Engineering a Better Asset Allocation: RJA Option Overlay ... · PDF fileEngineering a Better...

Engineering a Better Asset Allocation: RJA Option Overlay Strategies

September 2012

White Paper


1 | Ross, Jeffrey & Antle

1. Introduction

Traditional portfolio construction techniques have long emphasized the role of asset

allocation in determining optimal risk-return profiles. In his seminal work, Markowitz

(1952) pioneered the use of Mean-Variance Optimization in computing portfolio weights

among a group of assets. This research led to the notion of portfolio efficiency, where an

investor employs diversification to achieve the most desirable mix of risk and expected

return.

The set of asset class weights yielded by such optimization techniques, traditionally

referred to as a Strategic Asset Allocation, serves as a long-term guide for investment.

An investor may also choose to opportunistically adjust these weights to take

advantage of short-term opportunities; such deviations produce a Tactical Asset

Allocation.

In this paper, we propose a reframing of the investment process by judiciously

incorporating equity options into the traditional stock-bond allocation decision. We

show how the RJA approach to constructing such option portfolios can be used to

engineer an improved risk-return profile in a cost-effective manner. RJA’s tailored

options portfolios allow investors to enjoy the benefits of convexity in directional

market moves and enable fine-grained calibration of upside and downside exposures.

The remainder of this paper is organized as follows. In section 2, we briefly survey the

evolving perspectives on this topic. In section 3, we explain the methodology used to

include Option Overlay Strategies in an existing asset allocation. In section 4, we look

at the simulated performance of the new allocations. In section 5, we study the

efficiency of Option Overlay Strategies. In section 6, we explore the performance of

the Option Overlay Strategy in times of recent market crisis. In section 7, we

summarize our results and highlight the benefits of introducing an Option Overlay

Strategy into an existing allocation.



2. Academic Perspectives

In an important early work, Brinson, Hood and Beebower (BHB 1986) claimed that

nearly 90% of the variation in portfolio returns could be attributed to asset allocation

policy. This research influenced a generation of portfolio managers, who placed

disproportionate emphasis on the role of asset allocation in their performance. Since

then, academic opinion has turned dramatically on this result.

Starting with Jahnke (1997), many researchers have challenged the original BHB

hypothesis, claiming market exposure rather than asset allocation as the principal

determinant of portfolio variance. In one such work, Ibbotson and Kaplan (2000)

proposed that a high time-series explanatory power might occur because a portfolio

participates in the capital markets in general and not because of the specific asset

allocation policy. Expanding on this analysis, Xiong, Ibbotson, Idzorek and Chen (XIIC,

2010) split the total return of a portfolio into three parts:

The returns from overall market movements.

The incremental return from Strategic Asset Allocation (asset allocation policy).

The incremental return from Tactical Asset Allocation (timing, stock selection).

XIIC find that nearly 82%1 of time series variation in portfolio returns is due to variation

in the market. They also find that Strategic Asset Allocation and Tactical Asset

Allocation have comparable explanatory power after removing this market effect. Thus

the current literature emphasizes the overwhelming influence of the market in

determining portfolio volatility.

In response to these conclusions, modern alternatives to traditional asset allocation

attempt to control for the effect of market volatility. As a prominent example, the Risk

Parity approach weighs portfolio asset classes by their volatilities. This typically

produces portfolios that have low weight in Equities and high weight in Fixed Income,

with leverage being used to bridge the shortfall in returns.

Investors traditionally look to mitigate portfolio volatility by reducing market exposure,

leading to undesirable consequences. In a traditional asset allocation, this sacrifices

potential returns, while in a Risk Parity approach, the use of leverage introduces new

risks to the portfolio. In this paper, we propose an alternative solution, integrating

Option Overlay Strategies into an existing asset allocation. We show that the inclusion

of Option Overlay Strategies offers the best of both worlds, meaningfully reducing the

risk characteristics of a portfolio without notably reducing market exposure.

1 This is the average R2 across three fund universes – U.S. Equity Funds (83%), Balanced Funds (88%), and International Funds (74%).



