Introduction to the Infiniti Capital  Four Moment Risk Decomposition  By Peter Urbani and Mitchell Bristow
Higher Moments and Risk <ul><li>Classical Investment Theory assumes that investment returns are normally distributed. </li...
Normal versus Modified VaR In the case of a standard normal distribution (Mean=0, Std Dev=1, Skew=0, Kurt=3) both the Norm...
Normal versus Modified VaR In the case of a  slightly positive skewness  and slightly higher than normal kurtosis (Mean=0,...
Normal versus Modified VaR In the case of a  slightly negative skewness  and slightly higher than normal kurtosis (Mean=0,...
The Cornish Fisher Modification In Excel for use with Excess Kurtosis = (Skew*(ZScore^2-1)/6)+(Kurt*(ZScore^3-3*ZScore)/24...
Moving from the Univariate to the Multivariate (normal) Variance Covariance Matrix Std Devs (normal) Correlation Matrix We...
Infiniti Capital Modified VaR Decomposition
Normal & Modified VaR for a portfolio
Basic Portfolio Statistics
Covariance Matrix
‘ Modified’ Covariance Matrix
Correlation Matrix
‘ Modified’ Correlation Matrix
‘ Modified’ Volatility
Normal & Modified VaR from these Matrices
Infiniti Capital Four Moment Risk Decomposition http://www.infiniti-analytics.com
What can we learn from this Analysis  ? <ul><li>First we can see that the portfolio’s negative Skew of -1.28 and excess Ku...
Disclaimer <ul><li>The information and opinions in this presentation were prepared by the Infiniti Group (collectively “In...
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Four moment risk decomposition presentation

  1. 1. Introduction to the Infiniti Capital Four Moment Risk Decomposition By Peter Urbani and Mitchell Bristow
  2. 2. Higher Moments and Risk <ul><li>Classical Investment Theory assumes that investment returns are normally distributed. </li></ul><ul><li>The Normal distribution can be full described by its first two moments, Mean (Mu) and Standard Deviation (Sigma). </li></ul><ul><li>The empirical evidence indicates that only about 12% of Hedge Funds have returns that are normally distributed. </li></ul><ul><li>Hedge Fund returns exhibit significant amounts of skewness and excess ( > 3 ) kurtosis (third and fourth statistical moments). </li></ul><ul><li>Investors generally have a preference for positive skewness and moderate to low levels of kurtosis. </li></ul><ul><li>Consequently the impact of higher moments is of great interest to people building portfolios of hedge funds or managing their risk. </li></ul><ul><li>One way to include the impact of higher moments into the calculation of Value at Risk (VaR) for such portfolios is to use the Cornish Fisher modification to the Normal VaR calculation. </li></ul>
  3. 3. Normal versus Modified VaR In the case of a standard normal distribution (Mean=0, Std Dev=1, Skew=0, Kurt=3) both the Normal Var and Cornish Fisher Modified VaR give the same answer. Note this assumes Raw Kurtosis – Excels formula assumes Excess Kurtosis > 3 and subtracts 3 automatically. This is why Kurtosis is not 0 in the above example.
  4. 4. Normal versus Modified VaR In the case of a slightly positive skewness and slightly higher than normal kurtosis (Mean=0, Std Dev=1, Skew=0.5, Kurt=4) the Cornish Fisher Modified VaR is lower (less negative) than that given by the Normal VaR calculation.
  5. 5. Normal versus Modified VaR In the case of a slightly negative skewness and slightly higher than normal kurtosis (Mean=0, Std Dev=1, Skew=-0.5, Kurt=4) the Cornish Fisher Modified VaR is higher (more negative) than that given by the Normal VaR calculation.
