Retirement Portfolios Workbook E-Book

Michael J. Zwecher

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Wiley Finance Editions
• Sprache: Englisch

Seitenzahl: 197

Veröffentlichungsjahr: 2009

Beschreibung

A companion Workbook to the text Retirement Portfolios

Retirement is one of the most important parts of the financial planning process. Yet only two percent of financial advisors describe themselves as competent in retirement planning.

Constructing a retirement portfolio is viewed as a difficult endeavor, and the demands facing financial advisors responsible for this task continue to grow. The pressures are particularly intense due to events such as the financial crisis and oncoming rush of retiring baby boomers. It is imperative that financial advisors be equipped and ready to create appropriate retirement portfolios. That's why Michael Zwecher-a leading expert on retirement income-has created Retirement Portfolios and the Retirement Portfolios Workbook. In the text Retirement Portfolios, leading retirement income expert Michael Zwecher provides financial professionals with complete coverage of the most important issues in this field. The Retirement Portfolios Workbook offers you a wealth of practical information and exercises that will solidify your understanding of the tools and techniques associated with this discipline. This comprehensive study guide

• Provides chapter summaries and end of chapter questions to the main book
• Test your knowledge of the information addressed in Retirement Portfolios, before you put it to work in real world situations
• Helps you learn to solve problems while setting up tools you can use in practice
• Puts the management of risks related to retirement portfolios in perspective

If you want to gain a firm understanding of the information outlined in Retirement Portfolios, the lessons within this workbook can show you how.

Leseprobe

Table of Contents

Title Page

Copyright Page

Preface

BEFORE YOU GET STARTED: TOOLS YOU’LL NEED TO COMPLETE THE EXERCISES

PART One - Questions

CHAPTER 1 - Portfolio Focus and Stage of Life

CHAPTER RECAP

PROBLEMS

CHAPTER 2 - The Top-Down View

CHAPTER RECAP

PROBLEMS

CHAPTER 3 - The Importance of Lifestyle Flooring

CHAPTER RECAP

PROBLEMS

CHAPTER 4 - Monetizing Mortality

CHAPTER RECAP

PROBLEMS

CHAPTER 5 - Flooring with Capital Markets Products

CHAPTER RECAP

PROBLEMS

CHAPTER 6 - Building Retirement Income Portfolios

CHAPTER RECAP

PROBLEMS

CHAPTER 7 - Creating Allocations tor Constructing Practical Portfolios by Age ...

CHAPTER RECAP

PROBLEMS

CHAPTER 8 - Rebalancing Retirement Income Portfolios

CHAPTER RECAP

PROBLEMS

CHAPTER 9 - Active Risk Management for Retirement Income Portfolios

CHAPTER RECAP

PROBLEMS

CHAPTER 10 - The Transition Phase

CHAPTER RECAP

PROBLEMS

CHAPTER 11 - Putting Together the Proposal

CHAPTER RECAP

PROBLEMS

CHAPTER 12 - Market Segmentation

CHAPTER RECAP

PROBLEMS

CHAPTER 13 - Products and Example Portfolios

CHAPTER RECAP

PROBLEMS

CHAPTER 14 - Preparing Your Client for a Retirement Income Portfolio

CHAPTER RECAP

PROBLEMS

CHAPTER 15 - Salvage Operations, Mistakes, and Fallacies

CHAPTER RECAP

PROBLEMS

PART Two - Solutions

CHAPTER 1 - Portfolio Focus and Stage of Life

CHAPTER 2 - The Top-Down View

CHAPTER 3 - The Importance of Lifestyle Flooring

CHAPTER 4 - Monetizing Mortality

CHAPTER 5 - Flooring with Capital Markets Products

CHAPTER 6 - Building Retirement Income Portfolios

CHAPTER 7 - Creating Allocations for Constructing PracticalPortfolios by Age ...

