Stuart Schulman
April 18, 2016
Mr. Vincent M. De Sio
Chief Financial Officer
YMCA Retirement Fund
140 Broadway
New York, NY 10005-1197
Principal, Consulting Actuary
Buck Consultants, LLC.
485 Lexington Avenue
10th Floor
New York, NY 10017-2630
[email protected]
tel 212.330.1297
fax 212.330.1085
Dear Mr. De Sio:
We are writing to present our analysis of whether the interest rate used for the YMCA
Retirement Fund actuarial valuations is supported by the expected long-term return on assets of
the Fund.
The composite valuation interest rate, which is approximately 5.90%, is used to discount future
expected benefit payments to the current date, in order to determine the Fund’s liability for
various purposes. A composite interest rate that is unreasonably high would discount the
projected benefits too much and produce unreasonably low liability values. A pension plan that
can maintain an investment return that is at least equal to the valuation interest rate on a
compounded basis would have sufficient assets to meet its pension obligations. We therefore
need to assess whether the Fund can earn the compound (geometric) return implied by the
composite valuation interest rate.
Data on the Fund’s current asset allocation and the Target Investment Policy asset allocations
were provided to us on March 28, 2016. A summary of the Fund’s Current and Target asset
allocations used for the modeling is included in Appendix A. Based on our analysis of the
Fund’s investment policy and current allocation, we conclude that the Fund can be
expected to earn in excess of 5.9% in the long term and a rate in that range is fully
supported.
The average geometric returns presented in the table below were generated using data from the
GEMS Economic Scenario Generator licensed from Conning and Company. GEMS uses a
multifactor model to create internally consistent, realistic economic scenarios (paths) that reflect
the current economic environment as a starting point. Asset class correlations may vary from
year to year (just as in the real world), as well as from path to path. The model generates
results that are not normally distributed, with fatter tails, and should therefore estimate the
possibility of rare events (such as the market turmoil of 2008–2009) more realistically than a
mean-variance model. It is also important to note that inflation is an output from this model,
rather than an input to it. Additional information on the GEMS model is provided in Appendix B.
On each path, over a specified time horizon, annual investment returns for each asset class
were computed, using an appropriate benchmark for that asset class where required. Based on
the asset allocation percentages, a benchmark portfolio return was computed. The expected
investment management and other fees, estimated at 0.74% per annum, were subtracted from
the return each year on each path. In this way approximately 1,000 geometric returns were
generated over each time horizon, and this range of forecast results forms the basis of the
expected return analysis.
The results of the simulation at various time horizons are summarized in the following table:
Forecast
Period
5 Years
10 Years
15 Years
20 Years
Current Asset Allocation
Expected
Standard
Geometric Return*
Deviation
6.45%
10.61%
7.11%
11.21%
7.61%
11.46%
7.90%
11.52%
Target Policy Allocation
Expected
Standard
Geometric Return*
Deviation
6.63%
10.70%
7.28%
11.31%
7.78%
11.56%
8.06%
11.63%
* After subtracting 0.74% for investment and other expenses. No alpha has been added
to forecast benchmark returns.
Please note that:

The expected geometric returns over a 20-year period are well in excess of 5.90%
based on both the current asset allocation and the target policy allocation. Note
that the YMCA Retirement Fund is expected to be an ongoing fund with a long
investment horizon. Therefore, selecting a valuation interest rate based on expectations
over a longer period—20 years or even longer—is reasonable in our view.

You will notice that the Expected return on Assets over all time horizons has increased
compared to the results presented to you in 2013. This is due to changing asset class
return assumptions and updated allocations, slightly offset by a higher expense
assumption.
o At the 20-year horizon and assuming a 0.70% expense reduction, the 2013
actual allocation with current assumptions would result in a geometric return of
7.70%, compared to the 2013 result of 7.13%.

The GEMS model begins as of December 31, 2015, reflecting the state of the global
economy as of that time, including the low interest rate environment. Therefore initial
return expectations are low relative to historic norms. As the model projects results over
the next 20+ years, while each path will have unique results that may vary from the
norm, the central tendency is for the model to forecast that asset returns, interest rates,
standard deviations and so forth will revert to the norms of the last 60+ years.

The Standard Deviations shown reflect annual volatility.

The model assumes rebalancing annually.

No consideration has been given to the nature of the liabilities, since the promise to pay
a benefit is independent of how the monies to cover that promise are invested.
However, it must be acknowledged that any actuarial forecast includes some uncertainty
regarding the size and timing of expected benefit outflows. In addition, model error,
including future events not contemplated within the model, must be considered.
Therefore, a modest degree of conservatism is appropriate when selecting the valuation
interest rate. However, even allowing for a margin for conservatism for these factors,
the expected geometric return remains well in excess of 5.9%.
Based on the analysis, we are of the opinion that the Fund can on average expect to earn in
excess of 5.9%, and therefore the interest rate used for the Fund’s valuation is supported.
The undersigned is a Fellow of the Society of Actuaries, a Member of the American Academy of
Actuaries, an Enrolled Actuary and a CFA Charterholder, and is qualified to sign this Statement
of Actuarial Opinion. I am available to answer any questions on this matter.
Sincerely,
Stuart M. Schulman, FSA, CFA, FCA, EA, MAAA
Principal and Consulting Actuary
Retirement Risk Management Consultant
Cc:
James A. Stewart
Aaron Shapiro
Appendix A
Asset Allocation Information for YMCA Retirement Fund
Asset Class
Large Cap Equity
Small Cap Equity
International Developed Equity
Emerging Market Equity
Hedge Funds
Private Equity
Direct Real Estate
Commodities
Fixed Income
Cash
* As of March 23, 2016
Target Policy
Allocation
22.0%
6.0%
12.0%
8.0%
14.0%
8.0%
5.5%
5.0%
17.0%
2.5%
Current Asset
Allocation*
22.2%
4.4%
12.3%
6.7%
16.8%
8.8%
4.2%
3.7%
17.0%
4.0%
Appendix B
GEMS Overview
Development of Expected Asset Return Forecasts
Overview of Process

