Learning Objectives

In this chapter, you will formally learn the concept of diversification. In the process, you will become mindful of investment-performance claims and the roles of chance in obtaining above-average returns. You will also learn how you can construct an investment portfolio that is optimal for you given your risk preference and risk/return trade-off.

Impressive Investment Performance: Real or Fake

In the mid-1980s, a clever investment broker at a large American brokerage firm (in its Baltimore, Maryland branch) devised the following strategy in publishing his newsletters. He obtained a list of 2,000 high-net-worth individuals from a local golf club. In early January, he sent a letter to 1,000 of them (chosen at random) suggesting that they buy (i.e., long) soybean futures contracts. At the same time, he sent a different letter to the other 1,000, suggesting that they sell (i.e., short) soybean futures. By late January, soybean futures price dropped by about 10%, and so anyone in the second group who took his advice earned 10% in one month.

In early February, he sent follow-up letters to 500 of the “winners” (i.e., those who were told to short soybean futures contracts), advising them to buy German Deutschmark futures (at the time, Germany had not yet adopted the euro as their currency). The other 500 “winners” were sent a letter advising them to short Deutschmark futures. It turned out that the Deutschmark went up by 5% in February.

This book grew out of the deep frustration two of the three authors have experienced for many years, trying to teach a practical yet rigorous course on personal – in contrast to corporate or investment – finance, to undergraduate and graduate students at Canadian business schools. Although there are many college-level textbooks that discuss the tactical aspects of personal finance – nuggets such as: credit card debt is bad; reduce fees on mutual funds; regular saving is important; have a budget; and so on – we have not come across a textbook that integrated all these disparate concepts into a conceptual or strategic framework for financial decision making, based on sound economic principles.

For the most part, personal finance is being taught as a collection of standalone facts about “smart” money management. Most existing textbooks are written assuming a (very) basic background in mathematics on the part of the student, which limits the financial and economic level at which such a course can be delivered and the material discussed. Moreover, in today's Google and YouTube world, curious students could obtain more relevant, accurate, and up-to-date information about most (if not all) of the products that are part of the personal financial toolkit. In our opinion, a textbook that allocates most of its pages to the tactical aspects of financial planning, such as explaining how to read a credit card statement or how to get a copy of your credit report from your local credit bureau, or how to open up a brokerage account, is not advanced enough for a third or fourth year course in a business school.

Learning Objectives

In our day-to-day life, we face many risks. We can get sick or injured. We may get into an accident while we are driving to work. A fire or a flood can damage our houses. If that does not happen, someone may break into our houses and steal our belongings. In addition, we face the risk from not knowing exactly how long we will live. We may live shorter or longer than expected. If the former, our dependents may suffer from lack of financial support. If the latter, we may run out of retirement money. The list goes on. When these unpleasant events happen, their negative effects on our physical and/or financial well-being can be substantial.

Traditionally, there are insurance products that people can buy to manage these risks. In this chapter, we discuss the theoretical foundation of insurance. We look at insurance from both the buyers' and sellers' perspectives. Specifically, we want to determine when insurance should be used and how it is priced. In the process, we formalize the concepts of risks and people's attitudes toward them. The understanding from this chapter will be helpful to our discussion of life insurance in the next chapter.

The Concepts of Risk and Risk Preferences

Definition of Risk

Although there is no single, universally accepted definition of risk, a common one defines it as the variation in possible outcomes of an event that is subject to chance. The greater the variation, the more risky the event is. Risk can be classified into two distinct categories – speculative risk and pure risk.

Learning Objectives

In this chapter, we will learn how to calculate personal income taxes. We then talk about different types of investment income and how they are taxed. Finally, we explore a few ways to minimize the amount of taxes that we have to pay.

The Logic of Income Tax Calculations

In this section, we describe how income taxes are determined in Canada. Generally, income taxes in other countries follow a similar logic. In Canada, income taxes are assessed at both the federal and provincial levels. You are required to file a tax return in a given (tax) year if for that year you are a resident or a deemed resident of Canada with income above a certain level. Whether or not a person is a resident of Canada is determined by many factors. These factors include the amount of time spent in Canada in that year, ownership of a residence in Canada, and having relatives, bank accounts, and/or other social and economic ties to Canada. Except for residents of the province of Quebec, which administers its own personal income tax collection, Canadians file their tax return using a combined form in which both levels of taxes are calculated.

