Long Term Capital Market Assumptions Methodology Executive summary This paper offers a review of our framework for deriving return, volatility and correlation expectations for sovereign and corporate bonds, equities, alternative investments (hedge funds, private equity, commodities and real estate), and foreign exchange. QMS Advisors’ strategic asset allocation process involves 33 markets across seven asset classes for which our team provides long-term total return forecasts, volatility and correlation estimates. Our approach consists in obtaining a set of model-derived expectations, and to further refine our forecasts with numerous qualitative inputs; a process that relies on the contributions of a range of industry experts including economists, portfolio managers, and product specialists. Our rigorous quantitative and qualitative review processes ensure that our assumptions are based on sound economic and financial rationales. We further strive to utilize both comparable methodologies and common return drivers across assets to achieve consistency across our expectations (i.e. universal underlying macroeconomic assumptions):  Consistency with economic theory and practice: a wide array of economic and market factors are combined in order to derive robust return expectations for each asset class.  Consistency across business cycles: Macroeconomic factors are chosen for their ability to explain returns over multiple economic cycles.  Consistency across asset classes: Expected returns reflect a congruent pricing of risk, measured by the exposure of each asset class to economic and financial factors.  Capture dynamic market features: Interaction between economic and financial signals and the variations in asset classes’ potential returns and risks over time. We implicitly assume that -as suggested by empirical evidence- most of the key variables used in our models will converge over the long-run. Therefore bond yields, GDP and dividend growth are expected to converge over longer periods. For most asset classes we use clearly specified multi-linear regression models to forecast returns, while relying on traditional models in the cases of equities and foreign exchange (Dividend Discount Model and Fair Value Model, respectively). The object of this exercise is to arrive at five-year return and volatility forecasts for each of the assets, which are then used as inputs for the final optimization process. To an extent, forecasting returns for a five-year period is less error-prone than for a much shorter period and also lends itself to a greater reliance on longer-term fundamentals as drivers of future performance. It also implies that incorporating a mean-reverting element into the return forecasts is far less controversial than it would be over a shorter time horizon. Additionally, it is worth mentioning that all our models are supported by cross-checking procedures that aim to rationalize the initial forecast outputs. To a certain extent, return forecasts should have relatively little impact on forecasts of volatility and covariance. Risk, or volatility, is more a measure of the uncertainty of the return, rather than the forecast of the return. In the shorter term, underlying risk and covariance should be more stable than expected returns. With regard to volatility forecasts, we compute both historical volatilities and Ornstein-Uhlenbeck estimates for all assets, correcting for auto-correlation where necessary as suggested in econometric literature. Historical volatilities are taken as the best proxy for five-year average volatility forecasts for all alternative investments and equity indices. We employ the Ornstein-Uhlenbeck process to reflect the mean reversion process in volatility over time. We have found this process to produce more realistic out-of-sample forecasting results when compared to other volatility models such as variants of Arch or Garch-models. We use Ornstein-Uhlenbeck volatilit

1. QMS
. .
Advisors
Long Term Capital Market Assumptions
Methodology
Executive summary
This paper offers a review of our framework for deriving return, volatility and
correlation expectations for sovereign and corporate bonds, equities, alternative
investments (hedge funds, private equity, commodities and real estate), and foreign
exchange.
QMS Advisors’ strategic asset allocation process involves 33 markets across seven
asset classes for which our team provides long-term total return forecasts, volatility
and correlation estimates. Our approach consists in obtaining a set of model-derived
expectations, and to further refine our forecasts with numerous qualitative inputs; a
process that relies on the contributions of a range of industry experts including
economists, portfolio managers, and product specialists.
Our rigorous quantitative and qualitative review processes ensure that our
assumptions are based on sound economic and financial rationales. We further
strive to utilize both comparable methodologies and common return drivers across
assets to achieve consistency across our expectations (i.e. universal underlying
macroeconomic assumptions):
Ø Consistency with economic theory and practice: a wide array of economic and
market factors are combined in order to derive robust return expectations for
each asset class.
Ø Consistency across business cycles: Macroeconomic factors are chosen for
their ability to explain returns over multiple economic cycles.
Ø Consistency across asset classes: Expected returns reflect a congruent
pricing of risk, measured by the exposure of each asset class to economic
and financial factors.
Ø Capture dynamic market features: Interaction between economic and financial
signals and the variations in asset classes’ potential returns and risks over
time.
We implicitly assume that -as suggested by empirical evidence- most of the key
variables used in our models will converge over the long-run. Therefore bond yields,
GDP and dividend growth are expected to converge over longer periods.
For most asset classes we use clearly specified multi-linear regression models to
forecast returns, while relying on traditional models in the cases of equities and
foreign exchange (Dividend Discount Model and Fair Value Model, respectively). The
object of this exercise is to arrive at five-year return and volatility forecasts for each
of the assets, which are then used as inputs for the final optimization process. To an
extent, forecasting returns for a five-year period is less error-prone than for a much
Q.M.S Advisors | Tel: 078 922 08 77 | e-mail: info@qmsadv.com | website: www.qmsadv.com |

2. QMS
. .
Advisors
shorter period and also lends itself to a greater reliance on longer-term fundamentals
as drivers of future performance. It also implies that incorporating a mean-reverting
element into the return forecasts is far less controversial than it would be over a
shorter time horizon. Additionally, it is worth mentioning that all our models are
supported by cross-checking procedures that aim to rationalize the initial forecast
outputs. To a certain extent, return forecasts should have relatively little impact on
forecasts of volatility and covariance. Risk, or volatility, is more a measure of the
uncertainty of the return, rather than the forecast of the return. In the shorter term,
underlying risk and covariance should be more stable than expected returns.
With regard to volatility forecasts, we compute both historical volatilities and
Ornstein-Uhlenbeck estimates for all assets, correcting for auto-correlation where
necessary as suggested in econometric literature. Historical volatilities are taken as
the best proxy for five-year average volatility forecasts for all alternative investments
and equity indices. We employ the Ornstein-Uhlenbeck process to reflect the mean
reversion process in volatility over time. We have found this process to produce
more realistic out-of-sample forecasting results when compared to other volatility
models such as variants of Arch or Garch-models. We use Ornstein-Uhlenbeck
volatility forecasts for our fixed income indices when volatility clustering leads us to
expect a slow return to the long-term average volatility. The correlation matrix is
estimated using all available data from time series using the Stambaugh algorithm, a
process that is further combined to the Ledoit-Wolf shrinkage methodology is applied
to reduce estimation error in the calculations of the correlations, while taking into
account the different correlation patterns between major asset groups such as bonds
and equities. We combine a prior matrix with the Stambaugh matrix by calculating a
shrinkage factor. The result is a well-behaved correlation matrix with reduced
estimation error. The variance-covariance matrix is in turn obtained by multiplying
the correlation matrix with estimated variances.
For more on our methodologies, please visit us and register at:
www.qmsadv.com
Q.M.S Advisors | Tel: 078 922 08 77 | e-mail: info@qmsadv.com | website: www.qmsadv.com |