3. Including an Option Overlay Strategy

The Option Overlay Strategy we use for illustration in this paper has the following

characteristics2:

Targets 55% downside participation and 77% upside participation.

Six-month target date horizon.

Constructed and priced based on closing market inputs from August 15, 2012

with a 50 bps volatility bid-offer spread and assumes AUM of $1b.

Initiation cost3 of $3.37m for $1b AUM.

In order to perform our analysis, we compare the performance of two different

portfolios:

A portfolio that follows a traditional Asset Allocation Strategy by holding a given

proportion of Equities and Cash.

A portfolio that allocates among Equities, Cash, and an Option Overlay Strategy

as detailed in the next page.

We perform this comparison for three traditional allocations, 50-50, 40-60, and 60-40.

In each case, we determine a different allocation to Equities that, in conjunction with

the Option Overlay Strategy, improves the downside and upside return profile of a

traditional allocation portfolio.

2 RJA designs customized and cost effective Option Overlay Strategies based on client risk preferences and market positioning. Please contact RJA for further details on Option Overlay Strategy design and implementation. 3 RJA Fees are not included.



We outline our methodology with respect to a 50-50 allocation as follows:

Step 1: Show the payoff profile of a 50-50 allocation to Equities and Cash for

equity market moves in the range -75% to +75% (the dotted red line in Figure 1).

Step 2: Show the payoff profile of a 55-77 Option Overlay Strategy4, created

using RJA’s proprietary approach, for equity market moves in the range -75% to

+75% (the blue line in Figure 1).

Step 3: Modify the Step 2 allocation weights in Equities and Cash such that there

is equal downside and upside improvement5 upon the original 50-50 allocation

(the green line in Figure 1 shows modified allocations and the black shaded

region shows improvements).

Figure 1: Improvement in return from inclusion of the Option Overlay Strategy

-60%

-40%

-20%

0%

20%

40%

60%

80%

-75% -60% -45% -30% -15% 0% 15% 30% 45% 60% 75%

55-77 Overlay Strategy

50-50 Allocation

New Scaled Allocation

4 This Option Overlay Strategy targets 55% downside participation and 77% upside participation. 5 There are other equally valid methods to determine the scaling of the Option Overlay Strategy. These include matching the downside or upside return profiles, or matching the angle between the scaled Option Overlay and the 50-50 allocation on both the

upside and the downside.



In section 4, we use the results of a bootstrap simulation6 to compare the performance

of a portfolio with the Option Overlay Strategy to that of a traditionally allocated

portfolio. In this approach, we generate 5000 simulated six-month changes in the S&P

500 index level by sampling independently thirteen two-week intervals from the last

ten years of data7. Dividends on the S&P 500 have not been included in this analysis,

but we note that with dividend rates higher than cash yields, their inclusion would

further enhance the Option Overlay Strategy results. Appendix A explains bootstrapping

techniques in greater detail.

In Figures 2-4, we compare the spread of bootstrapped outcomes (in black) around a

central target line (in red) which represents the performance of a traditionally

allocated portfolio. Deviations from the red line represent Model Prediction Error and

arise primarily from errors in modeling future volatility. We show Model Prediction

Error for different market scenarios in Tables 2, 4, and 6, and confirm that on average,

the Option Overlay Strategy provides an improvement over the traditional allocation.

The figures that follow make a compelling case for the addition of an Option Overlay

Strategy to an existing portfolio. The convexity introduced by the Option Overlay

Strategy is valuable; it allows for increased participation in gains during large positive

market moves and dampened participation in losses during large negative market

moves.

This strategy provides structured risk reduction within the overall constraints of

portfolio allocation.

6 Bootstrapping is our preferred alternative to more traditional back-testing techniques, because it is less sensitive to the results in any particular historical period (which might not be representative of future outcomes) and it does not restrict testing to only the single historical return sequence that actually occurred. 7 The differences between realized and RJA modeled volatility levels are recorded at the same time as the two-week S&P 500 change to preserve the deviation’s correlation structure across strike, maturity, and the S&P 500 level change. The value of all options over time is generated by using the current interest rate and dividend forward curves, and the aforementioned RJA

volatility model.



