This document discusses risk budgeting and active manager allocation for multi-asset class funds. It defines the different types of risks that can be budgeted (systematic, active, etc.) and how the majority of a fund's risk comes from its systematic/beta exposures rather than active risk. The document provides mathematical formulas for decomposing total fund risk and return. It also discusses methods for determining manager allocations based on information ratios and evaluating whether returns come from alpha or beta.

1. Risk Budgeting & Active Manager Allocation
Risks To Budget
The goal of risk budgeting is to avoid losses above a risk threshold and to be adequately compensated
over time for the risks you choose to assume. Peter Bernstein noted that not all important risks can be
quantified. The moral risk associated with the principal-agent relationship is an example of a non-
quantifiable risk that cannot be budgeted. Fat tail risks that have a low probability of occurrence but a
potentially high impact are another example. Non quantifiable risks cannot be explicitly budgeted.
Of the risks that can be quantified (interest rate risk, yield curve, credit spread, volatility, liquidity,
currency, leverage, market, counter party and active decisions are examples), not all are normally
budgeted but most can be hedged. Hedging is not risk budgeting as discussed here.
Non normality of return distributions (fat tails) create challenges to risk budgeting. It is the fat tails
that you want to control but most ex ante risk budgeting assumes return distribution normality.
Assumptions of normality explain much of why risk budgets can fail when most needed.
Multi-asset class fund risk budgeting consists primarily of the asset allocation decision and the active
versus passive investment decision. These two risks determine the majority of quantifiable fund risk.
Asset allocation concerns itself with the various market exposures (also called beta exposures) while
the active versus passive decision determines how much active risk (variance from the policy
benchmark) the fund can tolerate in its search for alpha.
It is a basic tenet of Modern Portfolio Theory that multi-asset class fund total risk is reduced when
asset class correlations are low. When volatility increases asset class correlations tend to move
toward 1.0 negating the risk reducing effects of asset allocation. In the market down turn of July
2007-March 2009, correlations rose sharply, liquidity dried up and risk budgets were breached in
unanticipated ways. A lesson to remember is that all beta exposures are correlated and correlations
are unstable. During periods of increased volatility correlations can be expected to rise. Leveraged
beta exposures (beta >1.0) can be particularly damaging when volatility rises unexpectedly so
controlling the risk associated with beta exposures is important. Many investors were surprised to
learn that much of their presumed alpha had been leveraged beta and this only became apparent to
them when correlations moved toward 1.0.
Most multi-asset class funds that use risk budgets focus on establishing explicit downside tolerances
for their various beta exposures and active risk exposures. Leverage is addressed in the beta risk
budget and liquidity in the asset allocation policy (via allocation to high quality, zero duration fixed
income and allocation limits on non-liquid investments like private equity). Currency risk budgets are
a part of the domestic-foreign asset allocation decision. Currency risk can easily be hedged but at a
cost of increased correlations. Fixed income risks (interest rate, credit, yield curve, volatility) can be
addressed specifically in the fixed income composite allocation policy. Allocations between passive
and active strategies and among active managers determine the fund’s active risk.
It is my intention to focus on systematic and active risk budgeting in this paper.
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2. Defining Alpha and Beta
At Georgia Pacific alpha was defined as risk adjusted excess return and measured by subtracting the
manager’s net of fee return from their benchmark return adjusted for the manager’s beta (BM return x
Manager Beta). This levered or delevered the benchmark return to the manager’s beta allowing an
apples to apples risk adjusted return comparison. Any positive number was considered positive alpha.
We defined beta as our various market related or systematic exposures. Each external manager had a
broad market or custom benchmark which was used when evaluating each manager’s performance.
Manager betas were determined relative to their assigned market benchmark. We also used the policy
benchmark of the Master Trust as the market portfolio (beta = 1.0) when making decisions about
changes to manager structures or when considering the addition of new strategies. We could then
determine correlations of the manager or strategy with the rest of the Master Trust to see if the
strategy would have added risk adjusted excess return in various market regimes via back testing.
