Optimal Global Equity Allocation With Individual Stocks

|
Includes: AI, ARLP, ATW, AWLCF, BWLLY, CJREF, CSCO, DLAKY, ECIFY, ERJ, F, GKNGY, GM, IVR, LYB, NOBGY, NTAP, POAHY, RXEEY, SCRPY, SDRL, SIETY, TCLAF, TEVA, VR, WLMIY, WLWHF, WMC
by: Mark James Thompson

Summary

Even a smallish portfolio of stocks can be well diversified internationally.

Individual investors typically do not rely on asset correlations in their investment decisions.

Portfolio risk-return efficiency can be enhanced by exploiting asset correlations.

An "optimized" portfolio doesn't neutralize stock risk: returns are likely to issue from well-known risk factors.

In previous articles, I have discussed both minimum volatility portfolios and domestic equity allocation. In the former article, we saw both that accounting for the volatility and correlation how expanding the equity set can lead to better investment outcomes in terms of terms Sharpe ratios (risk-reward efficiency). In the latter article, we saw how a collection of individual stocks with a bit of discretion can perform better than a portfolio of risk-diluted ETFs. This article blends the two approaches by creating a stock-based portfolio with some of the qualities of an allocation-based strategy, but using individual stocks.

The goal is to develop a portfolio of 20-50 stocks - this is about the number needed to create a reasonably diversified portfolio whilst remaining tractable enough to manage. Individual investors with small portfolios typically reduce risk through large-cap and dividend stocks, emphasizing careful stock selection over portfolio construction. In contrast to that intuitive and legitimate approach, the idea here is to reduce risk by exploiting the statistical covariance of the entire global equity market. This will be done using constrained mean-variance optimization.

The next section describes the process and structures that define the solution portfolio, but if you want to use this article as a "quick pick list" for risk-efficient stocks with low correlation, feel free to jump down to results and discussion.

Investable Universe

With over 37,000 equities to invest in worldwide, security selection is a daunting process. Like most ETF benchmark indices that number needs to be winnowed down for reasons of both tractability and investability. What might be considered the closest proxy for the world portfolio, (NYSEARCA:VT), has only about 7,300 securities. In this exercise, the initial pool screened for stocks with at least 3 analyst estimates left about 6,200 assets. This screen acts as an implicit liquidity screen, and biases the sample toward large-cap stocks and well-followed small/mid-caps. The next screen limits stocks to those with dividend yield greater than the median (1.9%) and the forward earnings yield (EPS/price) is likewise greater than the median (5.25%). The expected dividend has to be less than expected profit, and book value must be positive. This leaves about 1,100 stocks.

The equities are divided into 4 market capitalization based classes: micro (<150m), small (<1,500m), mid (<6,000m), large (>6,000m). These correspond roughly to the break points in the major indices. Micro-cap stocks are screened out for two reasons: the first is liquidity as many of the stocks do not trade each day - this makes the covariance of the stock difficult to ascertain; the second reason is that the asymmetries of information between management and the public are quite large in my experience (I have had micro-caps triple and halve in price without any inkling as to why).

Each capitalization class of these is limited to 33% of the portfolio, corresponding roughly to a large/mid/small-cap ETF allocation that an investor might choose.

The stocks, assigned to 1 of 109 industries, are aggregated into about 19 sectors. The industry weights are proportional to the number of stocks in those industries: credit and financial services comprise about 13.1% based counts, and aerospace & defense comprises about 1% of the population. To prevent empty industry allocations, these smallest sectors are allocated up to 5% to allow at least one stock.

The portfolio is further constrained by corporate domicile based on the number of companies within a region. For example, the US-based stocks, which are ca. 34% of the population, receive a weight of 34% - using counts instead of market value tilts the portfolio more towards small- and mid-caps. Similarly, the countries are split between Developed (81%), Developing (17%), and Other Markets (2%). This generally reflects the 10-20% standard allocation to developing countries.

The final portfolio is allowed to drift from this market-neutral allocation by 10%. Each stock is constrained to 5% of the portfolio, with each industry requiring at least a 2.5% position.

Optimization

There are a number of ways to account for risk in portfolio construction, but mean-variance analysis is still probably the most common optimization technique where the idea is to minimize fluctuations in value while maximizing returns however measured.