CHAPTER 8 - Rebalancing Retirement Income Portfolios

CHAPTER 9 - Active Risk Management for Retirement Income Portfolios

CHAPTER 10 - The Transition Phase

CHAPTER 11 - Putting Together the Proposal

CHAPTER 12 - Market Segmentation

CHAPTER 13 - Products and Example Portfolios

THE ENVIRONMENT

FOCUSING THE CLIENT

FRAMING THE CLIENT

SUMMARIZING THE PROCESS

CHAPTER 14 - Preparing Your Client for a Retirement Income Portfolio

BIG PICTURE

CHAPTER 15 - Salvage Operations, Mistakes, and Fallacies

Founded in 1807, John Wiley & Sons is the oldest independent publishing company in the United States. With offices in North America, Europe, Australia, and Asia, Wiley is globally committed to developing and marketing print and electronic products and services for our customers’ professional and personal knowledge and understanding.

The Wiley Finance series contains books written specifically for finance and investment professionals as well as sophisticated individual investors and their financial advisors. Book topics range from portfolio management to e-commerce, risk management, financial engineering, valuation and financial instrument analysis, as well as much more.

For a list of available titles, please visit our Web site at www.WileyFinance.com.

Copyright © 2010 by Michael J. Zwecher. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, [phone], fax [phone], or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, [phone], fax [phone], or online at http://www.wiley.com/go/permissions.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at [phone], outside the United States at [phone] or fax [phone].

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our web site at www.wiley.com.

eISBN : 978-0-470-58622-8

Preface

This workbook is the companion to Retirement Portfolios: Theory, Construction, and Management. The workbook allows you to delve deeper into the main book’s topics and create the proficiency required for professional designation as a life-cycle investment or retirement investment professional.

The problems in Part One of this workbook are correlated with each chapter. By reading each chapter and performing corresponding chapter problems, you will better understand the problems and assimilate the material in the text. The readings and problems provide mutual reinforcement.

With the exception of a handful of warm-ups, the workbook problems are each designed to make a point directly related to the text, the larger discussion of retirement income in particular, and portfolios in general. In designing these problems, it is assumed that you are well versed in financial products and portfolio management; broadly familiar with portfolio theory; and competent but “rusty” in mathematics. The problems are designed to take you through the conceptual and bring you to the practical—that is, the problems should build you up rather than trip you up.

In Part Two of this workbook, detailed solutions are provided for every problem. In some cases, the problems require tools that are more advanced than expected from the typical user. In such cases, I try to provide enough detail to help walk you through the problem and get to the issue that the problem is trying to address.

Some of the problems address concepts, but many are trying to walk you through what you may want to do in practice, or how you can build tools that you can readily use. If you come away from a problem saying to yourself either “I get it, that’s good to know” or “Well that would be easy to add to my practice,” then I will have accomplished my goal. I want you to come away from these problems knowing how to build a viable business that you can be proud of.

Most of the questions are associated with Chapters 1 through 9 and Chapter 15. These 10 chapters constitute the bulk of the material that is suitable to a workbook format. For the other chapters, I have created thought provoking questions and provided some ancillary material that you will find useful in practice.

Just as the main book went to great lengths to avoid promoting any particular firm’s products or techniques, the same is true of the tools used here. I do not mean to endorse or promote any particular tool or software for working through these problems.

BEFORE YOU GET STARTED: TOOLS YOU’LL NEED TO COMPLETE THE EXERCISES

Most books on investments focus on single-period investment problems and topics. However, the focus here is on the long term, where issues like cumulative returns and cumulative risk take on added importance. In a sense, you can think of the emphasis of both books as adding through time instead of adding across assets or choosing a particular asset at a particular point in time.

Most of the problems in this workbook can be easily handled by tools that you use every day. Occasionally, we’ll use the tools that you are used to using in an unfamiliar way, or we have to tweak the tools to make them more amenable to multiperiod analysis.

In the next few pages we’ll first cover a boot-camp version of some formulas related to present and future values of annuities, both level and growing. I hope that this first part is familiar territory for you.

Next, we switch gears to cover the basics of asset returns useful for multiperiod problems. We cover the random nature of returns and the ways that it is typically shown. We then adapt the typical view to cover the multiperiod problem of building a portfolio through time. This second part may be somewhat new, but it is only a small change from what you are used to—and to make this topic more interesting, we cover a common but dangerous fallacy.

