Modeling Illiquidity Premia for
Alternative Investments
The Swiss CFA Society, Zurich & Geneva
Renato Staub, November 6 & 7, 2008
Problem
‹ Most alternative investments are illiquid.
‹ This reduces the investor’s flexibility.
‹ In a rational world, this should be compensated.
‹ For asset allocation, we need to know how illiquidity is compensated.
‹ The Capital Asset Pricing Model (CAPM) does not deal with illiquidity.
2
Examinations
‹ How do we define illiquidity?
‹ How does literature define illiquidity?
‹ What does literature say about compensation for illiquidity?
‹ How do we approach illiquidity compensation?
‹ How does our approach fit into our framework for modeling asset returns?
3
Liquidity: Definition
‹ Definition
— Finance 101 Class: “Liquidity is the price elasticity with regard to the
turnover of the respective security.”
— Gastineau: “Liquidity is a market condition in which enough units […]
are traded […] without significant impact on price stability.”
‹ In most instances, “liquidity” is associated with the costliness of a trade, and
it is measured in terms of its bid-ask spread.
‹ However, we are concerned about the fact that alternative assets are…
4
Liquidity: Definition
…not traded at all for a significant period.
5
Literature
‹ Irrelevant literature (for asset mgt.) – trading based (90% of all literature)
— Amihud/Mendelson (1986/1, 1986/2)
— Longstaff (1995, 1999)
‹ Relevant literature – discount based
— Silber (1991) examines restricted stocks (SEC 144) and finds a 34%
average discount for a 2-year illiquidity.
— Chaffe (1993) thinks a fair discount for illiquidity equals the value of a
put option. The discounts turn out to be very large in some instances.
— Smith/Smith/Williams (2000) think large illiquidity discounts are not
justified economically. They claim that studies providing large discounts
are flawed.
6
Literature: Judgement
‹ Literature
— Often operates with biased data
— Concentrates on particular selected aspects
— Provides stand-alone investigations
— Is trading based (in 90% of all instances)
— Makes unrealistic assumptions
‹ Probably, most studies overestimate illiquidity compensation .
‹ We have hands-on experience with illiquidity compensation: UBS EIP stocks
— 3-year lock in
— 13% discount (pay 100, get 115)
— UBS saves about a 9% in pension fund contribution
— Hence, 4% net discount
— Further, UBS is not forced to issue EIP stocks
7
Alternative Assets – Volatility
The fact that you cannot see the bat moving in the dark tunnel…
Tunnel
8
Alternative Assets – Volatility
… does not mean that the bat does not move up and down. Alternatives are just
like a bat flying through a dark tunnel; due to their missing mark-to-market,
you cannot see their movement.
9
Alternative Assets – Correlation
Internal Rates of Return for 5-Year Holding Periods
50
S&P 500 (lhs)
Venture Capital (rhs)
25
45
40
35
20
30
25
20
15
15
Annual Percent Return
Annual Percent Return
30
10
10
5
0
5
1985
'87
'89
'91
'93
'95
'97
1999
End Year
Sources: Venture Economics, Standard & Poor’s
10
Risk and Correlation of Alternative Assets
‹ It is often claimed that alternative assets have little risk at low or even
negative correlations
‹ This illusion is
— caused by a missing mark-to-market
— overstated by appraisal smoothing
‹ In reality, asset values are driven by underlying fundamentals.
‹ These have nothing to do with the legal form in that assets are offered.
‹ There are alternative assets with
— moderate risk/correlation
(like real estate)
— high risk/correlation
(like private equity)
11
Required Returns: Framework
Segmentation
- compensation for home bias
Integration
- compensation for systematic risk
Illiquidity
- compensation for lock-in time
12
Integration vs. Segmentation
‹ Integration means a world of no market imperfection.
‹ The risk premia are based on a CAPM-like, single factor.
‹ Greatest challenge in practice: defining “the market”.
‹ Segmentation depicts a world without free capital flows between markets.
‹ In a segmented world, the marginal investor is a local investor.