Traditionally, the mean expected returns have been estimated from the asset return data themselves; however, past returns predict future returns only weakly. Reasonably efficient markets do not allow for any strong predictors. Some investors have dispensed with the exercise altogether by adopting an equal weight approach, or choose to minimize just risk assuming returns to be equal and/or random.

The financial literature is not quite so pessimistic about predictors: value and momentum are well known and widely used predictors of returns. In addition, the financial literature documents other small but statistically significant predictors.

In this article, analysts' forward earnings estimates are used as the rational expected return. The first caveat of this value metric is that firms with higher earnings yield are inherently riskier: either because they employ more leverage or the earnings are less certain. Moreover, as any experienced equities trader knows, earnings estimates do not necessarily predict price: a stock can get crushed even beating estimates by less than expected; the converse is the same true for an earnings miss. Furthermore, all analyst appraisals likely exhibit systematic positive bias given the incentives of the financial industry (Kubik 2003; Womack 1996). Hence they're best interpreted relatively rather than absolutely. Using momentum, price to book, dividends, would be empirically founded alternatives to earnings estimates.

Risk and asset correlation are based on the annualized volatility of 2 years of daily adjusted returns from Yahoo! Finance. As a practical empirical note, mean variance analysis becomes intractable with too many assets. The ca. 1,100 stocks passing the screen are ordered by expected Sharpe ratios, and the top 10 stocks from each industry are included. Conceptually, this approach does not exploit the entire asset global covariance matrix, but since the most risk-efficient assets typically dominate the solution portfolio, this represents a reasonable approximation.

Table 1 shows the correlation matrix of the solution portfolio, where yellow indicates low correlation. The heat map underscores why global equity allocation is a useful diversifier.

Table 1: Correlations and Annual Standard Deviation

-\-

1378

2777

3336

552

685

832

PPH

(NYSE:AI)

(NASDAQ:ARLP)

(NYSE:ATW)

(AWDR)

(OTCPK:AWLCF)

(BWLPG)

(OTCPK:BWLLY)

(CJR.B)

(OTCPK:CJREF)

(NASDAQ:CSCO)

(DIE)

(OTCPK:SIETY)

(EDF)

(OTCPK:ECIFY)

(NYSE:ERJ)

(F34)

(OTCPK:WLMIY)

(NYSE:F)

(NYSE:GM)

(GNK)

(OTCPK:GKNGY)

(NYSE:IVR)

(LHA)

(OTCQX:DLAKY)

(NYSE:LYB)

(N21)

(OTCPK:NOBGY)

(NASDAQ:NTAP)

(POR3)

(OTCPK:POAHY)

(RXL)

(OTCPK:RXEEY)

(NYSE:SDRL)

(SQM)

(TCL.A)

(OTCPK:TCLAF)

(NYSE:TEVA)

(U96)

(OTC:SCRPY)

(NYSE:VR)

(NYSE:WMC)

(NYSE:WOW)

(OTC:WLWHF)

1378

0.43

0.40

0.24

0.41

0.04

0.30

0.05

-0.02

0.05

0.04

0.15

0.07

0.05

-0.01

-0.02

0.01

0.02

0.10

0.03

0.04

0.01

-0.05

0.11

0.03

0.12

0.02

0.12

0.01

0.01

0.00

0.04

-0.01

0.01

-0.02

-0.02

0.05

 

2777

0.36

0.18

0.32

0.04

0.39

0.02

0.01

0.04

-0.01

0.04

0.03

0.04

0.06

0.05

0.01

0.06

0.08

0.06

0.09

0.02

-0.01

0.07

-0.02

0.08

0.07

0.16

0.02

-0.01

0.08

0.01

0.00

0.01

-0.08

0.00

0.06

   

3336

0.43

0.18

0.07

0.12

0.01

-0.01

0.03

-0.01

0.06

0.03

-0.04

-0.01

-0.05

0.01

0.00

0.02

0.04

0.01

0.00

-0.04

0.07

0.06

0.00

0.04

0.10

-0.01

0.00

0.03

0.03

-0.08

0.05

-0.08

-0.01

-0.02

     

552

0.31

0.02

0.28

-0.01

0.03

0.00

0.03

0.08

0.06

0.00

0.06

0.01

0.02

0.10

0.02

0.01

0.06

0.03

0.02

0.03

0.05

0.09

0.02

0.14

0.04

0.00

0.00

0.03

0.04

0.05

-0.01

0.02

0.02

       