We also cover a brief description of efficient frontiers and the capital-market line. These are concepts that are fundamental building blocks of modern portfolio construction. While conceptually appealing, there are extraordinary difficulties with trying to build portfolios that are mean/ variance efficient. That few clients seem interested in buying mean/variance efficient portfolios is covered in Chapter 2; even economically optimizing, rational investors may prefer portfolios that protect lifestyle rather than meet the overly simple criteria of mean/variance optimization. Those caveats in place, the concept of the capital market line is still extraordinarily useful.

Annuity Formulas

All of these formulas are related to finding present values or future values of cash flows. Annuities are payments that are expected to recur at a stated frequency. Annuities in our usage can either be level payments or payments that grow at a constant rate. Annuities may be of fixed duration or potentially infinite duration. Throughout most of the workbook, I’ll differentiate between the typical financial textbook definition of annuities used here and the colloquial usage of the term as a way to refer to the insurance-related subset of annuities.

I’ll go through the derivation of the formulas, but your main interest will probably be in the formulas themselves. The formulas are easy to incorporate into spreadsheets for a wide variety of uses. I go through the derivation to try to pitch the idea so that you don’t need to memorize the formulas, you just have to remember the simple idea behind them.

Although the formulas for annuities were more useful before the advent of spreadsheet programs, it is still helpful to take a brief detour and provide some background material on payment streams, present values, and future values that you might find helpful. Also, by reading through this part, it should help brush away some cobwebs and make the remainder of the workbook more enjoyable.

The General Rule Underlying Annuities Some formulas have 1,001 uses. The annuity formula is one of them. So let me present it in a slightly different way that starts out looking like rather unappealing math but allows you to adapt the formula for a multitude of uses and doesn’t require that you commit much to memory.

First, let’s look at geometric sums, defining the sum of a geometric series as SN:

SNx + x2 + x3 + ... + xN

This series is hard to add up by itself and would have to be added term by term if we couldn’t find a way to simplify the problem, but we have a trick: Multiply every element of the sum by x, that is,

xSN=x2+ x3+ x4+ ... + xN+1

If we subtract the second expression from the first, we calculate the difference SN- xSN, and all that we are left with is the following:

Our trick allowed us to create what is called a telescoping series. This is all you ever have to commit to memory and from which all of the annuity results follow. The previous expression can be simplified to

Ordinary Annuities For present value of an ordinary annuity, replace x with, where r is the discount rate and N is the number of years in the annuity. Making the substitution and performing some messy algebra yields the following familiar formula:

The typical uses for this formula are in permutations of the following:

Generally the preceding is used either for figuring out the present value of a payments stream given N, r, Pmt or in figuring out the payment stream required to pay off a present value given N, r, Value.

The formulas that we will go through are very easy and useful to set up in a spreadsheet. For your spreadsheets, try the following example:

DataR0.04N10.00Intermediate Step1 + r1.04Calculations1/r251/(1 + r)N0.6755641 - 1/(1 + r)N0.324436Result (rounded)8.11

Example: A $12,000 annual payment annuity for 10 years at 4 percent would have an unrounded present value of $97,330.75.

Annuities Growing at a Constant Rate If the payment is growing at a constant rate g, then instead of using the substitution x =, use x =. In this case the formula changes a little bit.

If g < r and N becomes large, then the term on the right, inside of the parentheses, approaches zero and the formula will approach, which may look familiar to many of you as the “guts” of the dividend growth formula for fundamental valuation of equity, where D0is the current dividend.

Example: A $12,000 annual payment annuity for 10 years at 5 percent, growing at 2 percent would have an unrounded present value of $102,670.40.

Deferred Annuities For annuities that are deferred, you have two choices, either subtract from individual elements representing the deferral or use the previous formula to subtract from an annuity of the same duration as the deferral.

