The data sample in this study covers the January 1990 to December 2009 period and includes monthly returns on various asset classes including US equity, international equity, fixed income, real estate and alternative assets. We use the Russell 3000, MSCI EAFE, Barclays Capital US Aggregate Bond, FTSE NAREIT Equity Only and HFRI Fund Weighted Composite Index as proxies for US equity, international equity, fixed income, real estate and alternative assets, respectively. Table 1 shows the summary statistics of the asset class returns during the sample period and Table 2 shows the asset allocation weights used by the typical US DB plan.
We investigate the risk-return trade-offs implicit in the tactical band size decision by using the stationary bootstrap methodology proposed by Politis and Romano (1994). The stationary bootstrap procedure involves resampling a time series in data blocks of random length, where the block length follows a geometric distribution. The resulting resampled time series is stationary and the serial correlation structure of the observations within each block of the original time series is preserved. The stationary bootstrap procedure has been used in a variety of studies in finance (see for example Norsworthy et al, 2001; Balcombe and Tiffin, 2002; Koopman et al, 2005; Boyson, 2008; Ledoit and Wolf, 2008; Cao, 2009; James and Yang, 2010; and Nomikos and Pouliasis, 2011).
In our base case, we use the typical allocation of a US DB plan (2008 Pyramis Defined Benefit Research Round, 2008) as the starting strategic asset mix (that is, policy mix) consisting of 45 per cent US equity, 16 per cent non-US equity, 28 per cent fixed income, 5 per cent real estate and 6 per cent alternatives/other. Our first rule set is as follows: (i) a +/−5 per cent bandwidth for each asset class is established, (ii) when any asset class exceeds its band, the entire portfolio is rebalanced to policy weights, (iii) allocations are monitored on a monthly basis but a rebalancing is only implemented during a month when asset weights move outside the established bandwidth. Using the stationary bootstrap methodology proposed by Politis and Romano (1994), we generate monthly return series for each asset class resampled from our sample data covering the January 1990 to December 2009 period. Then, we apply our rule set to the portfolio of asset classes using the resampled return series for each asset class.
For each resulting portfolio, we calculate the arithmetic average return, standard deviation of the returns, correlation of the returns with the benchmark portfolio returns, information ratio and two different measures of tracking error. We define the information ratio as follows:
is return for portfolio i in month t, r
is return for the benchmark portfolio in month t, is the standard deviation of the differences in portfolio i returns and benchmark portfolio returns, and T is the number of months in the sample period.
We calculate TE1 and TE2 using the following equations:
where is the standard deviation of returns for portfolio i and ρ
is the correlation of returns of portfolio i and the benchmark portfolio.
We repeat this procedure by generating a set of 5000 resampled return series for each band size between 1 and 5 per cent enabling us to calculate distributions for each portfolio metric. The benchmark used for performance analysis is the portfolio rebalanced to policy weights in every period.
Table 3 shows the summary statistics of selected portfolio metrics across simulation runs. Correlation of the portfolio with the benchmark is very high for band sizes of 1–5 per cent. The mean value of the portfolio correlation is 99.9 per cent for each band size as shown in Panel B of Table 3. Similarly, these portfolios generate very low tracking error within the band size range of 1–5 per cent, as shown in Table 3. The value of the information ratio of the portfolio ranges between −0.41 and 0.93 across the simulation runs.
Figure 1 illustrates an interesting finding. As the band size increases from 1 to 5 per cent, the mean information ratio across simulation runs increases and peaks at around 0.45 at the 2 per cent band size before declining to around 0.35 at the 5 per cent band size. Figure 2 shows that the mean value of the tracking error across simulation runs increases from around 26 basis points (bps) at the 1 per cent band size to around 13 bps at the 5 per cent band size. When DB plan sponsors experiment with delegating greater authority to their managers to shift among asset classes, it may make sense to start with a 2 per cent band. The strength of the information ratio at the 2 per cent level should be attractive to plan sponsors who tend to allow small adjustments, rather than big shifts, in asset class allocations. Providing investment managers with this limited flexibility in asset allocation may seem conservative, but may still allow DB plans the potential to weather down markets better. For plan sponsors who are considering larger shifts, the simulation suggests they should be cautious. The average increase in returns may be offset by greater risk above the 2 per cent band size.
As some plan sponsors may provide their managers with additional flexibility to deviate from their policy weights based on their skill level, it is important to investigate the impact of manager’s skill on a plan’s portfolio performance. We use a perfect foresight assumption and the following rule set to calculate performance metrics across simulation runs: (i) a +/−5 per cent bandwidth for each asset class is established, (ii) each month the asset classes are ranked by next month’s return, (iii) the best performing asset class is over-weighted by underweighting the worst performing asset class, (iv) the trade amount is the maximum weight that can be traded between the best and worst asset class without exceeding either bandwidth.
Table 4 presents the summary statistics of selected portfolio metrics across simulation runs under the perfect foresight assumption. It shows that tracking error is very low within the band size range of 1–5 per cent. As expected, the mean of the information ratio increases as the band size increases. Figure 3 shows that as the band size increases from 1 to 5 per cent, the mean information ratio across simulation runs increases from around 3.2 at the 1 per cent band size to around 4.3 at the 5 per cent band size. Figure 4 indicates that, under the perfect foresight assumption, the mean value of the tracking error across simulation runs increases from around 8 bps at the 1 per cent band size to around 38 bps at the 5 per cent band size.
Portfolio managers may demonstrate their skill through successful uses of strategies such as momentum investing. To examine portfolio performance for a manager using a momentum strategy we use the following rule set: (i) a +/−5 per cent bandwidth for each asset class is established, (ii) the previous 36 months are used to calculate the total return from each asset class, (iii) each month the two asset classes with the highest return receive the maximum weight while the two asset classes with the lowest return receive the minimum weight, (iv) the remaining asset class receives a neutral weight.
Table 5, which includes the selected portfolio metrics across simulation runs for a momentum scenario, shows that the portfolio has high correlation with its benchmark and its tracking error is low within the band size range of 1-5 per cent. The mean information ratio for the simulated portfolios is positive and shows slightly increasing values across the band size spectrum. Figure 5 demonstrates this graphically. Figure 6 indicates that the mean value of the tracking error across simulated momentum portfolios increases from around 7 bps at the 1 per cent band size to around 35 bps at the 5 per cent band size.