Total Fund Risk = Σ Systematic Risks + Σ Active Risks (1)
This equality is the basis for risk budgeting in a multi-asset class fund. Total fund risk is measured by
the variance of the fund’s returns, the systematic risk by the weighted sum of its betas and active risk
by tracking error variances. We assumed that any non-compensable risk was diversified away or
hedged and we did not budget for risks from which we expected no positive return over time.
Mathematically we decomposed risk into: σ 2 = (β 2 x σ 2 bm) + ω 2. Where σ2 is variance, β2 is beta
squared. σ2bm is the variance of the policy benchmark and ω2 is tracking error variance.1 (Variance is
easier to work with mathematically than standard deviation or tracking error).
An example: if fund beta is 1.0, variance is 144 (12% standard deviation) and active variance is 25
(5% tracking error) then total fund risk is (1.02 x 144) + 25 = √169 = 13.0% standard deviation.
Market related risk exposures accounted for 12%/13% or 92% of the total risk of the fund. In most
multi-asset class funds the risks associated with its various market exposures account for more than
90% of total fund risk2.
What we see from the equality is that the greatest potential impact on total fund risk is not active risk,
but systematic risk which we measure using beta and that is why asset allocation policy is of such
concern to the investment committee. The asset allocation policy determines the beta risk exposures
of the fund and the upper limit on total risk of the fund in most cases. At Georgia Pacific we set the
asset allocation policy based on a maximum two standard deviation downside risk that was
acceptable to the plan sponsor for funding purposes.
We can make an estimate of the active risk in a fund by taking the square root of the sum of weighted
active manager tracking error variances multiplied by the correlation between each manager. That is,
ω fund = sqrt ∑ (wt2i x ω 2i) x ρ ij. Active risks are not additive, total fund active risk is the square root
of the sum of the individual manager active risks in the portfolio and can be expected to be less than
the sum of the weighted active risk of each manager.3
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3. Systematic Risk versus Active Risk
Active risk exposure in a multi-asset class, multi-manager fund is determined by the active/passive
allocation decision and by active manager allocation decisions. The systematic risk exposure (beta) is
determined when the asset allocation policy is established. Since the majority of the expected risk and
return in the fund comes from the fund’s various beta exposures, risk budgeting starts with the asset
allocation policy.
The focus of risk budgeting by the investment staff should be on allocating the active risk budget
since underperformance relative to the policy results primarily from active risk and fees when a fund
is systematically rebalanced to the policy allocation. It is the responsibility of the investment staff to
identify and evaluate active managers. The chief investment officer usually focuses on asset
allocation policy, the allocation between passive and active management and the allocation among
active managers in setting the total risk tolerance of the fund.
Determining Whether Returns Are Due to Alpha or Beta
We can estimate whether an active manager has generated alpha or passed leveraged beta returns as
alpha by leveraging or deleveraging the benchmark return using the manager’s beta as follows:
Manager nominal net of fee return - (Benchmark Return x Manager Beta). Assuming that the
manager has been assigned the correct benchmark, any positive number indicates that the manager
added risk adjusted value above an equivalently leveraged market return.
Total Fund Return = Return due to systematic exposures + return due to alpha (2).
This equality demonstrates how we seek fund level return and helps us define how we expect to be
compensated for the risks we take. In a passive fund alpha = 0 so total return = return due to
systematic risk exposures and total risk = sum of the systematic risk exposures. In most funds, while
the search for alpha consumes much of the time of an investment staff, the expected alpha return is a
fraction of the expected return due to systematic exposures. Systematic exposures are also called
betas.
We can use equalities (1) & (2), above, to help measure how much return we actually earn per unit of
various risk taking activities. The Sharpe ratio (excess return/standard deviation) tells us how much
return we have earned per unit of total risk taking, The Treynor ratio (excess return/beta) tells us how
much return we earned per unit of systematic risk taking and the information ratio (alpha/tracking
error) tells us how much active return we earned per unit of active risk taking. These measures are
usually used as relative measures in comparing active to passive strategies or among active strategies
to help understand which has compensated investors more on a risk adjusted basis.
