Chapter 9 Notes -- Investments
Suppose $1million is discounted over a full calendar year of 365 days using a bank discount yield of 5% and an assumed 360-day business year. What is the resulting acceptance (current) price?
Acceptance Price = Face Value (1-DTM*discount) 360 $949,305. 56 = $1,000,000(1-365*0.05) 360
Pure discount security
An interest-bearing asset that makes a single payment of face value at maturity with no payments before maturity
What does APR stand for and what is the formula for it?
Annual Percentage Rate r*m (per period rate earned)(# of periods in a year)
Suppose you wanted to buy a T-bill with 85 days to maturity and a face value of $5,000,000. How much would you have to pay if the ask discount is 3.41%?
Ask Price = 5,000,000(1 - 85 * 0.0341) 360 Ask Price = $4,959,743.06
Suppose a T-bill has 45 days to maturity and an ask discount of 5%. What is the bond equivalent yield?
BEY = 365*0.05 360-45*0.05 BEY = 0.05101 (5.101%)
Suppose the ask discount rate on a T-bill with 170 days to maturity is 3.22%. What is the bond equivalent yield?
BEY = 365*discount 360-dtm*discount BEY= 365*0.0322 360-170*0.0322 BEY = 0.03315 (3.315%)
A T-bill has a face value of $1,000,000, a bid discount rate of 0.140%, and an ask discount rate of 0.130%. The T-bill matures in 240 days. What is the bid price? What is the ask price?
Bid Price = $1,000,000(1 - 240 * 0.00140) 360 Bid Price = $999,066.67 Ask Price = $1,000,000(1 - 240 * 0.00130) 360 Ask Price = $999,133.33
Suppose the bond equivalent yield for a $1,000,000 T-bill that matures in 170 days and has a 3.22% ask discount rate, is 3.315%. What is the T-bill ask price?
Bill Price = Face Value 1+BEY*DTM/365 Bill Price = $1,000,000 1+0.03315*(170/365) Bill Price = $984,795.03
Suppose a banker's acceptance has a face value of $1 million that will be paid in 90 days. If the interest rate, quoted on a discount basis, is 5%, what is the current price of the acceptance?
Current Price = Face Value(1-DTM*discount) 360 987,500 = $1,000,000(1 - 90 * 0.05) 360
Suppose a banker's acceptance has a face value of $1 million that will be paid in 90 days. If the interest rate, quoted on a discount basis, is 5%, what is the discount aka the interest earned over the 90-day period until the acceptance matures?
Current Price = Face Value(1-DTM*discount) 360 987,500 = $1,000,000(1 - 90* 0.05) 360 Discount = Face Value-Current Price $12,500 = $1,000,000-$987,500
If you receive $1,000 today, what is the equivalent amount of money received in 3 years What formula do we use and what does each acronym mean?
FV = PV (1+r)^N FV is the amount received in 3 years PV is the amount received today r is the per period interest rate as a decimal 0.0xx N is the number of periods
Suppose you have $1,000 to invest and you can invest at an annual rate of 3.5% per year. What is the amount you will have in 3 years from this investment? What formula do we use and what is the answer?
FV = PV(1+r)^N $1,108.718 = $1,000(1+0.035)^3
Suppose you invest $500 for 4% for 6 years. How much money will you have at the end of 6 years?
FV = PV(1+r)^N $632.66 = $500(1.04)^6
Suppose the yield on a two year STRIPS is 7% and the yield on a one year STRIPS is 6%. Based on the expectations theory, what will the yield on a one year STRIPS be one year from now?
Forward rate = (1+0.07^2) -1 (1+0.06^1) Forward rate = 0.0800943 (8.00943%)
London Interbank Offered Rate (LIBOR)
Interest rate that international banks charge one another for overnight Eurodollar loans
Certificate of deposit (CD)
Large-denomination deposits of $100,000 or more at commercial banks for a specified term
The maturity preference theory suggests that
Long-term interest rates contain a maturity premium necessary to induce lenders into making longer term loans
What is the formula for Nominal Interest Rate and what do the acronyms stand for?
