The MAS Academy – vol. 7 Correlation

PD&M Multi Asset Solutions

For internal use only.

Multi Asset Solutions:actively managed and

actively explained

Participation Stability PreservationAlternatives

2

This topic enables you to explain …

… what correlation is;

… the difference between ex-post and ex-ante correlation;

… why it is key for investment management to anticipate correlations correctly;

Key objectivesTime investment: ~15 minutes

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SECTION 1

Definition and significance of correlation

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Definition 1/2

Correlation is a statistical measure of the linear dependency betweentwo variables, e.g. investment returns.

Correlation is measured with a correlation coefficient ranging from+1 to -1; 0 means no linear dependency is detected.

Positive correlation means that investment returns tend to change in thesame direction.

Negative correlation means that investment returns tend to change in theopposite direction.

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Definition 2/2

Dependency of return developments

Increasing diversification benefit

Correlation coefficient:

Dispersion of returns:

Correlation:

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Let’s have a look at two markets – e.g. equities and bonds – and their day-to-day changes. The statistical dispersion of returns is the more linear the more correlated the two return developments are, and the more widespread the more uncorrelated they are:

perfectlypositive

un-correlated

perfectlynegative

Retu

rn o

feq

uit

ies

Return of bonds

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Backward looking: ex-post correlation 1/2

0

200

400

600

800

1000

1200

19871988

19891990

19911992

19931994

19951996

19971998

19992000

20012002

20032004

20052006

20072008

CH

F

Swiss Bonds Swiss Equities

The graph illustrates the cumulative performanceof Swiss bonds and Swiss equities, from which we conclude the followingrisk and return figures:

Based on these keyfigures, we calculate the correlation between the two markets as follows …

Data as at 31.07.2008 / Time horizon: 31.12.1987 – 31.07.2008

Risk Return

Swiss bonds 2.8% 4.2%

Swiss equities 16.4% 11.0%

How to measure it

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… We calculate the (ex-post) trailing correlation based on monthly returns:The first correlation value calculation includes the 36 monthly returns from 12/87 to 12/90, the last one those from 07/05 to 07/08;the trailing windows in between contain 36 months each.

Situation in October 1994:ex-post correlation = 0.5*

* estimated over the previous 36 month

Situation in December 2000:ex-post correlation = 0*

Ex post correlation between Swiss bonds and Swiss equities(36 month trailing window)

-0.60

-0.40

-0.20

-

0.20

0.40

0.60

0.80

Situation in December 2004:ex-post correlation = -0.5*

-60.0%

-40.0%

-20.0%

0.0%

20.0%

40.0%

60.0%

80.0%

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

12-M

onth

Rolli

ng R

etu

rn

Swiss Bonds Swiss Equities

Backward looking: ex-post correlation

2/2

A look in the rear-view mirror12-month rolling returns

The curve shows that ex-post correlations were rather unstable.

It is thus very difficult to predict future(ex-ante) correlations.

0

200

400

600

800

1000

1200

19871988

19891990

19911992

19931994

19951996

19971998

19992000

20012002

20032004

20052006

20072008

CH

F

Swiss Bonds Swiss Equities

1 2

3

…………………………..

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Forward looking: ex-ante correlationPredicting the future

Ex-ante ≠ ex-post correlation.

Modelling and predicting correlations is a complex task* and requires professional guidance.

Sound risk monitoring and risk management are impossible without tracking correlations closely!

* Usually part of sophisticated risk models which are not easy to understand by clients and many practitioners. UBS Global Asset Management workswith ex-ante risk models that are based on forward-looking capital market assumptions (derived from a multi-factor model and inverse

optimisation).

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Ex post correlation between Swiss bonds and Swiss equities(36 month trailing window)

-0.60

-0.40

-0.20

-

0.20

0.40

0.60

0.80

Ex ante correlationEx-post correlation Ex-ante correlation

?

?

?

SECTION 2

Anticipate correlations correctlyis key for investment management

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Why is correlation important? 1/2

The lower the correlation between assets / asset classes the bigger the diversification benefit to a portfolio.

Future (ex-ante) correlation is key:For every portfolio investment decision investors rely on a predicted correlation,as the following example illustrates:– Within a multi-asset portfolio investors expect a diversification benefit because the

correlation between asset classes like bonds, equities, commodities and hedge funds is not perfect and will therefore provide stability (e.g. if the economy overheats and interest rates rise, bonds(and partly equities) suffer, whereas commodities perform well).

– Worst-case scenario: extreme market turmoil putting all asset classes under pressure and making correlations between all asset classes increase.

If an investor relies on falsely predicted correlations which finally turn out to be higher, the portfolio risk may get out of control!

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Diversification effect

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A simplified example for illustration purposes:

Let’s assume a portfolio of Swiss bonds and Swiss equities andits portfolio manager predicting an ex-ante correlation of -0.5 between Swiss bonds and Swiss equities. The expected portfolio risk is 3.8%.

Finally, the correlation turns out to be +0.5. In this case, the expected portfolio risk is 8.5%, i.e. much higher!

… may have a detrimental impact on risk!

25.0%

75.0%

Swiss bonds

Swiss equities

Swiss bonds

Swiss equities

3%

Risk (volatility) Correlation

+0.5

Assumptions:

Results:

Weight

75%

25% 16%

Correlation

0

6.6%

Correlation

-0.5

Expected portfolio risk

Why is correlation important? 2/2

False correlation assumptions …

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3.8% 8.5%

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Conclusion

The lower the correlation between assets is, the bigger is the diversification benefit to a portfolio.

Assessing future (ex-ante) correlations is a challenging task and requires professional guidance.

Forecasting correlations correctly is key for every portfolio investment decision,for both strategic and tactical asset allocation.

Sound risk monitoring and risk management are impossible without tracking correlations closely!

Close correlation tracking and risk management

are key for all multi-asset solutions!

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SECTION 3

Frequently asked questions

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Frequently asked questions 1/2

Every risk model ultimately relies on patterns which have to be estimated based on historic observations. Therefore, they are always subject to some degree of estimation risk.

If correlations exhibit structural breaks, the likelihood of failing risk models is high. The latest example is the subprime / credit crisis, where all models known to us have underestimated risk inherent in seemingly safe positions.

1) How good are risk models?

It shows the realized past correlation of two variables, e.g. investment returns.

For multi-asset portfolios, it gives an indication of the past diversification potential.

For hedging strategies, it shows the past tracking characteristics. As an example: If you used an equity index future in order to hedge parts of your portfolio and ex-post correlation was 0.98, your hedge worked decently well. The question whether this relationship persists going forwardis covered by ex-ante correlation.

2) What does ex-post correlation tell?

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Frequently asked questions 2/2

Any relations between assets is influenced by many underlying factors, which might suddenly change. Therefore, sophisticated risk models like UBS’s proprietary one are based on forward-looking capital market assumptions (derived from a multi-factor model and inverse optimisation) and they are constantly monitored (short-term risk models are revised in shorter intervals than long-term risk models).

3) Why is it difficult to estimate ex-ante correlation?

4) Why is it dangerous to extrapolate a seemingly stable relationship?If you expect a given correlation and construct a portfolio taking the respective diversification benefits into account, any sudden increase in correlation impacts total risk, which may get out of control. In a worst case scenario, like an extreme market turmoil, all assets might come under pressure and, simultaneously, correlations between assets might increase.

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The end!

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Contact information

www.ubs.com

Pascal GuilletUBS Global Asset ManagementProduct Development & ManagementGessnerallee 3-5CH-8098 Zürich

+41-44-235 4314pascal.guillet@ubs.com

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