Investment Yield Formulas and Yield Case Studies
School of Government: Cash Management & Investment of Public Funds
Investment Yield Formulas and Yield Case Studies
Presented by : Gary Porter, C.F.A. Vice President Capital Management of the Carolinas, LLC distributors of the North Carolina Capital Management Trust Email: gporter@
School of Government: Cash Management & Investment of Public Funds
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School of Government: Cash Management & Investment of Public Funds
What is Yield?
n The annual return on an investment
n Yield on a bond is based on:
n Purchase Price of the bond n Interest or coupon received
n Coupon payments are generally fixed n Price of the bond after purchase fluctuates
n Bond prices change due to changing interest rates n Supply & demand, time to maturity, credit quality
School of Government: Cash Management & Investment of Public Funds
Computing Bond Yields
Yield Measure
Purpose
Nominal Yield
Measures the coupon rate
Current Yield
Measures current income rate
Yield to Maturity*
Measures expected rate of return for bond held to maturity
Yield to Call
Measures expected rate of return for bond held to a call date
* Probably the most widely used
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School of Government: Cash Management & Investment of Public Funds
Determinants of Interest Rates
where:
i = RFR + I + RP
RFR = real risk-free rate of interest I = expected rate of inflation
RP = risk premium
School of Government: Cash Management & Investment of Public Funds
Bond Pricing
n Bond prices move inversely to interest rates
Interest Rates go
Bond Prices go
Interest Rates go
Bond Prices go
If you learn nothing else about bond prices, learn this!
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School of Government: Cash Management & Investment of Public Funds
Bond Pricing
Ex: - Bond purchased at par (price = 100%) 2 year maturity, 5% coupon bond Cost = Principal Amt x Price ($1,000 x 100% = $1,000) Interest rate moves to 4% New Price = 101.9039% New Market Value = $1,019.04 Interest rate moves to 6% New Price = 98.1415% New Market Value = $ 981.42
School of Government: Cash Management & Investment of Public Funds
n Bond Pricing
n Bond Prices move inversely to interest rates n The longer the maturity of the bond, the more
sensitive (variable) its price is to changes in rates (10 yr. security price will move more than 2 yr.) n The lower the coupon of the bond, the greater the price sensitivity
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Yield (%)
School of Government: Cash Management & Investment of Public Funds
Treasury
Rates Example
o f
Dramatic
Rise
i n
Longer
Term
R ates
4.0
3.5
3.0
2.50% 2.5
2.0
1.41%
1.5
1.67%
1.0
4/30/ 2013
6/30/ 2013
0.5
.65%
0.0
0
2
5
10
30
Years
School of Government: Cash Management & Investment of Public Funds
* Modified Duration is used to approximate the percent change in bond value for a given percent change in yield, using the following formula: Percent change in bond value = (-DM * change in yield)
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School of Government: Cash Management & Investment of Public Funds
School of Government: Cash Management & Investment of Public Funds
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School of Government: Cash Management & Investment of Public Funds
Back to Yields
Alternative Methods to Calculate Yields
n Discount yield (DY) n Money market yield (MMY) n Bond equivalent yield (BEY) n Yield to maturity (YTM)
School of Government: Cash Management & Investment of Public Funds
ANNUALIZING INTEREST AND YIELD
I.
Typically invest for a portion of the year and must convert interest earned
to equivalent annual yield
II. What is the annual yield on $100,000 invested for 91 days and interest earned of $1,500?
A. $ 1,500 = 1.5% or .015 $100,000
B. Annualize .015 x 365 91 = .015 x 4.011 = .06016 = 6.016%
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School of Government: Cash Management & Investment of Public Funds
III. Given $100,000 invested for 91 days at an annual yield of 6.016%, what interest would be earned?
A.
Convert annual yield to yield for period invested
.06016 x 91
365
= .06016 x .2493
= .0150
= 1.5%
B.
Calculation of interest
$100,000 x 1.5% = $1,500
School of Government: Cash Management & Investment of Public Funds
CALCULATION OF YIELD DEPENDS ON NUMBER OF DAYS USED FOR YEAR I. Some securities for which yield is quoted using a 360-day year
Treasury bills Commercial paper Bankers acceptances Some others
II. Securities for which yield is calculated using a 365-day year
Treasury notes and bonds NC Capital Management Trust CDs sometimes Others occasionally III. To re-state the yield of a security quoted on a 360-day basis to a yield on a
365-day basis, multiply the 360-day yield by the ratio of 365/360.
6.7% x (365/360) = 6.7% x 1.0139 = 6.79%
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