equal, U8AX will be (as will all assets above the diagonal) a less desirable asset in an MV framework when ‘risk’ is defined by Levy downside risk estimates rather than the standard deviation of total return.
We highlight the fate of municipal indices to point out the sensitivity
of asymmetric distributions to few but rather severe market dislocations. Relative to ‘normal’ market environments, the 2008 time period was very cruel, and particularly so to historically tame municipals. The cost of accounting for asymmetric and severe downside risk can be the exclusion of otherwise very desirable assets from portfolio construction.
ALLOCATION OUTCOMES We
calculated MV asset
EXPECTED NET DEFAULTS
7.00 6.00 5.00 4.00 3.00 2.00
10.5011.50 12.5013.50
50. Base Vol OAY51. Levy OAY52. DIP OAY STDEV
SHARPE RATIO allocations (holding insurance products’
leverage, mix, margins and volatility constant) using three different measures of risk: standard deviation (Base), DIP and Levy. The first graph of Chart 4 displays the resultant enterprise total return and risk efficient frontiers. We forego SNEOP because its results are identical to those of the standard deviation risk metric.
The results in the first graph of Chart 4 present the allocation outcomes
in the same resultant risk metric although DIP and Levy allocations were initially based upon minimisation of downside risk rather than the traditional MV standard deviation risk metric. The vertical difference between the traditional MV efficient frontier and both DIP and Levy outcomes is the cost of minimising extreme event downside risk. That penalty varies across the return/risk spectrum. However, it is always the greatest in the case of Levy, the metric that best captures asymmetric/extreme events.
The remaining three graphs in Chart 4 display a further look at
the consequences of using downside risk metrics rather than the traditional risk metric of standard deviation. In top-down order, we show the prior enterprise total return/risk trade-offs, the fixed income portfolio duration, the fixed income expected annualised loss given defaults and the investment portfolios’ Sharpe ratios. The differences are quite pronounced, representing the consequences of attempting to contain downside risk when focusing upon extreme asymmetric adverse outcomes.
CHART 4. AFTER-TAX ENTERPRISE TOTAL RETURN ON EQUITY AND RISK EFFICIENT FRONTIERS
TOTAL RETURN
12.0 11.0 10.0 9.0 8.0 7.0 6.0
10.5
50. Base Vol OAY51. Levy OAY52. DIP OAY 12.5
11.5 STDEV 13.5 DURATION
8.0 6.0 4.0 2.0
10.5 11.5 12.5 13.5
50. Base Vol OAY51. Levy OAY52. DIP OAY STDEV
14.5 14.5
0.8 0.6 0.4 0.2 0.0
10.5 11.5 12.5 13.5
50. Base Vol OAY51. Levy OAY52. DIP OAY STDEV
In contrast to traditional MV asset allocations, portfolios constructed
using Levy downside risk estimates show the greatest variation across all metrics. As the enterprise expected total return requirements increase, the differences among all metrics narrow and eventually disappear. Contrasting portfolios having equal standard deviations of total return, Levy portfolios most often have lower-return, shorter-duration, less expected net default losses and higher Sharpe ratios. Using alternative risk metrics yielding diverse outcomes raises the question, ‘what matters most?’.
SUMMARY We believe that the greatest deficiency of an MV framework is that it is
identical to all other models, namely, its blind adherence to their calculated results. Similar are the practitioners’ assumptions regarding return, correlations, leverage (and for that matter, ‘risk’) that the user is in ‘dealer control’.
Asymmetric downside risk haunts all asset allocation tools. Whereas
we believe the greatest value of these tools is sensitivity stress-testing, we think it is wise to begin the process using risk metrics that have the greatest likelihood of capturing extreme events. Accordingly, we prefer Levy T-VaR downside risk estimates to SNEOP and DIP estimates, both of which yield similar outcomes as conventional standard deviation risk metrics.
In the context of (enterprise-based) asset allocation, we believe it is useful
to understand the allocation consequences of capturing downside extreme event volatility to guide the discussion about return/risk trade-offs and enterprise risk tolerance. In the context of solvency margin assessment, we believe it is critical to understand the required capital consequences; for example, Solvency II, to the sensitivity of selected risk metrics.
Source for charts and tables: GR-NEAM Analytics
Disclosure: This is not an offer to conduct business in any jurisdiction in which General Re–New England Asset Management, Inc. and its subsidiaries are not registered or authorized to conduct business.
Jim Bachman is a vice president of capital management and Tobias Gummersbach is a quantitative analyst at GR–NEAM. (Please contact the authors for references.) They can be contacted at:
jbachman@grneam.com and
tgummersbach@grneam.com
September 2011 | INTELLIGENT INSURER | 45 14.5 14.50
Duration
Total return
Sharpe
Default loss $m
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