Learning objectives: Describe Treasury rates, LIBOR, and repo rates, and explain what is meant by the “risk-free” rate. Calculate the value of an investment using different compounding frequencies. Convert interest rates based on different compounding frequencies.
Questions:
712.1. Interest rates are a fundamental and essential building block in finance. As Hull reminds us, "for any given currency, many different types of interest rates are regularly quoted. These include mortgage rates, deposit rates, prime borrowing rates, and so on" and, further, interest rates are a factor in the valuation of virtually all derivatives. Consequently, fluency in finance requires that we achieve proficiency with the different types of rates and an ability to manipulate them depending on the circumstance. Each of the following statements is true EXCEPT which is false?
a. A repo rate is essentially similar to the federal funds rate except that a repo rate can only be an overnight (i.e., one day) rate and will be slightly higher due to its additional credit risk
b. Treasury rates are (i) the rates earned on instruments issued by a government to borrows in its own currency, (ii) are generally regarded as risk-free, but (iii) tend NOT to be the risk-free rate used to value derivatives
c. The OIS rate is the agreed fixed rate in an overnight indexed swap (OIS). OIS rates are continually refreshed one-day rates, and subsequent to the Global Financial Crisis (GFC), OIS rates have been used as risk-free rates
d. LIBOR (London Interbank Offered Rate) is an unsecured short-term borrowing rate between banks. LIBOR rates are quoted for a number of different currencies and borrowing periods that range from one day to one year. LIBOR rates are used as reference for hundreds of trillions of dollars of global transactions. However, LIBOR is suboptimal reference rate for derivatives transactions because it is determined from estimates made by banks, not from market transactions
712.2. Richard plans to invest $10,000.00 today in a zero-coupon bond with a promised return of 7.0% per annum. This return is possible because he will not be repaid until the bond matures in ten years. He calculates the future principal repayment, but his calculation assumes the rate is an equivalent annual interest rate; aka, effective annual rate. His advisor informs him that the actual rate is 7.0% per annum with monthly compounding. Compared to his original future value, how many dollars greater is Richard's revised future principal repayment?
a. Zero
b. $39.80
c. $215.75
d. $425.10
712.3. If the six-year discount factor, df(6.0), is $0.820 then which of the following is nearest to the basis point difference between the implied semi-annual six-year spot rate and the implied continuously compounded six-year spot rate?
a. Zero
b. Three basis points
c. 27.5 basis points
d. 249 basis points
Answers here:
Questions:
712.1. Interest rates are a fundamental and essential building block in finance. As Hull reminds us, "for any given currency, many different types of interest rates are regularly quoted. These include mortgage rates, deposit rates, prime borrowing rates, and so on" and, further, interest rates are a factor in the valuation of virtually all derivatives. Consequently, fluency in finance requires that we achieve proficiency with the different types of rates and an ability to manipulate them depending on the circumstance. Each of the following statements is true EXCEPT which is false?
a. A repo rate is essentially similar to the federal funds rate except that a repo rate can only be an overnight (i.e., one day) rate and will be slightly higher due to its additional credit risk
b. Treasury rates are (i) the rates earned on instruments issued by a government to borrows in its own currency, (ii) are generally regarded as risk-free, but (iii) tend NOT to be the risk-free rate used to value derivatives
c. The OIS rate is the agreed fixed rate in an overnight indexed swap (OIS). OIS rates are continually refreshed one-day rates, and subsequent to the Global Financial Crisis (GFC), OIS rates have been used as risk-free rates
d. LIBOR (London Interbank Offered Rate) is an unsecured short-term borrowing rate between banks. LIBOR rates are quoted for a number of different currencies and borrowing periods that range from one day to one year. LIBOR rates are used as reference for hundreds of trillions of dollars of global transactions. However, LIBOR is suboptimal reference rate for derivatives transactions because it is determined from estimates made by banks, not from market transactions
712.2. Richard plans to invest $10,000.00 today in a zero-coupon bond with a promised return of 7.0% per annum. This return is possible because he will not be repaid until the bond matures in ten years. He calculates the future principal repayment, but his calculation assumes the rate is an equivalent annual interest rate; aka, effective annual rate. His advisor informs him that the actual rate is 7.0% per annum with monthly compounding. Compared to his original future value, how many dollars greater is Richard's revised future principal repayment?
a. Zero
b. $39.80
c. $215.75
d. $425.10
712.3. If the six-year discount factor, df(6.0), is $0.820 then which of the following is nearest to the basis point difference between the implied semi-annual six-year spot rate and the implied continuously compounded six-year spot rate?
a. Zero
b. Three basis points
c. 27.5 basis points
d. 249 basis points
Answers here:
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