  6. 6. The Cornish Fisher Modification In Excel for use with Excess Kurtosis = (Skew*(ZScore^2-1)/6)+(Kurt*(ZScore^3-3*ZScore)/24)-((Skew^2)*(2*ZScore^3-5*ZScore)/36) for use with Raw Kurtosis =(1/6)*(ZScore^2-1)*Skew+(1/24)*((ZScore^3)-3*ZScore)*(Kurt-3)-(1/36)*(2*Zscore^3-5*ZScore)*Skew^2
  7. 7. Moving from the Univariate to the Multivariate (normal) Variance Covariance Matrix Std Devs (normal) Correlation Matrix Weights (normal) VaR (normal) Variance Covariance Matrix Std Devs Co-Skewn ess Co-Kurtosis (modified) Correlation Matrix Weights (modified) VaR Mod Std Devs
  8. 8. Infiniti Capital Modified VaR Decomposition
  9. 9. Normal & Modified VaR for a portfolio
  10. 10. Basic Portfolio Statistics
  11. 11. Covariance Matrix
  12. 12. ‘ Modified’ Covariance Matrix
  13. 13. Correlation Matrix
  14. 14. ‘ Modified’ Correlation Matrix
  15. 15. ‘ Modified’ Volatility
  16. 16. Normal & Modified VaR from these Matrices
  17. 17. Infiniti Capital Four Moment Risk Decomposition http://www.infiniti-analytics.com
  18. 18. What can we learn from this Analysis ? <ul><li>First we can see that the portfolio’s negative Skew of -1.28 and excess Kurtosis of +4.51 contribute to the 95% Modified VaR being higher than the Normal VaR at </li></ul><ul><li> -2.28% versus -1.90%. </li></ul><ul><li>This is even more evident when we look at the Modified Conditional VaR (Modified CVaR) versus the Normal CVaR of -4.09% versus -2.56%. </li></ul><ul><li>Whilst the differences between the Normal and Modified VaR for individual positions may be small in some cases, those for the Normal and Modified CVaR (average tail expectation beyond the VaR a.k.a expected shortfall (ES)) tend to be far more pronounced. </li></ul><ul><li>Thus we can see that largest % Contributions to the portfolio’s Modified CVaR came from Emerging Markets, Convertible Arbitrage, Event Driven and Distressed. </li></ul><ul><li>However when we look at ratio of % Contribution to Weight we can see that although Distressed contributed 18.0% to the Risk (Modified CVaR), it also contributed 18.4% to the return. Comparatively Emerging Markets was far riskier as although it contributed 19.3% to return, it also contributed 39.6% to the Risk. </li></ul>
  19. 19. Disclaimer <ul><li>The information and opinions in this presentation were prepared by the Infiniti Group (collectively “Infiniti”).  This presentation is provided for information purposes only.  It is not an offer or solicitation to enter into any agreement or contract with Infiniti.  Whilst all reasonable care has been taken to ensure that the facts stated herein are accurate and that the opinions and expectations contained herein are fair and reasonable, Infiniti makes no representation or warranty, express or implied, with respect to the fairness, correctness, accuracy reasonableness or completeness of the information and opinions herein but has obtained the information from sources believed to be reliable.  </li></ul><ul><li>  </li></ul><ul><li>Analyses contained herein are based on assumptions that if altered can change the conclusions reached herein.  Infiniti has no obligation to update, modify or amend this publication or to otherwise notify a reader in the event that any matter stated herein, or any opinion, projection, forecast or estimate set forth herein, changes or subsequently becomes inaccurate.  The information is not intended to depict or predict actual investment performance of any financial product and is subject to change without notice.  Any opinions expressed herein reflect Infiniti’s judgment at the date and time hereof and are subject to change without notice. </li></ul><ul><li>  </li></ul><ul><li>Infiniti is not acting and does not purport to act in any way as your advisor.  We therefore strongly suggest that you seek your own independent advice in relation to any legal, tax, accounting and regulatory issues relating to the merits or otherwise of the products and services discussed.  Financial instruments that may be discussed herein may not be suitable for all investors and any investors must make any investment decision using their own independent advisors as they believe necessary and based upon their specific financial situation and investment objectives.  </li></ul><ul><li>  </li></ul><ul><li>If a financial instrument is denominated in a currency other than an investor’s currency, a change in exchange rates may adversely affect the price or value of, or the income derived from, the financial instrument, and any investor in that financial instrument effectively assumes currency risk.  Prices and availability of any financial instruments described in this presentation are subject to change without notice.  Nothing contained herein shall constitute any representation or warranty as to future performance of any financial instrument, credit, currency, rate or other market or economic measure as past performance is not necessarily indicative of future results.  </li></ul><ul><li>  </li></ul><ul><li>The information contained herein is CONFIDENTIAL.  It is intended only for the use of the person to whom this document is given and may not be reproduced or redistributed in whole or in part without the prior written consent of Infiniti.    </li></ul><ul><li>  </li></ul><ul><li>This does not constitute an offer to sell, or the solicitation of an offer to buy, any product.  An offer may only be made by means of the offering memorandum and governing documents of the relevant funds (the “Fund Documents”), which should be read in their entirety.  The information is not intended to be complete or final and is qualified in its entirety by the Fund Documents.  In the event the Information is inconsistent or contrary to the descriptions or terms of the Fund Documents, the terms of the Fund Documents shall prevail.    Infiniti (i) may be a market maker or specialist in securities issued by companies mentioned herein (ii) may act as an adviser, underwriter or lender to companies mentioned herein (iii) may have received or intend to seek compensation for investment services from companies mentioned herein (iv) along with its respective officers, directors and employees may affect transactions and/or hold long or short positions in the underlying securities or related financial products of companies mentioned herein. </li></ul><ul><li>  </li></ul><ul><li>The information contained herein is intended for illustrative purposes only, has been developed internally and has been based on variations of existing funds, managed accounts, simulations, extrapolations of other investment programs, pro forma data or taken from trade and statistical services and other sources that we deem reliable, although no warranty is made that the information is accurate or complete and it should not be relied upon as such. </li></ul><ul><li>  </li></ul><ul><li>Any securities discussed herein may not be suitable for all investors.  Transactions of the type described herein may involve a high degree of risk, and the value of such instruments may be highly volatile.  </li></ul><ul><li>  </li></ul><ul><li>Past performance is not guarantee of, and cannot be construed as an indication of, future results. </li></ul><ul><li>  </li></ul>
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