Carino Smoothing for Multiperiod Performance Attribution
Summary
The document presents a portfolio attribution problem across four periods. It gives sector returns and weights for a portfolio and benchmark, then reports their compounded returns and active return. The author calculates Carino linking coefficients and applies period coefficients to single-period asset allocation, security selection, and interaction effects, but the resulting total appears much smaller than the reported active return.
The central learning point is the reconciliation problem: linked attribution effects should explain cumulative active performance, so a mismatch suggests an error in the calculations or in how the method is applied. However, the document contains no answer or correction, only the example and the request for help. It therefore does not establish which coefficient, return convention, or attribution step is wrong. The figures are an illustrative case, not evidence that Carino smoothing itself fails or that a particular implementation is correct.
Key ideas
- The example compares portfolio and benchmark returns and weights over four periods.
- The author applies Carino coefficients to period attribution effects and gets a cumulative result that does not reconcile to active return.
- A valid multiperiod attribution should reconcile its linked effects to cumulative active performance.
- The document poses the discrepancy but does not provide a diagnosis or worked solution.
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# Portfolio Performance Attribution Using Carino Smoothing
# Portfolio Performance Attribution Using Carino Smoothing
I'm trying to conduct portfolio performance attribution using Carino smoothing, but it seems that the active returns do not match and I don't know why. Here is the example I use:
\begin{array} {|r|r|r|r|r|r|r|r|r|r|} \hline portfolio &R_{t1} &R_{t2}&R_{t3}&R_{t4}&w_{t1}&w_{t2}&w_{t3}&w_{t4}\\ \hline sector1 &-0.06& 0.04& 0.04& 0.04 &0.30& 0.40& 0.20 &0.20\\ \hline sector2 &0.02 & -0.12 &-0.02 &0.06 & 0.10 & 0.40 &0.10 & 0.20 \\ \hline sector3 &-0.12 &0.04 & 0.21 & 0.06 & 0.60 &0.20 & 0.70 & 0.60 \\ \hline \end{array}
\begin{array} {|r|r|r|r|r|r|r|r|r|r|} \hline benchmark &R_{t1} &R_{t2}&R_{t3}&R_{t4}&w_{t1}&w_{t2}&w_{t3}&w_{t4}\\ \hline sector1 &0.00 & 0.03 & -0.06 &0.08 &0.10 & 0.10 &0.30 &0.40 \\ \hline sector2 &0.04 & 0.00 & -0.04& 0.06 & 0.20 & 0.40 & 0.20 & 0.20 \\ \hline sector3 &0.14 &0.00 & -0.10& 0.00 & 0.70 &0.50 &0.50 & 0.40 \\ \hline \end{array}
So I calculate the portfolio return 15.06% and benchmark return 10.84%, and thus the active return is 4.21%. Then, by using Carino smoothing, I get those coefficients: $k = 0.8854, k_1 = 0.9996, k_2 = 1.0054, k_3 = 1.0004, k_4 = 0.8696 $. I also calculate the asset allocation, security selection and interaction term for single period and use those coefficients to adjust them. For example: $$Asset Allocation_{t, adjusted} = Asset Allocation_t * k_t / k$$
After the adjustment, I sum up all those effects for 4 periods and find that the portfolio return minus the benchmark return becomes nearly 2% (I'm quite confused about this). I would expect the active return should be the same as the previous one, but it's far less than 4.21%. I guess there are some problems with how to use adjusted returns. Could someone explain how to use Carino attribution when I want to calculate the asset allocation, security selection, interaction for multiperiod for this example?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.