Correlation[1]

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 Preservation Alternatives   

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 objectives Time investment: ~15 minutes For internal use only.

SECTION 1 Definition and significance of correlation For internal use only.

Definition 1/2 Correlation is a statistical measure of the linear dependency between two 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 the same direction . Negative correlation means that investment returns tend to change in the opposite direction . For internal use only.

Definition 2/2 Dependency of return developments Increasing diversification benefit Correlation coefficient: Dispersion of returns: Correlation: For internal use only. 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: perfectly positive uncorrelated perfectly negative Return of equities Return of bonds

Backward looking: ex-post correlation 1/2 The graph illustrates the cumulative performance of Swiss bonds and Swiss equities, from which we conclude the following risk and return figures: Based on these key figures, we calculate the correlation between the two markets as follows … Data as at 31.07.2008 / Time horizon: 31.12.1987 – 31.07.2008 How to measure it For internal use only. 11.0% 16.4% Swiss equities 4.2% 2.8% Swiss bonds Return Risk

… 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* Situation in December 2004: ex-post correlation = -0.5* Backward looking: ex-post correlation 2/2 A look in the rear-view mirror 12-month rolling returns The curve shows that ex-post correlations were rather unstable . It is thus very difficult to predict future (ex-ante) correlations . 1 2 3 ………………………… .. For internal use only.

Forward looking: ex-ante correlation Predicting 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 works with ex-ante risk models that are based on forward-looking capital market assumptions (derived from a multi-factor model and inverse optimisation). For internal use only. Ex ante correlation Ex-post correlation Ex-ante correlation ? ? ?

SECTION 2 Anticipate correlations correctly is key for investment management For internal use only.

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 ! For internal use only. Diversification effect

A simplified example for illustration purposes: Let’s assume a portfolio of Swiss bonds and Swiss equities and its 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 ! Why is correlation important? 2/2 … may have a detrimental impact on risk! 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 False correlation assumptions … For internal use only. 3.8% 8.5%

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! For internal use only.

SECTION 3 Frequently asked questions For internal use only.

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 forward is covered by ex-ante correlation. 2) What does ex-post correlation tell? For internal use only.

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. For internal use only.

The end! For internal use only.

Contact information www.ubs.com Pascal Guillet UBS Global Asset Management Product Development & Management Gessnerallee 3-5 CH-8098 Zürich +41-44-235 4314 [email_address] For internal use only.

Correlation[1]

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