‹ In a segmented world, an asset is compensated according to its total rather than its
systematic risk.
‹ In reality, a market is neither fully integrated nor absolutely segmented.
‹ Its risk premium is estimated based on a weighted mean between integration and
segmentation.
13
Integration vs. Segmentation: Compensation
9%
EQ US
EQ CH
8%
BD USA
BD CH
7%
RE US
INFRASTRUCTURE US
VENTURE EARLY CH
Risk Premium
6%
VENTURE LATE CH
VENTURE VY2 US
5%
VENTURE VY7 US
LBO CH
LBO US
4%
MEZZANINE CH
MEZZANINE US
3%
DISTRESSED DEBT US
TIMBER US SOUTH
TIMBER US WEST
2%
FARMLAND US ROW CROP
FARMLAND US PERM. CROP
1%
GIM
RE US
0%
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Beta
14
Illiquidity Compensation: Approaches
‹ Jaffe’s put option approach
‹ Our Sharpe ratio approach
‹ Our put option approach
15
Jaffe’s Put Option Approach
‹ It is the most common approach for modeling the liquidity premium.
‹ It claims that the discount for illiquidity should equal the value of a put option.
Its exercise price equals the asset’s marketable price at purchase.
‹ The following two charts show the resulting discounts according to BlackScholes.
Chaffe's Approach - According Discount
Chaffe's Approach - According Discount
25%
25%
20%
20%
15%
10%
15%
10%
20%
20%
30%
10%
30%
10%
40%
40%
5%
5%
0%
0%
0
1
2
3
Illiquidity Horizon (Years)
4
0
10
20
30
40
50
60
70
80
90
Illiquidity Horizon (Years)
16
Jaffe’s Approach seems too generous
‹ The discount increases with a rising illiquidity horizon, turns at some point and
approaches zero asymptotically.
‹ In the short run, this means free shortfall insurance combined with unlimited
upward potential. It litterally implies no real risk-return trade-off.
‹ For longer horizons, the implied illiquidity premium decreases with an
increasing illiquidity horizon, whereas practical evidence implies the contrary.
‹ Full shortfall insurance is fairly arbitrary from a statistical perspective, as there is
no inherent relationship with both the asset’s risk and the length of the lock-in.
17
Sharpe Ratio Approach
E[S(T) ] = Se μ*T
M[S(T) ] = Se μT
E[S(T, r)] = Se rT
Illiquidity Horizon (T)
‹ We assume that the risky asset follows a Brownian Motion.
‹ Expected excess wealth after T:*)
E[S(T) − S(T, r)] = Se μ*T − Se rT
‹ Distribution of excess wealth after T:*)
σ2 [S(T) − S(T, r)] = σ2 [S(T)] = S 2 e 2μ*T (e σ T − 1)
‹ Sharpe Ratio of excess wealth after T:
*) See Hull, 1993.
2
SR(T ) =
E[S(T) − S(T, r)]
σ2 [S(T) − S(T, r)]
=
e μ*T − e rT
2
e μ*T e σ T − 1
18
The Sharpe-Ratio Approach
‹ SR(T) is a non-linear function in T. First, it increases with increasing horizon, T,
and then it decreases.
‹ Considering annualized Sharpe ratios, i.e. T=1, is arbitrary.
SR(T)
T
‹ In particular, annualized risks and returns are misleading if the lock-in horizon
is substantially longer than one year.
‹ We consider instead the Sharpe Ratio of the excess wealth which is expected
to be generated until the end of the lock-in.
19
Our Sharpe Ratio Approach - Example
‹ Assume
μ=10%
σ=20%
r=5%
(continuous return of asset, fully reinvested)
(risk of asset)
(riskless return, fully reinvested)
‹ SR = (10-5) / 20 = 0.25 (excess return / distrib. of excess return)
‹ After a time horizon, T, of 5 years for instance, we get
V=182% (expected value of asset)
Σ=60% (distribution of asset’s value)
W=128% (expected value of riskless asset)
‹ SR(T) = (182-128) / 60 = 0.90 (excess value / distrib. of excess value)
SR(T) is the excess value divided by its distribution, rather than the
annualized excess return divided by its distribution.