Returns associated with a fund’s beta exposures are correlated with each other while returns due to
alpha are uncorrelated with the returns due to beta and with all other alpha returns. This has
implications for the expected return of the fund in down markets.
Active Risk Budgeting
For most multi-manager funds underperformance of the policy benchmark caused by active manager
risk is a major concern. The information ratio (IR) is the manager’s alpha divided by active risk or α/
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4. ω. It tells us how much active return we earned for our active risk exposures. Setting a realistic target
IR is an important first step in allocating the active risk across a multi-asset class fund with multiple
external managers.
The maximum potential alpha for a manager = Information Coefficient x Transfer Coefficient x
breadth of active decisions.4
Mathematically this takes the form: αmax = IC x TC x Sqrt(n) where:
• Information Coefficient (IC) = Measure of forecasting skill. Measures correlation of the
manager’s forecast with actual outcome. A typical IC range for a successful active manager is
0.0 to +.10.
• Transfer Coefficient (TC)5 = % of potential alpha captured in the manager’s investment
process (primarily reflects the impact of constraints and fees)
• n= square root of # of buy/sell decisions made (# of active decision opportunities)
This equality is Ginold and Kahn’s Fundamental Law of Active Management and states that the
maximum expected alpha for a manager is a function of active manager skill, investment process
implementation efficiency and the number of active decision opportunities.
A manager can have a high information ratio due to some combination of active decision skill
(superior stock picking is an example), implementation ability (an efficient quantitative process, few
constraints or low fees), or making lots of active decisions by a skilled manager.
In the manager allocation process we can determine the IR we wish to target at the fund level with
each composite IR usually being proportional to the allocation to the asset class it represents. We can
also assign a target IR to each active manager based upon our expectations for risk and return for
each manager. Detailed manager research should give us some idea of what IR we should expect
from each active manager. The use of the IR recognizes that active management can have a positive
impact on both active risk and active return in the fund. In the restrictive condition where beta is
equal to 1.0 then either the Sharpe ratio or IR can be used interchangeably.
The chief investment officer normally determines how much under performance of the policy
benchmark caused specifically by active risk the fund will accept. This active risk underperformance
is expressed in terms of tracking error variance and can be used in determining the target IR of the
overall fund. Composite IR targets and individual manager allocations are set from there. A larger
active risk budget can result in a greater under performance of the policy benchmark if active
managers underperform.
Active Manager Allocation
According to Markowitz and Treynor the correct way to allocate among active managers with
uncorrelated alphas is to allocate to each in proportion to their contribution to the composite IR.
Mathematically, the allocation would be determined by the manager’s α/ω2 where α is the manager’s
alpha and ω2 is tracking error variance. (1Waring, page 27).
The IR recognizes that an active manager can help the fund with some combination of risk and return
and not just active return. If alpha drops but active risk drops farther, IR rises. If active risk rises but
alpha rises farther, IR rises. A passive manager always has an IR of 0 since there is no active return
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5. and no active risk. However, an IR of 0 can be higher than the realized IR of many active managers.
A completely indexed fund has an IR of 0 and any underperformance of the policy benchmark is
normally caused by fees and cash flows.
I have observed in practice that using this methodology tends to reward low tracking error managers
that possess consistent (and usually more modest) alpha at the expense of higher tracking error
managers who may have the potential to generate larger alpha less consistently. It also offers an
opportunity for the chief investment officer to make bets on higher potential alpha generating
managers (spend more of the active risk budget) when they feel confident in the long term active skill
of a particular manager. The IR establishes a risk/return benchmark that the chief investment officer
can use to make active manager allocation bets.
An alternative active manager allocation method is described by Waring and Ramkumar (2008)6
using the Fundamental Law of Active Management. W&R demonstrate how to create explicit
forecasts of manager alpha to build optimized portfolios of external managers which improve the
manager allocation process. Their methodology includes an explicit assessment by the plan sponsor
of each individual manager’s skill at beating their benchmark, net of fees and takes into account the
plan sponsor’s ability at estimating manager skill and incorporates both quantitative and qualitative
assessments. If an investment staff has high confidence in its ability to select skilled active managers
and the fund can tolerate a higher active risk budget, this method may be attractive.