4. Performance

Case 1: Improve downside and upside profile of a 50% Equities 50% Cash Allocation.

Portfolio consists of 76.6% Equities, 23.4% Cash, and the Option Overlay Strategy scaled

for $ 766m (76.6% of $1b). This scaling is calculated using the methodology described in

section 3. The red line represents the performance of a 50-50 allocation and the spread

of bootstrapped outcomes (in black) represents Model Prediction Error.

Figure 2: Performance comparison against 50-50 Allocation

Table 1: Bootstraps vs. 50-50 Allocation Table 2: Model Prediction Error

-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

60%

50% 60% 70% 80% 90% 100% 110% 120% 130% 140% 150%

Overlay Strategy + Equities 50-50 Allocation

Retu

rn

S&P 500 Level

S&P 500 % Change Mean

ALL 1.39%

< -30% 2.63%

-30% to -20% 1.76%

-20% to -10% 0.99%

-10% to 0% 0.37%

0% to 10% 0.46%

10% to 20% 1.18%

20% to 30% 4.47%

≥ 30% 14.83%

Average Difference in Returns8

S&P 500 % Change Stdev

ALL 1.47%

< -30% 0.51%

-30% to -20% 0.47%

-20% to -10% 0.38%

-10% to 0% 0.78%

0% to 10% 1.60%

10% to 20% 2.15%

20% to 30% 2.15%

≥ 30% 2.63%

Deviation of Bootstraps from Model9

8 The six-month initiation cost of the Overlay Strategy has been included in the calculation of returns. Initiation cost of $2.59m is 76.6% of the $3.37m six-month initiation cost for a $1b portfolio. Dividends on the S&P 500 are not included. RJA fees are not included in the calculation of returns. 9 This is sample standard deviation within each bucket.




Portfolio consists of 61.3% Equities, 38.7% Cash, and the Option Overlay Strategy scaled

for $ 613m (61.3% of $1b). This scaling is calculated using the methodology described in





-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

60%

50% 60% 70% 80% 90% 100% 110% 120% 130% 140% 150%


Retu

rn

S&P 500 Level


ALL 1.11%

< -30% 2.10%

-30% to -20% 1.41%

-20% to -10% 0.79%

-10% to 0% 0.29%

0% to 10% 0.37%

10% to 20% 0.95%

20% to 30% 3.58%

≥ 30% 11.86%



ALL 1.18%

< -30% 0.41%

-30% to -20% 0.37%

-20% to -10% 0.31%

-10% to 0% 0.62%

0% to 10% 1.28%

10% to 20% 1.72%

20% to 30% 1.72%

≥ 30% 2.10%


10 The six-month initiation cost of the Overlay Strategy has been included in the calculation of returns. Initiation cost of $2.07m is 61.3% of the $3.37m six-month initiation cost for a $1b portfolio. Dividends on the S&P 500 are not included. RJA fees are not included in the calculation of returns. 11 This is sample standard deviation within each bucket.




Portfolio consists of 92% Equities, 8% Cash, and the Option Overlay Strategy scaled for

$ 920m (92% of $1b). This scaling is calculated using the methodology described in





-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

60%

50% 60% 70% 80% 90% 100% 110% 120% 130% 140% 150%


Retu

rn

S&P 500 Level


ALL 1.66%

< -30% 3.15%

-30% to -20% 2.12%

-20% to -10% 1.19%

-10% to 0% 0.44%

0% to 10% 0.55%

10% to 20% 1.42%

20% to 30% 5.36%

≥ 30% 17.80%



ALL 1.76%

< -30% 0.61%

-30% to -20% 0.56%

-20% to -10% 0.46%

-10% to 0% 0.94%

0% to 10% 1.91%

10% to 20% 2.58%

20% to 30% 2.57%

≥ 30% 3.16%


12 The six-month initiation cost of the Overlay Strategy has been included in the calculation of returns. Initiation cost of $3.1m is 92% of the $3.37m six-month initiation cost for a $1b portfolio. Dividends on the S&P 500 are not included. RJA fees are not included in the calculation of returns. 13 This is sample standard deviation within each bucket.