NI = RI + IP + RP + LP + DP NI = Nominal rate RI = Real rate IP = Inflation premium RP = Interest rate risk premium LP = Liquidity premium DP = Default premium
If you are going to receive $1,108.718 in 3 years from an investment, how much is the investment worth today? What formula do we use and what does each acronym mean?
PV = FV/(1+r)^N FV is the amount received in 3 years PV is how much the investment is worth today r is the per period interest rate as a decimal 0.0xx N is the number of periods (3 years)
Suppose you will be getting $800 in 4 years. What is an equivalent amount today if you discount at 3.7%?
PV = FV/(1+r)^N $691.79 = $800/(1.037)^4
US Treasury STRIPS
Pure discount securities created by stripping coupons and principal payments of Treasury notes and bonds. Stands for Separate Trading of Registered Interest and Principal of Securities
Term structure of interest rates
Relationship between time to maturity and interest rates for default-free, pure discount instruments
Eurodollars
US dollars denominated deposits at foreign banks or foreign branches of US banks
Basis point
With regard to interest rates or bond yields, one basis point is 1 percent of 1 percent
If you need to calculate a STRIPS ask yield using its price, what would you do? Use the following info: N = 2M r = YTM/2 Maturity = 6 years Ask Price = $73.031 Face Value = $100 (it will always be 100)
YTM = 2[(Face Value)^1/2M - 1] [(STRIPS Price) = 2 [( 100 )^1/(2*6) - 1] [(73.031) STRIPS Ask Yield = 0.05307 (5.307%)
reinvestment risk is the risk that
a bond's future coupon payments may have to be invested at a rate lower than the bond's yield to maturity
The preferred habitat theory is
a compromise between market segmentation and maturity preference, where the market has different investors with different preferred maturities and can be induced to move to less preferred maturities by a higher interest rate
Treasury yield curve
a graph of treasury yields plotted against maturities
Bank discount basis
a method for quoting interest rates on money market instruments
Banker's acceptance
a postdated check on which a bank has guaranteed payment; commonly used to finance international trade transactions
For Treasury STRIPS, the number of periods is "a" and the interest rate is "b"
a. 2M (2*number of years until maturity) b. YTM/2
The formula used to calculate the acceptance price (current price) assumes a "a" day business year, with exactly "b" "c" day quarters because it made the calculation simpler and less subject to error.
a. 360 day business year b. 4 c. 90 day quarters
Medium credit quality corporate debt is denoted as "a" while high credit quality corporate debt is denoted as "b"
a. Triple B rated b. Double A rated
High yield bonds refers to corporate bond with
above average default risk
In the maturity preference theory, the preferred habitat is
always toward shorter maturities rather than longer maturities
An ask yield for a US Treasury STRIPS is
an Annual Percentage Return (APR)
The bond equivalent yield on a T-bill is also just
an Annual Percentage Return (APR)
Forward rate
an expected future interest rate implied by current interest rates (what you can expect in the future based on quotes today)
Fisher Hypothesis
assertion that the general level of nominal interest rates follows the general level of inflation
What are tax exempts
bonds issued by municipal governments that are exempt from federal income taxes and are often exempt from state income taxes too
If you intend to buy a T-bill, you must pay the (bid/ask) price
buyers pay the ask price
The market segmentation theory suggests that
debt markets are segmented by maturity, with the result that interest rates for various maturities are determined separately in each segment
Triple B rated bonds pay "higher/lower" interest rates compared to Double A rated bonds?