20
The Sharpe-Ratio Approach
‹ SR(T) increases with μ
SR(T)
μ >>
T
‹ The key is to compare the horizon-dependent Sharpe Ratio SR(T) of the asset
with SR(T) of the reference portfolio, i.e. the Global Investable Market (GIM).
21
The Sharpe-Ratio Approach
1.20
1.00
This is the standard horizon used in practice
This is the the lock-in period
for the alternative asset
GIM
SR(T)
0.80
0.60
μ too small
T = 6 years
Alternative Asset
0.40
0.20
μ too small
0.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Illiquidity Horizon (T)
Note: all holding period estimates are cumulative rather than annualized values
22
Our Put-Option Approach
‹ Only the risk-induced portion of the return is insured, because only this portion
is generated by holding the risky asset.
‹ The compensation is measured as the difference of two put options.
‹ Discount = Put1 - Put2
Exercise Price of Put1
Exercise Price of Put2
}
limited
downside
risk
Illiquidity Horizon
23
Integration into our Existing Framework
‹ Calculate illiquidity compensation with total risk of the alternative asset as an
input: full integration.
‹ Calculate illiquidity compensation with the systematic risk of the alternative
asset as an input: full segmentation.
‹ Define the weighting scheme for integration / segmentation of alternative
assets.
‹ Total premia (risk premia plus liquidity premia) is the weighted mean.
24
EQ US
1.89
4.70%
3.31%
EQUILIBRIU
M RETURN
ILLIQUIDTY
PREMIA
4.38%
RISK
PREMIA
3.04%
RISK-FREE
RATE
SEGMENTE
D RISK
PREMIA
17.6%
INTEGRATE
D RISK
PREMIA
EQ SWITZERLAND
BETA
RISK
Results
8.17%
14.6%
1.96
3.14%
3.63%
4.70%
3.24%
8.09%
BD SWITZERLAND
5.2%
0.36
0.58%
1.31%
4.70%
0.73%
5.46%
BD USA
4.6%
0.40
0.65%
1.14%
4.70%
0.74%
5.48%
RE AUSTRALIA
16.4%
0.81
1.31%
4.08%
4.70%
2.14%
0.43%
7.40%
RE FRANCE
16.1%
0.89
1.42%
4.02%
4.70%
2.46%
0.56%
7.88%
RE GERMANY
15.9%
0.89
1.42%
3.97%
4.70%
2.44%
0.55%
7.85%
RE NETHERLANDS
13.6%
0.76
1.23%
3.39%
4.70%
2.09%
0.43%
7.35%
RE SWITZERLAND
14.3%
0.70
1.13%
3.55%
4.70%
2.10%
0.44%
7.37%
RE UK
12.7%
0.67
1.08%
3.17%
4.70%
1.71%
0.31%
6.82%
RE US
10.2%
0.71
1.14%
2.53%
4.70%
1.55%
0.26%
6.60%
RE JAPAN
17.3%
0.89
1.44%
4.30%
4.70%
2.58%
0.61%
8.06%
RE BELGIUM
15.4%
0.52
0.83%
3.83%
4.70%
2.03%
0.46%
7.32%
RE ITALY
17.2%
0.90
1.45%
4.29%