5. Efficiency

In our analysis to this point, our simulations have implicitly incorporated the effects of

Model Prediction Error, primarily from volatility forecasting, in their results. To

objectively analyze portfolio efficiency metrics, we now run our simulations in an

alternate universe14 where realized volatility is assumed to precisely track modeled

volatility.

Table 7: Comparison of Efficiency Metrics

Gains in efficiency from the addition of the Option Overlay Strategy are shown in

Table 7 where one can see a marked improvement in the Sharpe Ratio and the

Gain/Loss Ratio16. The value added by the strategy during market downturns is also

supported by an improvement in the Sortino Ratio to 1.03 from 0.58.

Investing in Fixed-Income:

We perform a bootstrap simulation in Appendix B assuming that the non-Equity portion

of the portfolio is invested in Fixed-Income instruments instead of Cash. Thus far, the

analysis did not include dividends on the S&P 500, but we account for this yield in the

analysis in Appendix B. The rationale behind this is to treat income from Fixed-Income

instruments in a symmetric manner to income from dividends.

The results of this analysis make a strong case for using Option Overlay Strategies in

today’s low interest rate environment.

S&P 500

Option Overlay

Strategy

50-50

Allocation

40-60

Allocation

60-40

Allocation

Mean 8.78% 8.54% 4.38% 3.50% 5.26%

Stdev 15.15% 11.09% 7.58% 6.06% 9.09%

Gain/Loss Ratio 2.84 4.68 2.84 2.84 2.84

Sharpe Ratio 0.23 0.29 0.23 0.23 0.23

Sortino Ratio 0.58 1.03 0.58 0.58 0.58

Strategy Simulation

Bootstrapped simulation based on 5000 six-month return periods constructed from monthly data sampling 15

(1/4/1960 – 12/30/2011)

14 While there is no Model Prediction Error in these simulations, there is randomness in the particular sequence of S&P 500 returns. 15All returns have been annualized for both the strategies and the S&P 500. The strategies assume an underlying portfolio of $1 b invested in the S&P 500. Fees are not included in returns. Historical S&P 500 price and dividend data, and risk-free rate data are from Bloomberg LP. Strategy initiation costs have been subtracted from returns. 16 Gain/ Loss Ratio = Expected Gain * % of Positive Returns / Expected Loss * % of Negative Returns



6. Performance during 2008 crisis

Generally, market volatility rises when the market falls and decreases with increases in

the market. This is most pronounced for short dated options. For large market moves,

we can expect to see a notable volatility change across the entire term structure of

options. At RJA, we model the change in the shape of the volatility surface for a given

market movement. As in all modeling, there exists a degree of error in forecasts. One

way in which we mitigate some of this error is by sensibly sizing positions, keeping in

mind the interaction of all the factors that can cause option prices to move. The

simulation below generates market scenarios resembling those in the second half of

2008. The results demonstrate that our Model Prediction Error is well controlled even in

extreme market scenarios.

Our reference time frame for this analysis is the six-month window from July 1, 2008 to

Dec 31, 2008. During this period, the S&P 500 decreased 29.7% and the VIX increased

69%. In the following analysis, we assume that the S&P 500 decreases by 29.7% in the

six-month period from August 15, 2012 to February 15, 2013. We also assume that the

volatility surface moves in the exact same way it did in 2008, i.e., the volatility

increase at different tenors over the six-month period is the same as the corresponding

increase in 2008.



Table 8: Simulated Performance during 2008 crisis

During the 2008 crisis, the Option Overlay Strategy would have returned $126m instead

of $137m, underperforming the target by 0.80% as outlined in Table 8. Given the

extreme nature of market and volatility movements during this period, we believe this

is testament to the robustness of our underlying process.

