REAL ESTATE MATHEMATICS Applied analytics and quantitative methods for private real estate investing Edited by David Lynn and Tim Wang 2 Published in October 2011 by PEI Second Floor Sycamore House Sycamore Street London EC1Y 0SG United Kingdom Telephone: +44 (0)20 7566 5444 www.peimedia.com © 2011 PEI ISBN 978-1-904-696-93-3 eISBN 978-1-908783-52-3 This publication is not included in the CLA Licence so you must not copy any portion of it without the permission of the publisher. 3 All rights reserved. No parts of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means including electronic, mechanical, photocopy, recording or otherwise, without written permission of the publisher. Disclaimer: This publication contains general information only and the contributors are not, by means of this publication, rendering accounting, business, financial, investment, legal, tax, or other professional advice or services. This publication is not a substitute for such professional advice or services, nor should it be used as a basis for any decision or action that may affect your business. Before making any decision or taking any action that may affect your business, you should consult a qualified professional adviser. Neither the contributors, their firms, its affiliates, nor related entities shall be responsible for any loss sustained by any person who relies on this publication. The views and opinions expressed in the book are solely those of the authors and need not reflect those of their employing institutions. Although every reasonable effort has been made to ensure the accuracy of this publication, the publisher accepts no responsibility for any errors or omissions within this publication or for any expense or other loss alleged to have arisen in any way in connection with a reader’s use of this publication. PEI editor: Wanching Leong Production editor: Julie Foster 4 Printed in the UK by: Hobbs the Printers (www.hobbs.uk.com) 5 Contents Figures and tables About the editors Introduction and acknowledgements By David Lynn, Clarion Partners SECTION I: FUNDAMENTALS 1Private real estate allocations in multi-asset investment portfolios By Greg MacKinnon, Pension Real Estate Association Introduction The standard arguments for real estate Mean-variance optimisation Portfolio theory issues An alternative allocation paradigm: liability-driven investing Conclusion 2Forecasting real estate returns 6 By Timothy Bellman Introduction Why forecast real estate performance? What to forecast? How to forecast? Qualitative approaches Forecasting in practice 3Real estate investment capital structure By Hugh Kelly, Real Estate Economics Introduction Capital structure at the industry level Industry structure reflects individual investment characteristics Leverage generates risk and opportunity for the equity investor – and the lender Why not ‘borrow to the max’? What is the lender paid for? 7 The premium for taking real estate equity investment risk The mezzanine How the mezzanine preferred equity solution works Concluding observation 4Contrasting approaches to quantifying risk in real estate investments By Jon Southard, CBRE Econometric Advisors Introduction Scenario approach Stochastic Monte Carlo analysis Using the standard error of the estimate (SEE) Combinations of the three approaches Conclusion Appendix A: Procedure for approximating VaR level of a specific scenario 5Modelling uncertainty: Monte Carlo analysis and the pricing of real estate 8 By Randall Zisler and Matthew Zisler, Zisler Capital Associates, LLC The nature of real estate and recent encounters with risk Monte Carlo analysis Building a Monte Carlo model A sample application of Monte Carlo modelling The future of real estate risk analysis 6Analysing and pricing risk in international real estate markets By Maurizio Grilli and Richard Barkham, Grosvenor Introduction Hurdle rates The risk-return equation The risk premium Target versus expected returns Conclusion 7Special considerations in sustainable property financial analysis 9 By Scott Muldavin, Green Building Finance Consortium Introduction Step 1: Selecting the financial model Step 2: Evaluating property sustainability Step 3: Assessing the costs/benefits of sustainability Step 4: Evaluating the financial implications of costs/ benefits Step 5: Determining financial model inputs Step 6: Conducting a risk analysis and presentation (RAP) Sustainability investment performance Conclusion 8Real estate loans and real estate debt By Sam Chandan, Chandan Economics Introduction Leverage and the incentive to borrow Why borrow? When to borrow 10