Once an allocation has been made to each active manager we can observe over time which manager
helped and which hurt the composite IR. Those that help can be allocated a larger portion of the risk
budget if the investment staff feels confident in the active skill of the manager. While historic risk-
return information on managers can be used, predictive models like that described in W&R may be
more appropriate since we should be in a forward looking mode when allocating to active managers.
It is important to keep in mind that active manager alpha tends to be cyclical and that skilled active
managers do not necessarily add alpha in every market environment so a periodic review of manager
performance across multiple market environments should be a part of every active manager’s
performance analysis.
The goal in establishing an active risk budget should be to allocate to active managers who are most
likely to consistently compensate the fund adequately for the risks they take. That means we must
have the ability to separate returns due to various market risk exposures from returns associated with
active risk and to identify whether active returns are due to selection or allocation decisions. We
should be willing to pay more for consistent alpha but we need to recognize that returns from beta
will always do the heavy lifting. Beta sources are easier to identify and obtain than alpha, are more
persistent than alpha and are not a zero sum game or capacity constrained. In addition, beta returns
can be sourced more cheaply than can alpha. Breaking out returns due to various market risk
exposures (beta exposures) from returns due to active decision risks is important for proper risk
management and to avoid paying alpha prices for beta. Since most active managers assume all of
their excess return is alpha and is due to their unique skill, investment staffs and their managers may
not always agree on the definition of alpha but it is important to have a quantitative risk analysis
framework in place for every multi-asset class fund. In volatile markets when correlations tend to
rise, levered beta will magnify losses while true alpha will reduce losses relative to the benchmark.
Greg Johnsen, CFA. This was originally written in 2005 for Georgia Pacific’s pension investment department internal
use. Updated in 2009.
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6. References
1
Waring, M. Barton. “The Dimensions of Active Management”, in AIMR Conference Proceedings,
Improving the Investment Process Through Risk Management no. 4. 2003. pp 22-29.
2
Brinson, Gary, Hood, Randolph and Beebower, Gilbert. “Determinants of Portfolio Performance”,
Financial Analysts Journal, vol 51, no. 1 (January/February 1995): pp 133-138.
3
Kozun,Wayne. “The Integration of Risk Budgeting into Attribution Analysis”. AIMR Conference
Proceedings, Benchmarks and Attribution Analysis. No 3, 2001. pp 38-45.
4
Grinold, Richard and Kahn, Ronald. “Active Portfolio Management”, second edition. McGraw Hill,
NY. 2000.
In chapter 6 of their book, Grinold and Kahn articulate the basic fundamental law of active
management, Clarke, et al expand it with their incorporation of the Transfer Coefficient.
5
Clarke, Roger, De Silva, Harindra and Thorley, Steven. “Portfolio Constraints and the Fundamental
Law of Active Management”, Financial Analysts Journal, (September/October 2002), pp 48-66.
6
Waring, M. Barton and Ramkumar, Sunder R. “Forecasting Fund Manager Alphas: The Impossible
Just Takes Longer”, Financial Analysts Journal, vol 64, no 2 (March/April 2008): pp 65-80.
Waring, M. Barton, Whitney, Duane, et al. “Optimizing Manager Structure and Budgeting Manager
Risk”, The Journal of Portfolio Management, vol 26, no 3 (Spring 2000).
Berkelaar, Arjan, Kobor, Adam and Tsumagari, Masaki. “The Sense & Nonsense of Risk
Budgeting”, Financial Analysts Journal, vol 62, no 5 (September/October 2006), pp 63-75.
Clarke, Roger, de Silva, Harindra and Thorley, Steven. “Investing Separately in Alpha and Beta”.
Research Foundation of the CFA Institute monograph. March, 2009.
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