As with most countries, Canadian incomes taxes (both federal and provincial) are determined using the following three steps:

1. Figure out your total income from all sources. In Canada, you have to report income earned from every source, domestic or foreign. From this, you subtract deductions that are allowed by the tax laws, to arrive at a taxable income.

2. You then apply (federal and provincial) tax rates to your taxable income. The result is the total tax amount.

3. Finally, you subtract tax credits from your total tax to arrive at the amount of tax payable.

Learning Objectives

In this chapter, we talk about personal balance sheets, which are snapshots of our financial position at a point in time. We then discuss the concept of human capital that, as we will argue, should be included in everyone's personal balance sheet.

Personal Balance Sheets

A starting point in the personal financial-planning process is to assess our current financial situations. This is typically done by preparing a personal balance sheet. It is a good exercise for you to create your own balance sheet. Please take out a blank sheet of paper and draw a straight line down the center, splitting the sheet into two equal parts. Write “Assets” on the top left-hand side, and write “Liabilities” at the top right-hand side. On the left-hand side, list the value of your assets, including money in bank accounts, stocks, savings bonds, pension accounts, mutual funds, equity in a small business, house, car, and any other items you can think of. The list does not have to be exhaustive (e.g., you can disregard personal-use assets such as clothing). On the upper right-hand side, make sure to include what you owe on credit cards, consumer loans, student loans, mortgage loans, and any other financial obligations.

Once you have listed all your assets and all your liabilities, add them up to get summary numbers for both. On one side of the balance sheet is the value of everything you own, and on the other side is the value of everything you owe.

The last two chapters might have been a bit more than what you were expecting (or bargaining for) from a book on personal financial planning. Indeed, when we mention the terms Ito's lemma, control theory, or diffusion processes to graduate students and university colleagues – when asked about the tools of our research trade – they immediately assume that we work in the esoteric field of option pricing or derivative hedging. For most of the 1980s and 1990s that would have been the only conclusion to draw, but not anymore.

Indeed, most people are surprised to learn that one can actually use these mathematical concepts to analyze and provide guidance on practical questions such as how much and which type of life insurance you should purchase, the best age at which to start drawing a retirement pension annuity, or the optimal home mortgage loan for their family. Indeed, the models of quantitative finance that spawned a revolution in the 1970s and 1980s, which then filtered through to corporate finance and strategy in the 1980s and 1990s, have arrived at your personal doorstep in the last decade or two. The objective is crystal clear: to use the concept of “consumption smoothing” – in all its mathematical glory – to help individuals make better personal wealth and risk management decisions. We call it strategic financial planning (SFP) over the lifecycle. In the last decade financial luminaries such as Harry Markowitz, William Sharpe, and Robert Merton have penned articles, given presentations, and encouraged research on this same topic.

Learning Objectives

In this chapter, we discuss mortality risk and life insurance. Specifically, we examine the necessity of having life insurance and the appropriate amount of coverage. We then study how the premiums are determined. We also look at different types of life insurance policies.

Who Needs Life Insurance?

Life insurance is a contract whereby an insurance company promises to pay a sum of money to the designated beneficiary if the insured passes away. That sum of money is referred to as the death benefit or the face value of the policy. In exchange, the insured has to pay an insurance premium to the company. Typically, an insurance premium is paid monthly while the insured is still alive. However, the insured can choose to pay it in one lump sum at the start of the policy. In some cases, the person who pays the premiums is not the insured. That person is referred to as the owner of the policy. For example, if you purchase life insurance for your spouse, you are the owner while your spouse is the insured.

The primary reason for getting life insurance is to protect against financial problems associated with the insured's premature death. These financial problems include the loss of the insured's future earnings, which could lead to a lower standard of living for his or her family (i.e., dependents). They also include funeral expenses, unpaid medical bills, and outstanding debts.

Learning Objectives

People invest their savings in order to attain some specific objectives. The objectives can be short term (such as for education or for a down payment on a house) or long term (such as for retirement). The goal of an investment decision is to choose a portfolio that is optimal for the investor's objective and risk preference.