4.70%
2.59%
0.61%
8.07%
RE SPAIN
16.2%
0.86
1.38%
4.03%
4.70%
2.44%
0.55%
7.85%
RE SWEDEN
15.1%
0.81
1.30%
3.77%
4.70%
2.29%
0.50%
7.63%
RE NORWAY
17.2%
0.89
1.43%
4.28%
4.70%
2.57%
0.61%
8.04%
INFRASTRUCTURE AUSTRALIA
13.7%
0.66
1.06%
3.41%
4.70%
2.00%
0.80%
7.65%
INFRASTRUCTURE CANADA
13.7%
0.67
1.07%
3.41%
4.70%
2.01%
0.81%
7.67%
INFRASTRUCTURE EUROPE
13.7%
0.69
1.11%
3.42%
4.70%
2.03%
0.82%
7.70%
INFRASTRUCTURE JAPAN
13.7%
0.68
1.09%
3.42%
4.70%
2.03%
0.82%
7.69%
INFRASTRUCTURE UK
13.7%
0.66
1.06%
3.41%
4.70%
2.00%
0.80%
7.65%
INFRASTRUCTURE US
13.7%
0.67
1.08%
3.40%
4.70%
2.01%
0.80%
7.66%
25
ILLIQUIDTY
PREMIA
EQUILIBRIU
M RETURN
7.32%
12.54%
4.70%
9.41%
11.36%
27.57%
RISK
PREMIA
4.56
RISK-FREE
RATE
SEGMENTE
D RISK
PREMIA
50.3%
INTEGRATE
D RISK
PREMIA
VENTURE EARLY BENELUX
BETA
RISK
Results
VENTURE EARLY FRANCE
47.9%
4.30
6.91%
11.94%
4.70%
8.92%
9.52%
24.90%
VENTURE EARLY GERMANY
47.1%
4.26
6.84%
11.73%
4.70%
8.80%
9.01%
24.17%
VENTURE EARLY ITALY
49.5%
4.30
6.92%
12.34%
4.70%
9.08%
10.49%
26.20%
VENTURE EARLY SCANDINAVIA
46.4%
4.81
7.73%
11.57%
4.70%
9.26%
9.39%
25.14%
VENTURE EARLY SPAIN
50.1%
4.55
7.31%
12.48%
4.70%
9.38%
11.18%
27.32%
VENTURE EARLY SWITZERLAND
46.3%
3.93
6.32%
11.54%
4.70%
8.41%
8.27%
22.89%
VENTURE EARLY UK
44.0%
4.23
6.80%
10.95%
4.70%
8.46%
7.55%
22.13%
VENTURE LATE BENELUX
41.4%
4.19
6.73%
10.31%
4.70%
8.16%
4.74%
18.61%
VENTURE LATE FRANCE
39.0%
3.89
6.25%
9.71%
4.70%
7.63%
4.11%
17.33%
VENTURE LATE GERMANY
38.1%
3.80
6.11%
9.50%
4.70%
7.46%
3.92%
16.92%
VENTURE LATE ITALY
41.4%
4.17
6.70%
10.32%
4.70%
8.15%
4.74%
18.61%
VENTURE LATE SCANDINAVIA
35.7%
3.69
5.94%
8.89%
4.70%
7.12%
3.49%
16.06%
VENTURE LATE SPAIN
41.1%
4.17
6.70%
10.25%
4.70%
8.12%
4.69%
18.51%
VENTURE LATE SWITZERLAND
37.3%
3.47
5.57%
9.30%
4.70%
7.06%
3.57%
16.09%
VENTURE LATE UK
35.9%
3.75
6.02%
8.95%
4.70%
7.19%
3.56%
16.22%
VENTURE VY1 US
43.2%
4.15
6.67%
10.76%
4.70%
8.31%
7.75%
22.19%
VENTURE VY2 US
41.5%
4.08
6.55%
10.35%
4.70%
8.07%
6.50%
20.51%
VENTURE VY3 US
39.9%
3.95
6.35%
9.94%
4.70%
7.78%
5.50%
19.06%
VENTURE VY4 US
38.3%
3.85
6.19%
9.53%
4.70%
7.53%
4.72%
17.90%
VENTURE VY5 US
36.7%
3.75
6.03%
9.13%
4.70%
7.27%
4.09%
16.90%
VENTURE VY6 US
35.1%
3.65
5.87%
8.74%
4.70%
7.02%
3.56%
16.03%
VENTURE VY7 US
33.5%
3.57
5.74%