It is important to remember that the S&P 500 derivative market remained very liquid

throughout the crisis both in terms of volume and pricing. SPX Index options were also

insulated from the basis risk and ensuing breakdown in correlation faced by such

securities as VIX options. While counterparty default emerged as a prominent risk

factor during the crisis, improved settlement procedures and collateral management

systems are likely to mitigate the effects of counterparty failures going forward.



7. Conclusion

When properly implemented, Option Overlay Strategies are of benefit to the traditional

asset allocation approach providing additional tools to control risk and return

outcomes. Instead of a vanilla strategy buying puts or put spread collars, RJA

implements Return Engineering© to create overlay portfolios composed of put and call

options and spread positions diversified in tenors and strikes.

Within the Asset Allocation framework, Option Overlay Strategies can be used to free

the risk budget for Tactical Asset Allocation. Such strategies enable the fine tuning of

portfolio risks without encroaching upon long-term strategic allocation decisions.

Traditional Asset Allocation assumes a normal distribution of returns which does not

reflect real world experience. Option Overlay Strategies can be thought of as an

inexpensive way to offset this inherent non-normality in asset returns. The addition of

convexity to an existing portfolio can be used to dampen overall portfolio losses in

extreme tail risk scenarios.

Within the Risk Parity framework, the Option Overlay Strategy allows managers to

reduce portfolio risk without radically compromising returns. This gives managers

greater discretion over the use of leverage in such an allocation, and depresses the tail

risk exposure that leverage amplifies.

Finally, in times of constrained market liquidity, initiating derivative transactions is a

more effective way to reallocate risk exposure than selling existing assets in the

market.

We intend the results presented in this paper to be the start of a meaningful discussion

on how RJA Option Overlay Strategies can be used to enhance existing portfolio risk-

return profiles. Please send any feedback or questions to [email protected].

mailto:[email protected]



Appendix A: Bootstrapping

What is bootstrapping?

Mathematically speaking, if we uniformly and independently sample from an unknown

distribution we recover the same unknown distribution.

What does this mean for us?

We do not know the true distribution of the S&P 500 but we need to use it to get an

idea of the type of returns that can occur in the future. Using bootstrapping we can

randomly pull pieces of the past (sample historical returns) and string them together to

get a possible outcome for the future. This can be done many times to get many

possible future S&P 500 returns.

How do we generate these possible future returns?

We use realized historical S&P 500 returns to generate a broad range of possible future

S&P 500 returns. Absent reliable estimators of future possible returns, these

“bootstraps” serve as our best alternatives.

What if the realized historical returns are poor indicators of the future, and the past

never repeats itself exactly?

Bootstrapping has low sensitivity to the results in any particular historical period and it

does not restrict testing to only the realized sequence of historical returns.

How does the sampling process underlying bootstrapping work?

The key idea is of sampling with replacement. Suppose our sample contains only five

observations of S&P 500 returns, represented by five balls labeled A through E.



In this example, we assume the following returns

Ball A represents a 0.8% return of the S&P 500.

Ball B represents a -1% return of the S&P 500.

Ball C represents a -20% return of the S&P 500.

Ball D represents a 4.5% return of the S&P 500.

Ball E represents a -3.1% return of the S&P 500.

We put the five balls into a basket and then draw a ball randomly, note its value, and

replace it before making another random draw. Our recorded sequence of S&P 500

returns may look like any one of the examples below:

A, B, E, C, D

This would imply an S&P 500 return of -19.2%.

C, C, C, C, C

What if C is a period in Fall 2008? The above sequence is one where this worst of

2008 period occurs repeatedly.


C, C, E, E, E

What if E is a period in Summer 2011 (when the United States lost its AAA rating)?

The above sequence is one where this worst of 2008 period occurs twice followed

thrice by 2011’s market events.


D, D, D, A, D

This would imply an S&P 500 return of 20.2%.

This method of sampling allows us to test for a wide variety of possible S&P 500

scenarios.



