Diversifying Portfolios With
Concentrated Stock Exposure
Hedging Client Specific Concentration Risks
Q M S Advisors
. .
Av. C.-F. Ramuz, 85 | 1009, Pully | CH
This material does not constitute investment advice and should not be viewed as tel: 078 922 08 77 | 021 711 40 89
a current or past recommendation or a solicitation of an offer to buy or sell any e-mail: info@qmsadv.com
securities or to adopt any investment strategy. website: www.qmsadv.com

Optimal Portfolio Allocation For
Portfolios With Concentrated Risks
Efficient Risk Mitigation Methodologies
TARGET
To help clients with concentrated equity positions achieve
optimal portfolio diversification
To devise asymmetric hedging solutions allowing our clients to
reduce their exposure to concentrated stock positions; and to
effectively reduce their portfolio level idiosyncratic risks
To porting our clients’ risk budgets to strategies offering
maximum potential diversification from a total portfolio
perspective.
Q.M.S Advisors Av. C.-F. Ramuz, 85 | 1009, Pully CH | tel: 078 922 08 77 | 021 711 40 89 | e-mail: info@qmsadv.com | website: www.qmsadv.com Page 1

Optimal Portfolio Allocation For
Portfolios With Concentrated Risks
Efficient Risk Mitigation Methodologies
Objective
To diversify into alternative strategies, using a highly concentrated and volatile
equity position as collateral
Determine the most potent combination of alternative assets to introduce in the
portfolio in order to provide the maximum possible diversification
Determine the optimal joint leverage/collar strategy to minimize the likelihood
of margin calls under cost constraints
Approach
Design quantitative models to analyze complex levered portfolios
Build binomial term structure and option models to analyze clients’ potential
risks of facing margin calls over multiple time horizons
Design non-linear asset pricing models to assess the potential risks and cost
impact of implementing collar strategies
Assess the probability of margin calls over multiple time horizons and test the
efficiency of the chosen collar structure
Q.M.S Advisors Av. C.-F. Ramuz, 85 | 1009, Pully CH | tel: 078 922 08 77 | 021 711 40 89 | e-mail: info@qmsadv.com | website: www.qmsadv.com Page 2

Optimal Portfolio Allocation For
Portfolios With Concentrated Risks
Optimal joint leverage/collar strategy to minimize the likelihood of margin calls
Margin Calls At 30% Leverage Without Collars Margin Calls At 35% Leverage Without Collars
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.78% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.39% 1.76% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.20% 0.98% 2.69% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.10% 0.54% 1 %
.61 3.49% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.05% 0.29% 0.95% 2.22% 4.17% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.02% 0.16% 0.56% 1.39% 2.78% 4.72% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.09% 0.32% 0.85% 1.82% 3.27% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.05% 0.18% 0.52% 1 7%
.1 2.22% 3.70%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.02% 0.10% 0.31% 0.74% 1.48%
0.00% 0.01% 0.00% 0.00% 0.00% 0.00% 0.01% 0.06% 0.18% 0.46%
0.00% 0.01% 0.03% 0.00% 0.00% 0.01% 0.03% 0.1 %
1
0.00% 0.00% 0.02% 0.00% 0.00% 0.02%
0.00% 0.00% 0.00% 0.00%
0.00% 0.00%
Cumulative Probability Cumulative Probability
0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .7 8 % 0 .3 9 % 1.9 5 % 1.0 7 % 3 .2 7 % 1.9 3 % 4 .6 1% 2 .8 7 % 5 .9 2 % 3 .8 4 % 7 .17 % 4 .8 1% 3 .18 % 5 .7 7 %
Margin Calls At 30% Leverage With Collars Margin Calls At 35% Leverage With Collars
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.10% 0.54% 1 %
.61 3.49% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.05% 0.29% 0.95% 2.22% 4.17% 6.67% 0.00% 0.00% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.02% 0.16% 0.56% 1.39% 2.78% 4.72% 7.08% 0.00% 0.00%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.09% 0.32% 0.85% 1.82% 3.27% 5.18% 7.39%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.05% 0.18% 0.52% 1 7%
.1 2.22% 3.70%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.02% 0.10% 0.31% 0.74% 1.48%
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.06% 0.18% 0.46%
0.00% 0.01% 0.03% 0.00% 0.00% 0.01% 0.03% 0.1 %
1
0.00% 0.00% 0.02% 0.00% 0.00% 0.02%
0.00% 0.00% 0.00% 0.00%
0.00% 0.00%
Cumulative Probability Cumulative Probability
0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 1% 0 .0 4 % 0 .0 2 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .0 0 % 0 .10 % 0 .5 9 % 1.9 3 % 4 .6 1% 2 .8 7 % 5 .9 2 % 10 .5 1% 7 .17 % 11.8 9 % 8 .3 5 % 13 .16 %
Q.M.S Advisors Av. C.-F. Ramuz, 85 | 1009, Pully CH | tel: 078 922 08 77 | 021 711 40 89 | e-mail: info@qmsadv.com | website: www.qmsadv.com Page 3

Optimal Portfolio Allocation For
Portfolios With Concentrated Risks
Efficient Risk Mitigation Methodologies
Conclusions
Hedge level on the equity collateral is determined by the amount of risks
the client intends taking
Collars, when included in the debt covenants, help lower the probability of
margin calls over the defined time horizon
Collars in a dynamic framework can provide inexpensive portfolio
protection
Addition of hedge funds and other alternative investments to the client’s
portfolio helps reduce total portfolio risks while enhancing returns
Q.M.S Advisors Av. C.-F. Ramuz, 85 | 1009, Pully CH | tel: 078 922 08 77 | 021 711 40 89 | e-mail: info@qmsadv.com | website: www.qmsadv.com Page 4