8.35%
4.70%
6.78%
3.12%
15.30%
VENTURE VY8 US
32.0%
3.46
5.55%
7.97%
4.70%
6.52%
2.73%
14.58%
VENTURE VY9 US
30.5%
3.36
5.39%
7.60%
4.70%
6.28%
2.41%
13.95%
VENTURE VY10 US
29.1%
3.26
5.23%
7.24%
4.70%
6.04%
2.13%
13.38%
26
EQUILIBRIU
M RETURN
ILLIQUIDTY
PREMIA
RISK
PREMIA
RISK-FREE
RATE
SEGMENTE
D RISK
PREMIA
INTEGRATE
D RISK
PREMIA
BETA
RISK
Results
LBO BENELUX
32.2%
3.14
5.04%
8.03%
4.70%
6.24%
2.92%
14.47%
LBO FRANCE
33.3%
3.18
5.11%
8.30%
4.70%
6.38%
3.09%
14.82%
LBO GERMANY
30.3%
3.00
4.82%
7.56%
4.70%
5.91%
2.59%
13.77%
LBO ITALY
38.8%
2.77
4.45%
9.66%
4.70%
6.53%
3.74%
15.71%
LBO SCANDINAVIA
29.9%
2.76
4.43%
7.45%
4.70%
5.64%
2.40%
13.26%
LBO SPAIN
35.8%
3.01
4.84%
8.91%
4.70%
6.47%
3.35%
15.21%
LBO SWITZERLAND
34.2%
3.04
4.89%
8.51%
4.70%
6.34%
3.13%
14.82%
LBO UK
30.0%
2.78
4.46%
7.47%
4.70%
5.67%
2.43%
13.32%
LBO US
28.3%
3.13
5.03%
7.05%
4.70%
5.84%
2.44%
13.52%
MEZZANINE BENELUX
16.6%
1.18
1.89%
4.13%
4.70%
2.79%
0.69%
8.36%
MEZZANINE FRANCE
16.5%
1.12
1.81%
4.10%
4.70%
2.73%
0.67%
8.27%
MEZZANINE GERMANY
15.9%
1.17
1.87%
3.97%
4.70%
2.71%
0.65%
8.24%
MEZZANINE ITALY
16.7%
0.96
1.54%
4.15%
4.70%
2.59%
0.64%
8.10%
MEZZANINE SCANDINAVIA
16.0%
1.18
1.89%
4.00%
4.70%
2.73%
0.66%
8.27%
MEZZANINE SPAIN
16.6%
1.01
1.63%
4.13%
4.70%
2.63%
0.65%
8.15%
MEZZANINE SWITZERLAND
16.6%
1.04
1.67%
4.14%
4.70%
2.66%
0.66%
8.19%
MEZZANINE UK
17.0%
1.18
1.90%
4.24%
4.70%
2.83%
0.71%
8.44%
MEZZANINE US
17.8%
1.47
2.36%
4.43%
4.70%
3.19%
0.84%
8.94%
DISTRESSED DEBT US
20.2%
1.90
3.05%
5.03%
4.70%
3.84%
0.93%
9.73%
TIMBER ARGENTINA
29.0%
0.74
1.18%
7.22%
4.70%
4.80%
3.69%
13.78%
TIMBER AUSTRALIA
20.7%
1.17
1.89%
5.17%
4.70%
3.53%
1.61%
10.13%
TIMBER BRAZIL
24.0%
0.68
1.09%
5.97%
4.70%
4.02%
2.25%
11.36%
TIMBER CHILE
20.0%
0.53
0.85%
4.98%
4.70%
3.33%
1.46%
9.77%
TIMBER NEW ZEALAND
22.0%
0.78
1.25%
5.47%
4.70%
3.36%
1.75%
10.11%
TIMBER US SOUTH
15.1%
0.91
1.46%
3.76%
4.70%
2.61%
0.81%
8.30%
TIMBER US WEST
17.5%
0.96
1.54%
4.36%
4.70%
2.95%
1.08%
8.95%
TIMBER URUGUAY
25.7%
0.96
1.54%
6.40%
4.70%
3.97%
2.31%
11.37%
FARMLAND US ROW CROP
13.5%
0.51
0.82%
3.37%
4.70%
2.10%
0.51%
7.44%
FARMLAND US PERMANENT CRO 18.0%
0.68
1.08%
4.50%
4.70%
2.79%
0.86%
8.55%
27
Conclusions
‹ Illiquidity premia are a compensation for locking in investments.
