Performance
Comparison of The PBGC Total Fund Return
Performance to the Dynamic Benchmark
Return Performance in the Asset-Liability Context
A comparison of the PBGC Total Fund net-of-liability return performance to the net-of-liability return performance of the Dynamic Benchmark indicates that the PBGC Total Fund portfolio underperforms the Dynamic Benchmark in risk-adjusted terms on an asset-liability basis. In contrast to the results for the asset-only analysis, the PBGC Total Fund had weaker performance than the Dynamic Benchmark in that its Adjusted Sharpe ratio was lower for the overall time period (October 1976 to December 2009).24 Despite the switch in the performance rankings of the PBGC Total Fund and the Dynamic Benchmark, there are many similarities between the asset-liability performance analysis results and the asset-only performance analysis returns. The areas of similarity are as follows:
1. Under- or over-performance pattern across “decade” and asset allocation periods. The PBGC Total Fund underperformed the Dynamic Benchmark for two out of the four decade subperiods and two out of the four asset allocation regimes on a risk-adjusted,
24One factor that complicates the analyses in this section and the interpretation of the traditional Sharpe ratio is that all of the portfolios exhibit negative mean excess returns and hence negative Sharpe ratios for the overall time period and many subperiods. As mentioned in the performance statistics section, this renders the interpretation of the Sharpe ratio unclear. Thus, in executing portfolio performance comparison on a net-of-liability returns basis, greater emphasis is placed on the Adjusted Sharpe ratio, which is specifically designed to address this problem and provide logically consistent ranks to portfolios in a fashion that appropriately reflects the impact of risk aversion on portfolio choice and asset allocation decisions.
liability return basis, according to the Adjusted Sharpe ratio statistic values.
2. Lack of materiality of investment expenses. Deducting investment expenses from the PBGC Total Fund returns in the asset-liability context did not affect the performance ranking of the PBGC Total Fund relative to the Dynamic Benchmark on an Adjusted Sharpe ratio basis (in those periods for which investment expenses data were available).
3. Tendency to perform relatively worse in regimes where equity asset allocation is greater or rising. The PBGC Total Fund’s relative
performance has tended to be worse in asset allocations periods where there is an elevated or rising allocation to the equity asset class. For example, as in the asset-only analysis, the PBGC Total Fund returns, net of the liability returns, had an Adjusted Sharpe ratio below that of the Dynamic Benchmark in allocation period 1 (which was
characterized by a rising allocations to the equity sector). Also, as in the asset-only case, the PBGC Total Fund underperformed the Dynamic Benchmark on a net of liability return basis in allocation period 3, according to the Adjusted Sharpe ratio scores. In allocation period 4, when the average allocation to equities in the PBGC Total Fund portfolio was lower than in allocation regime 3, the PBGC Total Fund had a higher Adjusted Sharpe ratio than the Dynamic Benchmark did. However, unlike the asset-only case, the PBGC Total Fund
Adjusted Sharpe ratio was less than that of the Dynamic Benchmark in allocation period 2, when the PBGC Total Fund allocation to equities was falling and to bonds was rising. The similarity of the seemingly inverse relation between the PBGC Total Fund Adjusted Sharpe ratio value and the magnitude of the allocation to the equities asset class reinforces the impression that elevated allocations of the PBGC Total Fund to the equity asset class had adverse impact on PBGC Total Fund returns net of the liability returns in an asset-liability context as well as when the portfolio returns are considered in isolation from the liability returns in an asset-only context. However the patterns in the equity asset allocation and its relationship to performance should not be viewed as implying causality.25
4. Mean excess return prominence as a driver of risk-adjusted
performance metric values across subperiods. In every sub-period and
25For example, this finding should not be interpreted as equity causing the underperformance.
asset allocation regime where the excess mean return (net of the liability return) for the PBGC Total Fund exceeded the excess mean return (net of the liability return) for the Dynamic Benchmark
portfolio, the Adjusted Sharpe ratio for the PBGC Total Fund exceeded the Adjusted Sharpe ratio for the Dynamic Benchmark.
Given all of the similarities between the results of the performance comparisons in the asset-liability and asset-only contexts, the reason for the contrast between the PBGC Total Fund’s underperformance of the Dynamic Benchmark in the asset-liability context and its outperformance in the asset-only context appears to be risk. In the asset-only performance comparison analysis, the PBGC Total Fund’s riskiness—as measured by the standard deviation and semi-standard deviation of the returns—-was lower than that of the Dynamic Benchmark portfolio. However, in the asset-liability context, the results indicate that the PBGC Total Fund returns have greater standard deviation and semi-standard deviation values than the returns for the Dynamic Benchmark, suggesting that the PBGC Total Fund returns (net of the liability returns) are riskier and more volatile than the Dynamic Benchmark returns (net of the liability returns).
One factor that likely played a role in elevating the PBGC Total Fund’s riskiness above that of the Dynamic Benchmark is the correlation of the actual asset returns with the liability returns (not the correlation between the liability returns and the asset returns net of the liability returns). For the overall sample period, the PBGC Total Fund actual returns had lower correlation with the liability returns —both scaled by the funding ratio and unscaled—than the Dynamic Benchmark. Higher correlation makes it more likely that movements in the liability return are accompanied by movements in the asset portfolio return in the same direction and of similar magnitude. Such co-movement of the actual asset returns and the liability returns helps reduce the volatility of the asset returns net of the liability returns.
Lower correlation has the opposite effect of higher correlation—lower correlation reduces co-movement between asset returns and liability returns and thus elevates the riskiness of asset returns net of the liability returns. Thus, the extent to which the riskiness of the PBGC Total Fund exceeds the riskiness of the Dynamic Benchmark on a net-of-liability return basis probably reflects, at least in part, the extent to which the liability returns are less correlated with the PBGC Total Fund’s actual returns than with the Dynamic Benchmark actual returns. However, the question of why the PBGC Total Fund would be less correlated with liability returns than the Dynamic Benchmark would require a more detailed investigation.