685

0.19

-0.01

-0.08

-0.02

0.05

-0.02

-0.05

0.06

0.08

-0.02

0.00

0.00

-0.03

0.02

0.01

0.03

-0.04

-0.04

0.04

0.00

0.03

0.06

0.00

-0.09

0.06

0.09

0.02

-0.16

0.04

-0.05

-0.01

0.05

         

832

0.32

0.03

0.05

0.03

0.06

0.07

0.00

0.03

0.03

0.10

-0.03

0.02

0.05

0.12

0.09

0.11

0.07

0.08

0.06

0.08

0.05

0.09

0.02

0.04

0.04

0.05

0.00

0.05

-0.06

0.07

0.01

           

PPH

0.14

0.00

0.01

-0.04

0.04

0.03

0.00

0.04

0.01

-0.05

0.00

-0.06

0.10

-0.03

0.04

0.08

0.03

0.02

-0.02

0.04

0.07

0.05

-0.08

0.03

0.02

-0.01

-0.06

0.07

0.05

-0.07

             

AI

0.19

0.15

0.16

0.03

0.03

0.06

0.19

0.06

0.01

0.21

0.02

0.31

0.24

0.11

0.46

0.10

0.29

0.04

0.13

0.17

0.06

0.05

0.12

0.15

0.15

0.07

0.11

0.48

-0.04

               

ARLP

0.25

0.26

0.03

0.06

0.00

0.08

0.11

0.02

0.13

0.05

0.17

0.12

0.07

0.11

0.02

0.29

0.05

0.18

0.03

0.09

0.14

0.14

0.04

0.06

0.11

0.06

0.07

0.06

                 

ATW

0.35

0.11

0.08

0.10

0.14

0.11

0.02

0.22

-0.04

0.21

0.18

0.02

0.10

0.02

0.46

0.00

0.11

0.01

0.06

0.39

0.21

0.13

0.05

-0.05

0.14

0.12

0.06

                   

AWDR

0.37

0.22

0.03

0.07

0.07

0.05

0.08

0.06

0.01

0.00

-0.01

-0.02

-0.02

0.17

0.07

0.05

0.02

0.05

0.21

0.10

-0.03

0.01

0.04

-0.02

0.00

-0.01

                     

BWLPG

0.33

0.06

0.10

0.05

0.01

0.12

0.07

0.07

0.08

0.08

-0.03

0.10

0.20

0.04

0.08

0.14

0.15

0.25

0.03

0.03

0.08

0.12

0.14

0.00

0.08

                       

CJR.B

0.23

0.00

-0.01

0.09

0.05

0.02

0.07

0.12

0.06

-0.05

0.03

0.09

0.06

-0.02

0.08

0.08

0.02

0.03

0.15

-0.02

-0.05

0.08

-0.03

0.03

               

Diagonal is annualized standard deviation. Off diagonal are correlations.

CSCO

0.20

0.10

0.04

0.24

0.06

0.35

0.32

0.14

0.10

0.14

0.24

0.03

0.21

0.24

0.18

0.09

0.13

0.18

0.12

-0.01

0.18

0.10

-0.01

                   

DIE

0.15

0.15

0.06

0.03

0.14

0.08

0.15

0.03

0.11

0.13

-0.02

0.12

0.16

0.31

0.04

0.05

-0.02

0.04

0.12

0.14

0.08

-0.05

                     

EDF

0.17

0.17

0.09

0.09

0.09

0.10

0.03

0.12

0.07

-0.02

0.14

0.21

0.29

0.08

0.06

0.03

0.02

0.23

0.14

0.01

0.08

                       

ERJ

0.26

0.04

0.28

0.28

0.16

0.18

0.18

0.27

0.04

0.18

0.19

0.16

0.15

0.17

0.18

0.13

0.10

0.22

0.14

0.07

                         

F34

0.10

0.06

0.03

0.06

0.02

-0.02

0.06

0.21

0.11

0.09

0.07

0.04

0.00

0.01

0.06

0.29

0.08

-0.01

0.16

                           

F

0.20

0.59

0.20

0.19

0.22

0.36

0.10

0.22

0.25

0.16

0.05

0.14

0.19

0.17

0.02

0.25

0.19

0.06

                                     

