Newly issued hybrid ARMS are frequently quoted in the secondary market using a Z-spread to Treasuries and a 15 percent "CPB". This method assumes a 15% CPR until the roll date and a balloon repayment of outstanding principal on the roll date. This pricing method fails to price the cap, floor and prepayment options inherent in hybrid ARMs and masks their true return and risk characteristics. The following analysis provides a better perspective on hybrid ARM relative value and risk using OAS analysis that captures the essence of hybrid ARM options. In this analysis, we focus on the value of the "tail" - the principal balance remaining of the ARM at the first reset date. It is well known that this value comes from an "excess margin" embedded in the ARM; we show, however, that the tail values can be considerably limited by reset caps.
Table 1 below details the indicative data related to the FN/FH hybrid ARMs analyzed.
Table 1: Indicative Hybrid ARM Data
ARM Index Cap Structure
Table 2 details the OAS-based results calculated using the Andrew Davidson & Co., Inc. prepayment model. The results compare price, OAS, effective duration and convexity of the hybrids using the ballooned pay-off and the alternate assumption, whereby hybrid cash flows run out to maturity. The market rates, volatilities and price quotes used in the comparison were as of the close on 11/20/2003.
Table 2: Tail's Value Added
|
ARM
Type
|
Price Balloon
|
Price
Maturity*
|
Chg
|
OAS
Bal
|
OAS
MAt**
|
Chg
|
Dur
Bal
|
Dur
Mat
|
Chg
|
Cvx
Bal
|
CVx
Mat
|
Chg
|
|
3/1
YR
|
101.38
|
101.15
|
(0.23)
|
104
|
95
|
(8)
|
1.99
|
2.31
|
0.31
|
-0.21
|
-0.33
|
(0.13)
|
|
5/6
MO
|
101.00
|
101.23
|
0.23
|
65
|
74
|
9
|
2.14
|
2.17
|
0.03
|
-0.70
|
-0.76
|
(0.06)
|
|
5/1
YR
|
100.03
|
99.93
|
(0.10)
|
74
|
70
|
(4)
|
2.39
|
2.61
|
0.21
|
-0.26
|
-0.36
|
(0.10)
|
|
5/1
YR
|
102.56
|
102.83
|
0.26
|
55
|
64
|
9
|
1.95
|
1.98
|
0.03
|
-1.02
|
-1.10
|
(0.08)
|
|
5/1
YR
|
102.06
|
102.43
|
0.37
|
66
|
78
|
12
|
2.20
|
2.24
|
0.05
|
-0.84
|
-0.94
|
(0.10)
|
|
5/1
YR
|
102.25
|
102.39
|
0.14
|
63
|
70
|
6
|
1.36
|
1.46
|
0.10
|
-0.58
|
-0.69
|
(0.11)
|
|
5/1
YR
|
101.31
|
101.31
|
(0.00)
|
65
|
65
|
(0)
|
2.15
|
2.28
|
0.13
|
-0.64
|
-0.73
|
(0.09)
|
|
7/1
YR
|
100.75
|
100.95
|
0.20
|
33
|
38
|
5
|
3.18
|
3.26
|
0.08
|
-0.69
|
-0.79
|
(0.10)
|
| *Same-OAS valuation **Same-Price valuation | ||||||||||||
The OAS ranges from 38 to 95 for the ARMs analyzed, while the effective duration ranges from 1.46 to 3.28 when the balloon prepayment assumption is relaxed. The analysis shows that the 3/1 hybrid ARM offers the highest OAS whereas the 7/1 hybrid ARM is traded more inline with fixed-rate agency MBS.
The price differences
in the table reflect the amount by which the tail contributes to the value
of the hybrid. We see that the tail value changes the ARM price by marginal
amounts within the range of -0.23 to +0.37 points in the current environment.
Similar changes in OAS indicate the annual earnings differences attributable
to the tail range between -8 to +12 basis points in the current environment.
Not surprisingly, the effective duration and negative convexity of the hybrids
extend modestly when cash flows extend to maturity and are not truncated by
the balloon payment.
It is not hard to figure the dark forces that cause sub-par tail values with few ARMs in the analysis: the reset caps. Table 3 decomposes the change in the ARM price attributable to the caps and floors inherent in the tail ARM under two rate scenarios, the base case and the up 200 bps. First, we show the total tail's value. Then we remove the 1st collar and measure the incremental result. Finally, we free the tail from all other collars.
The 1st collar is seen to be considerably binding, especially for the + 200 bps scenario. For the exception of the 5/2/5 and 5/1/6 cap structures where it is totally or mainly absorbed by the life cap, the 1st collar generally accounts for more than a half of the total value of all collars.