Beginning October 2009, Buck entered into an agreement to lease the GEMS Economic Scenario
Generator. This is a multifactor model developed by Conning and Company that is based on historic
returns, but forecasts future asset class returns based on multiple factors such as simulated GDP
growth, employment levels, interest rates, etc.

The modeling approach is somewhat different than most processes that use historic data. Historic
methods generally assume that asset returns are normally distributed with distribution of future results
driven by mean, standard deviation, and correlation parameters that do not change over time.
®
o

Buck generates projected asset returns based on scenarios created with GEMS. The model
simulates approximately 1,000 paths and results, which are collected and percentiles computed.
Returns on various asset classes are computed in a manner consistent with forecast economic
environments.
o

A feature of GEMS is that expected returns and correlations change over time and are
different on each path, consistent with forecast economic conditions on that path.
Sample statistics are computed from the model output, for reporting purposes, and can include the
following:
o
o
o
o

In contrast, GEMS does not assume normal distribution. Shape of future portfolio returns,
inflation, and interest rates is an output from the model, rather than an input as with the
historic returns model.
Expected short- and long-term returns
Expected inflation
Average standard deviation
Average correlations among asset classes
Real returns are equal to the Nominal returns less Inflation.
Additional Considerations

ASC 715 suggests that the Expected Long-term Rate of Return on assets reflect “the average rate of
earnings expected on the funds invested or to be invested to provide for the benefits included in the
projected benefit obligation.”

GEMS models asset benchmarks such as the Russell 1000. To the extent that active management
adds any value (alpha) above the benchmark return or management fees reduce total return, there is
latitude for selecting an Expected Rate of Return that does not precisely match the mean observed
from this model.
Summary of Outputs from Model

Expected asset returns for portfolio:
o
o
o
o

For various time horizons (for example 1, 10, 20 years)
At various percentiles (for example, 5%, 95%, the quartiles and median)
Sample mean returns
Sample standard deviations
Returns on a real and nominal basis:
o
o
Nominal return is the output from the model
Real return is the nominal return minus the assumed annual inflation
Estimates of Inflation—Output from GEMS Model
o
The GEMS Model produces inflation forecasts as an output of the model. Mean inflation observed
from the GEMS model is as follows.
Averaging Period
Expected (Mean) Inflation
5-year average
2.21%
10-year average
2.46%
15-year average
2.69%
20-year average
2.84%
25-year average
2.97%
Additional Detail on Process

GEMS captures the real-life fact that means, volatilities, and correlations are determined dynamically
and can change over time.
o
o
o

This means that expected returns over, say, a 10-year horizon may not equal those over a
20-year horizon.
Based on the Monte Carlo analysis, we derive sample means, sample standard deviations,
and sample correlations for reporting purposes.
GEMS can model the economies of the USA, Canada, Germany (Eurozone), UK, and
Switzerland in an internally consistent manner.
We can therefore capture forecast currency effects and interest disparities between and among the
US Dollar, Canadian Dollar, Euro, Pound, and Swiss Franc.
Additional Details on GEMS model
Cash

Cash is modeled as an investment in short term government paper paying a nominal or inflation
linked rate.
Treasuries

GEMS uses a three factor model of interest rates to model treasuries.
Corporate Bond Model

In the Conning Bond Model, individual bonds are modeled and zero coupon corporate yields are
generated by adding the credit spreads to the corresponding zero coupon treasury yield. The credit
spread is driven by a default intensity process, which also determines each bond’s rating. The
evolution of the default intensity determines the migration, if any, of a bond’s rating from one class to
another.

Bond indices are created based on characteristics of bonds currently representing the index in
question.

Throughout a given scenario, bonds that mature or default are replaced by bonds with characteristics
expected to prevail at that time.
Equity Indices

All equity return series are generated using stochastic volatility with jumps (SVJ). This means
that unlike a standard mean-variance model, the simulation incorporates the possibility of large
swings in values that would not be anticipated taking values from a standard normal (Gaussian)
distribution.

The equity models generate extreme behavior (fat tails) via the specification of an independent
stochastic jump (SVJ) process. The features of the returns generated by the model include
volatility clustering, low frequency/high severity jumps, and jump clustering behaviors, all of which
are observed in actual markets.
o

It has been Buck’s observation that results at the 5th and 95th percentiles are similar to a
pure mean-variance model, but there is more kurtosis, meaning that results tend to cluster
both toward the mean and toward in the extreme tails (1st and 99th percentiles and beyond)
than would a plain mean-variance model.
GEMS includes the major equity indices for all the economies it models. In addition, Buck has
created, with guidance from Conning, our own user-specified models of equity sectors and alternative
investment classes (e.g., hedge funds) using the GEMS Market Indices facility.