GM

0.23

0.11

0.17

0.17

0.27

0.04

0.21

0.22

0.12

0.01

0.07

0.18

0.19

0.01

0.25

0.17

0.04

                                       

GNK

0.18

-0.02

0.35

0.12

0.08

0.08

0.33

0.19

0.15

-0.04

0.12

0.05

0.08

0.04

0.01

0.10

                                         

IVR

0.17

0.01

0.16

-0.01

0.12

0.08

0.02

-0.04

0.06

0.03

0.08

0.04

0.12

0.52

0.02

                                           

LHA

0.30

0.04

0.00

0.08

0.37

0.29

0.01

0.03

0.12

0.06

0.01

0.05

0.03

0.05

                                             

LYB

0.27

0.10

0.24

0.18

0.16

0.29

0.25

0.17

0.21

0.10

0.24

0.17

0.12

On the diagonal are the annualized standard deviations of the stocks. The risks of the stocks in the optimized portfolio are in the 20-40% range. This range is much higher than the standard deviation of the US market in general on the order of 10-20% per year. Hence, much of the portfolio's overall risk efficiency is coming from the very low correlation amongst the stocks, which are spread amongst a half a dozen currencies and exchanges.

Results and Discussion

Table 1 shows the portfolio composition and weights of the optimized portfolio:

Optimized Portfolio

Market

Country

Company

Security

Sector

Ex{

Yield}

Ex{

Earnings

Yield}

Size

Weight

DM

ES

Embraer SA

ERJ@

NYSE

Aerospace

Defense

2.3%

6.7%

mid

2.5%

EM

CN

China Hongqiao Group Ltd

1378@

SEHK

Basic

Materials

4.1%

18.9%

mid

5.0%

EM

MY

Media Chinese International Limited

685@

SEHK

Business

Services

7.0%

11.6%

small

2.4%

DM

CA

Corus Entertainment Inc.

CJR.B@

TSE

Business

Services

7.7%

11.0%

small

0.1%

EM

CL

Sociedad Quimica y Minera de Chile

SQM@

NYSE

Chemicals

6.7%

9.4%

mid

1.4%

DM

US

LyondellBasell Industries NV

LYB

@NYSE

Chemicals

2.9%

10.6%

large

1.1%

DM

GB

Greene King plc

GNK

@LSE

Consumer

Discretionary

3.4%

7.0%

mid

2.2%

DM

NL

PPHE Hotel Group Ltd

PPH

@LSE

Consumer

Discretionary

2.4%

9.1%

small

0.4%

DM

US

General Motors Company

GM@

NYSE

Consumer

Durables

4.3%

14.5%

large

5.0%

DM

DE

Porsche Automobil Holding SE

POR3@

XETRA

Consumer

Durables

3.0%

15.4%

large

1.9%

DM

US

Ford Motor Company

F@

NYSE

Consumer

Durables

3.7%

11.0%

large

0.2%

DM

SG

Wilmar International Limited

F34@

SGX

Consumer

Staples

2.5%

8.4%

large

2.5%

DM

US

Arlington Asset Investment Corp

AI@

NYSE

Financial

Services

17.5%

27.0%

small

5.0%

OM

BM

Validus Holdings, Ltd.

VR@

NYSE

Financial

Services

2.7%

10.3%

mid

5.0%

DM

GB

Awilco Drilling PLC

AWDR@

OMXNO

Fossil Fuel

Production

63.4%

83.8%

small

5.0%

DM

US

Alliance Resource Partners, L.P.

ARLP@

NASDAQ

Fossil Fuel

Production

10.8%

15.8%

mid

5.0%

DM

US

Atwood Oceanics, Inc.

ATW@

NYSE

Fossil Fuel

Production

1.9%

31.7%

small

1.8%

DM

NO

Seadrill Ltd

SDRL@

OMXNO

Fossil Fuel

Production

11.9%

25.5%

mid

0.1%

DM

IL

Teva Pharmaceutical Industries Ltd.

TEVA@

NYSE

Healthcare

2.2%

8.4%

large

2.5%

DM

FR

Rexel SA

RXL@

SBF

Heavy

Industry

4.9%

7.2%

mid

2.5%

DM

CA

Transcontinental Inc.

