicit no-arbitrage argument.
Answer:
=$5/(1+0.08)^1+($5+$100)/(1+0.08)^2
=$94.65
The price of the bond using an explicit no-arbitrage argument is $94.65
Suppose that the bond in the previous question is actually trading for $92. Show how you could
6)
exploit the mispricing to make an arbitrage profit.
Answer: As we know that if trading price 92 is lower and current price is higher 94.65 as per calculation
then there is a chance to increase the trading price therefore investor can make arbitrage profit.
7)
Suppose that the bank from the previous question is still around. Consider a gold mine that will
produce annual cash flows of $100 (with certainty) for five years starting in two years, i.e. from t = 2 to t
= 6. What is the arbitrage-free price of the gold mine?
Present Value
Year
Cash Flow
Present Value
factor @ 8%
1.
0.9259
100.00
0.8573
85.73
100.00
0.7938
79.38
4
100.00
0.7350
73.50
5
100.00
0.6806
68.06
6
100.00
0.6302
63.02
Price of Gold mine
369.70
8)
Now suppose that the cash flows from the mine in the previous question are risky with a
standard deviation of = $50. How would your answer change?
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