Table 3: Tail's Contribution with Decomposed Cap Structure
|
ARM
Type
|
Cap Structure
|
Tail
with Full Cap Structure
|
Value of 1st Collar | Value of All Collars | |||
|
Base
|
+200
Bps
|
Base
|
+200
Bps
|
Base
|
+200Bps
|
||
|
3/1
YR
|
2/2/6
|
(0.23)
|
(1.05)
|
0.71
|
1.25
|
0.87
|
1.74
|
|
5/6
MO
|
5/1/6
|
0.23
|
0.07
|
0.02
|
1.04
|
0.14
|
0.14
|
|
5/1
YR
|
2/2/5
|
(0.10)
|
(0.66)
|
0.39
|
0.54
|
0.74
|
1.35
|
|
5/1
YR
|
5/2/5
|
0.26
|
0.09
|
0.00
|
0.00
|
0.16
|
0.47
|
|
5/1
YR
|
5/2/5
|
0.37
|
0.11
|
0.00
|
0.00
|
0.23
|
0.60
|
|
5/1
YR
|
2/2/5
|
0.14
|
(0.26)
|
0.19
|
0.44
|
0.34
|
0.93
|
|
5/1
YR
|
2/2/6
|
0.00
|
(0.41)
|
0.29
|
0.55
|
0.40
|
0.89
|
|
7/1
YR
|
5/2/5
|
0.20
|
(0.09)
|
0.00
|
0.00
|
0.25
|
0.63
|
Table 4 shows the forward value of the tail seen today for the reset date under various treatments of caps. These forward prices were estimated from the incremental present values shown in Tables 2, 3 and taking both the forward pool factor and the discount factor into consideration. For example, the 99.61 forward price for the 3/1 HARM retaining full cap structure was produced using a 0.23 point present value loss due to the tail, 14.3 ballooned-life CPR (coming from the dynamic AD&Co. prepay model) that results in a 0.65 pool factor 36 months forward, and a 0.90 discount factor, for the same period (0.23/0.65/0.9 = 0.39 of forward price discount). The value in the last column shows the value of the tail assuming no caps or floors and also assuming immediate reset to today's yield curve.
Table 4. Forward Values of theTail
|
ARM
Type
|
Full
Cap Structure
|
1st Collar Gone | No Collars | No Collars- Immediate Reset to the 11/20/93 steep yeild curve | ||||
|
Base
|
+200
Bps
|
Base
|
+200
Bps
|
Base
|
+200
Bps
|
Base
|
+200Bps
|
|
|
3/1
YR
|
99.61
|
98.15
|
100.83
|
100.35
|
101.09
|
101.22
|
101.51
|
101.42
|
|
5/6
MO
|
100.68
|
100.20
|
100.72
|
100.30
|
101.09
|
101.37
|
101.67
|
101.57
|
|
5/1
YR
|
99.73
|
98.15
|
100.76
|
99.67
|
101.64
|
101.93
|
102.02
|
101.88
|
|
5/1
YR
|
100.76
|
100.25
|
100.76
|
100.25
|
101.23
|
101.54
|
102.27
|
102.18
|
|
5/1
YR
|
100.97
|
100.30
|
100.97
|
100.30
|
101.59
|
101.97
|
102.38
|
102.28
|
|
5/1
YR
|
100.51
|
99.20
|
101.24
|
100.54
|
101.79
|
102.04
|
101.85
|
101.76
|
|
5/1
YR
|
100.00
|
98.83
|
100.78
|
100.40
|
101.09
|
101.34
|
101.83
|
101.72
|
|
7/1
YR
|
100.56
|
99.76
|
100.56
|
99.76
|
101.26
|
101.51
|
103.73
|
103.51
|
In particular, we see that the uncapped forward tails would be priced in a relatively steady 101-102 range for all the hybrids in the analysis. For example, for the 3/1 YR hybrid the dollar price at the reset, currently, is 99.61 with the cap structure intact. This price would rise to 100.83 with the first collar removed, and to 101.09 with no caps or floors.
The tail's premium comes from the "excess margin", an IO component conventionally embedded in every ARM. The size of this margin, the prepay speeds (after reset) and discount rates are key contributors to valuation. The value for an IO is higher with lower discount rates and lower prepayment speeds, and this explains the difference between uncapped tail valuation for the actual (i.e. forward) and an immediate reset.
We conclude that, as a rule, the hybrid ARM's tails carry values above par, which is limited by reset caps; some tails may have sub-par values due to the caps. The tail's contribution may change with both rate levels and the curve's shape.