TCL.A@

TSE

Industrial

Commercial

Services

4.6%

15.5%

small

5.0%

DM

SG

SembCorp Industries Limited

U96@

SGX

Industrial

Commercial

Services

4.1%

10.5%

mid

2.6%

DM

HK

Noble Group Limited

N21@

SGX

Industrial

Commercial

Services

6.7%

16.1%

mid

0.4%

DM

HK

Ju Teng International Holdings Limited

3336@

SEHK

IT

Hardware

4.4%

20.1%

small

4.7%

DM

US

Cisco Systems, Inc.

CSCO@

NASDAQ

IT

Hardware

2.7%

7.9%

large

4.7%

DM

US

NetApp Inc.

NTAP@

NASDAQ

IT Services

and Software

1.9%

8.8%

large

2.5%

DM

US

Western Asset Mortgage Capital Corp

WMC@

NYSE

Real

Estate

18.8%

20.0%

small

5.0%

DM

US

Invesco Mortgage Capital Inc

IVR@

NYSE

Real

Estate

12.8%

13.0%

mid

5.0%

EM

CN

Central China Real Estate Ltd

832@

SEHK

Real

Estate

10.1%

31.9%

small

2.5%

EM

CN

Guangzhou R&F Properties Co Ltd

2777@

SEHK

Real

Estate

7.0%

25.7%

mid

0.3%

DM

BE

D'Ieteren SA

DIE@

SBVM

Retail

2.6%

7.5%

mid

2.4%

DM

AU

Woolworths Limited

WOW@

ASX

Retail

4.9%

6.9%

large

0.1%

EM

CN

China Communications Services Corp. Ltd.

552@

SEHK

Telecom

3.7%

11.8%

mid

2.5%

DM

NO

BW LPG Ltd

BWLPG@

OMXNO

Transport

16.8%

25.6%

small

5.0%

DM

DE

Deutsche Lufthansa AG

LHA@

XETRA

Transport

3.3%

15.6%

large

3.2%

DM

FR

Electricité de France SA

EDF@

SBF

Utilities

5.9%

9.4%

large

2.6%

Markets: developed (DM); emerging (EM); other (OM). Ex{}: represents 1Y forward dividend and earnings yield.

The absolute position sizes issuing from this type of numerical technique are of dubious utility; it likely makes no practical sense to have one stock with 50x the weight of another. Both transaction and monitoring costs likely outweigh the gain from diversification here.

The solution portfolio has an expected earnings yield of about 18% and an annualized standard deviation of about 6%, giving an expected earnings Sharpe of about 3. For comparison, the US stock market median earnings yield is currently about 5%.

That substantially higher yield comes from a number of known risk factors: it tilts towards small caps, emerging markets, cyclical industries, and anti-momentum from China's recently shattered equity market. Aside from systematic risk, the portfolio serves up plenty of business risk with contrarian picks in the form of Awilco Drilling in the North Sea oil or Alliance Resource Partners in the declining US coal industry (both of which have their SA advocates).

At the same time, the portfolio also comprises some widely covered blue-chip value stocks in the form of Cisco, General Motors, and Electricité de France. These are likely the result of the constraints placed on the optimization.

In short, there is no risk-free lunch at the stock level. The portfolio leans almost exclusively on portfolio diversification and large market discounts to the estimated earnings power.

Conclusion

Risk notwithstanding, this type of optimization technique offers a unique look at the equity universe, which is distinct from a stock-by-stock selection process. The extremely heterogeneous nature of the stocks in the solution portfolio put into strong relief the difference between a collection of stocks based on a particular screen or investing style and a portfolio that exploits the correlation amongst assets. In doing so, I hope to have provided some food for thought, and perhaps a stock or two worth considering for your risk-efficient portfolio.

In terms of future work in this vein, things worth discussing are the types of constraints, investability filters, and objective functions. For example, aggressive investors might use momentum or price-to-book as objective functions with even more relaxed constraints; risk-adverse investors might opt for some measure of business quality and constrain the emerging markets and/or small-cap allocations.

Disclosure: I am/we are long GM, CSCO, ARLP.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

Additional disclosure: I own some of the stocks in the solution portfolio as similar optimization techniques belong to my normal repertoire of security selection.

Editor's Note: This article discusses one or more securities that do not trade on a major U.S. exchange. Please be aware of the risks associated with these stocks.