Alternative Compounding Periods If the compounding period is something other than annual, say M times per year, then in all of the formulas replace the annual rate r with rlM and replace N with M*Nyears. One thing to remember is that the payments of the annuity need to match up with the frequency. For example, if the annuity pays $12,000 and the compounding and payments are monthly then the monthly payments of $1,000 should be used.

Example: A $12,000 annual payment annuity for 10 years at 4 percent, payable quarterly would have an unrounded present value of $98,504.06.

Constant Growth with Alternative Compounding Periods If the compounding period is something other than annual, say M times per year, then in all of the formulas replace the annual rate r with r/M, g with g/M and replace N with M * N years. Once again, remember that the payments of the annuity need to match up with the frequency. For example, if the annuity pays $12,000 and the compounding and payments are monthly then the monthly payments of $1,000 should be used.

If we place the formula into a spreadsheet, it is easy to see how the time to pay off the loan amount owed can be impacted by changing P. The most common use for this formula is in the estimated time to pay off a mortgage if some extra amount is regularly included with the monthly payment.

Try on your own: Notice the intuitive result that if the payments are constant rather than growing, the payment stream will last longer.

Future Value For future values of ordinary annuities, the date of reckoning is made on the date that last deposit is made. This means that there is one less compounding period and instead of running from x to xN, the sum SN runs from 1 to xN-1

In this case, the substitutions required for compounding at a rate that is not annual is left as an exercise.

Notation of Asset Returns and Basics

When we construct portfolios of assets, return is usually denoted rp. The heavy machinery of the central limit theorem and the normal distribution is usually brought in at this point. For simplicity, we usually start by constructing an equally weighted portfolio such that for a portfolio of N assets rpri. Importantly, this means that µpµiand that; if variance is constant across assets then. That the variance of a sample average is lower than the variance of an individual element of the sample is a property of random variables that is not specific to returns. Since standard deviation is the square root of variance, the standard deviation of a sample average becomes σp =. Confusing the standard deviation of a sample average with the standard deviation for cumulative returns is the source of one of the most common and dangerous fallacies in finance.

The Fallacy: The long-run risk of a portfolio being lower than the risk in the short run.

This fallacy shows up far too often, usually backed up by the arithmetic for sample averages to claim that the volatility of a portfolio declines over time at the square root of T. A typical example is that if the annual volatility is 30 percent, then the volatility over 16 years would only be 7.5 percent. Not only is this a fallacy, but it also leads to results that are somewhat humorous. An implication is that if we run the problem in reverse, the shorter the interval, the higher the volatility. If the annual volatility were 30 percent, then the implication of the fallacy would be that the volatility over one trading day would be about 480 percent.

The fallacy, mistaking properties of an average of random variables for properties of a sum of random variables, can be seen easily for what it is; but first we need to adapt our notation to the way that returns are typically viewed in multiperiod analysis.

To see the fallacy, we expand the component showing the sum of returns:

The variable Z denotes the number of standard deviations that a particular portfolio’s path deviates from the mean. Remember, each client only gets one portfolio and one path.

The reason that the expression for portfolio changes looks a little messier under the assumption of lognormality is because if ln(X) is a random variable that is normally distributed with mean µand variance σ2, then the mean of Xwill be, that is, the subtracted term causing the apparent messiness keeps the mean growth of the portfolio at µ.

In the workbook we will make use of multiperiod analysis. The key thing to remember is that other than the returns being defined as log changes, random variables act as before.

You may also find it useful to refer to the following minitable of standard normal cumulative probabilities in order to make better sense of the impact of different portfolio paths. As an example of how to read the table is the following statement: There is a 10 percent chance that the return outcome will be lower than -1.282 standard deviations below the mean return.

ZValueCumulative Probability-2.3261.0%-1.9602.5%-1.6455.0%-1.28210.0%-1.03615.0%-0.84220.0%-0.67425.0%-0.52430.0%-0.38535.0%-0.25340.0%-0.12645.0%0.00050.0%0.12655.0%0.25360.0%0.38565.0%0.52470.0%0.67475.0%0.84280.0%1.03685.0%1.28290.0%1.64595.0%1.96097.5%2.32699.0%