higher because they are more risky
Federal Funds rate
interest rate that banks charge each other for overnight loans of $1 million or more
Bellwether rate
interest rate that serves as a leader or as a leading indicator of future trends, e.g., interest rates as a bellwether of inflation
Real interest rates are
interest rates adjusted for the effect of inflation, calculated as nominal - inflation
Nominal interest rates are
interest rates as they are normally observed and quoted, with no adjustment for inflation
Yankee bonds are
issued by foreign corporations for sale in the US and are denominated in US dollars so investors do not have to worry that changing foreign exchange rates will affect debt values
Money market securities are
short term debt securities
Commercial paper
short-term, unsecured debt issued by large corporations
For treasury bills, the ask discount is used by dealers to
state what price a dealer will accept to sell a treasury bill
For treasury bills, the bid discount is used by dealers to
state what they are willing to pay for a treasury bill
Prime rate
the basic interest rate on short-term loans that the largest commercial banks charge to their most creditworthy corporate customers
Call money rate
the interest rate brokerage firms pay for call money loans, which are bank loans to brokerage firms. The rate is used as the basis for customer rates on margin loans
Discount rate
the interest rate that the Fed offers to commercial banks for overnight reserve loans
Expectations Theory
the term structure of interest rates is a reflection of financial market beliefs regarding future interest rates
If you want to calculate the bond equivalent yield for T-bills, what do you do if there is a leap year?
use 366 days instead of 365 in the numerator if February 29 occurs within the next 12 months
Consider a STRIPS with an ask price of 55.568, a reported yield of 4.40, and 13.5 years to maturity. 1. What is the actual semi annual rate? 2. How many semi annual periods are there? 3. How would you find the STRIPS price if we did not already have it?
1. Semi Annual Rate SAR = 4.4/2 = 2.2% 2. Semi Annual Periods SAP = 2*13.5 = 27 periods 3. STRIPS Price = Face Value (1+sar)^sap
What are the 2 indexes shown on the Treasury yield curve and their specifications?
1. Treasury securities - Intermediate (1-10 year maturity) - Long term (10-30 year maturity) 2. Government Agency debt - debt with 10-20 year maturity - debt with 20+ year maturity
If an interest rate of 5.82% rose to 5.94%, how many basis points did it increase by?
12 = 5.94-5.82 = 0.12(100)
US Treasury bill (T-bill)
A short-term U.S. government debt instrument issued by the U.S. Treasury
According to the expectations theory, the forward rate is an accurate predictor of the rate to be realized how far in the future?
1 year
A typical credit card may quote an APR of 18%. On closer inspection, you will find that the rate is actually 1.5% per month. What annual interest rate are you really paying on such a credit card? (AKA, what is the effective annual rate?)
1+EAR = (1+APR)^m m EAR = (1 + 0.18)^12 - 1 12 EAR = 0.1956 (19.56%)
Suppose the ask discount for a $1,000,000 T-bill that matures in 170 days, is 3.22%. 1. What is the ask price? 2. What is the discount? 3. What % will you earn on the $1mil investment considering its ask price? 4. What is the APR? 5. What is the EAR?
1. Ask Price = 1,000,000 (1 - 170 * 0.0322) 360 = $984,794 2. Discount = 1,000,000 - 984,794.44 = $15,206 3. % Earnings = 15,206 984,794 = 1.544% 4. APR = 365/170 = 2.147pds/yr = 1.544%*2.147pds/yr = 3.315% 5. EAR = (1 + 0.03315)^2.147 - 1 2.147 = 0.03344 (3.344%)
A money market instrument with 60 days to maturity has a quoted ask price of 99, meaning $99 per $100 face value. 1. What is the banker's discount yield? 2. What is the bond equivalent yield? 3. What is the effective annual return?
1. Current Price = 100(1 - 60 * y) 360 99 = 100(1 - 60 * y) 360 99 = 100(1-0.167y) 99 = 100 - 16.7y -100 -100 -1 = -16.7y -16.7 -16.7 Banker's Yield = 0.059 (6%) 2. BEY = 365*0.06 360-60*0.06 Bond Equivalent Yield = 0.06145 (6.145%) 3. EAR = 1- (1 + 0.06145)^365/60 365/60 Effective Annual Return = 0.06305 (6.305%)
Who are the 3 government sponsored agencies that repackage home mortgages into mortgage pools, where each pool represents several tens of millions of dollars of home mortgages?
1. Federal Home Loan Mortgage Corporation (FHLMC) 2. Federal National Mortgage Association (FNMA) 3. Government National Mortgage Association (GNMA)