Why Existing Portfolio Management Models Fail – Part 1 Modern Portfolio Theory, introduced by Markowitz in 1952, is still used extensively as a tool for portfolio management of traditional, as well as alternative investments. Rather than selecting an asset based on its expected risk‐return profile, it considers how assets in a portfolio move in tandem. The fundamental concept is that of diversification. Given two assets, as long as there is less than perfectly positive correlation, the portfolio’s overall risk can be reduced. Although many of the model’s failings have been widely discussed, insufficient attention has been paid to the implications of constantly changing correlations. This paper is divided into two sections. The first section summarises the model’s key assumptions and limitations for managing traditional or alternative investment portfolios. Using data from 1999‐2010, we demonstrate that currency, commodity and equity returns are increasingly failing to follow a normal distribution. The second section tackles a less widely published topic: that of constantly changing correlations, as well as the impact of the time period under observation. The Key Assumptions and Limitations of Modern Portfolio Theory Mean‐Variance Analysis Major Limitations
‐ Assumes normally distributed returns ‐ Financial time series/hedge fund returns not distributed normally ‐ Employs two parameters: mean and variance ‐ Volatility treats good and bad risks as equal ‐ Defines risk as volatility (standard deviation) ‐ Volatility alone is an incomplete risk measure Modern Portfolio Theory (MPT) ‐ A portfolio with relatively low volatility may exhibit a far greater propensity for extreme losses, yet this is ignored by MPT ‐ Maximises portfolio’s expected return for given level of risk Efficient Markets Hypothesis (EMH) and MPT ‐ Information asymmetry exists: some are better informed
‐ Assume efficient markets and rational investors ‐ Behavioural economics/cognitive biases/financial bubbles Diversification ‐ Assumes constant volatilities and correlations, whereas volatilities and correlations are constantly changing ‐ Portfolio of assets, with less than perfectly positive correlations, produces lower overall risk than summing risks of individual assets ‐ Expected vs. actual volatilities and correlations may vary widely. Portfolio diversification based on MPT fails The normal distribution 1 , on which Modern Portfolio Theory (MPT) is based, assumes assets returns are symmetric, and caters for mildly volatile events. It does not handle extreme or fat‐tailed events. Tables 1 and 2 compare the actual frequency of 3% and 4.5% price moves with the frequencies expected under normally distributed returns. Since 1999 the EUR‐USD saw 3% price moves every 3yrs, yet traditional finance models, which measure risk and expected returns using the normal distribution, expect this event every 540 yrs. During 2005‐2010 the S&P 500 and DAX saw 4.5% price moves every 9‐10 weeks, yet traditional finance models expect this event once a year. These tables also demonstrate converging correlations amongst assets. Whereas 10 years ago the DAX was twice as likely to experience a 4.5% move as the S&P 500, both indices now seem to face similar levels of volatility. Frequency (Years) of 3% Price Move: Jan99‐Oct10 TABLE 1 Jan99+ 5yr EUR GBP CHF AUD ZAR S&P 500 Russell 2000 DAX RJ_CRB NormDist
540.00 3,262.00 269.00 9.38 0.58 0.14 0.06 0.06 0.38 Actual
3.00
1.70 2.00 0.43 0.21 0.10
0.07 0.06 0.23
NormDist
365.00
83.00 147.00 1.16 0.37 0.07
0.03 0.07 0.14
Frequency (Years) of 4.5% Price Move: Jan99‐Oct10 Jan99+ 5yr
TABLE 2 NormDist Actual
NormDist EUR 232,386,184 12.00
102,576,120
GBP 11,757,517,824 12.00 3,617,341 CHF 46,300,473 6.00 11,536,845 AUD 30,453 2.40 335.00 ZAR 80.00 1.10 31.00 S&P 500 4.05 0.35
0.95
Russell 2000 0.65 0.22 0.18 DAX 0.71 0.17 1.01 RJ_CRB 33.32 0.69
3.77
3yr Actual
1.67
0.83 0.83 0.19 0.17 0.07
0.04 0.08 0.11
NormDist 24.00 7.33 14.00 0.27 0.18 0.03 0.02 0.04 0.07 Actual
1.00
0.50 0.50 0.12 0.12 0.04
0.02 0.05 0.07
Actual
5.00
5.00 2.50 1.00 1.25 0.19
0.11 0.17 0.31
3yr NormDist 239,416 16,946 72,781 15.00 7.00 0.21 0.07 0.28 0.90 Actual
3.00
3.00 1.50 0.75 0.75 0.11
0.06 0.10 0.19
1
The normal distribution uses two parameters: the mean and variance, to describe asset returns. Variance explains how much returns vary either side of the mean (average). Volatility is measured by the standard deviation (the square root of the variance). Mean‐variance optimization models which select the lowest volatility for a given level of expected return may in fact create high risk portfolios. Let’s consider catastrophe insurers. The insurance company receives stable cash‐flows from policy premiums but when claims occur cash out‐flows can be extremely large. The same analogy applies to a fund that writes out‐of‐the‐money options. Stable cash‐flows from option premiums may mask large but infrequent losses. Statman Advisors Statman Advisors is an independent, employee‐owned hedge fund advisory, providing customized Hedge Fund portfolios for: wealth managers, family offices, endowments, foundations, charities, trusts, pension funds and plan sponsors. We employ a proprietary quantitative methodology for Asset Allocation and Risk Assessments, Manager Selection and intra‐day Portfolio Management. Deep knowledge of trading and risk management enables us to dig further during Manager interviews and risk‐adjusted performance assessments. Allocations through a top‐tiered Managed Accounts platform provides transparency, flexibility and control; facilitates real‐time risk management; and mitigates fraud risk. No fees to investors: additional layers of fees are avoided by allocating directly and charging underlying funds an ‘allocation fee’, enabling investors to pay an ‘all‐in 2% & 20% fee’. To discuss these research results in more depth or to inquire about our Advisory services, please contact: Sara Statman (President & Chief Investment Officer) (sara@statmanadvisors.com). Disclaimer The content of this presentation is for informational purposes only. Nothing shall be construed as soliciting investors or offering investment advice to buy or sell any securities, funds or private placements. Whilst Statman Advisors believes the enclosed information to be reliable neither Statman Advisors or any other affiliate provide any warranty or guarantee as to the accuracy or completeness of the information contained within, nor hold any liability for any direct, indirect, consequential or special losses or damages of any kind incurred as a result of the information contained within this material. Potential investors should not rely on the information enclosed within to form an investment decision but should instead take relevant and specific professional advice and read the terms and conditions of the relevant offering prospectus.