‹ Investors who are able to wait should expect to be rewarded for assuming
illiquidity.
‹ Mathematical modeling is necessary to derive appropriate illiquidity premia.
‹ Illiquidity premia are an integral part of an investment’s equilibrium return and
are an essential factor in deriving asset allocation policy.
‹ The illiquidity premium is not a free lunch – the higher expected return is
compensation for the cost of reduced investment flexibility.
‹ The premium for illiquidity is larger when:
— The length of the lock-in period is greater
(less flexibility)
— The riskiness of the investment is higher
(greater uncertainty)
28
Thank you very much for your attention
Thank you very much for your attention.
29
References
Aitchison, J., and J.A.C. Brown, 1966, The Lognormal Distribution. Cambridge University Press.
Amihud, Y., and H. Mendelson, 1986, Liquidity and Stock Returns. Financial Analyst’s Journal. May-June, 43-48.
Amihud, Y., and H. Mendelson, 1986, Asset Pricing and the Bid-Ask Spread. Journal of Financial Economics 17, 223-249.
Brinson, Gary P., Jeffry J. Diermeier, and Gary G. Schlarbaum, 1986. A Composite Portfolio Benchmark for Pension Plans.
Financial Analysts Journal, March/April, 15-24.
Chaffe, David B.H., 1993, Option Pricing as a Proxy for Discount for Lack of Marketability in Private Company Valuations.
Business Valuation Review. December 1993, 182-188.
Hodges, Charles W., Walton R.L. Taylor, and James A. Yoder, 1997. Stocks, Bonds, the Sharpe Ratio, and the Investment
Horizon. Financial Analysts Journal, November/December, 74-80.
Hull, Jon C., 1993, Options, Futures, and other Derivatives, Second Edition. Prentice Hall, Englewood Cliffs, NJ.
Longstaff, Francis A., 1999, Optimal Portfolio Choice and the Valuation of Illiquid Securities. Working Paper.
Longstaff, Francis A., 1996, Placing No-Arbitrage Bounds on the Value of Nonmarketable and Thinly-Traded Securities.
Advances in Futures and Options Research 8.
Longstaff, Francis A., 1995, How much Can Marketability Affect Security Values?, The Journal of Finance, Vol. L, No. 5.
Mercer Capital, 1998, Why Not Black-Scholes Rather than the Quantitative Marketability Discount Model? Internet-memo
(www.bizval.com).
Perold, Andre F., and William F. Sharpe, 1988. Dynamic Strategies for Asset Allocation. Financial Analysts Journal.
January-February, 16-27.
Silber, W.L., 1991. Discounts on Restricted Stock: The Impact of Illiquidity on Stock Prices, Financial Analysts Journal,
July/August, 60-64.
Singer, Brian and Kevin Terhaar, 1997. Economic Foundations of Capital Market Returns. The Research Foundation of the
Institute of Chartered Financial Analysis.
Smith, Janet Kiholm, Richard L. Smith, and Karyn Williams, 2000. The SEC’s “Fair Value” Standard for Mutual Fund
Investment in Restricted Shares and Other Illiquid Securities, Working Paper.
Terhaar, Kevin, Renato Staub, and Brian Singer, (2003). The Appropriate Policy Allocation for Alternative Investments.
Journal of Portfolio Mangement, Vol. 29, No. 3, 2003.
The New York Times, Thursday, May 10, 2001. A Lifeline, With Conditions, C1 and C7.
Wilmott, Paul, Sam Howison, and Jeff Dewynne, 1995, The Mathematics of Financial Derivatives. Cambridge University
Press, Cambridge, UK.
