A m ba s s ad o r F i n a n c i a l G ro u p, i n c .
AMBASSADOR ALERT • 2011 • 1st Quarter
Why the Realized Yield Can Be Very Different
Than the Promised Yield
In our office there are several indices we keep track of on a regular basis. One such index is the U.S. Commercial Bank
Assets Index issued on a weekly basis by the Federal Reserve. This index details the amount of cash in the banking
sector which is currently almost $1.4 trillion. Furthermore, banks have been aggressively building their cash position
since mid 2008. Many of these institutions have been receiving monthly cash flows on both the loan and investment
portfolio and holding these assets in fed funds. While reviewing this cash index recently, it occurred to me that realized
portfolio yields are going to be drastically different than the book yields these institutions are expecting to earn.
To understand this phenomenon, let’s first look at the different types of risk in the fixed income market. Every fixed
income investor will tell you that when buying a bond you must consider the amount of interest rate risk and reinvestment
risk regardless of whether credit risk is a factor. Interest rate risk can be defined as the risk that an investment’s value
will change due to a change in the level of interest rates. Reinvestment risk is the risk that future proceeds—whether
that is principal or coupon payments—will have to be reinvested at a lower potential interest rate. These two types of
risk can be thought of as substitutes. For instance, if you buy a bond without reinvestment risk, such as a zero-coupon
issue, you will inherently assume more interest rate risk as the duration will be higher than a comparable issue with
semiannual coupon payments. These two risks can’t be completely eliminated; in the process of reducing exposure to
one, exposure to the other will be increased. Although interest rate risk is very important, this article is going to focus
on reinvestment risk.
An investor can measure the “compensation” they will receive by comparing the yield to maturity on several issues
or yield to call/put if the bond has embedded options. The yield to maturity is the interest rate that will make the
present value of a bond’s cash flows equal to its market price. The yield, sometimes referred to as the internal rate
of return or the promised yield, makes the critical assumption that all interim cash flows (i.e., interest and in some
cases principal) will be reinvested at an interest rate equal to the yield to maturity. Therefore, the yield is made up
of three components: coupon payments made by the issuer, capital gain/loss and reinvestment income. Reinvestment
income is generated from investing all interim cash flows of either interest or a combination of interest and principal
in the case of amortizing securities.
Most investors understand the importance of the coupon and
Coupon Interest:
$60.00
capital gain, but few realize how important the reinvestment
assumption can be. To help illustrate the importance of
Capital Gain:
$7.11
reinvesting coupon payments, consider the following example.
Reinvestment Income:
$24.84
Say we purchase a non-callable corporate bond with
a 10-year maturity that has a 7.00% bond-equivalent yield.
PMT (1+i) n − 1
The coupon is 6.00% and it pays semiannual interest. Using
FV =
i
a simple bond calculator, we can plug in these assumptions
to calculate a present value or current price of $92.89. We
can now decompose the yield to separate the coupon interest,
capital gain and reinvestment income on the bond. The total coupon interest is the sum of all coupon payments. The
capital gain or loss is the difference between the maturity price, in this case $100, and the purchase price. The future
value of the income from coupon payments plus the interim cash flow from reinvestment of those coupons is slightly
continued on page 2 …
Why the Realized Yield Can Be Very Different Than the Promised Yield
1
Ambassad or alert • 2011 • 1st quarter
continued from page 1 …
more complex, but it can be calculated using an annuity formula shown below. After calculating the future value of the
coupon payments received and reinvested with the aforementioned formula, subtract the total coupon interest and you
will be left with $24.84. This is the component of the yield calculation where we will focus our attention.
If an investor purchases this non-callable bond and reinvests coupon payments in fed funds at 0.25%, the actual yield
would be 5.56%, 21% lower than the expected yield to maturity of 7%. This illustration shows how misleading the yield
to maturity can be if its components are not fully understood.
The previous example was straight forward in that only coupon payments had to be reinvested. Next we will show
how this problem can be compounded when dealing with an amortizing security such as a mortgage backed security.
In this situation an investor will have to reinvest scheduled principal and prepayments in addition to interest payments.
There are two types of prepayments: voluntary and involuntary. Voluntary prepayments occur when a homeowner
decides to make an extra mortgage payment to reduce the amount of principal on the loan or refinance the loan altogether
at a more favorable interest rate. Involuntary prepayments happen when a borrower defaults. For the sake of this
article, we will examine an agency pass-through, so defaults will not cause losses to invested principal but instead
only a prepayment of principal.