Appendix B: Investing in Fixed-Income

In this analysis, we use the Barclays Capital U.S. Aggregate Bond Index17 as a broad-

based market representative for Fixed-Income instruments. Any portion of the portfolio

that is not invested in Equities is now assumed to be invested in the Barclays Index. To

calculate the implied yield on this index, we add the Barclays Index OAS spread to six-

month LIBOR. This implies a yield18 of 1.48% for the Fixed-Income portion of the

portfolio. We choose to use the OAS-based methodology to calculate yields to avoid

making assumptions about the correlation between stocks and bonds. In addition, we

now include a dividend yield of 2.1% for the S&P 500. The figures that follow are a

testament to the robustness of the Option Overlay Strategy19.

17The Barclays U.S. Aggregate Bond Index contains approximately 8,200 fixed-income issues and includes U.S. Treasuries, government-related issues, corporate bonds, agency mortgage-backed passthroughs (MBS), consumer asset-backed securities (ABS), and commercial mortgage-backed securities (CMBS). 18Implied Yield = OAS + six-month LIBOR. OAS of 76 bps has been obtained from Barclays for Aug 15, 2012. Six-month LIBOR of 71.82 bps has been obtained from Bloomberg for Aug 15, 2012. S&P Dividend Yield of 2.1% has been obtained from Bloomberg for Aug 15, 2012. 19Percent allocation to Equities has been maintained the same as the previous example for ease of comparison.



Case 1: Improve downside and upside profile of a 50% Equities 50% Fixed-Income

Allocation.

Portfolio consists of 76.6% Equities, 23.4% Barclays Aggregate Bond Index, and the

Option Overlay Strategy scaled for $ 766m (76.6% of $1b). This scaling is calculated

using the methodology described in section 3. The red line represents the performance

of a 50-50 allocation and the spread of bootstrapped outcomes (in black) represents

Model Prediction Error.

Figure 5: Performance comparison against 50-50 allocation


-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

60%

50% 60% 70% 80% 90% 100% 110% 120% 130% 140% 150%

Overlay Strategy + Equities + Fixed-Income 50-50 Allocation

Tota

l R

etu

rn

S&P 500 Level


ALL 1.47%

< -30% 2.71%

-30% to -20% 1.85%

-20% to -10% 1.07%

-10% to 0% 0.45%

0% to 10% 0.54%

10% to 20% 1.26%

20% to 30% 4.55%

≥ 30% 14.91%



ALL 1.47%

< -30% 0.51%

-30% to -20% 0.47%

-20% to -10% 0.38%

-10% to 0% 0.78%

0% to 10% 1.60%

10% to 20% 2.15%

20% to 30% 2.15%

≥ 30% 2.63%


20The six-month initiation cost of the Overlay Strategy has been included in the calculation of returns. Initiation cost of $2.59m is 76.6% of the $3.37m six-month initiation cost for a $1b portfolio. RJA fees are not included in the calculation of returns. The fixed-income portion of the portfolio is assumed to have an implied yield 1.48%. The S&P 500 is assumed to have a dividend yield of 2.1%. 21This is sample standard deviation within each bucket.




Allocation.

Portfolio consists of 61.3% Equities, 38.7% Barclays Aggregate Bond Index, and the

Option Overlay Strategy scaled for $ 613m (61.3% of $1b). This scaling is calculated

using the methodology described in section 3. The red line represents the performance

of a 40-60 allocation and the spread of bootstrapped outcomes (in black) represents

Model Prediction Error.



-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

60%

50% 60% 70% 80% 90% 100% 110% 120% 130% 140% 150%


Tota

l R

etu

rn

S&P 500 Level


ALL 1.17%

< -30% 2.17%

-30% to -20% 1.48%

-20% to -10% 0.85%

-10% to 0% 0.36%

0% to 10% 0.43%

10% to 20% 1.01%

20% to 30% 3.64%

≥ 30% 11.93%



ALL 1.18%

< -30% 0.41%

-30% to -20% 0.37%

-20% to -10% 0.31%

-10% to 0% 0.62%

0% to 10% 1.28%

10% to 20% 1.72%

20% to 30% 1.72%

≥ 30% 2.10%


22The six-month initiation cost of the Overlay Strategy has been included in the calculation of returns. Initiation cost of $2.07m is 61.3% of the $3.37m six-month initiation cost for a $1b portfolio. RJA fees are not included in the calculation of returns. The fixed-income portion of the portfolio is assumed to have an implied yield 1.48%. The S&P 500 is assumed to have a dividend yield of 2.1%. 23This is sample standard deviation within each bucket.