30
Renato Staub, PhD
Senior Asset Allocation and Risk Analyst
Executive Director
Years of investment industry experience: 13
Education: Federal Institute of Technology (ETH)
University of St. Gallen (HSG)
MSc
MA, PhD
‹ Renato Staub’s responsibilities include risk analysis, valuation analysis, and portfolio
construction of liquid and alternative assets for asset allocation. This involves building and
maintaining risk and valuation systems as well as quantitative and simulation analysis.
‹ Renato joined the firm in 1996 as a quantitative analyst and was involved in the development
of alternative investments such as the global leveraged portfolio, market neutral portfolio,
and risk controlled portfolio. This contained risk measurement and analysis, including stress
testing and performance simulation. Further, he was involved in the administration of
alternative asset portfolios.
‹ Renato has published articles in a variety of professional journals and serves as a referee. In
addition, he was a conference speaker for the Q-Group, Barra, Risk Waters Group, the
Society of Quantitative Analysis (New York), and the Quantitative Work Alliance for Applied
Finance, Education & Wisdom (Chicago).
Publications
‹ [1] Akers, Kurt, and Renato Staub. “Regional Investment Allocations in a Global Timber Market”. Journal of
Alternative Investments, Vol. 5, No. 4, 2003.
‹ [2] Calverley, John P., Alan A. Meder, Brian D. Singer, and Renato Staub. “Capital Market Expectations”. Managing
Investement Portfolios, CFA Institure, 3rd series, 2007.
‹ [3] Meder, Aaron, and Renato Staub. “Linking Pension Liabilities to Assets”. Society of Actuaries, 2007.
‹ [4] Brian Singer, Renato Staub, and Kevin Terhaar. “Appropriate Policy Allocation for Alternative Investments.” AMIR
Conference Proceedings, 2001.
‹ [5] Staub, Renato, and Jerrey Diermeier. “Illiquidity, Segmentation and Returns”. Journal of Investment Management,
Vol. 1, No. 1, 2003.
‹ [6] Staub, Renato. “Capital Market Assumptions”. UBS Global Asset Management, Working Paper, 2005.
‹ [7] Staub, Renato. “Multilayer Modeling of a Covariance Matrix.” Journal of Portfolio Management, Vol. 31, No. 3,
2006.
‹ [8] Staub, Renato. “Asset Allocation vs. Security Selection – Baseball with Pitchers only?” Journal of Investing, Vol. 15,
No. 3, 2006.
‹ [9] Staub, Renato. “Unlocking the Cage”. Journal of Wealth Management, Vol. 8, No. 5, 2006.
‹ [10] Staub, Renato. “Deploying Alpha Potential”. UBS Global Asset Management, Working Paper, 2006.
‹ [11] Staub, Renato. “Are you about to Handcuff your Information Ratio?”Journal of Asset Management, Vol. 7, No. 5,
2007.
‹ [12] Staub, Renato. “Deploying Alpha: A Strategy to Capture and Leverage the Best Investment Ideas”. A Guide to
130/30 Strategies, Institutional Investor, Summer 2008.
32
Publications
‹ [13] Staub, Renato. “Signal Translation and Portfolio Construction”. UBS Global Asset Management, Working Paper,
2008.
‹ [14] Terhaar Kevin, Renato Staub, and Brian Singer. “Appropriate Policy Allocation for Alternative Investments.”
Journal of Portfolio Management, Vol. 29, No. 3, 2003.
‹ [15] Staub, Renato. “Integration of Alternative Investments into the Market Covariance Matrix.” Working Paper, UBS
Global Asset Management, 2001.
‹ [16] Staub, Renato. “The Correlation between U.S. Equity and U.S. Bonds.” UBS Global Asset Management, Working
Paper, March 2002.
‹ [17] Staub, Renato. “Quarterly Focus: Capital Market Assumptions.” UBS Global Asset Management, Quarterly
Investment Strategy, March 31, 2004, p. 4-7.
33