continued on page 3 …
Assumptions
Security
FN MA0704
Original Face
$1,000,000
Settle Date
3/1/11
YTM
2.65%
Market Price
$1,046,250.00
Scenario 1
Scenario 2
Scenario 3
Reinvestment Rate
2.65%
1.00%
0.25%
IRR
2.64%
1.58%
1.10%
Interest
Principal
(Scheduled +
Prepayments)
Balance
Net Cash Flow
4/25/11
$3,333.33
$7,162.60
$992,837.40
$10,495.93
$13,611.17
$11,580.01
$10,757.13
5/25/11
$3,309.46
$7,634.73
$985,202.67
$10,944.19
$14,161.25
$12,064.51
$11,214.20
3
6/25/11
$3,284.01
$8,098.85
$977,103.82
$11,382.86
$14,696.47
$12,537.64
$11,661.27
4
7/25/11
$3,257.01
$8,554.27
$968,549.55
$11,811.28
$15,216.05
$12,998.69
$12,097.65
5
8/25/11
$3,228.50
$9,000.28
$959,549.27
$12,228.78
$15,719.24
$13,446.95
$12,522.66
6
9/25/11
$3,198.50
$9,436.20
$950,113.07
$12,634.70
$16,205.29
$13,881.74
$12,935.64
7
10/25/11
$3,167.04
$9,861.37
$940,251.70
$13,028.41
$16,673.50
$14,302.39
$13,335.95
8
11/25/11
$3,134.17
$10,275.15
$929,976.54
$13,409.32
$17,123.22
$14,708.29
$13,722.99
9
12/25/11
$3,099.92
$10,676.92
$919,299.62
$13,776.84
$17,553.83
$15,098.83
$14,096.17
10
1/25/12
$3,064.33
$11,066.07
$908,233.55
$14,130.40
$17,964.70
$15,473.42
$14,454.91
11
2/25/12
$3,027.45
$11,442.02
$896,791.53
$14,469.47
$18,355.31
$15,831.53
$14,798.69
12
3/25/12
$2,989.31
$11,804.23
$884,987.30
$14,793.54
$18,725.12
$16,172.63
$15,126.98
110
5/25/20
$83.13
$2,786.65
$22,150.94
$2,869.78
$2,927.24
$2,891.38
$2,875.17
111
6/25/20
$73.84
$2,718.14
$19,432.80
$2,791.98
$2,841.61
$2,810.65
$2,796.64
112
7/25/20
$64.78
$2,650.96
$16,781.84
$2,715.74
$2,757.94
$2,731.62
$2,719.70
113
8/25/20
$55.94
$2,585.07
$14,196.76
$2,641.01
$2,676.14
$2,654.24
$2,644.31
114
9/25/20
$47.32
$2,520.46
$11,676.30
$2,567.78
$2,596.21
$2,578.50
$2,570.46
115
10/25/20
$38.92
$2,457.11
$9,219.19
$2,496.03
$2,518.12
$2,504.36
$2,498.11
116
11/25/20
$30.73
$2,394.98
$6,824.21
$2,425.71
$2,441.79
$2,431.78
$2,427.23
117
12/25/20
$22.75
$2,334.07
$4,490.14
$2,356.82
$2,367.23
$2,360.75
$2,357.80
118
1/25/21
$14.97
$2,274.35
$2,215.79
$2,289.32
$2,294.37
$2,291.23
$2,289.80
119
2/25/21
$7.39
$2,215.79
$0.00
$0.00
$0.00
$0.00
$1,359,267.74
$1,223,474.93
$1,166,705.65
Payment
Number
Date
1
2
FV of Cash
FV of Cash
FV of Cash
Flow Reinvested Flow Reinvested Flow Reinvested
Why the Realized Yield Can Be Very Different Than the Promised Yield
2
Ambassad or alert • 2011 • 1st quarter
continued from page 2 …
We choose to conduct this analysis on a recently issued, 10-year 4.00% mortgage backed security. If we use Bloomberg
and run a simple yield table function, the yield to maturity is calculated at 2.65% under the current prepayment speed
assumptions. As the formula is a little more complex, we have exported the cash flows to Excel and detailed the
estimated principal and interest payments for each of the next 119 months as shown in the table on page 9. We have
detailed three scenarios demonstrating the effect of the reinvestment rate on the actual yield an investor will earn.
Under the first scenario, the reinvestment rate is equal to 2.65%, so our internal rate of return approximately equals
the stated yield to maturity of 2.65%. These yields differ by one basis point due to rounding. Under the second and
third scenarios, each interim cash flow is reinvested at 1% and 0.25%, respectively. If an investor purchased this bond
and held interim cash flows in fed funds, the actual yield earned would be 1.10% or 58% below the stated book yield!
After looking at these examples, the importance of reinvesting interim cash flows becomes very clear. With rates near
all time lows, it is understandable that investors are worried about rates going up, thus focusing their attention on interest
rate risk. But we can’t lose sight of the big picture that these two types of risk—interest rate risk and reinvestment risk—
are tradeoffs. Keep in mind next time you make an investment that there are three key components to the yield
calculation. While the reinvestment component may be the most difficult to quantify, it could cause the realized yield
to be markedly different than the anticipated promised yield. If you are building up a large amount of fed funds or cash
equivalents, it might be crucial to deploy some of this liquidity in order to achieve estimated yields. Look on the bright
side; although rates are low, the yield curve is historically steep and it might be a good time to invest.
– Joshua A. Albright
Senior Vice President, Fixed Income Trading
Why the Realized Yield Can Be Very Different Than the Promised Yield
3
A m ba s s ad o r F i n a n c i a l G ro u p, i n c .
THE AMBASSADOR TEAM:
1605 North Cedar Crest Blvd.
Suite 508
Allentown, PA 18104
toll-free 866.240.3898
Joshua A. Albright
Senior Vice President,
Fixed Income Trading
Allen Collins
Managing Director,
Chief Compliance Officer
Ryan Epler
Senior Vice President,
Fixed Income Trading
Heidi Geist
Administrative Assistant
Robert J. Pachence, Jr.
Managing Director
Eric R. Tesche
Managing Director
James R. Gillen
Managing Director,
Business Development
Michael Rasmussen
Managing Director,
Investment Banking
Mark B. Trinkle
Senior Vice President,
Fixed Income Trading
Timothy J. McDonald
Chairman
Matthew T. Resch, CFA
Managing Director
John S. Walker, Ph.D., CFA
Director of Research &
Chief Economist
The information presented is for informational purposes only. This is not an offer or solicitation to purchase or sell any security through Ambassador Financial Group, Inc.,
a current member of FINRA/SIPC. For more information contact us at 610.351.1633. © 2011 Ambassador Financial Group, Inc.