Allocation.

Portfolio consists of 92% Equities, 8% Barclays Aggregate Bond Index, and the Option

Overlay Strategy scaled for $ 920m (92% of $1b). This scaling is calculated using the

methodology described in section 3. The red line represents the performance of a 60-40

allocation and the spread of bootstrapped outcomes (in black) represents Model

Prediction Error.



-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

60%

50% 60% 70% 80% 90% 100% 110% 120% 130% 140% 150%


Tota

l R

etu

rn

S&P 500 Level


ALL 3.89%

< -30% 0.66%

-30% to -20% 0.63%

-20% to -10% 0.46%

-10% to 0% 0.92%

0% to 10% 1.93%

10% to 20% 2.63%

20% to 30% 3.05%

≥ 30% 11.35%



ALL 1.76%

< -30% 0.61%

-30% to -20% 0.56%

-20% to -10% 0.46%

-10% to 0% 0.94%

0% to 10% 1.91%

10% to 20% 2.58%

20% to 30% 2.57%

≥ 30% 3.16%


24The six-month initiation cost of the Overlay Strategy has been included in the calculation of returns. Initiation cost of $3.1m is 92% of the $3.37m six-month initiation cost for a $1b portfolio. RJA fees are not included in the calculation of returns. The fixed-income portion of the portfolio is assumed to have an implied yield 1.48%. The S&P 500 is assumed to have a dividend yield of 2.1%. 25This is sample standard deviation within each bucket.



References

Markowitz, Harry (1952), “Portfolio Selection.” The Journal of Finance, vol. 7, no. 1:

77-91.

Brinson, Gary P., L. Randolph Hood, and Gilbert L. Beebower (1986), “Determinants of

Portfolio Performance.” Financial Analysts Journal, vol. 42, no. 4: 39–44.

Jahnke, William (1997),“The Asset Allocation Hoax.” Journal of Financial Planning, vol.

1, no.2: 109-113

Ibbotson, Roger G., and Paul D. Kaplan (2000), “Does Asset Allocation Policy Explain 40,

90, or 100 Percent of Performance?” Financial Analysts Journal, vol. 56, no. 1: 26–33.

Xiong, James, Roger G. Ibbotson, Thomas Idzorek, and Peng Chen (2010), “The Equal

Importance of Asset Allocation and Active Management.” Financial Analysts Journal,

vol. 66, no. 2.



Disclaimer

This document is confidential and may not be reproduced without the written consent

of Ross, Jeffrey & Antle LLC (RJA). It is not intended for distribution and may not be

distributed without the written consent of RJA.

The ideas and material contained herein are the intellectual property of RJA. The

information contained herein is believed to be reliable and has been developed in good

faith but no representation or warranty expressed or implied, is made by RJA as to the

accuracy or completeness of the information.

This document is not intended to be an offer or a solicitation of an offer to buy or sell

relevant securities. Any historical results presented herein should not and cannot be

viewed as indicators of future performance.

RJA is not an advisor as to legal, taxation, accounting or regulatory matters in any

jurisdiction and is not providing any advice as to such matters to the recipient. The

recipient should discuss such matters with the recipient’s advisors or counsel and make

an independent evaluation and judgment with respect to them.

Hypothetical performance results have many inherent limitations that may adversely

impact actual results, some but not all of which are described below. They may benefit

from hindsight, do not reflect actual trading under actual market conditions and

therefore do not reflect the impact that unforeseen economic and market factors may

have had on the advisor’s investment decisions. No representation is made that the

performance would have been the same or as good as such simulated performance;

there are frequently sharp differences between hypothetical results and the actual

record subsequently achieved. The simulated results do not take into account

enhancements that may be made to the proprietary computer models over time.

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