In this chapter and the next, you will learn about investment decisions – how you should invest your savings and what factors you have to take into consideration when making an investment decision. Because investment is now a very large topic, it is not possible to cover every aspect of it in detail in this book. We concentrate on the most important issues and also on how investment decisions are related to the concept of consumption smoothing.

This chapter discusses the basic principles of investment. It starts by identifying the investment choices that are available to you. We classify these choices into five categories (or asset classes), and examine the risk and return of each asset class. Finally, you learn the concept of asset allocation and diversification.

Investment Decisions and Consumption

Saving and investing for retirement is what most people have to do. Recall from Chapter 4 that under the consumption-smoothing framework, you choose a consumption pattern that maximizes your total standard of living over your lifetime. One factor that determines the pattern of your optimal discretionary consumption is the rate of return that you can get on your savings.

Learning Objectives

In this chapter, we cover various issues concerning usage of debt. In particular, we look at how mortgage financing works. We then talk about the advantages and shortcomings of investment loans (i.e., borrowing money to invest). Finally, we discuss the benefits of debt consolidation (i.e., combining debts of various sources into one).

Mortgage Financing

Suppose you want to buy a house. After visiting several potential choices, you decide on one house that you like the most. You then negotiate with the seller on the price. Now, you have to decide how much ofthe payment will come from your own money (i.e., down payment) and how much from borrowing.

In many countries, there is a rule governing the minimum down payment that a buyer needs to make. Typically, the minimum is expressed as a percentage of the house's price or appraised value. For Canada, that minimum is 5% (as of early 2011). Obviously, you can make a larger down payment than the minimum if you want. Depending on the amount of your down payment, your mortgage can be classified as conventional or high-ratio. A conventional mortgage is one where the buyer makes a down payment of at least 20% of the purchase price and borrow the rest (or, equivalently, the loan-to-value ratio is 80% or below). On the other hand, a high-ratio mortgage is one where the down payment is between 5% and 20% (or the loan-to-value ratio between 95% and 80%).

Learning Objectives

In this chapter, we look at consumption/investment decisions. During your working years, you have to decide how much of your salary you want to spend immediately and how much to save for the future. We use an economic concept called consumption smoothing, which suggests that people want to optimize their standard of living over their lifetime. They do so by balancing the spending and savings during different stages of their lives. We will see that under this concept, people's standard of living will not wildly fluctuate. Rather, it either remains the same or changes in a smooth fashion over their lifetime.

You will learn to derive your optimal consumption and savings at various ages. You will also see how your financial and economic net worth change over time.

Consumption Smoothing

Imagine the following situation. You are twenty-five years old, and your long-lost and rather eccentric uncle, whom you rarely met and barely know, has just passed away. When the lawyers vet his will, they discover that he left you $25 million as an inheritance. Unbeknownst to your family, he was quite wealthy and he took a liking to you personally. Unfortunately (and there always is abut), themoney has been placed in an iron-clad trust that you cannot access for the next twenty-five years. Even the best lawyers in town cannot break or dissolve the trust documents. Your uncle was concerned about your financial maturity, and he decided it would be best to wait until you are (much) older before giving you the title to this unprecedented sum of cash.

Learning Objectives

In this chapter we offer a (more) mathematical formulation of the main ideas behind strategic financial planning for individuals. The intended audience for this chapter is upper level or graduate students with sufficient calculus training. We start by reviewing some earlier results – which we presented back in Chapters 2 to 5 without much justification – and then move on to obtain some newer ones. Some of the concepts might seem familiar (and perhaps even repetitive), but we urge you to pay special attention to the new context in which they are being presented. As this chapter (and then Chapter 14) progress, the material will get exceedingly mathematical and involve some advanced concepts from differential equations to stochastic processes. Hang in there (or skip to the numerical examples). Our objective is to provide a complete representation of the model for those who want to derive the equations themselves.

Wages and Salary in Continuous Time

In this section we introduce the notation we will be using in continuous time. Start by assuming that you are x years old, still in school (i.e., not earning any money) and you plan to graduate, start your working life, join the labor force, and earn an income at an age denoted by I. From a modeling perspective, it helps to consider the remainder of your lifecycle as consisting of three distinct stages: study, work, and retirement, although we do acknowledge that in practice some people alternate between and merge these stages over their life.