Return Attribution of a Portfolio (January to May)  
The month of May saw a significant rise in the long rate, or the yield curve has steepened a lot, as  
depicted by Figure 1. The results show that the 10 year rate has dropped 30 bpts from January to April.  
But the rate rose 50 bpts in the month of May. The 2 year has not changed significantly. Based on a  
sample portfolio, the weighted average OAS of the bonds rose in the first three months but then fell  
last month, resulting in negligible OAS change over the four months. How do these market factors  
impact our bond portfolio performance? If we expect market rates continue to rise, then how should  
we manage our portfolio? Using return attributions, we can gain some insight into answering these  
questions.  
The performance of a bond portfolio is affected by many other factors, such as the change in the level  
of yield curve, the option adjusted spreads, riding down the curve and many others. In fact, the THC  
model uses 11 components to provide traders and portfolio managers to identify the sources of total  
returns of the portfolio. Using return attribution to identify the key sources of returns, we do find  
something that gives us some insights: in recent month, with the Fed’s impact on the shape of the  
yield curve, there are several major contributors to the total return of a bond portfolio.  
We consider a fixed income portfolio that has bullet and structured agency bonds, corporate bonds,  
municipals, and MBS. A summary description of the portfolio is given below in Table 1.  
Table 1 | Portfoilo Descriptions  
Coupon Maturity Face  
Market  
Price  
YTM  
(%)  
2.94  
Yield to Spread  
OAS  
(%)  
1.13  
OAS  
WAL  
Eff.  
Dur  
5.7  
Eff.  
Conv  
-0.51  
CUSIP  
Rate(%) (year) Value  
Worst  
(%)  
1.17  
Duration (year)  
Portfolio  
Agency  
Bullet  
3.24  
15.46 76,000  
101.88  
2.88  
6.05  
8.65  
1.28  
1.96  
5.62 10,000  
10.1 10,000  
100.4  
99.22  
1.17  
1.17  
0.19  
0.23  
0.13  
-0.11  
5.32  
2.91  
5.38  
8.84  
5.32  
3.52  
0.35  
Structured  
Munis  
2.04  
2.03  
-5.45  
Tax Exempt  
Taxable  
Corporate  
Investment  
High yield  
MBS  
4.62  
3.34  
23.33 10,000 100.85  
4.38  
2.94  
4.25  
2.94  
1.73  
1.18  
1.62  
1.32  
9.24  
7.47  
16.71  
8.61  
9.98  
7.47  
0.84  
0.87  
10.58  
8,000  
102.7  
2.63  
6.08  
13.86  
9,000  
99.3  
2.61  
5.76  
2.33  
5.7  
0.46  
4.15  
0.74  
4.11  
8.28  
6.32  
10.9  
8.28  
6.46  
1.55  
9.94 10,000  
101.81  
7.96  
0.74  
Fixed MBS  
ARM  
3.28  
2.61  
24  
9,000  
105.23  
2.29  
2.23  
2.29  
2.23  
1.14  
0.53  
0.63  
4.92  
4.4  
6.02  
4.94  
4.43  
0.84  
-1.6  
25.22 10,000 105.78  
1.36  
-1.05  
The total return of the portfolio over the four months is 0.20%. Figure 2 below presents the  
contributors of returns, where the sum of all the components must equal the total return of the  
portfolio. The results show that among the 11 components, there are only three main contributors:  
yield curve flattener, OAS shift and riding down the curve. As we mention above, the yield curve has  
steepened and therefore the “flattener” component shows a loss of 0.90%. While the shift of OAS  
has not affected the portfolio performance, the OAS over time has released over 0.38% return. More  
importantly, because of the Fed’s quantitative easing program, the market yield curve has remained  
steep. For this reason, portfolio managers can accrue returns by riding down the yield curve, and that  
has contributed significantly to the portfolio performance. The riding down the curve has contributed  
0.66% returns to the 0.20% of the total return over the four month period.  
Figure 2 | Jan-May Return Attribution  
Residual  
Actual Prepayment Effect  
Vol Curve Chg  
OAS Shift  
Conv Return  
YC-Curvature shift  
YC-flattener shift  
YC-Parallel shift  
time-riding down return  
time-oas return  
time-risk free return  
total return  
-1.00%  
-0.80%  
-0.60%  
-0.40%  
-0.20%  
0.00%  
0.20%  
0.40%  
0.60%  
0.80%  
As we need to balance risk and returns, we need to analyze the risk of these components. Figure 3  
below provides us some insights. Figure 3 presents the cumulative returns of each component over  
the period of analysis. The result clearly shows that the two components (1) release of returns from  
option-adjusted spreads (OAS) and (2) riding down the curve provide steady returns of the portfolio  
while the yield curve risk poses significant total return uncertainty.  
Implications of these results are clear. As long as the Fed keeps the short term rates low, then riding  
down the curve and investing in cheap sectors or bonds (as measured by OAS) can enhance a bond  
portfolio performance. Also based on these observations, there are other strategies that a portfolio  
manager can implement. For example, exploiting mean reversion of OAS, controlling the yield curve  
risk and more.  
To construct a portfolio strategy, we need to understand the return attribution of each sector or bond  
type. For example, what is the return attribution of a step-up coupon callable agency bond, where the  
callability significantly affects the components of the total returns? Similarly, premium hybrid 3-1  
ARMs prepayment risk also affects the riding down the curve as well as yield curve risk components.  
We will analyze these issues in our following bulletins.